Philosphy of Science

Contents

Preface iii

Acknowledgements v

1 Science Teaching: The Role of History and Philosophy of Science 3Michael R. Matthews

2 Does Science Teaching Need History and Philosophy of Science? 21Peter Slezak

3 Teaching History and Philosophy of Science: Experience at IIT Kanpur 39P.R.K. Rao

4 Multiculturalism in Science Education and the Question of Universalism. 51William W. Cobern & Cathleen C. Loving

5 Varieties of Constructivism and their (Ir-)Relevance to Science Education 71Peter Slezak

6 Social Constructivism and the Science Wars 85Peter Slezak

7 Re-examining the Image of Science in the School Science Curriculum 111William W. Cobern

8 Linking Science Pedagogy with History and Philosophy of ScienceThrough Cognitive Science: A Proposal 133Amitabha Gupta

9 Conceptual Change in the Learning of Science 167Stella Vosniadou

10 How did Galileo Discover the Law of Free Fall? An EpistemologicalReconstruction of the Episode 177Nagarjuna G.

11 Introducing History of Science in Science Education: A Perspectivefrom Chemical Education 197Prajit K. Basu

12 Multicultural Mathematics, Anti-racist Mathematics: What can that be? 213George Gheverghese Joseph

2

13 Infinite Series Across Three Cultures: Background and Motivation 227George Gheverghese Joseph

14 How should ‘Euclidean’ Geometry be Taught? 243C. K. Raju

15 The Axiomatic Method: Its Origin and Purpose 263S. D. Agashe

16 Approaches to the Periodic Table 281Rudolf Kraus

17 Alternative Frameworks in Electricity 291A.B.Saxena

18 Common Man’s Science 303Rakesh Popli

19 Attitude Towards Science: An Analysis 321Daya Pant

20 Emergence of Science Textbooks in Tamil—Encounter of ModernScience with Traditional Knowledge Forms 343T.V. Venkateswaran

Index 367

Science Teaching: The Role of History and Philosophy of Science

Michael R. MatthewsUniversity of New South Wales, Sydney, Australia. Email: [email protected]

Science teachers contribute to the overall education of students, thus they need somemoderately well-formed view of what education is, and the goals it should be pursuing.Teachers and administrators need some conception of an educated person, as this is thetelos of their individual classroom teaching and policy development. Teachers need tokeep their eyes on the educational prize, the more so when social pressures increasinglydevalue the intellectual and critical traditions of education.

The conviction that the learning of science needs to be accompanied by learningabout science is basic to liberal approaches to the teaching of science. If studentsdo not learn and appreciate something about science—its history, its interrelationswith culture, religion, worldviews, and commerce, its philosophical and metaphysicalassumptions, its epistemology and methodology—then the opportunity for science toenrich culture and human lives is correspondingly minimised. If science is taughtmerely as a technical subject devoid of its cultural and philosophical dimensions, thenthe positive results of science education are less able to fructify in society. We havesome inkling of this situation of lost cultural opportunities when we look at the purelytechnical teaching of the sciences in the former USSR where the wide-spread teachingof science did not appear, with a few courageous exceptions, to generate critical andindependent thinking, in many parts of contemporary southern USA where racism andbelief in creation science go hand-in-hand with sophistication in technical science, andperhaps in Japan where it seems that technical science is taught fairly well, but thescientific competence gained seems not to contribute very much to Japanese culturalunderstanding or philosophy (on this complex matter see Kawasaki 1996).

The Science Literacy Crisis

It is widely recognised that there is a crisis in Western science education. Levels ofscience literacy are disturbingly low. This is anomalous because science is one of thegreatest achievements of human culture. It has a wonderfully interesting and complexpast, it has revealed an enormous amount about ourselves and the world in which welive, it has directly and indirectly transformed the social and natural worlds, and thehuman and environmental problems requiring scientific understanding are pressing—yet, disturbingly, students and teachers are deserting science.

This flight from the science classroom by both teachers and students has beendepressingly well documented. In the US in the mid-1980s it was estimated that eachyear 600 science graduates entered the teaching profession whilst 8,000 left it (Mayer1987). In 1986, 7,100 US high schools had no course in physics, and 4,200 had nocourse in chemistry (Mayer 1987). In 1990 only four states required the three yearsof basic science recommended by the sobering 1983 report A Nation at Risk, the rest

2 Science Teaching: The Role of HPS

allowed high school graduation with only two years science (Beardsley 1992, p. 80).Irrespective of years required, seventy percent of all school students drop science atthe first available opportunity—which is one reason why in 1986 less than one in fivehigh school graduates had studied any physics. In 1991 the Carnegie Commissionon Science, Technology and Government warned that the failings of science educationwere so great that they posed a ‘chronic and serious threat to our nation’s future’(Beardsley 1992, p. 79). And the American National Science Foundation charged that‘the nation’s undergraduate programs in science, mathematics and technology havedeclined in quality and scope to such an extent that they are no longer meeting na-tional needs. A unique American resource has been eroded’ (Heilbron 1987, p. 556).The Second International Science Study indicated that the scientific knowledge of UScitizens was among the lowest in the industrialised world (Anderson 1989).

In the US, science illiteracy is disturbingly high among the educated classes. A 1986survey of 1,000 college students in Connecticut, Texas, and California revealed that58% believed in a literal Adam and Eve, and 25% thought that humans and dinosaursonce lived together (Harrold & Eve, 1987). A survey of US biology teachers estimatedthat 35% believe that psychic powers can be used to read other people’s minds, 30% percent reject the theory of evolution, and 20% believe in ghosts (Martin, 1994, p. 359).

In the UK, recent reports of the National Commission on Education and the RoyalSociety have both documented similar trends. One commentator has said that ‘wher-ever you look, students are turning away from science . . .. Those that do go to universityare often of a frighteningly low caliber’ (Bown 1993, p. 12). In Australia in 1989 scienceeducation programmes had the lowest entrance requirement of all university degrees.

A 1991 study in New Zealand by the Ministry of Research, Science and Technologyrevealed how little citizens of that country knew and cared about science. The study(based on the US tests of Jon Miller) of 1012 representative adults showed that:

• Fully 90% were scientifically illiterate, having less than a minimum understand-ing of the processes, terms and social impact of science.

• Only 13% were even attentive or interested in science, with an even smallerpercentage of women in the sample being interested.

• Only 3% were both literate and interested; that is most of the 10 per cent whowere scientifically literate, were not interested in science!

• Overall there was a negative attitude to science. (MORST 1991, p. 4).

There are complex economic, social, cultural, and systemic reasons for this rejectionof science. These are beyond the scope of teachers to rectify. But there are alsoeducational reasons for the rejection of science that are within the power of teachersand administrators to change. In 1989, for example, a disturbing number of the verytop Australian school science achievers gave ‘too boring’ as the reason for not pursuinguniversity science. It is these curriculum and pedagogical failings that the history andphilosophy of science (HPS) can help rectify.

Michael Matthews 3

Science and Cultural Health

Studies of scientific illiteracy reveal a situation that is culturally alarming, not justbecause they indicate that large percentages of the population do not know the meaningof basic scientific concepts,1 and thus have little if any idea of how nature functions andhow technology works, but because they suggest widespread antiscientific views, andillogical thought.

The defense of science in schools is important, if not necessary, to the intellectualhealth of society. Pseudoscientific and irrational world views already have a stronghold in Western culture; antiscience is on the rise.2 Newspaper astrology columnsare read by far more people than science columns; the tabloid press, with their Elvissightings and Martian visits, adorn checkout counters and are consumed by millionsworldwide each day. A 1991 Gallup Poll revealed that nearly half (47%) of all UScitizens believe that human life began on earth just a couple of thousand years ago(Smith, Siegel & McInerney 1995). A study at one Canadian university found that amajority of students believed in astrology, extrasensory perception, and reincarnation;while another estimated that 11% of US citizens claim to have seen a ghost (Cromer1993, p. 34). Surveys conducted over a three year period at the University of Texasrevealed that 60 per cent of students thought that some people could predict the futureby psychic powers, 35% believed in Black Magic, and the same percentage believed inghosts. A recent survey by the Australian Institute of Biology of 4,225 first-year biologystudents from 17 universities in all States showed that one in eight (12%) believed that‘God created man pretty much in his present form at one time within the last 10,000years.’ Old-fashioned chemistry sets are no longer even marketed, while tarot cardsand crystals are available on almost every street corner.

When thought becomes so free from rational constraints, then outpourings of racism,prejudice, hysteria and fanaticism of all kinds can be expected. For all its faults, sciencehas been an important factor in combating superstition, prejudice and ignorance. Ithas provided, albeit falteringly, a counterinfluence to the natural inclinations of peopleto judge circumstances in terms of their own self-interest. It instills a concern forevidence, and for having ideas judged not by personal or social interest, but by how theworld is; a sense of ‘Cosmic Piety,’ as Bertrand Russell called it. These values are underattack both inside and outside the academy. When people en masse abandon science,or science education abandons them, then the world is at a critical juncture. At such atime the role of the science teacher is especially vital, and in need of all the intellectualand material support possible.

1Jon D. Miller has conducted a series of large-scale studies on scientific literacy in the US. On the basis ofability to say something intelligible about concepts such as ‘molecule,’ ‘atom,’ ‘byte,’ in 1985 he judged only 3%of high-school graduates, 12% of college graduates, and 18% of college doctoral graduates to be scientificallyliterate. See Miller (1983, 1987, 1992.)

2For discussion of the anti-science phenomena see Passmore (1978), Holton (1993), Gross & Levitt (1994),and Grove (1989).


International History, Philosophy and Science Teaching Group

My work grows out of, and is a contribution to, the International History, Philosophy,and Science Teaching Group. This is a heterogenous group of teachers, scientists,educators, historians, mathematicians, philosophers of education and philosophers ofscience who have, since 1989, staged four international conferences3 and have ar-ranged the publication of many special issues of academic journals devoted to HPSand science teaching.4 Some basic papers in the field have been gathered togetherand published in my History, Philosophy, and Science Teaching: Select Readings (OISEPress, Toronto, and Teachers College Press, New York, 1990). These might be usefulfor further reading. The International History, Philosophy, and Science Teaching Groupis also associated with a new journal devoted to the subject of this paper—Science &Education: Contributions from the History, Philosophy, and Sociology of Science andEducation.5

The Rapprochement between History, Philosophy, and Science Education

In 1985 a paper was published titled ‘Science Education and Philosophy of Science:Twenty-Five Years of Mutually Exclusive Development’ (Duschl 1985). This was anaccount of the missed opportunities and shortsighted curricular projects that resultedfrom the development of science education largely separate from the disciplines ofhistory and philosophy of science. Pleasingly, in recent times there has been somerapprochement between these fields. The well-documented crisis in science educationand analyses of its causes and remedies are resulting in both the theory and, impor-tantly, the practice of science education becoming more informed by the history andphilosophy of science.

The present rapprochement between HPS and science education represents in parta renaissance of the long-marginalised liberal, or contextual, tradition of science edu-cation, a tradition contributed to in the last hundred years by scientists and educatorssuch as Ernst Mach, Pierre Duhem, Alfred North Whitehead, Percy Nunn, JamesConant, Joseph Schwab, Martin Wagenschein and Gerald Holton. The once-upon-a-time widespread acceptance of this liberal view of science teaching can be attested toby a comment made in a popular science teacher education text written over sixty years

3The proceedings of the 1989 Tallahassee conference are available in Hergret (1989, 1990); those of the1992 Kingston conference are in Hills (1992); the 1995 Minneapolis conference in Finley et al. (1995). The1999 conference was held in Pavia, Italy, and information can be obtained from Professor Fabio Bevilacqua,Dipartimento di Fisica, A. Volta,’ Universita di Pavia, Via A.Bassi 6, 27100 Pavia, Italy. The 2001 conferenceis being held in Denver, Colorado, USA and information can be obtained from William McComas, ProgramChair School of Education, WPH 1001E University of Southern California Los Angeles, CA 90089-0031, USAEmail: [email protected]

4The journal special issues include the following: Educational Philosophy and Theory 20(2), (1988);Synthese 80(1), (1989); Interchange 20(2), (1989); Studies in Philosophy and Education 10(1), (1990); ScienceEducation 75(1), (1991); Journal of Research in Science Teaching 29(4), (1992); International Journal ofScience Education 12(3), (1990); and Interchange 23(2,3), (1993).

5The journal is published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, TheNetherlands. It is available at reduced rates through the international HPS & ST group (inquiries to theauthor).

Michael Matthews 5

ago. The author, F.M. Westaway, writes that a successful science teacher is one who:

. . . knows [his/her] own subject . . . is widely read in other branches of science . . . knows how toteach . . . is able to express [him/her self] lucidly . . . is skillful in manipulation . . . is a logician. . . is something of a philosopher . . . is so far an historian that [he/she] can sit down with acrowd of [students] and talk to them about the personal equations, the lives, and the workof such geniuses as Galileo, Newton, Faraday and Darwin. More than all this, [he/she] is anenthusiast, full of faith in [his/her] own particular work. (Westaway, 1929, p. 3)

This is a nice sketch of the liberal, realist and contextual approach to the teachingof science that I advocate. If universities, and colleges of education, produced anabundance of such science teachers, many of the Western world’s science educationproblems would be diminished.

The liberal tradition is characterized by a number of educational commitments.6One is that education entails the introduction of children to the best traditions of theirculture, including the academic disciplines, in such a way that they both understandthe subject discipline, and know something about the discipline—its methodology, as-sumptions, limitations, history and so forth. A second feature is that, as far as ispossible and appropriate, the relations of particular subjects to each other, and theirrelation to the broader canvas of ethics, religion, culture, economics and politics shouldbe acknowledged and investigated. The liberal tradition seeks to overcome intellectualfragmentation.

One part of the contribution of HPS to science teaching is to connect topics inparticular scientific disciplines, to connect the disciplines of science with each other,to connect the sciences generally with mathematics, philosophy, literature, psychology,history, technology, commerce and theology. And finally, to display the interconnectionsof science and culture—the arts, ethics, religion, politics—more broadly. Science hasdeveloped in conjunction with other disciplines, there has been mutual interdepen-dence. It has also developed, and is practiced, within a broader cultural and socialmilieu. These interconnections and interdependencies can be appropriately exploredin science programs from elementary school to graduate study. The result is far moresatisfying for students than the unconnected topics that constitute most programs ofschool and university science. Courses in the sciences are too often, as one studentremarked, ‘forced marches through unknown country without time to look sideways.’

The routine topic of pendulum motion, for instance, when taught in such a way thatincludes consideration of its history and philosophy, results in the following kind ofintegrated learning experience for students. The science of pendulum motion connectswith important topics in religion, history, philosophy and literature.7

Contributors to the liberal tradition believe that science taught from such a per-spective, and informed by the history and philosophy of the subject, can engenderunderstanding of nature, the appreciation of beauty in both nature and science, and the

6There is a large literature on the theory and practice of liberal education. Peters (1966, chs. 1, 2) andBantock (1981, ch. 4) are useful introductions. See also Dressel (1979) and Mark (1994). The contributionsto Obler & Estrin (1962) focus on the contribution of science to a liberal education, as do the arguments inHolton (1973) and Schwab (1945).

7For further details see Matthews (1999).


RELIGION HISTORY SCIENCE PHILOSOPHY LITERATURE

PE

NDULUM

MOT ION

1

2 3

456

1. The Design Argument2. European Voyages of Discovery3. Aristotelian Physics and Methodology

4. Romantic Reaction5. Idealisation and Theory Testing6. Industrial Revolution

Figure 1: HPS-informed curriculum.

awareness of ethical issues unveiled by scientific knowledge and created by scientificpractice.

The liberal tradition maintains that science education should not just be an edu-cation or training in science, although of course it must be this, but also an educationabout science. Students educated in science should have an appreciation of scientificmethods, their diversity and their limitations. They should have a feeling for method-ological issues, such as how scientific theories are evaluated and how competing theo-ries are appraised, and a sense of the interrelated role of experiment, mathematics andreligious and philosophical commitment in the development of science. All students,whether science majors or others, should have some knowledge of the great episodes inthe development of science and consequently of culture: the ancient demythologizingof the world picture; the Copernican relocation of the earth from the centre of the solarsystem; the development of experimental and mathematical science associated withGalileo and Newton; Newton’s demonstration that the terrestrial laws of attractionoperated in the celestial realms; Darwin’s epochal theory of evolution and his claimsfor a naturalistic understanding of life; Pasteur’s discovery of the microbial basis ofinfection; Einstein’s theories of gravitation and relativity; the discovery of the DNAcode, and research on the genetic basis of life. They should, depending upon their

Michael Matthews 7

age, have an appreciation of the intellectual, technical, social and personal factors thatcontributed to these monumental achievements. Clearly all of these goals for generaleducation, and for science education, point to the integration of history and philosophyinto the science curriculum of schools and teacher education programmes. Teachersof science need to know something of the history and nature of the discipline they areteaching.

James Conant in the early 1950s expressed this perennial undercurrent in scienceeducation when he said “Being well-informed about science is not the same thing asunderstanding science . . . What is needed is methods for imparting some knowledge ofthe tactics and strategy of science” (Conant 1951). Conant realised that understandingscience’s local tactics (methods and processes of science), and the more global strategies(methodology and epistemology of science) required familiarity with the history ofscience, and some knowledge of the philosophy of science. For Conant, and the liberaltradition more generally, school science should be taught in such a way that it not onlybrings about scientific understanding, but also that it contributes to what is now called‘cultural literacy’ (Hirsch 1987).

Philosophy and Technical Science Education

The rapprochement between HPS and science education is not only dependent upon thevirtues of a liberal view of science education: a good technical science education alsorequires some integration of history and philosophy into the program. Knowledge ofscience entails knowledge of scientific facts, laws, theories—the products of science; italso entails knowledge of the processes of science—the technical and intellectual waysin which science develops and tests its knowledge claims. HPS is important for theunderstanding of these process skills. Technical—or ‘professional’ as it is sometimescalled—science education is enhanced if students know the meaning of terms thatthey are using and if they can think critically about texts, reports and their ownscientific activity. Their abilities as scientists are enhanced if they have read examplesof sustained inquiry, clever experimentation, and insightful hypotheses.

The US science educators James Rutherford (now director of the AAAS Project2061) and Joseph Schwab both stressed the importance of pupils acquiring skills inscientific method, but they recognised behind method lay important issues of method-ology. Methodology is the theory of method, it is the explanation of why method works,of why particular methods results in scientific knowledge. The distinction is somewhatakin to that between a chef and someone who follows a cookbook recipe. The chefknows why water is added after flour and baking powder to a cake mix, why certainflours but not others are used in sauces and so on. Following a cookbook does requireits own skills and these are not to be minimised, but successful following of cookbooksdoes not make people chefs. Training in cookbook recipes is not the same as theeducation of a chef. The latter requires some understanding of why the recipes work,why the ingredients are chosen, what the alternatives could be and so on. Likewisecompetence in scientific method, processes and skills—measuring rolling balls, lightingbunsens, choosing equipment, drawing graphs, devising hypotheses, thinking of controlconditions, locating errors, etc.—are all important competencies and are not be to


minimised, but such competencies do not make students scientific; they do not makethem any wiser about how these processes relate to the creation or testing of scientificknowledge. Method may not require philosophy but methodology does. And in as muchas technical science education aims to develop an appreciation of both scientific methodand methodology, then philosophy needs to be part of science education.

Consider for instance common laboratory work. Students might conduct an exper-iment on bodies rolling down an inclined plane, or on the period of different lengthpendulums, or on the ratio of tall versus short pea plants in different generationsof plants. These experiments might vary from, at the one end, routinised teacherdirected cookbook following, to at the other end, genuine open inquiry experiments. Inall cases there are important scientific method and process skills to be acquired; withthe inquiry experiments requiring more of the cognitive skills of hypothesis generationand experimental design. But across the spectrum there are methodological questionsthat transcend the simple method skills. How does the data relate to the phenomena?How do descriptions relate to observations? What can be legitimately inferred fromthe data? How do singular statements (the experimental data) bear upon universalstatements (supposed scientific laws)? In what circumstances can experimental datafalsify hypotheses or laws? In what circumstances, if any, can data verify laws? Howcan data confirm laws? These questions all give rise to standard methodological issuesabout induction, falsification, theory dependence of observation, the epistemologicalstatus of theory, the ontological status of theoretical terms, and so on. These questionsare the bread and butter of philosophy of science, and students can be encouraged todine on them.

Others have made the same point about logic and science education. A 1966 paper inThe Science Teacher is titled ‘Use Philosophy to Explain the Scientific Method’ (Berlin& Gaines 1966). An informative 1977 paper, drawing on Matthew Lipman’s Philosophyfor Children material, and published in Science Education is titled ‘Philosophic Inquiryand the Logic of Elementary School Science Education’ (Wagner & Lucas 1977). Thereasoning dimension of science competence has been recognised in curriculum doc-uments. Ehud Jungwirth in a comprehensive study of the issue, lists a number ofcurriculum statements that make reference to critical-logical-analytical thinking skills(Jungwirth 1987).

Alfred North Whitehead expressed this view of good technical education when, justafter World War II, he said:

The antithesis between a technical and a liberal education is fallacious. There can be no ade-quate technical education which is not liberal, and no liberal education which is not technical:that is, no education which does not impart both technique and intellectual vision. (Whitehead1947, p. 73)

A common occurrence in science classrooms is a child asking: If no one has seenatoms, how come we are drawing pictures of them? Such a child is raising one of themost interesting questions in philosophy of science: the relationship of evidence tomodels, and of models to reality. Good science teachers should encourage such ques-tions and be able to provide satisfactory answers, or suggestions for further questions.

Michael Matthews 9

To reply “I do not know,” or “because it is in the book” is to forego the opportunityof introducing students to the rich methodological dimensions of science. Einsteincaught this philosophical dimension of science when he once described physicists as“philosophers in workmen’s clothes.” Science teachers, as well as being competent inscience, psychology, pastoral care, crisis management and everything else demandedof them, need also to be philosophers. Students commonly ask: Why are we studyingthis? How do we know this is true? Does this make sense to anyone? Teachers shouldtake advantage of such questions to widen the intellectual horizons of their students,to give them a sense that there are many big issues about that deserve reflection andconsideration.

Philosophy is not far below the surface in any scientific investigation. At a most ba-sic level any text or scientific discussion will contain terms such as ‘law,’ ‘theory,’ ‘model,’‘explanation,’ ‘cause,’ ‘truth,’ ‘knowledge,’ ‘hypothesis,’ ‘confirmation,’ ‘observation’ andso on. Philosophy begins when students and teachers slow down the science lessonand ask what these terms mean and what the conditions are for their correct use. Allof these concepts contribute to, and in part arise from, philosophical deliberation onissues of epistemology and metaphysics: questions about what things can be knownand how we can know them, and about what things actually exist in the world and therelations possible between them. Students and teachers can be encouraged to ask thephilosopher’s standard questions: What do you mean by ? and How do youknow ? of all these concepts. Such introductory philosophical analysis allowsgreater appreciation of the distinct empirical and conceptual issues involved when forinstance Boyle’s Law, Dalton’s model, or Darwin’s theory is discussed. It also promotescritical and reflective thinking more generally.

Lee Shulman, a US educational researcher and policy analyst, has developed thisfeature of the teacher’s role with his notion of Pedagogical Content Knowledge. Of thishe has said:

To think properly about content knowledge requires going beyond knowledge of the facts orconcepts of a domain. It requires understanding the structures of the subject matter . . . Teach-ers must not only be capable of defining for students the accepted truths in a domain. Theymust also be able to explain why a particular proposition is deemed warranted, why it is worthknowing, and how it relates to other propositions, both within the discipline and without, bothin theory and in practice. (Shulman 1986, p. 9)

The abilities sought by Shulman are enhanced if teachers are interested in andfamiliar with the history and philosophy of whatever subject they are teaching. The USNational Standards in Science Education group is urging teachers to ask themselvesand their students not just what do we know in science, but how do we know what weknow. These are routine methodological questions that lead into and are answered bythe philosophy of science.

Current Curriculum Proposals

Integration of HPS and science education has been proposed recently by numerousgovernment and educational bodies. Among these have been the American Association


for the Advancement of Science in two of its very influential reports Project 2061 (AAAS1989) and The Liberal Art of Science (AAAS 1990); the British National CurriculumCouncil (NCC 1988); the Science Council of Canada (SCC 1984); the Danish Scienceand Technology curriculum, and in The Netherlands, the PLON curriculum materials.8In these cases HPS is not simply another item of subject matter added to the sciencesyllabus; what is proposed is the more general incorporation of HPS themes into thecontent of curricula. The American Association for the Advancement of Science, in itsProject 2061 proposal, has written that:

Science courses should place science in its historical perspective. Liberally educated students—the science major and the non-major alike—should complete their science courses with anappreciation of science as part of an intellectual, social, and cultural tradition. . . . Sciencecourses must convey these aspects of science by stressing its ethical, social, economic, andpolitical dimensions. (AAAS 1989, p. 24)

The AAAS in its proposal for the reform of college science teaching, The LiberalArt of Science, recognises that science education is enriched, and is more faithful to itssubject, if aspects of the interesting and complex interplay of science and philosophycan be conveyed in the classroom. It says:

The teaching of science must explore the interplay between science and the intellectual andcultural traditions in which it is firmly embedded. Science has a history that can demonstratethe relationship between science and the wider world of ideas and can illuminate contemporaryissues. (AAAS 1990, p. xiv)

The advocates of a contextual approach to science teaching are not just educationaldreamers. There has been a tradition of attempts to teach science in an HPS-informedor liberal manner. The strengths and weaknesses of these attempts can be examined.Perhaps the outstanding example was the Harvard Project Physics course developed forschools in the early 1960s by Gerald Holton, James Rutherford and Fletcher Watson.9Over sixty studies of the effectiveness of the program were published (Welch 1973)and these were all positive and encouraging. Measures such as retention in science,participation of women, improvement on critical thinking tests and understandingof subject matter all showed improvement where the Project Physics curriculum wasadopted. Another example of a widely adopted HPS-influenced course was the YellowVersion of the BSCS Biology course developed by John Moore and Joseph Schwab.10

8The British National Curriculum is documented in NCC (1988). It is discussed in Akeroyd (1989), Ray(1991), and Solomon (1991). The Danish curriculum in the History of Science and Technology is discussedin Nielsen & Nielsen (1988), and Nielsen & Thomsen (1990). In The Netherlands there has been a ‘Physicsin Society’ course since 1981 (Eijkelhof & Swager 1983), and since 1972 various materials generated bythe PLON project have incorporated a HPS dimension (Project Curriculum Development in Physics, POBox 80.008, 3508 TA Utrecht, The Netherlands). The Project 2061 proposals are contained in AAAS (1989)and republished in Rutherford & Ahlgren (1990); they are discussed in Stein (1989). A discussion of STSprogrammes and a guide to the literature can be found in McFadden (1989) and Yager (1993).

9Fifteen per cent of US high school physics students were following this program at its peak, and it waswidely used outside the US. The philosophy behind this program can be read in Gerald Holton (1978a), andin the symposium published in The Physics Teacher (1967, vol. 5 no. 2). Other evaluations of Harvard ProjectPhysics can be found in Aikenhead (1974), Brush (1978, 1989), Russell (1981), and Welch & Walberg (1972).

10This was first published in 1963 and went through four editions up to 1980.

Michael Matthews 11

Contributions of HPS to Science Education

The inclusion of history and philosophy of science does not, of course, provide all theanswers to the present science education crisis—ultimately these answers lie deep inthe heart of culture and economics. But the history and philosophy of science has acontribution to make to the overall task of improving science teaching and learning.Aspects of this contribution might be itemized as follows:

• HPS can humanize the sciences and connect them to personal, ethical, cultural,and political concerns. There is evidence that this makes science and engineer-ing programmes more attractive to many students, and particularly girls, whocurrently reject them.

• HPS, particularly basic logical and analytic exercises—Does this conclusion fol-low from the premises? and, What do you mean by such and such?—can makeclassrooms more challenging, and enhance reasoning and critical thinking skills.

• HPS can contribute to the fuller understanding of scientific subject matter—it canhelp to overcome the ‘sea of meaninglessness,’ as Joseph Novak once said, whereformulae and equations are recited without knowledge of what they mean or towhat they refer.

• HPS can improve teacher education by assisting teachers to develop a richer andmore authentic understanding of science and its place in the intellectual andsocial scheme of things. This has a flow-on effect, as there is much evidence thatteachers’ epistemology, or views about the nature of science, affect how they teachand the message they convey to students.

• HPS can assist teachers appreciate the learning difficulties of students, becauseit alerts them to the historic difficulties of scientific development and conceptualchange. Galileo was forty years of age before he formulated the modern conceptionof acceleration, despite prolonged thought he never worked out a correct theoryfor the tides. By historical studies teachers can see what some of the intellectualand conceptual difficulties were in the early periods of scientific disciplines. Thisknowledge can assist with the organization of the curriculum and the teaching oflessons.

• HPS can contribute to the clearer appraisal of many contemporary educationaldebates that engage science teachers and curriculum planners. Many of thesedebates—about constructivist teaching methods, multicultural science education,feminist science, environmental science, inquiry learning, science-technology-societycurricula and so forth—make claims and assumptions about the history and epis-temology of science, or the nature of human knowledge and its production andvalidation. Without some grounding in HPS, teachers can be too easily carriedalong by fashionable ideas which later, sadly, ‘seemed good at the time.’


There are various ways in which the interplay between science and philosophy canbe conveyed: reading of selections from original sources; joint projects with history, so-cial science, divinity or literature classes; dramatic reenactments of significant episodesin the history of science; essays on selected themes; debates on topical matters; or low-level philosophical questioning about scientific topics being studied or practical workbeing conducted. All philosophy of science begins with analytical and logical matters:What does a particular concept mean? How do we know the truth of a proposition? Doesa conclusion follow from the premises adduced? These analytic and logical questionsand habits of thought can be introduced as early as preschool—as Matthew Lipmanand the Philosophy for Children programs attest—and they can be refined as childrenmature (Lipman & Sharp 1978). Susan Johnson and Jim Stewart (1991) provide a niceexample of the incorporation of philosophy of science into a high school genetics course.They focus on the ‘three Ps’ of science: problem posing, problem solving, and persuasionof peers.

School courses in Science-Technology-Society (STS) are another area in which sci-ence courses connect with philosophy, particularly ethical and political philosophy. A1990 Department of Education guide to STS education issued by the provincial govern-ment of Alberta, Canada—Unifying the Goals of Science Education—gives prominenceto teaching about the nature of science. Its reading list includes the work of Hawking,Einstein, Holton, Kuhn, Latour, Polanyi and Ravetz. A recent list of common STS topicsincludes: abortion, AIDS, endangered species, genetic engineering, organ transplants,nuclear war, space exploration, and waste management (Rubba et al.1991). These STScourses in England, Holland, Canada, and the US11 deal explicitly with political andethical issues involving notions such as justice, equality, the fair distribution of goods,responsibility and the like—all of which are clarified by philosophical analysis, andby reference to the history of these ideas. Without philosophical input, STS coursesrun the risk of just repeating fashionable and shallow ideology about pollution, nuclearenergy, conservation and so on. This was seen in the 1940s in Science for Consumerscourses. Shallow views on these vital matters tend to be blown away at the first gustof national- or self-interest that the student encounters upon leaving school.

There is not, of course, a single HPS-informed view of science or of science education.There are two broad camps discernible in the literature: those who appeal to HPS tosupport the teaching of science, and those who appeal to HPS to puncture the perceivedarrogance and authority of science. The second group stress the human face of science,the fallibility of science, the impact of politics and special interests, including racial,class and sexual interests, on the pursuit of science; they argue for skepticism aboutscientific knowledge claims. For this group, HPS shows that science is one among anumber of equally valid ways of looking at the world, it has no epistemic privilege;its supposed privilege derives merely from social considerations and technological suc-cess. This group includes those influenced by postmodernist philosophy, and certainsociologies of science.

11See the two NSTA Yearbooks Redesigning Science and Technology Education (Bybee et al. 1984) andScience, Technology, Society (Bybee 1985), and their volume The Science, Technology, Society Movement(Yager 1993).

Michael Matthews 13

Conclusion

There are many reasons why study of the history and philosophy of science shouldbe part of preservice and in-service science teacher education programs. Increasinglyschool science courses address historical, philosophical, ethical and cultural issuesoccasioned by science. Teachers of such curricula obviously need knowledge of HPS.Without such knowledge they either present truncated versions of the curricula, orrepeat uncritical gossip about the topics mentioned. Either way their students aredone a disservice. But even where curricula do not include such ‘nature of science’sections, HPS can contribute to more interesting and critical teaching of science.

Beyond these ‘practical’ arguments for HPS in teacher education, there are com-pelling ‘professional’ arguments. A teacher ought to know more than just what he orshe teaches. As an educator, they need to know something about the body of knowledgethey are teaching, something about how this knowledge has come about, how its claimsare justified and what its limitations are. Teachers should have a feel for, or appreci-ation of, the tradition of inquiry into which they are initiating students. HPS fostersthis.

Education systems have a responsibility to identify and transmit the best of ourcultural heritage. Science is one of the most important parts of this heritage. Thehistory and philosophy of science allows science teachers to better understand theirown social and professional responsibilities as part of a great tradition.

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Does Science Teaching Need History and Philosophy of Science?

Peter SlezakUniversity of New South Wales, Australia. Email: [email protected]

The place of History and Philosophy of Science (HPS) in the science curriculum derivesfrom the rationale for teaching science itself. The point is best appreciated by meansof an illustration. We see one familiar rationale for teaching science in the remarks ofCollins & Pinch (1992):

It is nice to know the content of science—it helps one to do a lot of things such as repair thecar, wire a plug, build a model aeroplane, use a personal computer to some effect, know wherein the oven to put a souffle, lower one’s energy bills, disinfect a wound, repair the kettle, avoidblowing oneself up with the gas cooker, and much much more. (Collins & Pinch 1992, p. 150)

Such a utilitarian view of science has consequences not only for how science istaught, but also for how research is pursued. If seen primarily in terms of its use-fulness, even this practical aspect of science may be jeopardised, for curiosity-driven re-search is not merely a dispensable luxury, but the very mechanism of scientific progress.Thus, the prosaic, pragmatic conception of science education of Collins and Pinch isa view which might be thought to leave out something important. It is no accidentthat this view of science and its value in the curriculum is articulated by sociologistswho are among the foremost proponents of a ‘constructivist’ and relativist conceptionaccording to which science is not to be understood in terms of its rational, intellectual,explanatory content but rather as a merely consensual, negotiated and culturally con-tingent convention based on interests and politics. This approach has been an avowedlydeflationist one, skeptical of the claims of science as a privileged form of knowledge and,therefore, concerned to demote it from its exalted status and unwarranted pretensions.

The view of science as merely instrumentally useful, at best, is in keeping witha widespread anti-science sentiment, indeed hostility, which has fuelled the recent‘science wars’ (Gross & Levitt 1994). Laudan (1990, p. x) has scathingly describedsociological relativist views as “the most prominent and pernicious manifestation ofanti-intellectualism in our time.” The charge of anti-intellectualism points to the aspectof social constructivism which has the most direct pedagogical implications. Such meta-scientific, philosophical views will inevitably have some influence on the teaching ofscience content. On such constructivist views (Ashmore 1993, Pinch & Collins 1984)there is no more warrant for teaching currently accepted science than discreditedtheories since there are no intellectual grounds to distinguish between them, only socialand political ones (see Slezak 2000).

At the opposite end of the spectrum, we may note an actual example of scienceteaching which is informed by a different outlook, namely, one which seeks to conveya picture of science as the highest achievements of the human intellect. Densmore’s(1995) text reconstructs the central argument of Newton’s Principia and suggests whatit means for a student to make the attempt to appreciate Newton’s achievement:

20 Does Science Teaching Need History and Philosophy of Science?

. . . one can feel the sense of adventure and intrigue, the challenge of solving the puzzle. It canbe viewed as one views many games and puzzles people buy and play voluntarily for fun. Itcan be viewed as one views a good detective story: all the clues are there . . .. (Densmore 1995,p. xxxi)

This conception is in the spirit of those such as Jacob Bronowski (1960, 1964, 1978)who writes of science as the highest romantic adventure with intellectual, aestheticand inspirational qualities equal to those of the arts. Indeed, beyond these, Bronowskihas emphasized the fundamental moral dimension of science which echoes the valuesemphasized by Popper and other philosophers of science.

The Inevitability of HPS in the Curriculum.

The contrast between the foregoing views of science raises precisely the issue of whetheror not it is possible to teach the content of science without explicitly addressing issuesabout science. I will suggest that HPS cannot be avoided in the science curriculumsimply because some position on fundamental questions will be implicitly assumedeven where it is not explicitly addressed. Arguably, therefore, it is better to addresssuch conceptions openly as part of science teaching rather than to insinuate themtacitly. However, this, in turn, requires familiarity with the range of opinions anddoctrines in the discipline of HPS. The value of a self-conscious concern with meta-scientific issues is attested by Einstein in the following remarks:

How does a normally talented research scientist come to concern himself with the theory ofknowledge? Is there not more valuable work to be done in his field? I hear this from manyof my professional colleagues; or rather, I sense in the case of many more of them that thisis what they feel. I cannot share this opinion. When I think of the ablest students whom Ihave encountered in teaching—i.e., those who distinguish themselves by their independence ofjudgement, and not only by mere agility—I find that they had a lively concern for the theoryof knowledge. They liked to start discussions concerning the aims and methods of the sciences,and showed unequivocally by the obstinacy with which they defended their views that thissubject seemed important to them. (Einstein 1916, quoted in Holton 1973)

As if responding directly to Collins and Pinch, Einstein adds:

. . . For when I turn to science not for some superficial reason such as money-making or ambi-tion, and also not (or at least exclusively) for the pleasure of the sport, the delights of brain-athletics, then the following questions must burningly interest me as a disciple of this science:What goal will and can be reached by the science to which I am dedicating myself? To whatextent are its general results ‘true?’ What is essential, and what is based only on the accidentsof development? (Einstein 1916, quoted in Holton 1973)

Naive Philosophy of Science

Just as people have a naive, intuitive, commonsense understanding of the physicalworld which is Aristotelian, so they have a naive meta-knowledge or commonsenseconception of the nature of science itself. Thus, what philosophers have dubbed the‘pessimistic historical meta-induction’ is, in fact, the most widespread view amonglaypersons and the scientifically illiterate. Echoing a popular skepticism, Laudan(1981, p. 232) has argued that a difficulty for realism is the fact that the history of

Peter Slezak 21

science offers a long list of successful theories which turn out to be wrong. Specifically,they appear to be nonreferential with respect to central explanatory concepts andposits. Thus we no longer believe in the existence of crystalline spheres, bodily humors,phlogiston, caloric, vital forces or the luminiferous ether, inter alia. The ‘pessimisticmeta-induction’ is captured in Glymour’s (1992) observation:

Since all [scientific] theories in history have been false, . . . we should conclude that the methodsof science do not generate true theories; hence our present scientific theories, which wereobtained by the same methods, are false as well. (Glymour 1992, p. 126)

Even if knowing little else, everyone is aware that science is historically changeable.The important question, then, is what conclusions may be drawn from this undeniablefact about the history of science. For non-experts, the mutability of science seemsto warrant a general belief in the need to remain “open minded” about miraculousor paranormal phenomena which are contrary to accepted scientific theories. Thus,for example, a standard popular response to skepticism about psychic phenomenais to cite the supposed lessons of the history of science and its ever changing bodyof beliefs. This lesson is taken to dictate an “open-mindedness” about unorthodoxand even disreputable theories rather than “dogmatic” dismissal. This “tolerance” isallegedly inferred from earlier mistakes and is often justified with the slogan “Theylaughed at Galileo too.” However, an apt answer which has been given by skeptics is“Yes, but they laughed at Bozo the clown too.” Being unorthodox is not, in itself, avirtue.

Recruited in this way as support for some currently unfounded pseudo-science, theargument from history is entirely vacuous despite being almost universally seen asself-evident. The ‘insight’ is only the wisdom of hindsight, because it cannot providegrounds for deciding what to believe in any given case today. However difficult toexplicate, warranted belief must be based on the usual considerations of evidence,explanatory coherence, comprehensiveness, elegance, and whatever other factors playa role. None of these are weighted differently in the light of the historical mutabilityof science. Based on past practice, knowing only that what we believe tomorrow willbe different from what we believe today carries no specific implication or prescriptionfor current beliefs. Nevertheless, generally deployed in this way, an inexplicit, naivephilosophy of science is taken to warrant either credulity or global skepticism.

Closed Mind or Open Mind?

In his characteristically ironic way, Bertrand Russell (1925) has noted a well-knownfeature of education:

A certain percentage of children have the habit of thinking; one of the aims of education is tocure them of this habit. (Russell 1925, p. 378)

When faced explicitly as a question about the place of HPS in the curriculum, theissue of open-mindedness poses a seeming paradox. Undeniably, one of the centralfeatures of science emphasized by many scholars has been its critical nature. Popper


(1963) has emphasized that the origin of science among the Presocratics was specif-ically founded in their inauguration of a tradition of critical inquiry as opposed todogmatic acceptance of orthodoxy. The same moral has been emphasized by schol-ars such as Guthrie (1962) and Farrington (1961) who share Popper’s view that theessence of the scientific enterprise was first captured by these Milesian Greeks in theircommitment to criticism as the means for improving and advancing our understandingof the world. For Popper, this theme of ‘conjectures and refutations’ found expression inhis doctrine of falsifiability as the mark of science, distinguishing it from metaphysicsor other pseudo-scientific inquiries. Thus, he asserts “Criticism is the lifeblood of allrational thought” (Popper 1974). In view of this widely held conception of science, anacute paradox is presented by T.S. Kuhn who writes:

To turn Sir Karl’s view on its head, it is precisely the abandonment of critical discourse thatmarks the transition to science. (Kuhn 1970b, p. 6)

For those wishing to teach science as an embodiment of rationality and critical think-ing, it is important to reconcile this Popperian conception with Kuhn’s radically alter-native picture of science as founded on dogmatism. In a famous essay The EssentialTension, Kuhn observes that:

. . . exclusive exposure to a rigid tradition has been immensely productive of the most conse-quential sorts of innovations. . . . each of [the natural sciences] acquired something like thattechnique [of rigid education] at precisely the point when the field began to make rapid andsystematic progress. (Kuhn 1959, pp. 229-231)

The dilemma for science educators arises from recognizing the divergence betweenthe rhetoric and the reality of scientific practice. The theme of Kuhn’s essay is thetension between open and closed mindedness, that is, between ‘convergent’ and ‘diver-gent’ thinking . Divergent thinking is the flexible or ‘lateral’ thinking characteristic ofcreative discovery and innovation. Kuhn explains:

The basic scientist “must lack prejudice to a degree where he can look at the most ‘self-evident’facts or concepts without necessarily accepting them, and, conversely, allow his imagination toplay with the most unlikely possibilities” . . .

. . . “divergent thinking [is] the freedom to go off in different directions, . . . rejecting the oldsolutions and striking out in some new direction.”. . . gigantic divergences lie at the core of the most significant episodes in scientific development.(Kuhn 1959, p. 226)

Kuhn notes that a common criticism of science education complains that it empha-sizes narrow or convergent thinking at the expense of creative, divergent thinking.This criticism suggests “We have attempted to teach students how to arrive at ‘correct’answers that our civilization has taught us are correct . . .. Outside the arts . . . we havegenerally discouraged the development of divergent thinking abilities, unintentionally.”Kuhn acknowledges that this characterization of our educational practice is eminentlyjust, but he askes “whether it is equally just to deplore the product that results.” Kuhnis pointing to the function of science education and textbooks as indoctrination, and tothe crucial role of such indoctrination in the very success of science.

In an ironic defence of dogmatism Kuhn explains:

Peter Slezak 23

But both my own experience in scientific research and my reading of the history of scienceslead me to wonder whether flexibility and open-mindedness have not been too exclusivelyemphasized as the characteristics requisite for basic research.. . . normal research, even the best of it, is a highly convergent activity based firmly upon asettled consensus acquired from scientific education and reinforced by subsequent life in theprofession.Let me try briefly to epitomize the nature of education in the natural sciences . . .. The singlemost striking feature of this education is that, to an extent totally unknown in other creativefields, it is conducted entirely through textbooks . . . written especially for students. . . . Thereare no collections of “readings” in the natural science. Nor are science students encouragedto read the historical classics of their fields—works in which they might discover other waysof regarding the problems discussed in their textbooks, but in which they would also meetproblems, concepts, and standards of solution that their future professions have long sincediscarded and replaced. . . . These books exhibit concrete problem solutions that the professionhas come to accept as paradigms, . . . Nothing could be better calculated to produce “mentalsets” . . . Even the most faintly liberal educational theory must view this pedagogic techniqueas anathema. . . . Education in the natural sciences seems to have been totally unaffectedby [attitudes encouraging ‘divergent’ thinking, open-mindedness and creativity, innovationetc.]. . . . It remains a dogmatic initiation in a pre-established tradition that the student isnot equipped to evaluate. (Kuhn 1959, pp. 228-229)

Kuhn’s view reverses a traditional conception of science and how it should be taught.For example, on such a view one common picture of the Galileo affair is mistaken, sincethe orthodox Aristotelianism of the Catholic Church was not essentially different in itsconservatism from that of science itself.

History of Science as Subversive

Conventional goals of science teaching have been articulated in authoritative and influ-ential policy documents as inductive generalization from data, a venerable conceptionseen in historical figures such as Herschel and Planck. However, such pronouncements,like other methodological doctrines, are impossible to reconcile with the actual practiceof scientists themselves as revealed by the historical record. In this regard, historyhas a subversive effect in undermining widely held prejudices about science. Thus, forexample, S. Brush (1974) writes:

Once it has been pointed out that in Galileo’s statement, “I have discovered by experimentsome properties of [motion],” the words “by experiment” were added in an English translationand do not appear in the original Italian version, it is hard to maintain the traditional faith inGalileo’s empiricism. (Brush 1974, p. 1170)

Another distinguished historian of science remarks on Isaac Newton in the same vein:

If the Principia established the quantitative pattern of modern science, it equally suggesteda less sublime truth—that no one can manipulate the fudge factor quite so effectively as themaster mathematician himself. (Westfall, quoted in Brush 1974, p. 1167)

Contrary to a naive empiricist views, Newton’s approach is characterised by Densmore:

This attempt to give science a logically sound deductive basis constituted a radical departurefrom Francis Bacon’s inductive method, which was very influential at the time [and more


recently]. Bacon advocated collecting many and varied instances of the phenomena under studyand trying to see patterns.By contrast Newton used minimal experimental data. . . . Everything was deduced, usingmathematical demonstrations, from these few observation-based conclusions about how ourworld works. (Densmore 1995, p. xxi)

However, more surprising perhaps than Newton’s failure to employ inductive methodsis his commitment to quite radically different principles not usually thought compatiblewith scientific method. Thus, Newton writes in his Principia:

I had an eye upon such principles as might work with considering men for the belief of a Deity;and nothing can rejoice me more than to find it useful for that purpose.

Evidently, Newton’s goal was to demonstrate the dependence of matter on God. West-fall notes:

He sought as well to plumb the mind of God and His eternal plan for the world and mankindas it was presented in the biblical prophecies. (Westfall 1980, p. 105)

In the famous passages of the General Scholium of Book Three in Newton’s PhilosophiaeNaturalis Principia Mathematica, Newton not only utters his famous “hypotheses nonfingo”, that is, his unwillingness to speculate about the occult causes of gravitationalaction at a distance. More remarkably, though rarely noted, is the fact that Newtonalso expresses a conception of a designer deity:

This most elegant arrangement of the sun, planets, and comets could not have arisen but by theplan and rule of an intelligent and powerful being. And if the fixed stars be centers of similarsystems, all these, constructed by a similar plan, will be under the rule of One . . .

He governs everything, not as the soul of the world, but as lord of all things. And because ofhis dominion, he is usually called “Lord God Universal Emperor” . . . And from true absoluterule it follows that the true God is living, intelligent, or in the highest degree perfect. He iseternal and infinite, omnipotent and omniscient; that is, he endures from eternity to eternity,and is present from infinity to infinity. He reigns over everything, and knows everything thathappens or can happen. . . .

The whole diversity of created things according to places and times could only have arisenfrom the ideas and will of a being existing necessarily. . . . And this much concerning God,to discourse of whom, at least from the phenomena, is the business of natural philosophy.(Newton, in Densmore & Donahue 1985)

Such passages in the midst of the scientific theorising require us to qualify precon-ceptions about what is the properly “scientific” part of Newton’s work, and they serveto remind us of the arbitrariness of dismissing in retrospect those parts which we maynow regard as pseudo-scientific or religious. These distinctions appear not to have beenmeaningful to Newton himself. This is of course, the lesson of Kuhn’s (1970) work.

A further example is instructive. A common conception of science as driven byempirical data is amusingly illuminated by anecdotes about Einstein:

“But you don’t seriously believe,” Einstein protested, “that none but observable magnitudesmust go into a physical theory?” “Isn’t that precisely what you have done with relativity?” Iasked in some surprise. . . . “Possibly I did use this kind of reasoning,” Einstein admitted, “but

Peter Slezak 25

it is nonsense all the same. Perhaps I could put it more diplomatically by saying that it may beheuristically useful to keep in mind what one has actually observed. But on principle, it is quitewrong to try founding a theory on observable magnitudes alone. In reality the very oppositehappens. It is the theory which decides what we can observe.” (Heisenberg 1971, p. 63)

In the autumn of 1919, in the course of a discussion with a student, Einstein—now aged40—handed her a cable which had informed him that the bending of light by the sun wasin agreement with his general relativistic prediction. The student asked what he would havesaid if there had been no confirmation. Einstein replied, “Then I would have to pity the dearLord. The theory is correct anyway.” (Pais 1994, p. 127)

This last anecdote is interesting in part because the confirmation of the bending oflight was cited by Karl Popper as the very exemplary case of falsifiability. Einstein’sattitude reveals how little scientists conform to Popperian conceptions of rationality.However, more forceful than such anecdote is the systematic study of episodes such asthe famous Eddington expedition referred to in the story by Pais. Earman and Glymour(1980) reveal that the entire episode is a case study of Duhem-Quine adjustment of aux-iliary hypotheses in order to save a favoured theory faced with recalcitrant evidence.They write:

The initial reception of special relativity in English speaking countries was almost uniformlyhostile or disdainful. . . . One may imagine that in order to turn the tide of opinion the eclipseresults must have been unequivocal. They were not. (Earman & Glymour 1980, p. 50)In truth, while some aspects of Eddington’s [1919] handling of the deflection of light were in thefinest traditions of science, others were not. As he confessed in Space, time and gravitation, hewas “not altogether unbiased.” The bias showed in his treatment of the evidence: he repeatedlyposed a false trichotomy for the deflection results, claimed the superiority of the qualitativelyinferior Principe data, and suppressed reference to the negative Sobral results. (His discussionof the red-shift was sometimes no better . . .). . . all that was necessary to establish the red-shift prediction was a willingness to throw outmost of the evidence and the ingenuity to contrive arguments that would justify doing so.. . . The red-shift was confirmed because reputable people agreed to throw out a good part ofthe observations. They did so in part because they believe the theory; and they believed thetheory, again at least in part, because they believed that the British eclipse expeditions hadconfirmed it. Now the eclipse expeditions confirmed the theory only if part of the observationswere thrown out and the discrepancies in the remainder ignored: Dyson and Eddington, whopresented the results to the scientific world, threw out a good part of the data and ignored thediscrepancies.This curious sequence of reasons might be cause enough for despair on the part of those whosee in science a model of objectivity and rationality. That mood should be lightened by thereflection that the theory in which Eddington placed his faith because he thought it beautifuland profound—and, possibly, because he thought that it would be best for the world if itwere true—this theory, so far as we know, still holds the truth about space, time and gravity.(Earman & Glymour 1980, pp. 84-85)

Contextual Approach: Is Content Knowledge HPS-free?

For the reasons indicated, there seems to be no alternative to a contextualist approachas advocated by Matthews (1992, p. 12) in which students learn about the ‘nature ofscience’ simultaneously with learning the substantive content of science. In particular,the intention is not that HPS topics be extraneous, added on to science courses, or thatHPS be substituted for content knowledge. Rather these themes should be integratedinto the curriculum material itself as an intrinsic part.


No one expects children to solve the realism/instrumentalism debate, nor should they learncatechism-like that there were fifteen reasons why Galileo was right and the cardinals wrong.Rather they are expected to appreciate something of the intellectual issues that are at stakein these matters; to appreciate that there are questions to ask and to begin to think not justabout answers, but what would count as answers, and what kinds of evidence would supportour answers. (Matthews 1992, p. 14)

The understanding of content knowledge cannot be HPS-free because even learningthe bare ‘facts’ and theories of science inherently requires understanding such things asthe evidential warrant for one theory and why it might be preferred over another, whatcounts as an explanation, refutation etc. For example, how else can one explain whyevolution is to be preferred to creationism without some appeal to weight of evidence,explanatory force and other such concepts central to the philosophy of science? Notleast of all, this example inevitably raises the issue of demarcation between scienceand pseudo-science which has been a central theme in the philosophy of science atleast since David Hume and Immanuel Kant.

The educational significance of such philosophical questions is brought into sharprelief in the text-book and curriculum debates concerning creation science which haverecently been revived in the USA (See Ruse 1988, Laudan 1988).

Paradox of HPS in Science Teaching

If, as just suggested, science cannot be taught as bare content, facts, theories andformulae without some implicit philosophical doctrine, an apparent paradox arisesfrom the need to make such doctrine explicit. The theories of HPS are themselvescontroversial and changeable. The alternative to not teaching HPS explicitly seems tobe that of teaching more or less controversial philosophical views which are themselvesless secure than the science content itself. Thus, for example, teaching physics byintegrating something of the history of Galileo confronts the difficulty of finding a non-controversial picture. Galileo has been seen in the following ways. William Whewell(1840) wrote

Galileo was an inductivist and empiricist with “prepondering inclination towards facts, and didnot feel, so much as some other persons of his time, the need of reducing them to ideas. (Quotedin Matthews 1992, p. 19)

David Brewster (1830) suggested Galileo was a Baconian inductivist, while ErnstMach (1883) and the positivists suggest that “Galileo did not supply us with a theoryof the falling of bodies, but investigated, wholly without preformed opinions, the actualfacts of falling.” Alexandre Koyre (1939) claimed that Galileo was a Platonist whoinvented some experiments, while Stillman Drake (1978) argued that Galileo was apatient experimentalist. Notoriously, Paul Feyerabend (1975) argued that Galileo wasan anarchist, dadaist and propagandist with no “method.” Finally, Stillman Drake(1971) disputes a common view in claiming that Galileo fought not against religion orthe church but against authority. In light of these diverse accounts, it would seem thatHPS becomes something like Bertrand Russell’s parody of animal psychology:

Peter Slezak 27

Animals studied by Americans rush about frantically, with an incredible display of hustle andpep, and at last achieve the desired result by chance. Animals observed by Germans sit stilland think, and at last evolve the solution out of their inner consciousness. (Russell 1960, p. 33)

Matthews (1992) has characterised this as the ‘hermeneutical problem’ which hasimportant intellectual virtues, despite the inherent difficulty:

The hermeneutical problem of interpretation in the history of science, far from being an em-barrassment or impediment to the use of history, can be the occcasion to introduce students tothe significant questions of how we read texts and interpret events, to the complex problems ofmeaning: students know from their everyday life that people see things differently, the historyof science is a natural vehicle for illustrating how this fact impinges on science itself. (Matthews1992, p. 22)

A Role for History: The Bias of Science Textbooks

Following the theme of his Essential Tension noted earlier, a new sensitivity to historygiving rise to this ‘hermeneutical problem’ was inaugurated by T.S. Kuhn’s (1970)landmark work The Structure of Scientific Revolutions which opened with observationson the role of history and, in particular, the function of science textbooks.

History if viewed as a repository for more than anecdote or chronology, could produce a decisivetransformation in the image of science by which we are now possessed. That image has pre-viously been drawn, even by scientists themselves, mainly from the study of finished scientificachievements as these are recorded in the classics and, more recently, in the textbooks fromwhich each new scientific generation learns to practice its trade. Inevitably, however, the aimof such books is persuasive and pedagogic; a concept of science drawn from them is no morelikely to fit the enterprise that produced them than an image of a national culture drawn froma tourist brochure or a language text. This essay attempts to show that we have been misledby them in fundamental ways. Its aim is a sketch of the quite different concept of science thatcan emerge from the historical record of the research activity itself.. . . historians confront growing difficulties in distinguishing the “scientific” component of pastobservation and belief from what their predecessors had readily labeled “error” and “super-stition.” The more carefully they study, say, Aristotelian dynamics, phlogistic chemistry, orcaloric thermodynamics, the more certain they feel that those once current views of naturewere, as a whole, neither less scientific nor more the product of human idiosyncrasy than thosecurrent today. If these out-of-date beliefs are to be called myths, then myths can be producedby the same sorts of methods and held for the same sorts of reasons that now lead to scientificknowledge. If, on the other hand, they are to be called science, then science has included bodiesof belief quite incompatible with the ones we hold today. (Kuhn 1970a, p. 1)

Science & Subjectivity

One reaction to Kuhn’s work was a concern about its “irrationalism” in portrayingscience as the product of psychological and social forces rather than the pure cognitiveforce of evidence and argument. I. Scheffler wrote:

That the ideal of objectivity has been fundamental to science is beyond question. The philo-sophical task is to assess and interpret this ideal: to ask how, if at all, objectivity is possible.This task is especially urgent now, when received opinions as to the sources of objectivity inscience are increasingly under attack.The notion of a fixed observational given, of a constant descriptive language, of a sharedmethodology of investigation, of a rational community advancing its knowledge of the realworld—all have been subjected to severe and mounting criticism from a variety of directions.


The overall tendency of such criticism has been to call into question the very conception ofscientific thought as a responsible enterprise of reasonable men. (Scheffler 1967, p. 1)

This was undoubtedly an over-reaction to the work of Kuhn, though it seems am-ply warranted in relation to the more extreme sociological doctrines which saw theirorigins in Kuhn’s book. Acknowledging the non-rational elements in the science doesnot mean abandoning a conception of scientific thought as “a responsible enterprise ofreasonable men,” but only the need for reconciling these elements into a more subtleand complex overall picture.

Such a reconciliation is unquestionably a difficult and perhaps as yet unattainedideal. This poses a difficult question for the educator because the old verities andcomforting stereotypes about science and its virtues appear to be false. How, then,can science be taught in a way which is consistent with its history and sensitive to itsvagaries.

Should the History of Science be Rated X?

In view of the subversive nature of the history of science in the ways we have seen, oneanswer to the foregoing question offered ironically by S. Brush (1974) is ‘censorship.’

. . . young and impressionable students at the start of a scientific career should be shieldedfrom the writings of contemporary science historians . . . [because] these writings do violenceto the professional ideal and public image of scientists as rational, open-minded investigators,proceeding methodically, grounded incontrovertibly in the outcome of controlled experiments,and seeking objectively for the truth . . .. (Brush 1974, p. 1164)My point is that, if science teachers want to use the history of science, and if they wantto obtain their information and interpretations from contemporary writings by historians ofscience rather than from the myths and anecdotes handed down from one generation of text-book writers to the next, they cannot avoid being influenced by the kind of skepticism aboutobjectivity which is now so widespread.. . . I do not know how science teachers are going to respond to the new historical interpreta-tions. So far, most teachers seem to have ignored them.. . . I suggest that the teacher who wants to indoctrinate his students in the traditional role ofthe scientist as a neutral fact-finder should not use historical materials of the kind now beingprepared by historians of science: they will not serve his purposes. (Brush 1974, p. 1170)

Realism vs Instrumentalism

A striking feature of contemporary science is the way in which it evokes philosophicaldisputes essentially identical to those arising at the origins of modern science with thescientific revolution of the seventeenth century. Specifically, we see this illustrated ina book by Jauch (1989) titled Are Quanta Real? Significantly, the work is in the form ofa Galilean dialogue which is particularly apt in view of the fact that the issues raisedare identical with those at the heart of the Galileo affair. The issue between CardinalBellarmine and Galileo was centrally concerned with the literal interpretation of theCopernican heliocentric theory in view of the contrary teachings of Aristotle and theBible. The question at the heart of contemporary quantum physics is remarkable forbeing identical with the one facing Galileo’s Copernicanism as we see in van Fraassen’s(in Cushing et al. eds. 1984, p. 171) question regarding quantum theory: He asks:

Peter Slezak 29

How could the world possibly be the way physical theory says it is? For Bellarmine,as for quantum theorists today, the issue was the need to “save the appearances” andwhether any further commitment to the literal claims of the theory was justified. Thiswas, of course, the question raised in Osiander’s notorious preface to Copernicus’s DeRevolutionibus Orbium Coelestium of 1543. The correspondences of Bellarmine andGalileo reveal the same contrasting attitudes as those seen today (see appendix).

We see the dilemma for Galileo raised in an acute form today at the very inceptionof quantum theory with Max Planck’s treatment of Black-Body radiation in 1900. Theclassical Rayleigh-Jeans theory led to a distribution law for energies irreconcilablewith observations and even with the finiteness of the total energy of the radiation (theso-called ‘ultra-violet catastrophe’). Norton (1994) explains the problem arising fromthe fact that Planck’s ad hoc model managed to save the appearances by what Planckhimself regarded as physically meaningless mathematical tricks.

. . . [Planck’s] discontinuity theory was by no means a popular theory, and understandably so. Itrequired the falsity of a quite fundamental supposition of classical physics. The mere fact thatthe discontinuity [quantization] hypothesis “saved the phenomena” was certainly not sufficientto force its acceptance. Why should one not hope that the phenomena would be saved by someless traumatic variant of the classical theory that preserved continuity? (Norton 1994, p. 16)

In view of the experimental confirmation of the most counter-intuitive features ofquantum theory including Bohr’s predictions against those of Einstein’s EPR thought-experiment, the difficulties of accepting the literal meaning of quantum theory arehardly less today. As Feynman (1965, p. 129) has quipped, despite its unprecedentedsuccess, ‘nobody understands quantum mechanics.’

By contrast with instrumentalism and related anti-realist doctrines, Putnam (1975,p. 73) has said that “the positive argument for realism is that it is the only philosophythat doesn’t make the success of science a miracle.” However, one might rhetoricallyask “What success?” Thus, the philosopher’s standard ‘theoretical entity,’ the electron,serves to bring the difficult issues into relief. An affirmative answer to the question“Are electrons real?” is faced with the history sketched by Bain and Norton (1998):

For Thomson (1897), the electron was an electrified particle obeying Newtonian dynamic. ForEinstein (1905) the electron had instrinsic mass and relativistic dynamics; for Bohr (1910) theelectron had a mix of classical and discrete properties; for Pauli (1925) the electron obeyed anon-classical ‘exclusion principle’; for Jordan and Wigner (1928) the electron was an excitationof a fermionic field; for Wigner (1939) the electron had a spin 1/2 and was the irreduciblerepresentation of a Poincare group; for Glashow, Salam and Weinberg (1967) the electronhas massless left-handed and right-handed parts uniting to form a massive particle throughinteractions with a scalar Higgs field; and the current standard model (1990) takes the electronto be a member of first of three generations of similar leptonic particles related in a non-trivialway to three generations of hadronic quarks.

Anti-realism might be thought to follow from such a litany, but Hacking (1982)suggests that philosophers have placed too much emphasis on theory and not enoughon experiment. Hacking explains:

No field in the philosophy of science is more systematically neglected than experiment. Ourgrade school teachers may have told us that scientific method is experimental method, buthistories of science have become histories of theory. (Hacking 1982, p. 248)


No wonder that scientific antirealism is so permanently in the race. It is a variant on “thespectator theory of knowledge” [that is, Berkeley’s idealism]. (Hacking 1982, p. 258)I proceed from experimental practice. . . . [From] an interest in real life physics as opposed tophilosophical fantasy science. (Hacking 1982, p. 259)Once upon a time, it made good sense to doubt that there were electrons. . . . The best reasonfor thinking that there are electrons might have been success in explanation. But the ability toexplain carries little warrant of truth. . . . Antirealism about any submicroscopic entities wasa sound doctrine in those days. Things are different now. The “direct” proof of electrons andthe like is our ability to manipulate them using well-understood low-level causal properties.(Hacking 1982, p. 256/258). . . engineering, not theorizing, is the best proof of scientific realism about entities. (Hacking1982, p. 258)

Of course, Hacking’s final comment makes it difficult to see how one might ascribereality to black holes which are hardly amenable to engineering in the way he seemsto have in mind. Nevertheless, my concern here has been only to point to the ways inwhich the deepest questions of the history and philosophy of science bear directly on themanner and substance of science teaching. Toulmin (1970) has indicated the intimateintertwining in which, for example, both Planck and Mach had been influenced indifferent ways by the philosophical ideas of Immanuel Kant. Toulmin suggests that thepositivism of Mach worked its way into the very fabric of theoretical physics, shapingBohr’s interpretation of quantum mechanics.

Physics and philosophy have had a continuous relationship, but a fluctuating one. . . . Incertain periods, physical scientists have been content to acknowledge their partnership withphilosophers, and even to see their own fundamental theories and methods as resting on“metaphysical foundations.” (Toulmin 1970, p. ix)

As Matthews notes:

If science has developed as a dialogue with metaphysics . . ., then to teach science as a soliloquyin which science just talks to itself and grows entirely by self-criticism is to impoverish thesubject matter. (Matthews 1992, p. 36)

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Kuhn, T. S.: 1959, The Essential Tension, The Essential Tension: Selected Studiesin Scientific Tradition and Change, The University of Chicago Press, Chicago,1977, pp. 225–239. Also reprinted in R. Boyd, P. Gasper & J.D. Trout eds., ThePhilosophy of Science, Cambridge, Mass.: Bradford/MIT Press, 1991, 139 -147.

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Teaching History and Philosophy of Science: Experience at IIT Kanpur

P.R.K. RaoFormerly of Indian Institute of Technology, Kanpur, India

As this book is about teaching and history, before I recall my fading memory tracesof my experience of teaching history and philosophy of science at IIT (Indian Instituteof Technology)-Kanpur, let me begin by reminding you of two cautionary remarks ofGeorge Bernard Shaw, “Teaching,” he said, “is ineffective except in those instances inwhich it is superfluous.” Perhaps, there is an element of truth in the claim that ourstudents learn inspite of us rather than because of us! About history, Shaw maintainedthat “the only lesson that we can learn from history is that nobody learns from it.”These two indictments, whatever their truth, can help moderate our, excessive en-thusiasm for and expectations of innovations in science education. Moreover, nothingwarrants the presumption that every civilized, vibrant nation must necessarily be alsoa scientifically advanced nation.

The kind of concerns and circumstances that prompted some of us at IIT Kanpur tointroduce a programme of courses in history of science, scientific method, science andtechnology and its linkages with society are best captured by the observations of thefirst and the last programme leaders of the Kanpur—Indo-American programme whichhelped establish IIT Kanpur with the participation of a consortium of nine leadingAmerican Universities. The first programme leader, Normal Dahl had observed that“IIT Kanpur has been an irrelevant factor in the industrial and social progress in India. . . a kind of isolated island of academic excellence but not part of the mainstream ofIndia’s development.” This assessment worried some of us for we were imbued withthe idea that institutions like IIT Kanpur were set upto to be able to attend to thescientific and technological needs of the country. What distressed us even more anddrove home our failure as educators was the telling observation of the last programmeleader Mr. Oakely. He said that IIT Kanpur students face no technological backgroundproblems of adjustment in M.I.T., one of the foremost symbols of ‘high-technology west,’and the same students show considerable enthusiasm when, possibly for the first timein their education, they are exposed to the ideas of growth of technology and its relationto percieved technological needs specific to a country.

Science is a selective cognitive enterprise. The nature of that selectivity, to my mind,is succintly described by Hertz in the introduction to his book, Principles of Mechanics.We form images or symbols of objects such that the logically necessary consequencesof those symbols or images are the same as the materially necessary consequencesof the objects that correspond to the symbols or images. What is interesting in Hertz’saccount is the feature of the considerable freedom that exists in the formation of imagesor symbols of objects even as they must obey the above stipulated important limitation.In the cognitive enterprise called science, while we are necessarily performing, whatHans Jonas has called the ‘primary ontological reduction’ of the actual objects of the

38 Teaching HPS

world (as for example, point masses in place of extended physical objects in rigid bodydynamics), there is no unique way of performing that primary ontological reduction.Earlier, successful scientific practices, cultural influences, environmental pressures,socioeconomic factors etc., may contingently further constrain a particular scientificcommunity in exercising the freedom involved in primary ontological reduction, but theexistence of that freedom is the condition of possibility of what we understand by theterm creativity. Our failure as teachers at IIT Kanpur consisted in not even sensitizingour students to the idea that science is a human and historical practice, let aloneprovoking them to draw on their creativity to perform such fruitful primary ontologicalreductions which will enable them to attend to the scientific and technological needsof the society to which they belong. Undoubtedly we have been quite successful intraining our students to use established recipes in their chosen disciplines. But wehave not even attended to the more important problem of orienting them so that theyperceive a relevant segment of reality around them, perform novel primary ontologicalreductions, formulate the pertinent problems and solve them creatively.

Our failure, it then appeared to us, can be traced, at least in part, to the situa-tion in which not only lay man but also practicing scientists are so overwhelmed bythe products of science that they pay scant attention to the processes by which theenterprise of science manufactures knowledge. One disastrous consequence of thislack of self-reflexivity, particularly in a third world country like India, has been thegradual weakening of critical, social and political forces that could mediate between therequirements of autonomy of the expert scientific community and the developmentalneeds of the country.

The above account should have made it clear that even in an institution like IITKanpur famous for its flexibility in procedures it is not going to be easy to introducenew courses that do not fall within the framework of established disciplinary divisions.Fortunately for us, at that point of time there was a circular from the Ministry of Edu-cation which desired the introduction in IITs and other educational institutions coursesdevoted to historical practices in India related to temple architectures, ship-building,metallurgy and other indigeneous pre-industrial technologies. We took advantage ofthis particular circular and constituted a committee, with Prof. Mohini Mullick asthe chairperson, to look into the possibilities of introducing courses in history andphilosophy of science with particular reference to India. A few years later this courseon History of Scientific Ideas was introduced as an open elective in the third year ofthe four year programme.

We also conducted a five day workshop in 1982 on the development of a curriculumin philosophy of science, history of science, science and technology and society. Basedon the discussions which took place in that workshop we subsequently formulated somecourses. We also made a largely unsuccessful effort to see that each instructor deliverssome three to four lectures on the historical aspects of whatever subject he is teachingin a semester. Many faculty members thought it to be a waste of time particularly whenthey have so much syllabus to cover. As always, there are notable exceptions: Prof.Amitabh Ghosh who is currently the Director of IIT Kharagpur, and Prof. A.K. Biswaswho used to offer a course on history of science in India.

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More often than not any effort to have faculty engagement with or study of anyhistorical, philosophical aspects of science met with resistance. Responses varied from“What is in it there for me?” to “Will it help me to publish more often?”

It was probably in 1982 that the course on History of Scientific Ideas was offered forthe first time IIT Kanpur. There were five of us as instructors (Professors Mohini Mul-lick, A.P. Shukla, K.S. Gandhi, V.K. Jairath and myself) sharing eight lectures each andwe had three students (two of them were students of physics and the third of computerscience)! None of the instructors was a professional historian. I must confess that eventoday it is not clear to me whether it was a setback or an advantage. Perhaps it is both.On the one hand, we have the eminent scientist and equally well known historian ofscience, Truesdell, assuring us that “it is the standard claim of scientists that mosthistorians do not have sufficient grasp of science, itself to understand the facts ratherthan the mere circumustances of its history.” On the other hand, we are alerted by theJ.B. Cohen, that “Professional historians are wont to complain of the attempts of thescientist whose approach to history often sufferes from the consequences of a purelyscientific training.” Kuhn, in his paper, ‘The Relations between History and Historyof Science’ (Daedalus, Vol. 100, No. 2) discuss the problem of teaching of history ofscience. I am inclined to believe that the problem involved is more complex than oneof teaching or of history or of science. We may remind ourselves of Kant’s famousinjunction that history without philosophy is blind and philosophy without history issterile. But we all know the consequences of riding two horses at the same time. TheNobel laureate poet, Czeslaw Milosz in his Charles Eliot Norton lectures at Harvardin 1982 summarized the situation thus—as far as poets are concerned: “Many learnedbooks on poetry have been written, and they find, at least in the countries of the west,more readers than poetry itself. This is not a good sign, even if it may be explained bothby the brilliance of their authors and by their zeal in assimilating scientific disciplineswhich today enjoy universal respect. A poet who would like to compete with thosemountains of erudition would have to pretend that he possesses more self-knowledgethan poets are allowed to possess.” What is the case with a poet is also in good measurethe case with a scientist or a historian or in fact with any one who is engaged inmaking valid knowledge claims. The necessarily historical character of the knowledgesystem of science and the limited role that the individual practicing scientist plays inthe production of cognitive goods by and large restricts the span of his philosophical,historical, ethical and social concerns in that production. This restriction of concernsnot merely at the level of the individual practitioner of science but also at the levelof knowledge claims of science detracts from the secular character of science in so faras it resists the critical examination of its own founding (un)concerns in its practices.And as long as this situation prevails, not only teaching of history of science will beplagued by charges of only attending to ‘the mere circumustances if its history’ or to thecounter-charges of the distorting ‘consequences of a purely scientific training,’ but moreimportantly, the freedom available in performing primary ontological reductions thatare comensurate with the philosophical, historical, ethical and social concerns cannotbe pressed into service for the generation of knowledges that are genuinely liberating.

The course, History of Scientific Ideas, has by now been offered for more than ten

40 Teaching HPS

years by me and Prof. A.P. Shukla (See Appendix B for a topic outline of the course).The number of students who registered in the course at any given time never exceededtwenty five. But one notable feature is that there always used to be a sizeable numberof auditors, some times as many as the creditors of the course. It is interesting toknow that between eighty to hundred thousand candidates appear in the joint entranceexamination of the IITs and out of them about three hundred get admitted into eachIIT. They are admittedly a bright lot but they are innocent of philosophy and ignorantof history. History to them is a boring chronology of events and philosophy a waste oftime. Moreover, in their schools they are indoctrinated with received cannon of whatscience is. To break the consequent resistance on their part and sensitize them to theidea that science is a historical activity and there can be alternative creative punc-tuations of reality more adequate to the lived life-world than those of contemporaryscience, I used to resort to pedagogical-shock treatment, so to speak: I would circulatean excerpt from the famous preface of the book, Order of Things, by Michel Foucault(see Appendix D) in which he talks about a particular Chinese encyclopaedia in whichanimals are taxonomically ordered in ways that cannot even be conceived by manyof us. Or I would distribute two excerpts on social order in early Hindu society, oneby Ananda K. Coomaraswamy and another by Kosambi (see Appendix A). Both refer tothe same empirical domain but each gives an interpretation which is antithetical to theother, Coomaraswamy interprets the entire social order in terms of the requirementsof ritual sacrifices. Kosambi, on the other hand, interprets the same social formationin terms of Marxist categories. I would invariably describe the episode in which NeilsBohr and Heisenberg went to the Kronberg Castle in Denmark. Here is what Bohr saidas recapitulated by Heisenberg:

Isn’t it strange how this castle changes as soon as one imagines that Hamlet lived here. Asscientists we believe that a castle consists only of stones, and admire the way architects putthem together. The stone, the green roof with its patina, the wood carvings in the church,constitute the whole castle. None of this should be changed by the fact that Hamlet livedhere, and yet it is changed completely. Suddenly the walls and the ramparts speak a differentlanguage. The courtyard becomes an entire world, a dark corner reminds us of the human soul,we hear Hamlet’s “To be or not to be.” Yet all we really know about Hamlet is that his nameappears in a thirteenth-century chronicle. No one can really prove that he really lived here.But everyone knows the questions Shakespeare had him ask, the human depths he was madeto reveal, and so he too had to be found a place on earth here, in Kronberg.

I would draw on Carr’s little book, What is History?, to drive home the idea thathistory is a continual dialogue of the present with the past and therefore historicaltruths are not frozen collection of facts but, like scientific truths, are eternally revisablein light of new evidence and new frameworks of interpretation. Sometimes, a littlemischievously, I would ask the students to imagine what would have happened if theMichelson-Morley experiment (which rendered ether the emperor’s new clothes) wereconducted before the earlier truth of geocentric theory was declared falsel in favour ofthe new thruth of heliocentric theory!

There is another important aspect of the course which I would like to mention.I used to give on a regular basis reading assignments. Each student was asked tosubmit a written summary of the article assigned and argue for his/her agreements and

Rao 41

disagreements with the epistemological or ontological or methodological or historical orrealist/anti-realist claims explicitly or implicitly made by the author of the article. Oneof my favourites is the article on roots of atomic physics from the book, Physics andPhilosophy, by Heisenberg. Another is the article, ‘The Dematerialization of Matter’,by N.R. Hanson. A third interesting paper, I often used to assign, is Nobel Laureatebiologist, George Wald’s ‘Innovation in Biology’. Sometimes, to place in evidence thechanging and the now discarded scientific vocabulary and the important role playedby text-books in influencing the cognitive orientation of future practitioners of science,I would assign for reading an eighteenth or nineteenth century scientific article orselection from a text-book. The main purpose of these assignments, as that of thecourse, is to let the student see for himself that whether or not science describes realityas it really is, as history of science demonstrates, it attempts to describe that realityby seeing it through a contingently chosen cognitive grid and that he and his relevantcommunity can draw on their cognitive resources to choose another cognitive grid moresuited to the life-world they belong to.

Appendix C also includes a sample examination paper. I take advantage of itsinclusion (the statement by Mazlish) to contest if not dispel the widespread beliefthat science and the church are in continuous conflict. In point of fact what one findsfrom the history of science is that many men of the establishment of the church madesignificant contributions to the enterprise of science in the latter’s formative years. Themen of God believed that reason can be enlisted in support of faith which of course tothem was of paramount importance.

A word about student and faculty response to the course. The student reactionsurveys always elicited a negative response to the idea of dropping the course fromthe curriculum. And more often than not they also expressed the view that there isa significant change in their understanding of the nature of scientific activity and itsplace in society. More surprisingly, many faculty who were earlier on suspicious aboutthe usefulness of this course based on whatever reports they probably got from othersbegan to consider the course as conceptually interesting and rigourous.

Finally, let me briefly state my views on the importance of courses on history andphilosophy of science in science education. I do not believe that teaching such courseswill make the students more creative scientists. Firstly, we do not have, and, I believe,we can never have, an algorithm for transforming people into creative scientists orartists or whatever. When Gauss was once asked as to how he finally succeeded inproving a theorem the proof of which eluded him for several years he is supposedto have answered: ‘By divine inspiration.’ An element of mystery must always en-velop the creative act. Secondly, the kind of self-reflexive, critical attitude that onedevelops through studies in history and philosophy of science, I suspect, dampens thebold, aggressive, adventurous asumption-making disposition that one asociates withcreativity. What I have argued for in the previous pages is that study of historyand philosophy of science suggests that doing science creatively involves performing aprimary ontological reduction of the objects of the world and that there are no groundsfor believing that only one such reduction is possible. If my claim is valid, study ofhistory and philosophy of science enables us to recognize what it takes to be creative.

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It does not make us creative. For we may lack the requisite capacity to perform primaryontological reduction even though we know that is what we must do to be consideredcreative. Moreover, such recognition is not necessary for one to be creative.

There can be other reasons for the importance of study of history and philosophy ofscience. Many of us as teachers have often encountered the situation in which a studentwho is admitted into, say, computer science programme considers that we are imposingan unnecessary burden on him when we prescribe a course on electromagnetic theoryor chemistry. What is not recognized by him is that transporting ideas from one domaininto another can sometimes help better understanding of ideas in the, latter domainand may even facilitate creativity. Transporting the familiar idea that all historyis contemporary history may help recognize that scientific truths are not ahistoricaltruths. Above all, the study of history and philosophy of science can be an intellectuallyenriching experience in so far as that study allows us to see the limits of liberationthat can be secured by the dominant knowledge system of our times. Indicating thelimits of a subject taught is an important responsibility of the teacher as the Germanscientists and intellectuals of the second world war generation painfully realized. Thepost second world war commission for university reform in Germany came up with thefollowing recommendation: “Every lecturer in the university must have the ability: 1.To see the limits of his subject material in his teaching to make the students aware ofthese limits and to show them that beyond these limits forces come into play which areno longer entirely rational, but arise out of life and human society itself. 2. To showin every subject the way that leads beyond its own narrow confines to broader horizonsof its own,” I am inclined to believe that study of history and philosophy of science canhelp a teacher in his efforts to acquire those abilities.

Appendix A

1. Hinduism by Ananda K. Coomaraswamy, Philosophical Library, New YorkThe Social Order: Where there is agreement as to the nature of man’s last end,and that the way by which the present and the paramount ends of life can berealised is that of sacrificial operation, it is evident that the form of society will bedetermined by the requirements of the Sacrifice; and that order (yatharthata) andimpartiality (samadrsti) will mean that everyman shall be enabled to become, andby no mis-direction prevented from becoming, what he has it in him to become.We have seen that it is to those who maintain the Sacrifice that the promise ismade that they shall flourish. Now the Sacrifice, performed in divinis by theAll-worker (Visvakarma), as imitated here demands a cooperation of all the arts(visva karmani), for example, those of music, architecture, carpentry, husbandryand that of warfare to protect the operation. The politics of the heavenly, socialand individual communities are governed by one and the same law. The patternof the heavenly politics, is revealed in scripture and reflected in the constitutionof the autonomous state and that of the man who governs himself.In this man, in whom the sacramental life is complete, there is a hierarchy ofsacerdotal, royal; and administrative powers, and a fourth class consisting of the

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physical organs of sense and action, that handle the raw material or ”food” tobe prepared for all; and it is clear that if the organism is to flourish, which isimpossible if divided against itself, that the sacerdotal, royal and administrativepowers, in their order of rank, must be the “masters,” and the workers in rawmaterials their “servants.” It is in precisely the same way that the functionalhierarchy of the realm is determined by the requirements of the Sacrifice onwhich its prosperity depends. The casted are literally “born of the Sacrifice.” Inthe sacramental order there is a need and a place for all men’s work: and there isno more significant consequence of the principle, Work is Sacrifice, than the factthat under these conditions, and remote as this may be from our secular ways ofthinking, every function, from that of the priest and the king down to that of thepotter and scavenger, is literally a priesthood and every operation a rite. In eachof these spheres, moreover, we meet with “professional ethics.” The caste sys-tem differs from the industrial “division of labor,” with its “fractioning of humanfaculty,” in that it presupposes differences in kinds of responsibility but not indegrees of responsibility; and it is just because an organisation of functions suchas this, with its mutual loyalties and duties, is absolutely incompatible with ourcompetitive industrialism, that the monarchic, feudal and caste system is alwayspianted in such dark colors by the sociologist, whose thinking is determined moreby his actual environment than it is a deduction from first principles.The Aryans had little difficulty in penetrating to within 50 miles of the Yamunariver. The thinner forest of the region could be burnt down. But the socialorganisation necessary for settling the land cleared by fire went beyond the simpletribe. The lowest caste—for caste had developed within the tribe—was now calledsudra possibly from the tribal name (e.g. the Oxydrakoi on the lower Indus whofought against Alexander). These were helots who belonged to the tribe or clangroup as a whole in much the same manner as the tribal cattle, without themembership rights of the tribe as granted to the three upper castes. These threehigher castes were properly recognised as Aryan and full members of the tribe:kshatriya (warrior and ruler), brahmana (brahmin priest), vaisya (the settler whoproduced all the food surplus by agriculture and cattle breeding). The word varnacame to mean one of these four class castes, which constituted a class structurewithin such of the tribes as had reached advanced forms of property-holding andindulged in trade exchange on a sufficiently large scale. This was not true ofevery single Aryan tribe, many of whom continued undifferentiated while othershad only the arya-sudra (free v. helot) division. That the sudra was not boughtand sold as in ancient Greece and Rome was due to no kindness on the part of theIndo-Aryans. It was simply that commodity production and private property hadnot developed far enough.The existence of the sudra caste had a peculiar effect upon later Indian society.Chattel slavery in the sense of classical European (specifically Graeco-Roman)antiquity was never to be of any size or importance in the means and relationsof production in India. The expropriable surplus could always be produced by

44 Teaching HPS

the sudra. The development of caste foreshadowed a general class society beyondthe exclusiveness of a tribe. A few of the brahmins had begun to officiate formore than one clan or tribe, which implied some type of relationship betweenseveral groups. A few brahmins at the other end of the economic scale hadbegun to advance into the dense forest to the east, in fairly small groups withtheir own cattle; sometimes even as individuals with no property and no arms fordefence or hunting. Their harmlessness was obvious, and they were of the utmostimportance in coming to terms with the food-gathering Naga savages of the forest,whom they often joined, or with whom they lived on friendly terms. Their soleprotection was their poverty and manifestly innocuous nature. The traders, onthe other hand, were convoyed at need by armed kshatriyas who would protectthem against the aborigines (nishada). These kshatriyas grew into mercenarygroups ready to fight in anyone’s service for hire.

2. Hinduism by D.D. KosambiWithout mincing words, the ritual books say: Like a vaisya . . . tributary to an-other, to be eaten up by another, to be oppressed at will . . .. Like a sudra . . .the servant of another, to be the primary producers, were to be enclosed be-tween the two upper castes during the sacrificial procession of the whole tribe,‘to make them submissive.’ After this the basic class nature of caste need hardlybe doubted, though it was still class on a primitive level of production. The firsttaxes were called bali because they were gifts brought to the chief at the sacrificeby members of the tribe or clan. There was a particular official known only at thistransitional period, the ‘king’ apportioner’ (bhaga-dugha). His job seems to havebeen the proper sharing out of the bali gifts among the tribal king’s immediatefollowers, and perhaps assessment of taxes as well.

Appendix B

Outline of the course on history of scientific ideas

1. Historical study as a means of understanding the nature of scientific mode ofthinking and its place in life and society. Role of philosophy of science in thestudy of history of science; metatheoretic concerns. Brief accounts of scientificmethod: Inductivism; Falsificationism; Methodology of Research Programmes;Paradigmatic shifts and scientific revolutions, Science as an extended metaphor.

2. Greek Thought as the bed-rock of Western civilization or the fabrication of a myth.Ionian Nature-philosophy, Pythagoreanism, Eleaticiam, Atomism, Sophism, Pla-tonism, Aristotelianism. Hellenistic Science: Mathematics, Astronomy, Mechan-ics.

3. Arab Ascendancy and Islamic Science: Brief outline of the contributions to phi-losophy, mathematics, astronomy, chemistry, medicine.

4. Middle Ages and European Intellectual Resurgence: Rediscovery of Greek Thought,Translation of “Greek Texts,” “Aristotelian Scholasticism” Interplay of Faith, Rea-

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son, Doubt, Criticism and Innovation. Copernican Revolution, Baconian empiri-cism, Galilean Platonism, Cartesian split of the Res Extensa and Res cogitans,Newton the last great magician, Newtonian Synthesis of the clockwork Universe,Mechanization of the World Picture, Leibnitzian Mathesis Universalis.

5. Nineteenth century as the Golden/Silly Age of Science; Development of Math-ematics. Astronomical, Kinetic, Atomic, Energetic, Psychophysical, Statistical,Morphological, Genetic Views of Nature. Microcosm after the microscope, Macro-cosm after the telescope, matter after the chemical Balance, life after vivisecton,Man after Darwin, Society after Marx, Psyche after Freud. Twentieth century’sRelativistic dethronement of common-sense, perceptions and Quantum mechani-cal mixed metaphors. Unity of Science vs Unity of Man.

6. From Plantocracy to Technocracy or the Historical Evolution of Institutions of Sci-ence: Mercantile Capitalism, Colonies & Plantations; Slave Trade and Saving theHeathens; Seed-beds of Science in Botanical Gardens and Monasteries. Scientis-tic Movements, Birth of Acadamies of Science and Technical Schools, Emergenceof the Scientist and the rise of the Expert; Migration of Science from Italy toEngland to France to Germany to U.S.A. Innovating Innovation and Managers ofScience and Technolgy.

7. Indian Science: Colonial, Nationalist and Post-Independence phases. Parasiticcharacter of and lopsided institutionalization of Science. People’s Science Move-ments. The question of Alternative Sciences.

Text-Books

• Chalmers, A.F.: 1982, What Is This Thing Called Science?, University of Queens-land Press, St. Lucia, Qld.

• Dijkterhuis, E.J.: 1986, The Mechanization of the World Picture, tr. by C. Dik-shoorn, Princeton University Press, Princeton.

• Merz, J.T.: 1903-1914, A History of European Thought in the 19th Century, W. Black-wood & Sons, Edinburgh, London.

Appendix C

Sample Examination PaperIndian Institute of Technology, Kanpur

Science, Metascience, SocietySE 862-History of Scientific ideas

II Mid Semester Examination

Time: 1 hour OPEN NOTES 11.3.86

Maximum length of answer for each question: 300 words

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Q.1.

In the Temple were, forged the hammers which destroyed the Temple. (A. France )

Bacon, Galileo and Descartes can veritably be called the founders of the methodof modern science. Identify the most important idea in each case, which became afoundation stone of Science and show how this self-same idea has become historicallytransformed into a better sapping science of its virality.

Q.2.

The warfare of Science with theology in christendom . . . . . . is simply part of a continuing conflict—a conflict which takes its rise from the contradictory nature of man: rational and irrational,creator of his own conditions, and conditioned by forces seemingly beyond his control. Thetension generated by these warring elements is not a mere transient phase of man’s existence:as long as he remains human, it will be his problem and his glory. When it ceases we will be nolonger recording history, which by definition deals with human beings. (D. Mazlish)

Logic and reason have been put to service of christian dogma and study of natureand science, both simultaneously and, to the mutual exclusion of each other. Elaborateon this dynamical process by the historical development of European thought from 11thto the middle of 16th century, as a concrete example.

Q.3. Every significant institution, individual, or thought of the past, must be a productof the travails of its times. And we can benefit by it only if we can currently relate itsrelevance and irrelevance with the present. Comment in this light on any four of thefollowing:

1. Pythagoras

2. Aristotelian causality

3. Hellenistic Astronomy

4. Ishale at-Kindi

5. Brethren of sincerity

6. Newtonian synthesis

Format of answers: You are expected first to elaborate on the views propounded onthese topics in the lectures, and then give reasons for your agreement or disagreement.

Appendix D

The Order of Things by Foucault, Preface, p. xv.This book first arose out of a passage in Borges, out of the laughter that shattered,as I read the passage, all the familiar landmarks of my thought—our thought, thethought that bears the stamp of our age and our geography—breaking up all theordered surfaces and all the planes with which we are accustomed to tame the wild

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profusion of existing things, and continuing long afterwards to disturb and threatenwith collapse our age-old distinction between the Same and the Other. This passagequotes a ‘certain Chinese encyclopaedia’ in which it is written that ‘animals are dividedinto: (a) belonging to the Emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens,(f) fabulous, (g) stray dogs, (h) included in the present classification, (i) frenzied, (j)innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having justbroken the water pitcher, (n) that from a long way off look like flies.’ In the wondermentof this taxonomy, the thing we apprehend in one great leap, the thing that, by meansof the fable, is demonstrated as the exotic charm of another system of thought, is thelimitation of our own, the stark impossibility of thinking that.

References

Carr, E.: 1974, What is History?, Penguin, London.

Coomaraswamy, A.: Hinduism, Philosophical Library, New York.

Foucault, M.: 1970, The Order of Things, Tavistock Publications, London.

Hanson, N. R.: 1958, The Dematerialization of Matter.

Heisenberg, W.: 1958, Physics and Philosophy, George Allen and Unwin Edition.

Kuhn, T.: 1971, The Relations between History and History of Science, Daedalus100(2).

Wald, G.: 1958, Innovation and Biology, Scientific American 199, 100.

48 Teaching HPS

Multiculturalism in Science Education and the Question ofUniversalism

William W. CobernWestern Michigan University, USA. Email: [email protected] C. LovingTexas A&M University. Email: [email protected]

Introduction

Is science universal? Only recently has this question been given any serious consid-eration at all. In the tradition of science as practiced in the West for the past 300years and in the tradition of school science, the answer has been, “Of course science isuniversal.” As Richard Dawkins likes to put it, there are no epistemological relativistsat 30,000 feet. But today some will say, “Not so fast!” Dawkins offers a brute definitionof universality completely devoid of any nuance of understanding and equally devoidof relevance to the question at hand. No one disputes that without an airplane of fairlyconventional description, a person at 30,000 feet is in serious trouble. The question ofuniversality does not arise over the phenomena of falling. The question of universalityarises over the fashion of the propositions given to account for the phenomena of falling,the fashion of the discourse through which we communicate our thoughts about thephenomena, and the values we attach to the phenomena itself and the various wayswe have of understanding and accounting for the phenomena—including the accountoffered by a standard scientific description. In today’s schools there are often competingaccounts of natural phenomena especially where schools are located in multiculturalcommunities. There are also competing claims about what counts as science. Thepurpose of our paper is to examine the definition of science put forward from multicul-tural perspectives in contrast to a universalist perspective on science, i.e., the StandardAccount. We will argue that good science explanations will always be universal evenif we do incorporate indigenous knowledge as scientific and broaden what is taught asscience. What works best is still of interest to most and although we hate to use theword hegemony—Western science would co-opt and dominate indigenous knowledgeif it were incorporated as science. Therefore, indigenous knowledge is better off as adifferent kind of knowledge that can be valued for its own merits, that can play a vitalrole in science education, and can maintain a position of independence from which itcan critique the practices of science and the Standard Account.

Multicultural Perspectives on Science

If there are different ways of accounting for a phenomena of nature then it is possiblethat some people will reject some of these accounts—including the account offeredby Western science—and accept others. Gibson (1996) tells of a time when she wasworking at a rainforest scientific station on a South Pacific Island and a conversation

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she had with an indigenous Islander. The Islander commented that Westerners onlythink they know why the ocean rises and falls on a regular basis. They think it hasto do with the moon. They are wrong. The ocean rises and falls as the great seaturtles leave and return to their homes in the sand. The ocean falls as the waterrushes into the empty nest. The ocean rises as the water is forced out by the returningturtles. Is this Islander scientific because he has accurate knowledge of the oceantides that affect his island? Is he unscientific because his explanation for tidal actionis scientifically inappropriate? Is science universal because the standard scientificaccount for tidal action applies to all local occurrences of tidal phenomena? Or, doesone grant the obvious brute factuality of actual phenomenon but reject universalistclaims for standard scientific accounts of actual phenomenon? Matthews well statesthe universalist perspective of the Standard Account:

Just as volcanic eruptions are indifferent to the race or sex of those in the vicinity, and lavakills whites, blacks, men, women, believers, non-believers, equally, so also the science of lavaflows will be the same for all. For the universalist, our science of volcanoes is assuredly ahuman construction with negotiated rules of evidence and justification, but it is the behaviorof volcanoes that finally judges the adequacy of our vulcanology, not the reverse. (Matthews,1994, p. 182)

The undeterred critic, however, will still ask: Though the phenomenon are experien-tially universal, can’t one argue that scientific accounts are not universal since suchaccounts are not universally accepted?

The resolution of such questions hinges on the definition of science, including theconcept of universality, and this resolution is of considerable importance for both ed-ucators and the public at large. When a discipline earns the title science it “acquiresthe authority to promulgate truthful and reliable knowledge, control over educationand credentials, access to money and manpower, and the kind of political clout thatcomes from possessing knowledge that is essential yet esoteric” (Fuller, 1988, p. 177).In science education the definition of science is a de facto gate keeping device for whatcan be included in a school science curriculum and what cannot. A very large amount ofmoney, for example, has been spent in the USA on litigating the question of whether ornot “creation science” can be properly included as an aspect of school science (Nelkin,1983; Overton, 1983). Moreover, if science is deemed universal it not only displacesscientific pretenders such as creation science, it as well displaces any local knowledgethat conflicts with it. Kawagley, Norris-Tull & Norris-Tull (1998, p. 134) argue that“such a narrow view of science not only diminishes the legitimacy of knowledge derivedthrough generations of naturalistic observation and insight, it simultaneously devaluesthose cultures which traditionally rely heavily on naturalistic observation and insight.”The record is fairly clear. Around the globe where science is taught, it is taught atthe expense of indigenous knowledge and this precipitates charges of epistemologicalhegemony and cultural imperialism.

People feel passionately about these issues. The passions in the academy have runso high that the controversies have been dubbed the “Science Wars” (Nature, 1997).At school levels, the struggle is over multicultural approaches to science and scienceeducation within multicultural situations. Actions taken are at times extreme. In

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1987, the Portland Oregon School District published the African-American BaselineEssays, a set of six revisionist essays providing resource materials and references forteachers on the knowledge and contributions of Africans and African-Americans. Thescience baseline essay, written by Hunter Havelin Adams (1990), has serious problems,but it is widely distributed because of the current pressure on school districts to incor-porate multicultural material into the classroom coupled with the dearth of this kind ofmaterial. Hundreds of copies of the Baseline Essays have been sent to school districtsacross the country and they have been adopted or are being seriously considered byschool districts as diverse as Fort Lauderdale, Detroit, Milwaukee, Atlanta, Chicago,Prince George County, MD, and Washington, DC. Even more widely distributed is itspredecessor, Blacks in Science: Ancient and Modern, edited by Ivan Van Sertima (1984).Vine DeLoria, who is involved with Indian science education through the AmericanIndian Science and Engineering Society (AISES) has recently published a book entitledRed Earth, White Lies: Native Americans and the Myth of Scientific Facts (DeLoria,1995). These supplements on multicultural science, expressly intended to “raise theself-esteem” of students, adopt a triumphalist approach to the material. That is, theypresent the achievements and the beliefs of the group described as superior and antic-ipatory to the achievements and beliefs of modern Western science. Thus, the Dogon ofMali supposedly studied Sirius B, which is invisible to the naked eye, hundreds of yearsago. The Egyptians foreshadowed the Theory of Evolution thousands of years ago;the Egyptians also anticipated many of the philosophical aspects of quantum theory(Adams, p. 21), and they knew the particle/wave nature of light (p. 26).

The Baseline Essays and similar publications represent a radical revisionist histo-riography of science and culture. There are other examples of multicultural materialsfor science education that are far less controversial. Books such as Robertta Barba’s(1995), Science in the Multicultural Classroom: A Guide to Teaching and Learningand the Addison Wesley (1993) teachers guide, Multiculturalism in Mathematics, Sci-ence, and Technology: Readings and Activities bring culture into the science classroomfor pedagogical purposes without rewriting history. The nature of science implicit inthese books, however, represents a subtle change from standard accounts. Lookingelsewhere, the question of how science is to be defined is brought into clear relief (e.g.,Kawagley, Norris-Tull, & Norris-Tull, 1998; Snivley & Corsiglia, 1998). With specificreference to First Nations people in Canada and the Yupiaq people of Alaska, one findsthat indigenous knowledge is reclassified as science—but not science according to theStandard Account and therein lies the controversy.

Multiple Culture-based Sciences?

The Standard Account of science can be called Western given its historic origins inAncient Greek and European culture. Speculative thought about Nature, natural phi-losophy and later what became known simply as science have always been engaged withWestern culture. The Western experience with science has been a long one and in asense they have matured in consort, but not without trials. “There has been, on the onehand, a disintegrating effect on traditional values and forms of representation, and, onthe other hand, a progressive integration into the dominant culture . . . of the scientific


mentality—the values, content of knowledge and patterns of action which underliescientific practice and are formed by it” (Ladriere, 1977, p. 12). This disintegratingeffect appears to have been recognized by Charles Darwin who late in life lamented:

I have said that in one respect my mind has changed during the last twenty or thirty years.Up to the age of thirty, or beyond it, poetry of many kinds . . . gave me great pleasure, and evenas a schoolboy I took intense delight in Shakespeare. . . I have also said that formerly picturesgave me considerable, and music very great, delight. But now for many years I cannot endureto read a line of poetry: I have tried to read Shakespeare, and found it so intolerably dull thatit nauseated me. I have also almost lost my taste for pictures or music . . . I retain some tastefor fine scenery, but it does not cause me the exquisite delight which it formerly did. . . . Mymind seems to have become a kind of machine for grinding general laws out of large collectionsof facts . . . (quoted in Owens, 1983, p. 38)

And of course the European Romantic poets echoed this lament (see Barber, 1963).Moreover, Europe was an expansionist culture, and European exploration, conquest

and colonization of lands beyond Europe brought Western science to those lands andtheir inhabitants. In these parts of the world where Western science is experienced asa relatively new phenomena, the interaction of science “with culture has taken a moreviolent form and the disintegrating effects have been much more sharply experienced”(Ladriere, 1977, p. 14). Indeed, colonial education designed for indigenous peoplesused science as the tool of choice to modernize and supplant indigenous culture. In thewords of one colonialist: “A literate nation is provided with the means for substitutingscientific explanations of everyday events—such as death, disease, and disaster—forthe supernatural, non-scientific explanations which prevail in developing societies . . . ”(Lord, 1958, p. 340). A more reflective colonial teacher remarked, . . . “In common withso many others, I used to think that we could get rid of Bantu ‘stupidities’ by suitabletalks on natural science, hygiene, etc., as if the natural sciences could subvert theirtraditional lore or their philosophy” (Tempels, 1959, p. 29). The point is, the Westjudged the rest of the world by its own measure of choice, Western science and Westerntechnology, and used education to enforce change on those societies found deficient.According to Adas (1989, p. 4) European “perceptions of the material superiority oftheir own cultures, particularly as manifested in scientific thought and technologicalinnovation, shaped their attitudes toward and interaction with peoples they encoun-tered overseas.” Why? Because:

In the late eighteenth and nineteenth centuries, most European thinkers concluded that theunprecedented control over nature made possible by Western science and technology provedthat European modes of thought and social organization corresponded much more closely tothe underlying realities of the universe than did those of any other people or society, past orpresent. (Adas, 1989, p. 7)

Western scientists did have scientific interests in the rest of the world. Many areasof the globe became field sites for the practice of Western science by Western scientists(Basalla, 1967). Darwin’s voyage on the Beagle is surely the best known example ofWestern scientific development derived from non-European field work. When scien-tists occasionally took note of indigenous knowledge of Nature, that knowledge wasdistinctively labeled ethnoscience (e.g., Berlin, 1972; Behrens, 1989; Boster & Johnson,

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1989)—never simply science. This is not to say that such indigenous knowledge wasregarded as without value. There is a long tradition of Western science finding valuein indigenous knowledge especially as an aide to pharmaceutical discovery (Linden,1991). But, finding value in indigenous knowledge is not the same as conferring thetitle, science, and admitting indigenous knowledge of Nature to the Standard Account.

In the 1990s, non-Western people and some scholars within the West began to for-mally and overtly resist this imperial Western attitude toward indigenous knowledgeof Nature. This movement was abetted by the program for the social study of science,founded in the 1970s at Edinburgh (Bloor & Barnes, 1996), which argued that all sci-ence is socially contingent and culturally embedded. New epistemological perspectivessuch as multiculturalism (Stanley & Brickhouse, 1994), post colonialism (McKinley,1997), and post modernism (Lyotard, 1995) rose to challenge the conventional Westernwisdom on the relationship between science and culture and the Standard Accountitself. In education Hodson (1993, p. 686) maintained that science curricula often“portray science as located within, and exclusively derived from, a western culturalcontext. The implicit curriculum message is that the only science is western science. . . ”Dr. Thom Alcoze is Native American and a forestry professor at Northern Arizona Uni-versity. In a taped interview for a science teacher development project (SmithsonianInstitution, 1996b) he poignantly presented a different perspective on science.

Science is often thought of [pause] America has science. Mainstream America has science.And if you are a minority culture in this country you don’t have science. We started lookingfor Indian science where science is expressed in Indian tradition. And found it with plants,starting off. Medicines. And of course the stereotype is well Indian medicine is just superstitionand mumbo-jumbo, slight of hand, and basically it’s a witch doctor kind of thing [pause] astereotype. A lot of strange noises and dancin’ and singin’ and a lot of shakin’ but that’s all itis [pause] superstitious. It’s not real. What we found out when we looked for facts, we foundthat even today in modern America there are over 200 medicines in the pharmacopoeia that weuse that have direct origins in Native American medical practice. Yes, in fact Indian people didhave science. They were using science all the time. They weren’t using scientific terminology.They did not publish in scientific journals [pause] that’s kind of facetious at that time. But theissue of science then started to be redefined in my definition of what science is all about whenwe started to see that science is just another word for nature.

Dr. Alcoze’ last sentence is of critical importance. He says, “science is just anotherword for nature” and therefore American Indians being greatly knowledgeable aboutNature had scientific knowledge of their own. This idea is further developed in Kawa-gley et al., (1998, p. 134): “We contend that no single origin for science exists; thatscience has a plurality of origins and a plurality of practices.” They contend “that thereis no one way to do or think about science” (p. 139). As their case in point, they contendthat Yupiaq culture in southwestern Alaska holds “a body of scientific knowledge andepistemology that differs from that of Western science” (p. 133).

Much of Yupiaq scientific knowledge is manifested most clearly in their technology. One mayargue that technology is not science. However, technology does not spring from a void. Toinvent technological devices, scientific observations and experimentation must be conducted.Yupiaq inventions, which include the kayak, river fish traps . . . represent technology that couldnot have been developed without extensive scientific study of the flow of currents in rivers, the


ebb and flow of tides in bays, and the feeding, resting, and migratory habits of fish, mammals,and birds. (Kawagley et al., 1998, p. 136)

Science from this perspective refers to descriptive knowledge of Nature developedthrough experience with Nature. The definition of science used here is consistent withOgawa (1995, p. 588) who refers to science simply as “a rational perceiving of reality”and which then allows him to argue for the existence of legitimate multi-sciences.

The knowledge described above is from a domain of knowledge that Snively & Cor-siglia (1998) call Traditional Ecological Knowledge (TEK). It is the descriptive ecologi-cal knowledge about Nature that First Nations peoples in Canada and Native Americasin the USA have acquired through long years of experience with their natural environ-ment, and which has been vital to their survival. Snively & Corsiglia (1998) show thatthis knowledge can be quite insightful and has much to offer Western science. Forexample, they tell the story of a Nisga’a fisherman in British Columbia who noticedthat the Dungeness Crabs he typically harvested were exhibiting strange behaviorpatterns. The crabs were “marching past the dock at the mouth of the Nass River,rather than staying in the deep water of Alice Arm” (Snively & Corsiglia, 1998, p. 22).He grew concerned about possible industrial pollution of the Alice Arm waters from anearby molybdenum mine and later his concerns were shown to be well founded. Giventhe life and practice of the Nisga’a this intuition should come as no surprise.

Among the Nisga’a, and among other aboriginal peoples, formal observation, recollection, andconsideration of extraordinary natural events is taken seriously. Every spring members ofsome Nisga’a families still walk their salmon stream to ensure spawning channels are clear ofdebris and that salmon are not obstructed in their ascent to spawning grounds. In the course ofsuch inspection trips, Nisga’a observers traditionally use all of their senses and pay attentionto important variables: what plants are in bloom, what birds are active, when specific animalsare migrating and where, and so forth. In this way, traditional communities have a highlydeveloped capacity for building up a collective data base. Any deviations from past patternsare important and noted. (Corsiglia & Snively, 1997, p. 25)

Similar accounts obtain for people living traditional lives in many other regions ofthe world from Australia to Africa (see Warren, 1991 & 1997).

Multicultural Science in the Classroom

The reasons for including such examples of knowledge as part of the Standard Accountor the reasons for expanding the definition of science under the Standard Account,have to do with education. Proponents of a multiplicity view of science argue thatthis will better serve the needs of students coming from diverse cultural backgroundsand will help to change the culturally corrosive effect that Western science has hadon non Western cultures. “The Harvard-Smithsonian Video Case Studies in ScienceEducation” (Smithsonian Institution, 1996a & 1996b) project on classroom scienceprovides a glimpse of how this multicultural perspective on science can play out in ascience classroom. The project produced videotape case studies of teachers. Each tapeshows vignettes of a teacher teaching science interspersed with interview segmentswith the teacher and a science education expert. One of the case studies was done at anelementary school in Flagstaff, Arizona where the students come from American Indian

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Nature is viewed as sacred

Humans are part of the web of life

Humans should live in harmony with nature

The entire world is viewed as being alive

Technology should be low impact

Figure 1: Native American views about nature (Simthsonian Institution, 1996b).

and non-Indian families. Donna is a fifth grade teacher and she has been teaching aunit on ecology. She also has drawn in her Native American students by collectinginformation on Indian culture. This information is publicly displayed on a large posterboard in the classroom (see figure 1).

Pointing to the poster board, the teacher speaks to her students.Donna: We were talking earlier in here about looking at different cultures and finding ideasform cultures that might help us understand science better. Now, some of the traditional NativeAmerican views about nature are on this chart. Can you find one [Native American view] thathelps us to understand this cycle of decompositions? (Smithsonian Institution, 1996b)

At this point a number of students raise hands. The teacher calls on them to speakand she asks each student to explain the relationship of the Native American viewpointto decomposition. Later, Donna is asked in an interview about the purpose of suchactivities.

Donna: My goal would be that all children would feel that they have a very important heritage.No matter what heritage they come from. And to be a scientist doesn’t mean that you have to beany particular race or any particular gender or from any particular culture but that all peoplehave contributed to the body of knowledge which we call science. (Smithsonian Institution,1996b)

In this vignette, Donna has set a very nice stage with her Native American posterabout views of nature. From here she can go on to have her class study what sciencehas learned about ecological cycles, balances of nature, decomposition, etc. Loving (inpress) and Cobern (1995a) offer similar views on using local culture to promote sciencelearning.

One would only hope that along the way, reference might be made back to the posterto see if science supports, ignores or rejects ideas from one’s culture and what evidencethere is to support that. In Donna’s case above the controversial questions are abouther meaning for the world “science” and will she lead her students to understand thatthere are different legitimate ways of thinking about Nature? “Nature is viewed assacred” is one such legitimate way but it is not the way of science. Thus, we wouldwant to know if Donna intends to help her students cognitively construct two different,though complementary, explanations for the same phenomena? Or, will the studentslearn the multiplicity view that all of this simply represents different forms of science?


The Universality of Science

As much as we support science teaching that is both informed by culture and sensitiveto culture, the issues raised by TEK and multicultural perspectives on science mustnot be accepted uncritically. We say this not in defense of science and the StandardAccount. We think that science has shown itself sufficiently useful and remarkableto humanity that there will be no withdrawal of science from modern life. And, it isarguable that science would suffer little harm if, for the purposes of curriculum, TEKand similar domains of knowledge were declared scientific tomorrow. In contrast, suchan action would actually be counterproductive with respect to the concerns people haveabout indigenous knowledge being shut out of science by the Standard Account. Beforedeveloping that thought, however, we clarify our meaning of the Standard Account andthe case for universality.

Defining the Standard Account

Loving’s (1991) Scientific Theory Profile gives a good indication of the breadth of philo-sophical views on the nature of science. Philosophers of science run the gamut fromrationalist to naturalist, anti-realist to realist, and the many combinations within theseranges. Within the philosophy of science and scholarship on the nature of scienceresides the important question of demarcation. How can science be distinguishedfrom other intellectual domains? How does science differ from (say) historiography ortheology or philosophy? According to Gieryn, Bevins, and Zehr (1985, p. 392) the goalsof demarcation are the “(1) differentiation of a valued commodity uniquely providedby science, and (2) exclusion of pseudo-scientists . . . ” and these goals “are importantfor scientists’ establishment of a professional monopoly over the market for knowledgeabout nature” (also see Gieryn, 1983). The demarcation of science from other disci-plines, however, is not easily accomplished. Laudan (1983, pp. 8-9) argues that,

philosophers have been regarded as the gatekeepers to the scientific estate. They are the oneswho are supposed to be able to tell the difference between real science and pseudo-science. . . .Nonetheless, it seems pretty clear to many of us. . . that philosophy has largely failed to deliverthe relevant goods. Whatever the specific strengths and deficiencies of certain well-knownefforts at demarcation . . . it can be said fairly uncontroversially that there is no demarcationline between science and non-science, or between science and pseudo-science, which would winassent from a majority of philosophers.

Though we do not wish to minimize the philosophical complexity of the issue towhich Laudan refers, nor are we immune to the ideological influences upon the Stan-dard Account (Hesse, 1980), there is a pragmatic view to science broadly acceptablein the scientific community and described in accounts by scientists themselves, suchas biologist Frederick Grinnell (1987) and physicist A.F. Chalmers (1982). In addition,science educators (Driver, Leach, Millar and Scott, 1996) who thoughtfully examinedthe range of philosophical, historical and sociological views of science were able toarrive at critical areas of consensus and were helpful in our Standard Account. Thefollowing is what we understand that definition of the Standard Account of science tobe. In providing this definition we have kept in mind Laudan’s (1996, p. 24) point that

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what “we need to provide is a way of distinguishing reliable knowledge claims fromunreliable ones.”

1.0 Science is a naturalistic, material explanatory system used to account fornatural phenomena that ideally must be objectively and empirically testable.

1.1 Science is about natural phenomena. It is not about the things that humansconstruct such as economic systems nor is it about spiritual phenomena. Here weconcur that TEK is about natural phenomena.

1.2 The explanations that science offers are naturalistic and material. It follows frompoint 1.1 that scientific explanations are not about the spiritual, emotional, economic,aesthetic, and social aspects of human experience. Snively & Corsiglia (1998) recognizethat with respect to TEK this aspect of the Standard Account poses a problem eventhough TEK is about natural phenomena. They note that many scientists refuse torecognize TEK as science “because of its spiritual base, which they regard as supersti-tious and fatalistic” (p. 30). In response, they argue that “spiritual explanations oftenincorporate important ecology, conservation, and sustainable development strategies”(p. 30); but nevertheless, they still assert that “the spiritual acquisition and expla-nation of TEK is a fundamental component and must be promoted if the knowledgesystem is to survive” (Johnson, 1992 quoted in Snively & Corsiglia, 1998, p. 31).

1.3 Science explanations are empirically testable (at least in principle) against naturalphenomena (the test for empirical consistency) or against other scientific explanationsof natural phenomena (the test for theoretical consistency). Science involves collect-ing data (i.e., evidence) and a scientific explanation must be able to account for thisdata. Alternatively, science involves the testing of proposed explanations against data(Driver et al, 1996, p. 43). This concept is nicely captured by Duschl in an interviewwhere he is commenting on the activities of some 1st graders. The 1st grade classare experimenting with sound. The children have some ideas about sound and theytest some of these ideas using rubber bands stretched over geoboard pegs. About thisepisode, Duschl remarks:

When kids are given the same phenomena to observe, they see very different things. Theirpersonal interpretations of the ideas are very different. And when we listen to the children incircle you can hear this and see it. This is an opportunity to get this consensus that we want, toget some discussion because the scientific ideas just aren’t any ideas. They are ideas groundedin evidence. (Smithsonian Institution, 1996a)

Duschl tells us that “the scientific ideas just aren’t any ideas.” They are tested ideas.They are tested either in the physical world following from point 1.2, or they are testedfor theoretical consistency with other scientific explanations, which in turn were testedin the physical world.

Moreover, scientific testing strives to be objective. In recent years this value inscience has been derided as “objectivism . . . a universal, value-free process” (Stanley& Brickhouse, 1994, p. 389; also see Guba & Lincoln, 1989). Perhaps some people


have overextended the concept of objectivity. In our view of the Standard Account,objectivity refers to the goal that experimental outcomes are not to be prejudged norunreasonably constrained by prior belief, that data is collected fairly and accurately,and that research methods are executed with fidelity.

Is it possible that TEK is tested knowledge? Borrowing a phrase form Sagan (1996,p. 251), Kawagley et al., (1998, p. 137) maintain that “Yupiaq traditional knowledgereflects an understanding of the natural world based on a massive set of scientificexperiments continuing over generations.” No one would doubt that the Yupiaq, alongwith every other group of people that ever lived, have and continue to engage in “trialand error” experimentation. People try different shampoos until they find the one theylike best but few would consider such “experimentation” scientific. It is not scientificbut it is an effective and valuable process. Similarly, the building up of traditionalknowledge through trial and error interactions with Nature has produced importantknowledge. But, it lacks the formal, controlled features of scientific experimentation.

1.4 Science is an explanatory system—it is more than a descriptive ad hoc accounting ofnatural phenomena. Science seeks to parsimoniously explain how things work invok-ing only natural causes and these explanations are woven into a system of theoreticalthought. Theories, however, are typically under-determined, that is they go beyondthe available data and are therefore conjectural. Scientists chose between competingtheories based on criteria such as accuracy of prediction, internal consistency and dataconsistency, breadth of scope (the more encompassing the theory, the more it is valued)simplicity and fruitfulness—all based, however, on human judgement (Driver et al.,1996). To this aspect of the Standard Account, the sociology of science adds thathuman judgment does not exist in a vacuum. It exists and is exercised within thecontext of social and cultural life. There is an inherently social aspect to all knowledgeconstruction. Thus, for example, to understand how Darwin came to his formulationof evolution it is not sufficient to know about the voyage of the Beagle, his variousobservations, his knowledge of domestic breeding practices and the like. One mustalso take into account the cultural environment in which Darwin lived (Cobern, 1995a;Desmond & Moore, 1991).

Moreover, it must be noted that scientific explanation (point 1.2) and scientifictheory (point 1.4) represent two complementary levels of scientific knowledge (alterna-tively, the difference between what students think of as “description” and “explanation”in the theoretical scientific sense—see Horwood, 1988 and Matthews, 1994). Thefirst level is strongly related to direct human experience. Thus, for example, thelocation of salmon at any one time of the year can be explained in terms of the salmon’slifecycle, where evidence relating to locality and lifecycle are both directly observable.This explanation has considerable creditability regardless of cultural variation. Incontrast, credibility at the second level is much more culturally dependent. At thesecond level, scientific theory would further explain that “lifecycle” can be viewed as anidealized pattern of sequenced events that is applicable across a great many organisms.Here credibility depends on how accustomed people are to abstract scientific theoriz-ing. In a different culture, people would find it more credible to explain “lifecycle”

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as the purposeful course of life uniquely belonging to each creature. Horton (1994)has demonstrated that much of traditional African thought at the lower level does notdiffer substantially from scientific explanation. The significant differences are at thesecondary level with the “webs of significance” (Geertz, 1973) that give meaning tothose first level explanations. Similarly, here is the fundamental problem with takingTEK as science—TEK is embedded in a spiritual system of meaning that cannot easilybe ignored, nor should it be ignored.

2.0 The Standard Account of science is grounded in metaphysical commit-ments about the way the world “really is” (e.g., see Burtt, 1967; Cobern, 1991 &1995b). These commitments take the form of necessary (or first order) presuppositions.They are not descriptive of what science is but what science presupposes about Nature.By themselves these necessary presuppositions are probably not sufficient motivationfor any individual to be involved with science, hence any individual scientist or scienceteacher likely will have augmented these necessary presuppositions with other (sec-ondary) presuppositions that are personally necessary. Our focus, however, is on themetaphysical minimum for science.

2.1 Science presupposes the possibility of knowledge about Nature. Realists viewthis as actual knowledge—Human thinking holds the potential for recognizing andunderstanding the actual order and causality inherent in the phenomena of Nature.Idealists view this as instrumental knowledge—Human thinking holds the potential forconstructing viable understanding about the instrumental order and causality in theexperience of natural phenomena. Roger Penrose and Stephen Hawking, respectively,are exemplars of the two positions (Hawking & Penrose, 1996). Closely linked to thepossibility of knowledge are the presuppositions of order and causality.

2.2 Science presupposes that there is order in Nature. The fact that the orbit ofthe earth can be represented as a mathematical equation or that tidal action can beestimated within predictable limits of accuracy is evidence of order. Realists view thisorder as actual order—There is order in nature. Idealists view this as instrumentalorder—Human experience with Nature is amenable to ordered thinking about experi-ence with Nature. Historically, presupposed order in Nature was profoundly importantto the development of science in Europe. Gernet (1993-94), following the pioneeringwork of Needham (1969), notes the crippling effect the lack of this presupposition hadon the development of Chinese science.

2.3 Science presupposes causation in Nature (Collingwood, 1940). For example, rain iscausally linked with factors such as air temperature and humidity. Given enough watervapor in the atmosphere and the right air temperature, it is going to rain. Realists viewthis causation as actual causation. Cause and effect are inherent attributes of Nature.Idealists view this as instrumental causation—Causal thinking is amenable with thehuman experience with Nature.


3.0 Nevertheless, what ultimately qualifies as science is determined by con-sensus within the scientific community. Thus, simply offering an idea whichfits all these parameters will still not be science until judged so by the communityof science. As we noted above, the problem is that there is no perfect account of sciencethat clearly represents all of science, past and present, and just as clearly eliminates allendeavors that scientists do not consider to be science. In the final analysis a humanjudgment must be made. However, the community of scientists is a community thatrequires that scientific knowledge be made public and withstand public scrutiny andtesting. Thus, in the long run there can be no conspiracies to include or exclude anydomain of thought.

The Universality of Science

Much of the multicultural literature on science seems to be saying that the problemwith the Standard Account is that it is taken to be the only account of science. It is anexclusive and universally appropriate account. But we wonder if this really is the boneof contention among multiculturalists? Is it the alleged universality of science or is itthe intellectual exclusiveness of science according to the Standard Account? We askthis because the post-colonialist arguments rejecting the universality of science seemto be arguments more about the exclusivity of science. It seems to us that even if thedefinition of science were broadened to include what is now excluded one would stillhave a “universal” science. Indeed, if there is no universal concept of science then howcan anything be either included or excluded as science?

It can be instructive to consider a different type of example altogether. Around theglobe “football” is a widely recognized sporting game. We in America have a game called“football” but it is significantly different from what the rest of the world calls football.In fact, the rest of the world for the sake of clarity refers to the American game as“American football” to distinguish it from real football. With enough political agitationand economic clout those of us Americans who resent this form of marginalizationcould possibly get the rest of the world to broaden its definition of “football.” Theterm “football” still is universal (we now all agree that the game of football includesthe varieties played in the USA and elsewhere) but it now has a new meaning that isgeneral enough to include what many previously took to be two rather distinct games.Undoubtedly, there are other games played with a ball and the feet. If the proponentsof these games agitate as successfully as did the American footballers, where will theprocess end? In our opinion, this is anti-reductionism made absurd and the end resultis that everyone loses. Diversity is lost. Meaning is lost. Communication is lost.

We thus conclude that the real difficulty multiculturalists have with the StandardAccount is not its claim to universality, but its exclusiveness. Though technicallydifficult to accomplish, conceptually the Standard Account could be broadened by sim-ply getting a consensus in the science community for the rewriting of the definitionof science in a more inclusive form. Then one could have “Maori science” or “FirstNations science,” (or for that matter, “Christian science” and Islamic science, etc.)—just as “football” could be broadened to include “American” football. We could be evenmore inclusive by simply taking science to be knowledge of Nature—but one needs to

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reconsider why would anyone want to do any of these things? Early in this article wequoted from Kawagley et al (1998, p. 134) on the relationship between the StandardAccount and indigenous knowledge:

such a narrow view of science not only diminishes the legitimacy of knowledge derived throughgenerations of naturalistic observation and insight, it simultaneously devalues those cultureswhich traditionally rely heavily on naturalistic observation and insight.

We see in this statement that some people are troubled about the dominant intellectualposition that modern Western science has come to hold in the public square. It is a po-sition of dominance that tends to disenfranchise competitors. One way for competitorsto regain that franchise is to oust Western science. Another way to regain access to thepublic square—and this is the approach many multiculturalists appear to be taking—isto get one’s ideas included in the definition of the dominant player, in this case Westernscience or the Standard Account.

If such a thing were to ever happen it would be a pyrrhic victory for indigenousknowledge. The new additions to science (TEK or any other form of indigenous knowl-edge) would soon face serious negative consequences. They would first lose their dis-tinctiveness as a form of thought as they became absorbed by the dominant discourseof science, that is the Standard Account. They would lose because the new additionswould inevitably be taken as mere “tokens” of cultural inclusiveness rather than as se-rious participants in the discourse of science. This tokenism would be reinforced by theinability of the new additions to compete where Western science is strongest—technicalprecision control, creative genius and explanatory power. And, the new additions wouldlose by being co-opted into the cultural chauvinism scientism now holds in much ofmodern life. Snively & Corsiglia (1998) rightfully question where is the wisdom inscience? As an incorporated part of science, that critique and challenge would be muchmore difficult to make.

The Problem of Scientism

The problem facing TEK and other forms of indigenous knowledge, as well as otherdomains of knowledge such as the arts and literature and religion, is the problem ofscientism—the cultural hegemony science. The problem is not that science dominatesat what it does best: the production of highly efficacious naturalistic understandingof natural phenomena. The problem is that too often science is used to dominate thepublic square as if all other discourses were of lesser value. This is a hierarchic viewof knowledge with science placed at the epistemological pinnacle (see figure 2). Forexample, the National Academy of Science out of fear over religious incursions in schoolscience issued this statement:

In a nation whose people depend on scientific progress for their health, economic gains, andnational security, it is of utmost importance that our students understand science as a systemof study, so that by building on past achievements they can maintain the pace of scientificprogress and ensure the continued emergence of results that can benefit mankind. (NAS, 1984,p. 6)


Natural Sciences

Social Sciences

Other Knowledge Domains

Figure 2: Epistemological pyramid.

More recently the International Council of Scientific Unions (ICSU) endorsed a sim-ilar perspective in the “Proposed ICSU Programme on Capacity Building in Science”(ICSU, 1996). The document epigram equates “the global gap of well-being” with “theglobal imbalance of science and technology development.” The ICSU intends to:

demonstrate to the world that having the capacity to understand and use science is economi-cally, socially and culturally profitable. Indeed, the very habitability of the planet will dependon global popular consensus. As such, the spread of scientific culture, of scientific ways ofthinking, and of knowledge is tied to the fate of humanity. (p. 1)

About these statements we can say, of course, few people question the productiverole that science has played in the development of modern life including medicineand contributions to good health, nor the economic gains due to technical innovationsgrounded in science (though the relationship between science and technology is notnearly so straightforward as these statements from the science community suggest).These claims by NAS and ICSU, however, are vastly overstated and singularly one-sided. Good health, economic well being and national security depend on many thingsonly one of which is science. Moreover, as important as science surely is, it does nothave an uncontested claim to be the most important of these many factors. Curiously,though the National Academy of Science and the ICSU appear eager to accept creditfor good technological innovations there is no parallel acceptance of technological dis-asters. If the science community wants credit for developing high yield grains thatease food shortages, how can the same community refuse credit for DDT? Something iswrong with this portrayal of science (we might even say betrayal of science). Garrardand Wegierski (1991, p. 611) suggest an explanation:

It can be argued that technology and scientific positivism constitute the dominant ideology ofWestern civilization today. Technology has indeed become, as Heidegger noted, the metaphysicsof our age, a totalistic form of secular religion ultimately incompatible with the existence ofrival, non-technological assumptions, beliefs, or thought systems.

The problem for TEK—as well as for so many other domains of knowledge—is notthe exclusivity of science as per the Standard Account but the transmogrification ofscience as scientism in the public square.

Cobern & Loving 63

Epistemological Pluralism

When there is a gatekeeper and you persuade the gatekeeper to let you in, althoughyou may have influenced the gatekeeper you have also conceded his legitimacy asgatekeeper. Similarly, getting TEK into the school curriculum as science does notaddress the fundamental problem that led to the devaluing of TEK and other forms ofindigenous knowledge in the first place. The task for educators is to develop curriculathat value knowledge in its many forms and from its many sources. Therefore bringingTEK into the science classroom is an excellent thing to do. It offers students a chanceto see how the practice of science can benefit from the insights of another domain ofknowledge. It helps students see that some of the insights from science can be arrivedat by other epistemological pathways. And, it helps students see what is unique aboutscience—what science can do that other domains of knowledge cannot do.

We therefore reject positions of scientific and epistemological relativism. Not allthoughts are equal. Not all ways of thinking are parallel. But life is a complicatedaffair and the skillful navigation of life requires a diverse repertoire of thought andreason. And what is essential for a suburbanite American to understand about Naturewill not be satisfactory for a Nisga’a fisherman living in a very different world. Thus,what we value is the best thinking for a given situation and the wisdom to changeone’s thinking when situations change. We advocate epistemological pluralism and theability to wisely discriminate amongst competing claims. This last point is importantbecause the issues of life typically cross epistemological categories. It is not alwaysobvious in the public when a problem does or does not call for a scientific solution.Should the USA spend four billion dollars to build a Super Collider? The scientificanswer is probably “yes” since the Collider would help make important advances inphysics. But, America is not building the Super Collider because science was out bid bythe competing discourse of economics. In other situations we may find other domains ofknowledge acting in consort with science. Snively & Corsiglia (1998) give a number ofexamples of ecologists and biologists profiting from the TEK of indigenous people. TheNative American Forestry Program at Northern Arizona University (1997) providesanother example where science and traditional knowledge work in consort.

In other situations, however, science rightly precipitates and influences culturalchange. Consider the following situation. At a recent NARST session a researcherread the script of dialogue between an Australian Aborigine and a health care workerindicating totally different perspectives regarding the value and use of high-proteinfoods. The food is valued as nutrition, especially for children, in the West and valuedas gifts in adult relationships to the Aborigines. The result of the latter perspec-tive is continued high infant mortality for children under two years of age despitehealth care workers’ careful use of Socratic methods to dignify the alternate viewswhile educating the Aborigines. From the perspective of traditional Aboriginal life,that of a hunter/gatherer culture, the elevated social and political status of the eldersmakes their health critical to the success of the tribe. From that perspective theywere correct to reject the science-based position. However, cultures cannot maintain astatus quo in the face of environmental change and expect to survive. The fact that the


researcher was involved with an education program for Aboriginal peoples indicatesthat the researcher knew this fully well. Thus in this case the possible cultural changesprecipitated by science education regarding young children’s need for high protein foodare likely to be in the groups’ long term best interests.

The unfortunate fact of this last example is that the researcher represented theAboriginal rationale for distributing the best food to important adults as equally scien-tifically valid as is a distribution based on confirmed nutritional value and nutritionalneed at various stages of human physical development. But if all explanations aremistakenly valorized as scientifically valid (and there is no attempt at understandingthe best scientific explanations), we are reduced to relativism of the worst kind. Privi-leging “what knowledge is of most worth” in science class is not the same as denying thevalue of other forms of knowledge (Loving, 1997). What is at issue here is the learningof when scientific knowledge should be appropriated over other competing domains ofknowledge because it is the best knowledge available for the particular situation.

Conclusion

Our position in this article is that science can be defined with sufficient clarity so as tomaintain a coherent boundary for the practical purposes of school science curriculumdevelopment. That boundary excludes most forms of indigenous knowledge, if notall, just as it excludes art, history, economics, religion, and many other domains ofknowledge. Being exclusive, however, does not confer science with any privilege vis-a-vis other domains. Science is properly privileged only within its own domain for thatis where its strength lies. When TEK and other forms of indigenous knowledge aredevalued it is not because of the exclusive nature of the Standard Account of science.It is because someone is involved in the scientistic practice of extending scientificprivilege from its proper domain in science and technology into other domains. Thesolution is to resist this scientistic practice by emphasizing throughout schooling theconcept of epistemological pluralism, bearing in mind that pluralism,

is not relativism. . . Pluralism is the civil engagement of our differences and disagreementsabout what is most importantly true. Against the monism that denies the variety of truth,against the relativism that denies the importance of truth, and against the nihilism thatdenies the existence of truth, we intend to nurture a pluralism that revives and sustains theconversation about what really matters, which is the truth. (First Things, 1995, p. 12)

Bearing also in mind that truth is never under the sole proprietorship of any singledomain of knowledge—not even science.

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Varieties of Constructivism and their (Ir-)Relevance to ScienceEducation

Peter SlezakUniversity of New South Wales, Austrialia. Email: [email protected]

Introduction

The post-modernist affectation in the title, referring to the (ir-)relevance of ‘construc-tivism,’ is intended to reflect the ambiguities which prevail under this broad head-ing and their varied implications. Despite these unclarities, the doctrines under thisheading enjoy an extraordinary popularity among educators. Paul Cobb (1994, p. 4)has referred to the “fervor that is currently associated with constructivism” and PaulErnest has written:

In the past decade or two, the most important theoretical perspective to emerge in mathematicseducation has been that of constructivism. . . . Ironically the attacks on radical constructivism. . . which were perhaps intended to fatally expose its weakness, served as a platform fromwhich it was launched to widespread international acceptance and approbation. (Ernest 1995)

In an important clarification of the varieties of ‘constructivism,’ D.C. Phillips (1997,p. 152) has noted that “Arguably it is the dominant theoretical position in science andmathematics education” and he remarks:

Across the broad fields of educational theory and research, constructivism has become some-thing akin to a secular religion. (1995, p. 5)

Phillips distinguishes the sociological form of constructivism from the psychologicalvariety. The psychological variety of constructivism is a theory of individual mentalactivity principally championed by Ernst von Glasersfeld (1995) and its origins canbe seen in Kant, Berkeley and Piaget, among others. There is a third variety ofconstructivism which deserves to be clearly distinguished from the others, namely,the ‘constructive empiricism’ of van Fraassen (1980) which has received no attentionamong educationalists, though it has been among the most important recent views inthe philosophy of science. This doctrine is a form of anti-realism or instrumentalismwhose provenance can be traced by at least as far as Osiander’s notorious preface toCopernicus’ De Revolutionibus and the Galileo affair, and still a major issue in thephilosophy of science.

The educational implications of these doctrines are markedly different, and in thisarticle I will be concerned to draw these out clearly. First, I will suggest that, despiteits overwhelming influence among educationalists, the ‘radical constructivism’ of vonGlasersfeld has absolutely no pedagogical consequences at all. By contrast, the so-ciological variety of constructivism at the centre of the recent ‘Science Wars’ has themost dramatic, and largely unnoticed, implications for education, to be discussed inthe following article. Finally, van Fraassen’s constructive empiricism has importance

70 Constructivism and Science Education

for educators as a part of the broader role of history and philosophy of science in anysound science curriculum, discussed in the paper ‘Does Science Teaching Need HPS?’(See the article on page ??.)

Radical Constructivism: Epistemology, Education and Dynamite

Ernst von Glasersfeld has remarked “To introduce epistemological considerations intoa discussion of education has always been dynamite” (quoted in P. Ernest 1995, p. xi).I am concerned to give an analysis of the explosive mixture.

A symptom of the problem may be seen in the remarkable range of philosophicalissues raised in the educational literature. These include extremely abstruse, esotericquestions whose relevance to any practical or theoretical problem in education is surelydoubtful. Thus, among the topics discussed are Berkeleyan idealism, Cartesian du-alism, Kantian constructivism, Popperian falsifiability, Kuhnian incommensurability,Quinean underdetermination, truth, relativism, instrumentalism, rationalism and em-piricism, inter alia. By seemingly plausible increments, we are led from the classroomto the most arcane problems of metaphysics.

Education←→ Learning←→ Psychology←→ Knowledge←→ Epistemology←→Metaphysics.

Thus, Gergen (cited in Steffe & Gale eds. 1995, p. xii) sees certain lapses in “Cartesianepistemology” and the “mind-body split,” though the concievable bearing of this oneducational matters remains obscure. Likewise Steffe (1995, p. xiii) contrasts variousconstructivist approaches with “the Cartesian model,” suggesting that they “differedfrom the Cartesian model in viewing knowledge in a nondualistic manner so as toavoid to mind-body split of endogenic (mind-centred) and exogenic (reality-centred)knowledge” (1995, p. xiii). In passing, we might note that the mind-body split is adifferent issue from that of the objective reality of a mind-independent world, thoughSteffe seems to conflate these. Unfortunately, Steffe also neglects to explain howCartesian dualism might have the slightest bearing on science teaching, or anythingelse for that matter. As a card carrying materialist, like most philosophers today, Idoubt that I am a better teacher for that reason. Some of my best friends are dualists,and great teachers. Not least, Descartes’ own exemplary foundational contributions tomodern science and mathematics were hardly inhibited by his alleged “lapses.”

Such examples suggest that we might be highly suspicious of constructivist claimsof von Glasersfeld and Gergen, among others, suggesting that for 2,500 years sincethe origin of science in ancient Greece, we have been somehow seriously misguidedin our conceptions of knowledge and science (see von Glasersfeld in Steffe & Galeeds. p. 6). Thus, von Glasersfeld suggests that his conception of constructivism arose“out of a profound dissatisfaction with the theories of knowledge in the tradition ofWestern philosophy” and he has suggested that adopting his constructivism “couldbring about some rather profound changes in the general practice of education” (1989,p. 135). His radical recommendation is: “Give up the requirement that knowledgerepresents an independent world” (in Steffe & Gale eds. pp. 6-7). This is, of course,Berkeley’s notorious idealism and undoubtedly a radical proposal. However, despite

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these extravagant claims, we will see that the educational recommendations whichvon Glasersfeld actually offers are rather modest.

Commonsense Realism

The prominent role of such metaphysical problems in the educational literature isperplexing in a way which goes beyond the intrinsic puzzles of the issues themselves.Undoubtedly, the issue of realism remains a central one in philosophy, though even herean important warning has been recently voiced by Hilary Putnam (1994) in his DeweyLectures. Putnam notes that “The besetting sin of philosophers seems to be throwingthe baby out with the bathwater” as each new generation or fashion ignores the insightsof earlier periods. In particular, concerning the disputes over realism, Putnam saysthat it is important to find a way “to do justice to our sense that knowledge claims areresponsible to reality without recoiling into metaphysical fantasy” (1994, p. 446). Theresponsibility proposed by Putnam is a familiar, commonsense, naive realism.

It is surprising enough that philosophers need to be reminded not to lose sight ofcommonsense realism. That educationalists need the same advice is somewhat harderto explain. Like Berkeley, Kant is explicitly cited by von Glasersfeld as one of thesources for his constructivism, though it is instructive to ponder how one might deriveeducational implications from the Critique of Pure Reason. Kant’s ‘transcendentalidealism’ as an attempt to find an alternative to a pure ‘phenomenalism’ is an unlikelybasis for pedagogical theory or instructional interventions.

Piaget’s “Construction of Reality?”

von Glasersfeld sees important consequences following from a person’s “cognitive iso-lation from reality.” However, Kant’s idea that knowledge of the world and of theself are two aspects of the same schema is not a denial of the objective reality ofa mind-independent world as von Glasersfeld appears to think. Kant’s idea is alsoexpressed by Piaget, clearly acknowledging a knowable objective world beyond oursense-data. Despite being chargeable with at least “flirting with idealism” (Boden 1979,p. 79), Piaget (1975) says that his epistemological position is “very close to the spiritof Kantianism” (Insights and Illusions of Philosophy, p. 57)—both in its constructivismand in its sensitivity to the need to avoid Berkeleyan idealism.

Thus Margaret Boden writes:

Piaget is aware that as a constructivist he must be careful to avoid idealism—or, to put itanother way, that he must answer the sceptic’s challenge that perhaps all our so-called ‘knowl-edge’ is mind-dependent illusion. He tries to buttress his commonsense realism by appealingto the biological basis of knowledge. (Boden 1979, p. 79)

Piaget himself explains clearly:

. . . So to attribute logic and mathematics to the general coordinations of the subject’s actions isnot an idealistic overestimation of the part played by the subject; it is a recognition of the factthat, while the fecundity of the subject’s thought processes depends on the internal resourcesof the organism, the efficacy of those processes depends on the fact that the organism is notindependent of the environment but can only live, act, or think in interaction with it. (Piaget1971, p. 345)


Although the title of Piaget’s (1955) book The Construction of Reality in the Childis suggestive of the constructivist doctrines which von Glasersfeld has championed,Piaget’s own text leaves little doubt about the significant difference between these two.Thus, while von Glasersfeld is at pains on every occasion to emphasize the unknowa-bility of reality and the need to abandon notions of objectivity and truth, Piaget bycontrast, writes in an altogether different mood. The conclusion of his book is titled‘The Elaboration of the Universe’ and he asks how the world is constructed by meansof the instrument of the sensorimotor intelligence. In particular, Piaget speaks of theshift from an egocentric state to one “in which the self is placed . . . in a stable worldconceived as independent of personal acitivity” (p. 395). Elsewhere Piaget explains:

. . . the universe is built up into an aggregate of permanent objects connected by causal relationsthat are independent of the subject and are placed in objective space and time. Such a universe,instead of depending on personal activity, is on the contrary imposed on the self . . .. (p. 397). . . During the earliest stages the child perceives things like a solipsist who is unaware ofhimself as a subject and is familiar only with his own actions. But step by step with thecoordination of his intellectual instruments he discovers himself in placing himself as an activeobject among the other active objects in a universe external to himself. (p. 397)

Thus Piaget is quite unselfconscious in speaking about the existence of an indepen-dent reality:

Accommodation of mental structures to reality implies the existence of assimilatory schemata.. . . Inversely, the formation of schemata through assimilation entails the utilzation of externalrealities to which the former must accommodate . . .. (p. 398)

He explains that the dual processes of assimilation and accommodation lead to ashift from egocentrism to an objectivity and enables “the subject to go outside himselfto solidify and objectify his universe . . .” (p. 402).

Elsewhere Piaget writes:

The theory of knowledge is therefore essentially a theory of adaptation of thought to reality,even if in the last analysis this adaptation (like all adaptations) reveals the existence of aninextricable interaction between the subject and the objects of study. (1972, p. 18)

The problem is that of “determining how knowledge comes to terms with the realworld, and therefore what relationships obtain between subject and object” (ibid, p. 6).

These are ways of talking which von Glasersfeld has emphatically repudiated, andso it is evident that his version of constructivism is quite different from Piaget’s.

The Philosophical Urge

von Glasersfeld has explicitly drawn his constructivist stance from what he takes to bethe insights of Berkeley and Kant. He says Berkeley’s insight

. . . wipes out the major rational grounds for the belief that human knowledge could representa reality that is independent of human experience. (von Glasersfeld 1995, p. 34). . . Kant’s ‘transcendental philosophy’ . . . is a purely rational analysis of human understandingand provides a model that is in many ways fundamental to the constructivist orientation. (vonGlasersfeld 1995, p. 39)

Slezak 73

von Glasersfeld is evidently suffering from what Rorty (1979) has called “the philo-sophical urge,” namely, to say that assertions and actions must not only cohere withother assertions and actions but “correspond” to something apart from what peopleare saying and doing . . . (1979, p. 179). By contrast, in the spirit of Putnam’s (1994)“second naivete,” Rorty says that a Quinean naturalism questions “whether, once weunderstand . . . when and why various beliefs have been adopted or discarded, there issomething left called “the relation of knowledge to reality” left over to be understood”(1979, p. 178).

Aside from the question of its possible bearing on pedagogy, von Glasersfeld isevidently led into his Berkeleyan worries by failing to distinguish questions of epis-temology from questions of metaphysics. That is, he conflates questions concerningthe reliability of knowledge with the question of metaphysical realism. In the follow-ing quotation we see the former concern in the first paragraph and the latter, quitedifferent concern in the second:

In most departments of psychology and schools of education, teaching continues as thoughnothing had happened and the quest for immutable objective truths were as promising as ever.For some of us, however, a different view of knowledge has emerged, . . . This view differs fromthe old one in that it deliberately discards the notion that knowledge could or should be arepresentation of an observer-independent world-in-itself . . .. (von Glasersfeld 1989)

Again, we see a non-sequitur from a concern about the reliability of knowledge toidealism:

The existence of objective knowledge . . . has been taken for granted by educators. Recentdevelopments in the philosophy of science and the historical study of scientific accomplishmentshave deprived these presuppositions of their former plausibility. Sooner or later, this must havean effect on the teaching of science. . . . I am presenting an alternative theory of knowing thattakes into account the thinking organism’s cognitive isolation from ‘reality.’ (von Glasersfeld1989, p. 121)

Any solution to our “cognitive isolation from reality” is unlikely to help solve theproblem of objective knowledge since the arguments for realism are not the same asarguments for this latter problem. That is, the epistemological problem of “objectiveknowledge” is left untouched by “recoiling into the metaphysical fantasy” of Berkeleyanidealism. Rather, the current philosophical answer to the epistemological problem isthe acknowledgement that there is no absolutely certain foundation. Instead, philoso-phers settle for a fallibilistic naturalism captured in Quine’s epigraph from Neurath:

Wie Schiffer sind wir, die ihr Schiff auf offener See umbauen mussen, ohne es jemals in einemDock zerlegen und aus bestend Bestandteilen neu errichten zu konnen. (Otto Neurath, quotedas epigraph in Quine 1960)

That is, we are like the sailor who must repair his ship while sailing in it. Theentire ship may be rebuilt, but only one plank at a time. von Glasersfeld’s concernsabout metaphysics are addressed in Quine’s following remarks:

Ontological questions, under this view, are on a par with questions of natural science. (Quine1961a, p. 45)


. . . our statements about the external world face the tribunal of sense experience not individu-ally but only as a corporate body. (Quine 1961a, p. 41)Hence it is meaningless, I suggest, to inquire into the absolute correctness of a conceptualscheme as a mirror of reality. Our standard for appraising basic changes of conceptual schememust be, not a realistic standard of correspondence to reality, but a pragmatic standard. (Quine1961b, p. 79)

Charitably construed, von Glasersfeld’s concerns may be seen as expressing—if nota “post-epistemological” view as he is pleased to call it, or a “successor epistemology”as Gergen (p. 23) says,—the familiar epistemological position of Quine himself. vonGlasersfeld’s notion of “viability” seems best understood as a “coherentist” positionconcerned with what he calls “the goal of a coherent conceptual organization of theworld as we experience it,” (Steffe & Gale eds. p. 7) and “the goal of constructing ascoherent a model as possible of the experiential world” (ibid, p. 8). It is in this sensethat we may acknowledge that von Glasersfeld’s words need not be construed as anidealism or solipsism as they have often been taken. Instead, they can be read as aQuinean holism and fallibilism. It is in the spirit of von Glasersfeld’s constructivismand in keeping with his insistence on rejecting an unknowable ontological reality toread his remarks as a Quine’s holism since this seems to be the sense of some of vonGlasersfelds remarks. Thus he says: “I claim that we can define the meaning of ‘toexist’ only within the realm of our experiential world and not ontologically.” (ibid, p. 7).The talk of ontology is misleading and confusing here, however, because, followingQuine, our ontological commitments are ipso facto the posits of our theories and havenothing to do with an inaccessible, unknowable reality lying beyond our experience,our theories or the ‘veil of ideas.’ It is this repeated emphasis on an inaccessible orunknowable reality by von Glasersfeld which warrants the repeated charge of idealism.

Direct Objects of Knowledge

von Glasersfeld is victim to a notorious problem in philosophy concerning the directobjects of perception and knowledge. This is the problem of the ‘veil of ideas’ whichseems to intervene between the mind and the world and which has posed the difficultyfor philosophers at least since the Cartesians, Malebranche and Arnauld, throughLocke and Berkeley and the sense-data theories of A.J. Ayer in the 20th Century. Inpsychology, too, the problem has given rise to Gibson’s ‘ecological’ or direct realism asa response to traditional representationalist theories (see Slezak 1999). We see thisclearly in von Glasersfeld’s articulation of his doctrines:

. . . it is this construction of the individual’s subjective reality which, I want to suggest . . . shouldbe of interest to practitioners and researchers in education . . .

One of Vico’s basic ideas was that epistemic agents can know nothing but the cognitive struc-tures they themselves have put together. . . . God alone can know the real world . . . In contrast,the human knower can know only what the human knower has constructed. (von Glasersfeld1989)For constructivists, therefore, the word knowledge refers to a commodity that is radicallydifferent from the objective representation of an observer-independent world which the main-stream of the Western philosophical tradition has been looking for. Instead, knowledge refersto conceptual structures . . .. (von Glasersfeld 1989, p. 123)

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It is precisely this idea that we know only our own ideas or “conceptual structures”directly rather than the world which is the source of the traditional puzzle. Putnam(1994) provides a succinct diagnosis of this “disastrous idea”:

. . . our difficulty in seeing how our minds can be in genuine contact with the “external” worldis, in large part, the product of a disastrous idea that has haunted Western philosophy sincethe seventeenth century, the idea that perception involves an interface between the mind andthe “external” objects we perceive. (Putnam 1994)

Besides this “disastrous idea,” the conflation of the metaphysical problem of realismwith epistemology is encouraged by much “post-modern” “post-positivist” “post-epistemological”writing. Thus, for example, in their recent book Barnes, Bloor and Henry (1995) denytheir own idealism, but accuse all their sociogical constructivist colleagues of thischarge (see Slezak 1997, 2000). Nevertheless, despite being explicitly repudiated byBloor, as by von Glasersfeld, such disavowals are not quite enough to exculpate themsince there are grounds for seeing a confusion in their writings between idealism andfallibilism. They reject the external world when they evidently wish to reject absolute,infallible truth claims.

Whatever may be the educational interest in these matters, von Glasersfeld is atleast in good philosophical company. His worry about the gap between thought andreality mediated by ideas is the familiar one posed by Locke and Malebranche and,more recently, by John McDowell (1994) in his significantly titled work Mind andWorld. However, in the present context, whatever the philosophical merits of vonGlasersfeld’s concerns, the question is how these bear on any issue of conceivableeducational interest.

Epistemology or Pedagogy?

Apropos this very issue, at a meeting von Glasersfeld was explicitly asked whetherconstructivism is to be understood as an epistemology or pedagogy. His answer ismost revealing for what it fails to say. von Glasersfeld responded by restating theformula of Berkeley: “. . . there is no way of checking knowledge against what it wassupposed to represent. One can compare knowledge only with other knowledge” (1993,p. 24). The questioner is unlikely to have found this answer satisfying. Other questionssought to clarify the “differences between constructivism and idealism.” Again, vonGlasersfeld’s answer is rather unhelpful, simply re-iterating that “we can only knowwhat our minds construct” and that “the ‘real’ world remains unknowable” and that“I could be one of Leibniz’ monads” (1993, p. 28). Teachers might wonder how thiscould help them in the classroom. When pressed on this question concerning “theimplications of contructivism for a theory of instruction,” von Glasersfeld suggests thatthere are many. These include the following: “It is . . . crucial for the teacher to get someidea of where they [the students] are,” that is, “what concepts they seem to have andhow they relate them (1993, p. 33). This inference seems a modest recommendationwhich is far from the “rather profound changes” promised. Similar platitudes aretypical:


Asking students how they arrived at their given answer is a good way of discovering somethingabout their thinking. (1993, p. 33)Whatever a student says in answer to a question (or “problem”) is what makes sense to thestudent at that moment. It has to be taken seriously as such, regardless of how odd or “wrong”it might seem to the teacher. To be told that it is wrong is most discouraging and inhibiting forthe student. (1993, p. 33)If you want to foster students’ motivation to delve further into questions that, at first, are of noparticular interest (from the students’ point of view), you will have to create situations wherethe students have an opportunity to experience the pleasure inherent in solving a problem.(1993, p. 33)

We may assume that such profundities are what K. Tobin (1993) has in mind whenhe refers to constructivism as “A paradigm for the practice of science education”. Tobinhas his own deeply insightful contributions to offer:

A most significant role of the teacher, from a constructivist perspective, is to evaluate stu-dent learning. In a study of exemplary teachers, Tobin and Fraser found that these teachersroutinely monitored students in three distinctive ways: they scanned the class for signs ofimminent off task behavior, closely examined the nature of the engagement of students, andinvestigated the extent to which students understood what they were learning. If teachersare to mediate the learning process, it is imperative that they develop ways of assessing whatstudents know and how they can represent what they know. (Tobin & Tippins 1993, p. 12;emphasis added)

In brief, good teachers make sure students pay attention and understand the lesson!Inevitably one wonders how differently a teacher might do things if not operating “froma constructivist perspective.”

From the Metaphysical to the Mundane

We have seen von Glasersfeld promise:

. . . if the theory of knowing that constructivism builds up on this basis were adopted as aworking hypothesis, it could bring about some rather profound changes in the general practiceof education. (von Glasersfeld 1989, p. 135)

Elsewhere he has suggested that “taken seriously” radical constructivism “is a pro-foundly shocking view” which requires that “some of the key concepts underlying edu-cational practice have to be refashioned.” Among these “profoundly shocking” recom-mendations he suggests the following:

. . . students will be more motivated to learn something, if they can see why it would be usefulto know it.Teaching and training are two practices that differ in their methods and, as a consequence,have very different results. . . . rote learning does not lead to ‘enlightenment.’. . . in order to modify students’ thinking, the teacher needs a model of how the student thinks.Students should be driven by their own interest.. . . talking about the situation is conducive to reflection.To engender reflective talk requires an attitude of openness and curiosity on the part of theteacher, a will to ‘listen to the student’ . . .

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These are all undoubtedly sound recommendations, though hardly deserving tobe regarded as “profoundly shocking.” Indeed, such platitudes are characteristic ofconstructivist instructional advice, though they are typically dressed up in a gratuitoustechnical jargon which serves only to hide their banality. Thus, it is instructive tosubject an example to careful analysis.

Driver et al. (1995) writes:

. . . learning science involves being initiated into scientific ways of knowing. Scientific entitiesand ideas, which are constructed, validated, and communicated through the cultural insti-tutions of science, are unlikely to be discovered by individuals through their own empiricalinquiry; learning science thus involves being initiated into the ideas and practices of the scien-tific community and making these ideas and practices meaningful at an individual level. Therole of the science educator is to mediate scientific knowledge for learners, to help them makepersonal sense of the ways in which knowledge claims are generated and validated, rather thanto organize individual sense-making about the natural world. (Driver et al. 1995, p. 6)

A critical reading of the foregoing passage reveals it to reduce without remainder tothe following:

Learning science involves learning science. Individuals cannot rediscover science by them-selves. So, the role of teachers is to teach.

Consider the first sentence of Driver et al. “. . . learning science involves beinginitiated into scientific ways of knowing.” The ring of plausibility, if not profundity,in this assertion derives from its being pure tautology. “Learning science” presumablymeans, or may be paraphrased as, “being initiated into scientific ways of knowing.”Likewise their remark that “The role of the science educator is to mediate scientificknowledge for learners” is like saying that the role of the butcher is to mediate animalproducts for consumers or the role of the bus driver is to mediate automotive vehiculartransportation for commuters. Their assertion is merely a circumlocution for sayingthat the role of teachers is to teach. It is perhaps tedious to pursue this analysisin exhaustive detail, but the illustrations serve to indicate a widespread tendency torecast truisms in pretentious polysyllabic jargon to create a superficial illusion of deeptheory. Tobin and Tippin (1993) provide another typical illustration:

Constructivism suggests that learning is a social process of making sense of experience interms of what is already known. In that process learners create perturbations that arise fromattempts to give meaning to particular experiences through the imaginative use of existingknowledge. The resolution of these perturbations leads to an equilibrium state whereby newknowledge has been constructed to cohere with a particular experience and prior knowledge.(Tobin & Tippins 1993, p. 10)

Translation: Students sometimes learn new things.

A most significant role of the teacher, from a constructivist perspective, is to evaluate stu-dent learning. In a study of exemplary teachers, Tobin and Fraser found that these teachersroutinely monitored students in three distinctive ways: they scanned the class for signs ofimminent off task behaviour, closely examined the nature of the engagement of students, andinvestigated the extent to which students understood what they were learning. If teachersare to mediate the learning process, it is imperative that they develop ways of assessing whatstudents know and how they can represent what they know. (Tobin & Tippins 1993, p. 12)


Translation: Good teachers make sure students pay attention and understand thelesson.

Tobin and Tippins conclude their article with the following remarks:

. . . it is our contention that constructivism is an intellectual tool that is useful in many edu-cational contexts. . . . We do not claim that use of constructivism as a referent is the only wayto initiate changes of . . . a comprehensive and significant scope, but from our experience wecan assert that constructivism can assume a dialectical relationship with almost every otherreferent in a process that culminates in a coherent world view consisting of compatible referentsfor action. (Tobin & Tippins 1993, p. 20)

Translation: Constructivism is consistent with some other theories.Constructivist ‘buzz-words’ serve to give an air of profundity but all have ordinary

synonyms which reveal the platitudinous nature of the assertions they are used tomake. These include the following list:

mediating negotiating appropriatingdiscursive practices community of discourse social constructionmeaning-making appropriating meaning interventionsco-construction of knowledge dialogic interaction process symbolic realitiescultural tools representations perturbationsnegotiation of meaning in enculturationsocial interaction

Thus we can see how we might render an ordinary phrase in a more impressivemanner: Instead of merely saying “talking among teachers and students” we can say“the discursive practices that support the coconstruction of scientific knowledge byteachers and students” (Driver et al. 1994, p. 9). Instead of saying simply that “teachersexplain new ideas” we can say the “teacher’s role is characterized as that of medi-ating between students’ personal meanings and culturally established mathematicalmeanings of wider society” (Cobb 1994b, p. 15). Rather than the truism that “teachersand students exchange ideas” we can say “speaking from the sociocultural perspective,[we] define negotiation as a process of mutual appropriation in which the teacher andstudents continually coopt or use each others’ contribution” (Cobb 1994b, p. 14). Wheresomeone might wish to say only that “students figure things out for themselves inclass with others,” a more impressive rendering would be “learning is characterizedby the subjective reconstruction of societal means and models through negotiationof meaning in social interaction” and “students’ interactive constitution of the class-room microculture” (Cobb 1994b, p. 15). “Learning through lessons in school” is betterrendered as “students’ subjective reconstruction” through “teacher’s and students’ in-teractive constitution of the class-room microculture” (Cobb 1994b, p.15). And sayingthat “students learn different things at different times” may be recast as “Ratherthan successive equilibrations, . . . learning may be better characterized by parallelconstructions relating to specific contexts” (Cobb 1994a, p. 7).

The following dictionary may be helpful for translating between constructivese andEnglish.

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Constructivese English“cultural apprenticeship” learning“neutralizing a perturbation” learning something new“personal construction understandingand meaning making”“the mediation process teachinginvolving interventionand negotiation with anauthority”“community of discourse” group“communities characterized different groupsby distinct discursive practices”“appropriate experiential scientific data andevidence, cultural tools theoriesand conventions of thescience community”“dialogic process” talking“discourse practices” talking“unbroken contingent flow of talkingcommunicative interactionbetween human beings”“the way in which novices talking in classare introduced to acommunity of knowledgethrough discourse in thecontext of relevant tasks”“The discursive practices kids in school don’t doin science classrooms differ the same thing assubstantially from the scientistskids in school practicesof scientific don’t do theargument and enquiry thatsame thing take place withinvarious as scientists communitiesof professional scientists”“engagement” paying attention“off task behaviour” not paying attention“experiential constraints of the real worldthe ever-presentsocio-physical context”

Between Metaphysical and Mundane

Though intended to be entertaining, the foregoing analysis has a serious purpose. It isin the venerable tradition of C.W. Mills’ (1959) expose of Talcott Parsons’ pretentious‘grand theory.’ Mills reduced long passages of Parsons’ sociological verbiage to a briefplatitude. Here, too, the serious question raised is whether there is any substance be-hind the mystification of jargon-ridden polysyllabic prose, or whether, in Orwell’s (1946)


phrase, it merely gives the “appearance of solidity to pure wind.” I have suggestedthat the psychological variety of ‘radical’ constructivism has little to offer between themetaphysical and the mundane.

References

Barnes, B. Bloor D. Henry, J.: 1996, Scientific Knowledge: A Sociological Analysis, TheUniversity of Chicago Press, Chicago.

Boden, M.: 1979, Piaget, Fontana, London.

Cobb, P.: 1994a, Constructivism in Mathematics and Science Education, EducationalResearcher 23(7).

Cobb, P.: 1994b, Where Is the Mind? Constructivist and Sociocultural Perspectives onMathematical Development, Educational Researcher 23(7), 13–20.

Driver, R. Asoko, H. Leach, J. Mortimer, E. and Scott, P.: 1994, Constructing ScientificKnowledge in the Classroom, Educational Researcher 23(7), 5–12.

Ernest, P.: 1995, Radical Constructivism: A Way of Knowing and Learning, The FalmerPress, London. Preface by Series Editor, E. von Glasersfeld.

McDowell, J.: 1994, Mind and World, Harvard University Press, Cambridge, Mass.

Mills, C.: 1959, The Sociological Imagination, Oxford University Press, New York.

Orwell, G.: 1946, Politics and the English Language, The Penguin, 1946, Essays ofGeorge Orwell, Penguin Books, Harmondsworth, 1984.

Phillips, D.: 1995, The Good, the Bad, and the Ugly: The Many Faces of Construc-tivism, Educational Researcher 24(7), 5–12.

Phillips, D.: 1997, How, Why, What, When, and Where: Perspectives on Constructivismin Psychology and Education, Issues in Education 3(2), 151–194.

Piaget, J.: 1955, The Construction of Reality in the Child, Routledge and Kegan Paul,London.

Piaget, J.: 1971, Biology and Knowledge, Edinburgh University Press, Edinburgh.

Piaget, J.: 1972, Psychology and Epistemology: Towards a Theory of Knowledge,Penguin, Harmondsworth.

Piaget, J.: 1975, Insights and Illusions of Philosophy, Meridian Books, New York.

Putnam, H.: 1994, Sense, Nonsense, and the Senses: An Inquiry Into the Powers of theHuman Mind, The Journal of Philosophy XCI(9), 445–517. The Dewey Lecturesat Columbia University 1994.

Quine, W.: 1960, Word and Object, MIT Press, Cambridge, Mass.

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Quine, W.: 1961a, Two Dogmas of Empiricism, From a Logical Point of View, Harper,New York.

Quine, W.: 1961b, Identity, Ostension, and Hypostasis, From a Logical Point of View,Harper, New York.

Rorty, R.: 1979, Philosophy and the Mirror of Nature, Princeton University Press,Princeton.

Slezak, P.: 1997, Review of Barnes, Bloor & Henry: Scientific Knowledge: A SociologicalAnalysis, Metascience 11, 44–52.

Slezak, P.: 1999, Situated Cognition: Empirical Issue, ‘Paradigm Shift’ or ConceptualConfusion?, in J. Wiles and T. Dartnall (eds), Perspectives on Cognitive Science,Ablex Publishing Corporation, Stamford.

Slezak, P.: 2000, Radical Social Constructivism, in D. Philips (ed.), National Society forthe Study of Education (NSSE) Yearkbook, Forthcoming.

Steffe, L.: 1995, Title, Publisher.

Steffe, L. and Gale, J. (eds): 1995, Constructivism in Education, Lawrence ErlbaumAssociates, Inc., New Jersey.

Tobin, K. (ed.): 1993, The Practice of Constructivism in Science Education, AAA Press,Washington D.C.

Tobin, K. and Tippins, D.: 1993, Constructivism as a Referent for Teaching andLearning, in K. Tobin (ed.), The Practice of Constructivism in Science Education,AAA Press, Washington D.C., pp. 3–21.

van Fraassen, B.: 1980, The Scientific Image, Oxford University Press, Oxford.

von Glasersfeld, E.: 1989, Cognition, Construction of Knowledge, and Teaching,Synthese 80, 121–140.

von Glasersfeld, E.: 1993, Questions and Answers about Radical Constructivism, inK. Tobin (ed.), The Practice of Constructivism in Science Education, AAA Press,Washington D.C.

von Glasersfeld, E.: 1995, Radical Constructivism: A Way of Knowing and Learning,The Falmer Press, London.

Social Constructivism and the Science Wars

Peter SlezakUniversity of New South Wales, Australia. Email: [email protected]

The dispute concerning Social Constructivism has emerged from being an isolatedand esoteric epistemological debate among relatively few academic scholars to beinga notorious public scandal. Challenges to traditional conceptions of science whichseverely polarised philosophers, historians and sociologists have erupted into heatedpublic disputes—the so-called ‘Science Wars’. The issues at stake concern the mostfundamental questions about the nature of science, and these controversies have be-come prominent in educational literature where a variety of ‘constructivist’ doctrineshave become entangled (see Phillips 1997b and Matthews 1998).

If social constructivist doctrines are correct, the implications for science educationare revolutionary. On these views, knowledge is merely a consensus upon arbitraryconvention; and education involves not learning as a cognitive process of reason andunderstanding, but merely conformity to power and political interests. There could beno more fundamental challenge to education than the one posed by social construc-tivism, since it purports to overturn the traditional conception of knowledge. The self-advertising grandiosely proclaims: “The foundations of modern thought are at stakehere” (Pickering 1992).

A major battle in these Science Wars has been fought over the book Higher Supersti-tion by Paul Gross and Norman Levitt (1994), which brought the polemics surroundingsocial constructivism to wide popular attention. Adding piquancy and greater publicattention to social constructivism was the fallout from the ‘Sokal Hoax’ . Unwittingly,the editors of the journal Social Text published a spoof article written in post-moderniststyle by the mathematical physicist Alan Sokal without realizing that it was deliberatenonsense (Sokal and Bricmont 1997).

In their different ways, the Sokal article and the Gross and Levitt book exposedwhat they claim to be the bankrupt, fraudulent and pernicious nature of social con-structivism in a broad variety of post-modern guises. The colourful epithets and purpleprose conveyed the enormity of what Gross and Levitt call the post-modernist game of“intellectual subversion” (1994, p. 85) and “philosophical styrofoam” (1994, p. 98).

Even in the more sober academic literature there had been outrage about socialconstructivism going well beyond normal intellectual disagreement. The disputes inthe technical journals have been characterised by ad hominem assaults of an unusualferocity. For example, Mario Bunge (1991) described most of the work in the field as“a grotesque cartoon of scientific research.” In a similar vein, the philosopher DavidStove (1991) called these doctrines a form of lunacy which is “so absurd, that it eludesthe force of all argument” (1991, p. 31), a “philosophical folly” and “a stupid and dis-creditable business” whose authors are “beneath philosophical notice and unlikely tobenefit from it.” In his scathing remarks, Stove describes such ideas as an illustration

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of the “fatal affliction” and “corruption of thought” in which people say bizarre thingswhich even they must know to be false. Larry Laudan (1990b, p. x) who has been amongthe first philosophers to make systematic critical analyses of social constructivism, hascharacterized this “rampant relativism” as “the most prominent and pernicious man-ifestation of anti-intellectualism in our time.” Laudan’s charge of anti-intellectualismpoints to the source of concern for educators.

Ideas or Ideology? Pedagogy or Propaganda?

In important clarifications of the varieties of ‘constructivism’, D.C. Phillips has notedthat “Arguably it is the dominant theoretical position in science and mathematicseducation” (1997b, p. 152) and he remarks “Across the broad fields of educationaltheory and research, constructivism has become something akin to a secular religion”(1995, p. 5). Phillips (1997b) distinguishes the sociological form of constructivism ofinterest here from the psychological variety and observes: “It is the work of the socialconstructivists that had drawn the most dramatic attention in recent years; clearlythey have touched a raw nerve” (1997b, p. 154). As Phillips notes elsewhere, the reasonfor this is that “There is a lot at stake. For it can be argued that if the more radical ofthe sociologists of scientific knowledge . . . are right, then the validity of the traditionalphilosophic/epistemological enterprise is effectively undermined, and so indeed is thepursuit of science itself” (1997a, p. 86). The doctrines of social constructivism takescientific theories to reflect the social milieu in which they emerge and, therefore,rather than being founded on logic, evidence and reason, beliefs are taken to be thecausal effects of the historically contingent, local context. Accordingly, if knowledge isthe product of ‘external’ factors rather than ‘internal’ considerations of evidence andreason, then it is an illusion to imagine that education might serve to instil a capacityfor critical thought or rational belief. Education becomes indoctrination and ideas aremerely conformity to social consensus.

Before examining these doctrines in detail, it is worth observing a symptomaticview of education and its goals arising from social constructivism. Where traditionalviews see scientific knowledge as a source of insight, creativity and aesthetic pleasure,sociologists see something less exalted. Instead of fostering independent thought andthe pleasures of intellectual curiosity, science is offered as having a mere utilitarian,pragmatic value, at best. Thus, Collins and Pinch (1992) writing specifically on scienceeducation in schools suggest “It is nice to know the content of science—it helps oneto do a lot of things such as repair the car, wire a plug, build a model aeroplane . . .”(1992, p. 150). To be sure, science has such practical uses, but this prosaic view seemsto leave out something essential—namely, the intellectual dimension, the role of thecreative mind in providing an understanding of the world. Instead of conceiving ofscience education as fostering such intellectual values as understanding and criticalthinking, Collins and Pinch recommend that a science education should attend to thesocial negotiation, “myths” and “tricks of frontier science” as “the important thing”(1992, p. 151).

The relativism of social constructivist theories makes it impossible for teachers tooffer the usual intellectual grounds for distinguishing science from nonsense. Since

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the rational virtues of theories are taken to be irrelevant to their status, one cannotcomplain that some views are false or implausible or otherwise lacking rational, cogni-tive merit. For example, one cannot teach that Soviet Lysenkoism or Hitler’s racialismwere perversions of scientific truth. Their very success in winning consensus counts asexemplary scientific achievement according to social constructivist doctrines.

What is Social Constructivism?

A few special difficulties must be faced in attempting to characterise the field of socialconstructivism. First, in the years since its recent re-invention and promotion by theEdinburgh School, (Bloor 1976, Barnes 1974a, 1974b) there has been a fragmentationamong various factions which cannot be traced in detail here. Second, the historyof these changes is clouded by the questionable tactics of the constructivists. Never-theless, the original, fundamental ideas must be understood despite having becomeobscured in its more recent manifestations (Woolgar 1988).

David Bloor’s (1976) small book Knowledge and Social Imagery launched the so-called ‘Edinburgh Strong Programme’ in the sociology of scientific knowledge (SSK),and the appeal of this work was its iconoclastic approach to old-fashioned theories.Bloor self-consciously hoped to displace traditional philosophy and epistemology. Inbrief, the sociological enterprise announced the rejection of ‘the very idea’ of scienceas a distinctive enterprise. This effacing of any distinction between science and otherinstitutions is summarized by S. Woolgar (1988) as the rejection of the following tradi-tional “core assumption”:

The persistent idea that science is something special and distinct from other forms of culturaland social activity . . . Instead of treating them as rhetorical accomplishments, many analystscontinue to respect the boundaries which delineate science from non-science. (Woolgar 1988,p. 26)

On this view, not only is the very distinctiveness of science merely some kind of pro-paganda victory, a further “assumption” to be rejected is the curiously persistent view“that the objects of the natural world are real, objective and enjoy an independent pre-existence” (Woolgar 1988, p. 26). In place of the traditional “misconceptions” aboutscience and the independent pre-existence of the world, social constructivism proposedan amalgam of idealism and relativism according to which scientific theories are merely“fictions,” the product of social forces, interests and other contingent, historical aspectsof the milieu in which they arise. That is, scientific theories are not explanatory ordescriptive of the world, but are “rhetorical accomplishments” by some communityof discourse and constituted entirely by social consensus. Even scientific discoveryis a matter of “interpretative practice,” and “genius has no bearing on the pattern ofdiscovery in science” (Brannigan 1981. See the discussion in Slezak 1989.)

These are not merely radical or even revolutionary claims. They can only be de-scribed as extravagant doctrines which might be expected to require compelling ar-guments. In the absence of any arguments, sociologists had a ready explanation forthe predictable incredulity of philosophers. Foreshadowing the provocation of laterworks, Bloor’s preface to the first edition of his book already hints darkly that the


inevitable resistance by philosophers to his doctrines will be due, not to their unarguedabsurdity, but to uncomfortable secrets that they would wish to hide. Bloor assertsthat his approach to science from a sociological point of view encounters resistancebecause “some nerve has been touched.” He announces his bold intention to “despoilacademic boundaries” which “contrive to keep some things well hidden” (Bloor 1976,p. ix). Bloor was right about some nerve having been touched, though he misdiagnosedthe nature of the irritation. He devotes an entire chapter of his landmark book to akind of psychoanalysis of his opponents by speculating about the “sources of resistance”to the Strong Programme which he attributes to hidden, indeed primitive, motivesinvolving the fear of sociology’s desacralizing of science and its mysteries. One mightsuggest alternative reasons for the resistance to his sociological doctrines, but Bloorsees only repressed impulses concerning the “sacred” and the “profane” leading to “asuperstitious desire to avoid treating knowledge naturalistically” (Bloor 1976, p. 73).Bloor imagines that the “threatening” nature of any investigation into science itselfhas been the cause of a “positive disinclination to examine the nature of knowledgein a candid and scientific way” (1976, p. 42). However, this disinclination to examineknowledge and the need to keep it mystified through fear of desecration is difficult toreconcile with the fact that every philosopher since Plato has been centrally concernedwith the problem of knowledge and its justification. The inordinate space devoted tosuch fatuous speculations signifies the pre-eminent place they occupy in the social con-structivist enterprise as a substitute for serious, or indeed any, philosophical analysis.

“Knowledge As Such”: Contexts, Contents and Causes

In his manifesto, Bloor had declared that the central claims of the Strong Programmehe launched were “beyond dispute” (1976, p. 3), and Barnes begins an article assertingthat in the short time since its advent “developments have occurred with breathtakingspeed” and “the view that scientific culture is constructed like any other is now wellelaborated and exemplified” (Barnes 1981, p. 481).

This level of self-congratulatory hyperbole has prompted Thomas Gieryn (1982,p. 280) to comment upon these “defences and re-affirmations” as “expressions of hubris”and “exaggerations passing as fact.” Gieryn (1982, p. 293) has suggested that theradical findings of the new sociology of science “are ‘new’ only in a fictionalized readingof antecedent work.” In particular, Robert Merton’s article on “The Sociology of Knowl-edge” (Merton 1957) had specifically enunciated the central doctrine of the StrongProgramme:

The “Copernican revolution” in this area of inquiry consisted in the hypothesis that not onlyerror or illusion or unauthenticated belief but also the discovery of truth was socially (histori-cally) conditioned. . . . The sociology of knowledge came into being with the signal hypothesisthat even truths were to be held socially accountable, were to be related to the historical societyin which they emerged. (Merton 1957, p. 459)

Although it had appeared in different guises before in Hegel, Marx, and Durkheim, theradical idea at the heart of the Strong Programme was to go beyond those sociologicalstudies which stopped short of considering the actual substantive content, the ideas, of

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scientific theories as an appropriate domain for sociological investigation. Previously,sociological studies paid attention only to such things as institutional politics, citationpatterns and other peripheral social phenomena surrounding the production of science,but had not ventured to explain the cognitive contents of theories in sociological terms.Since this crucial point has been obscured, its importance for appreciating subsequentdevelopments cannot be overstated. The opening sentence of Bloor’s book asks “Canthe sociology of knowledge investigate and explain the very content and nature ofscientific knowledge?” (Bloor 1976, p. 1)—that is, “knowledge as such, as distinct fromthe circumstances of production.”

The alleged failure of previous sociological studies to touch on the contents of scien-tific belief was portrayed by Bloor as a loss of nerve and a failure to be consistent (1976,p. 8). Karl Mannheim, for example, is characterised as failing to extend his approachfrom knowledge of society to the knowledge of nature. The relativist challenge derivesfrom this thorough-going application of the sociological principle which seeks to explainthe hitherto exempted knowledge claims. The ambitions of Bloor’s program are explicit,for he complains that previous sociologists, in “a betrayal of their disciplinary stand-point” have failed to “expand and generalise” their claims to all knowledge: “. . . thesociology of knowledge might well have pressed more strongly into the area currentlyoccupied by philosophers, who have been allowed to take upon themselves the task ofdefining the nature of knowledge” (Bloor 1976, p. 1).

Causes and Case Studies

The extensive body of case studies repeatedly invoked by sociologists to answer theircritics has been taken to establish the thesis that the contents of scientific theories andbeliefs have social causes, in contradistinction to psychological ones. The causal claimconcerns such things as “connections between the gross social structure of groups andthe general form of the cosmologies to which they have subscribed” (1976, p. 3). That is,the cognitive content of the beliefs is claimed to be causally connected with immediate,local aspects of the social milieu. Of this general thesis, Bloor asserts “The causal linkis beyond dispute.” Indeed, Bloor (1981) and Shapin (1979) were evidently unable tobelieve that anyone might question the causal claims of the Strong Programme excepton the assumption that they must be unfamiliar with the extensive literature of thecase studies. However, in a parallel with Durkheim and Mauss (1903/1963), the claimsof social determination of beliefs are all the more extraordinary in view of the failureof these case studies to support them. Critics have challenged precisely the bearing ofthese studies on the causal claims, and so repeatedly citing the burgeoning literatureis to entirely miss the point.

Of course, scientific discoveries have always necessarily arisen in some social milieuor other. However, establishing a causal connection requires more than merely charac-terising the social milieu. These more stringent demands have not been met anywherein the voluminous case studies in the SSK literature. Thus, although Steven Shapinhas acknowledged that “the task is the refinement and clarification of the ways in whichscientific knowledge is to be referred to the various contextual factors and interestswhich produce it,” (1979, p. 42) and that “we need to ascertain the exact nature of


the links between accounts of natural reality and the social order,” nevertheless hismuch-cited case study of phrenology offers only a variety of anthropological approachesleading at best to a postulation of “homologies” between society and theories whichmay serve as “expressive symbolism” or perhaps function to further social interestsin their “context of use.” This argument falls far short of demonstrating the strongclaims of social determination, for it is a truism to assert, as Shapin does, merely that“Culture [taken to include science] is developed and evaluated in particular historicalsituations” (1979, p. 65). Shapin undertakes to refute the accusations of empiricalsterility by a lengthy recounting of the “considerable empirical achievements” of thesociology of scientific knowledge (1982, p. 158). But he is simply begging the questionwith his advice that “one can either debate the possibility of the sociology of scientificknowledge or one can do it.” Casting more horoscopes does not address concerns aboutthe causal claims of astrology.

When is a Cigar Just a Cigar?

The local, historical determination of scientific theories entails that theories wouldhave been different had the social milieu been different. We are inevitably led to ask:Would Einstein have theorised E = mc3, or would Newton have enunciated an inversecube law of gravitation, had their societies been different? The model of such empir-ical studies was Forman’s (1971) much-cited work which attributes the developmentof quantum physics to the prevailing milieu in Weimar Germany. However, in thesame vein, we might inquire: Did Godel’s ‘Incompleteness’ theorem arise from somelacunae in the Viennese social order of 1930? This example invokes the same sug-gestive metaphorical connections adduced by social constructivist case studies. Thereis, at best, a kind of affinity claimed between the social context and the contents ofthe theory in question. Thus, Shapin cites “homologies between society and nature”and sees theories as “expressive symbolism” which can be exploited to serve socialinterests. Given the tenuous nature of such “homologies” between theories and theZeitgeist, the distinction between parody and serious claims is difficult to discern.Shapin’s Rorschach homologies between theory content and social context recall theFreudian interpretation of dreams which involved a similar decoding of an allegedlysymbolic connection. Likewise, sociology pretends to disclose the hidden meaningunderlying our scientific theories. We may have imagined that 19th century theories ofphrenology were about the brain, but they were really “expressing a social experience”and about the “differentiation and specialization [in the social order] perceived by thebourgeois groups” (Shapin 1979, p. 57). Godel’s Incompleteness theorem, too, undoubt-edly expresses a collective longing for wholeness and fulfillment among the Vienneseintelligentsia. However, in the spirit of Freud’s famous remark one is tempted to ask:When is a cigar just a cigar?

The Social Construction of Social Constructivism

It is instructive to look at a recent, authoritative and sympathetic statement of so-cial constructivism in a book whose co-authors include two of its founders—Scientific

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Knowledge: A Sociological Analysis by Barnes, Bloor and Henry (1996). As founders ofthe field, these authors are uniquely well qualified to offer the book to anyone “seekinga text in the sociology of scientific knowledge.” However, borrowing earlier words of oneof its authors, this sociological enterprise appears to “contrive to keep some things wellhidden” (Bloor 1976, p. ix). A study of the index is revealing. Georg Cantor, infinitecardinal numbers and the continuum hypothesis get several entries whereas socialconstructivism and the Strong Programme get none at all. In view of the status ofthe Strong Programme, being the radical new approach proclaimed with great fanfareas revolutionizing the study of science and epistemology, its omission is revealing.The Duhem-Quine thesis, mentioned en passant in an obscure footnote, gets no indexentry either, though the book is an extended essay on the alleged consequences of thisphilosophical doctrine.

Other omissions from the index are equally curious. The truth of the “teleological”view of rationalist philosophers was originally presented by Bloor (1976) as entailingthe falsity of the sociological programme. The ‘teleological’ view takes beliefs to beexplained by reasons. This rationalist view is taken by Bloor to be diametricallyopposed to the sociological account of belief since only the latter is supposed to ascribecauses to beliefs. In the second edition of his foundational text, Bloor (1991) hasreaffirmed his commitment to the tenets of the original Programme. Thus, in view ofthe decisive, foundational status of this diametrical opposition, as we will see presently,it is striking that this issue, too, has disappeared without trace in more recent accounts.This re-writing of history makes it impossible to understand both the social construc-tivist doctrines themselves and the scandal they have generated. However, failure tomention a vital, potentially refuting, doctrine is illuminated by certain judicious andunacknowledged changes in the text of the second edition of Bloor’s book (see Slezak1994).

The following questions encapsulate some of the fundamental issues on which thedisputes about social constructivism have centred—a kind of diagnostic class test forSocial Studies of Science 101:

1. What is the Edinburgh ‘Strong Programme’ in the sociology of scientific knowl-edge, what were its central tenets, and what was its self-proclaimed, radicalnovelty regarding the content of scientific theories?

2. What is the esential characteristic doctrine of social constructivism and whatis its relation to “rationalist,” “teleological” and “psychologistic” approaches oftraditional epistemology? How are the latest views in the sociology of sciencerelated to their earlier formulations twenty years ago?

3. What is the Duhem-Quine thesis of underdetermination of theory by evidence?How does it relate to the ‘theory-laden’ nature of observation? What follows fromthese theses for the determinants of ‘theory-choice’ in science?

4. What kinds of empirical evidence have been offered as support for the theoriesof the sociology of scientific knowledge and how exactly do they bear upon theclaims? Are theory contents caused by social contexts?


5. Which epistemological stance does the new sociology of science adopt?

(a) Realism (b) Idealism (c) Relativism(d) All of the above (e) None of the above

6. What are the scope and limits of sociological approaches to science in relation toindividual psychology?

As indicated, students who might wish to use the latest book of Barnes, Bloor andHenry as a text to study for the foregoing test would fail. These questions cannot beanswered by a conscientious study of the book, though any teacher would recognisethem as elementary ones basic to understanding the field. Cryptic references to issuessuch as the ‘rationalist’ philosophies against which the entire sociological enterprisewas directed are left entirely unexplained and so the innocent reader will not be ableto understand or assess the current claims. These failings might indicate only thatthe book is an inadequate text, which would not be unusual. However, the lapses andomissions appear to disguise a shift from vital doctrines which have become untenable.

Idealism

The book begins encouragingly, if somewhat mystifyingly for the newcomer, by ac-knowledging the existence of reality. This admission will undoubtedly be comfort-ing to those harbouring doubts about the matter, but it arises at all only throughcertain naive confusions. For their part, Barnes, Bloor and Henry are concerned todistance themselves from those—we are to assume other—sociologists who they say“Occasionally . . . may have given this impression” of denying the existence of tablesand chairs. Nevertheless, they admit that most other sociology of knowledge is, in fact,idealist. In repudiating this stance these authors emphasize their own contrasting‘naturalistic’ view, but on such good authority, then, idealism must be regarded as acentral philosophical issue for the understanding of social constructivism.

Notwithstanding these authors’ disclaimers, warrant for the charge of idealismagainst them too arises partly from their own misconceptions regarding the ‘rationalist’theories they oppose and partly from the social constructivism to which they remainfirmly committed—actually an amalgam of idealism and relativism. An unavoidabletemptation towards idealism arises from the sociologists’ desire to deny that sciencedescribes an independent world. Consequently, the opposing ‘rationalist’ philosophyof science has been seen as committed to a metaphysical realism involving access toabsolute truth about a world behind appearances. While science attempts to discoverthe nature of an independently existing reality, this concern is not a metaphysicalthesis about some Kantian ‘things-in-themselves.’ It is simply the truism that wetake our best theories literally to be talking about something. The reaction to theordinary practice of science as some kind of philosophical error requiring sociologicalremedy is simply a mistake, since the virtues and status of science as an enterpriseare independent of such metaphysical questions. Realists and idealists alike can enjoythe fruits of scientific knowledge. Specifically, whether or not scientific theories are

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socially constructed is an issue to be determined by arguments entirely independent ofidealism. Nevertheless, Barnes et al. offer their own “naturalist” stance as the contrastwith “idealism,” but their “naturalism” is simply a demand for empirical explanation interms of causes. However, Berkeley, like all other idealists, was an empiricist in goodstanding in this sense, and one can be an idealist at the same time as being committedto empirical, naturalistic science. Idealism is a metaphysical doctrine concerning theoverall status of our scientific theories as such, and not a specific approach to expla-nation within the overall enterprise like naturalism. The dispute concerning idealismis entirely indifferent to any debate about the practices of empirical inquiry as suchand, therefore, asserting credentials as “naturalistic” does not even amount to a pleaof ‘innocent’ to the charge of idealism—much less grounds for acquittal.

Revealing comments support the charge of idealism despite their disavowals. Barneset al. (1996, p. 48) point out that it is not “the existence of nature” which accountsfor certain behaviours and that “attention to nature” will not adjudicate the meritsof our theories and classifications. Of course, if appeal to nature, meaning empiricalevidence, cannot adjudicate our theories, it is not clear what would do so. We see herethe social constructivist dogma that scientific theories are somehow unconstrained bythe way things are in the world. However, Barnes et al. are confusing the supposedindirectness of our knowledge of the world, its inaccessibility beyond the ‘veil of ideas,’with the bearing of empirical evidence on our scientific theories. Stressing the formerkind of inaccessibility does not establish the latter kind. This is precisely to confuseidealism with relativism.

The declaration of Barnes et al. that they are not idealists, then, is paradoxicalsince it poses the following dilemma: Which reality is the one the sociologists professto believe in? Do they believe in an inaccessible Kantian ding an sich after all? Ordo they believe in the rationalists’ world as conveyed by our true (i.e. best) theories?In wishing to deny the former, they end up denying the latter and, thereby, becomeidealists as well as relativists. In brief, their needless entanglement in such notoriousproblems is symptomatic of sociologists’ absurd pretensions to overthrow “the subjectthat used to be called philosophy” (Bloor 1983).

Relativism

Despite characterising their book as focussed on “basic foundations,” Barnes et al.explain that it “gives little prominence” to such issues as relativism. Indeed, thisprefatory mention of relativism is the only one in the book. However, even morethan idealism, relativism has been the central, distinctive theoretical doctrine of socialconstructivism and the source of most dispute. Neglecting to discuss it is like a text onevolution professing to concentrate on “basic foundations” and choosing to give “littleprominence” to natural selection. The authors’ recent reticence about their own centraldoctrines is a telling feature of their work (Barnes and Bloor 1982).

Relativism is the claim that knowledge has no warrant beyond belief acceptanceitself. It is often a non-sequitur from the recognition that there is no absolute certainty.However, given that there can be no absolutely secure knowledge, the alternative torelativism is fallibilism: the idea that reliable knowledge is possible through revision


and improvement. Relativism is at the heart of social constructivism because thesupposed absence of constraints of independent “reality” is assumed to leave no othergrounds for adjudicating claims. Specifically, the freedom from a constraining reality istaken to warrant appeal to a sociological account of theory acceptance. Relativism,then, is the spurious assumption that there can be nothing more to say about thegoodness of our theories if one can’t meaningfully compare them to an independent,inaccessible reality. However, the question of ‘realism’ has been the subject of a vastphilosophical literature, and both sides of this dispute accept the rational force ofevidence and the usual considerations of explanatory virtue such as comprehensive-ness, coherence and simplicity as grounds for rational theory choice. Thus, CardinalBellarmine’s instrumentalism did not involve a challenge to the intellectual meritsof Galileo’s Copernicanism as such. More recently, van Fraassen’s (1980) celebrated‘constructive empiricism’ is concerned to ‘save the phenomena’ without postulatinga hidden underlying reality, but this does not entail rejection of the usual rationalconsiderations governing theory choice. Social constructivists mistakenly conclude thatthe inaccessibility of ‘things in themselves’ behind the veil of our theories (whateverthis might mean) precludes saying anything sensible about their cognitive virtues.

However, “rationalist” talk of observation, confirmation, evidence and truth etc., iswithin the sociologists’ own preferred framework on our side of the veil, as it were, ac-cording to which, as Bloor says, all we have and all we need are the theories themselves.Indeed, Bloor’s view could be a version of Quine’s (1960) well-known metaphor of thefabric or web of our knowledge, also articulated in his famous epigram from Neurathconcerning the sailor quoted on page ??. That is, we are inescapably dependent on ourtheories even as we seek to revise them. But, in terms of the metaphor, what counts asa repair of our boat is not a matter of arbitrary convention; social constructivism wantsto scuttle it.

Theory Choice: Underdetermination of Theory by Evidence

One consideration, above all, has been widely taken to warrant the appeal to soci-ological factors in the explanation of scientific theory ‘choice.’ An attempt is madeto exploit the so-called Quine-Duhem thesis concerning the underdetermination oftheory by evidence (Laudan 1990a). The thesis means that there can be no directinference from observational data to any particular theory since there must be indefi-nitely many theories equally compatible with the same empirical evidence. Therefore,other considerations must be invoked to explain the preference of scientists for onetheory over another which is equally consistent with the observational or experimentaldata. However, a non-sequitur from this thesis has become a foundational tenet ofsocial constructivism. Thus, when distilled to its essence, Bloor’s (1976) manifestoinvolves a spurious inference from underdetermination to social construction. How-ever, underdetermination is neutral among the various alternative resources whichmight be invoked to explain theory choice beyond conformity with the evidence. Ithas to be shown independently why it might be social factors rather than some others(say, astrological) which are the operative ones in determining theory choice among thepossible alternatives consistent with the evidence.

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Setting the pattern for subsequent discussions, Bloor relies on this issue as thecentral thesis of his book. Evidently no argument is thought necessary for this non-sequitur and Bloor gives none. In view of the foundational status that this book andthis “argument” have acquired, the situation is sufficiently peculiar to deserve empha-sis: The problem with Bloor’s discussion and the general reliance on this doctrine insocial constructivism is not merely that the arguments are weak or open to challengein some way. Rather, no arguments of any kind are offered whatsoever.

C. Boorse (1975) has pointed out that the underdetermination of theories by allpossible observational evidence does not make them indistinguishable on other criteriasuch as simplicity, fecundity, coherence, comprehensiveness, explanatory power, and soon. These are, of course, the kinds of rational considerations typically invoked by the‘rationalist’ or ‘teleological’ account. Part of the problem may have arisen from anexcessively literal construal of ‘theory choice’ which cannot be considered as an actualselection among equivalent available alternatives. Historians, above all, should recog-nise that the problem is typically to find even a single theory that is consistent with theobservations. Accordingly, what is termed ‘choice’ is more appropriately described asthe psychology of scientific invention or discovery—the subject of a burgeoning researchliterature (Langely, Simon et al. 1987; Tweney, Doherty & Mynatt 1981; Gorman 1992;Giere 1992).

Consensus as Conventional

Social constructivism rests on this idea that alternative theory choices are not onlyavailable, but equally good. Of course, this is the claim for the conventional characterof science and is the locus of sociological relativism. Barnes et al. assert, “Conventionscould always be otherwise . . . ” (Barnes, Bloor & Henry 1996, p. 154), presumablyentailing that knowledge might have been negotiated differently had the local interpre-tive milieu been different and, thereby, inviting the facetious question about Newton’sinverse cube law. Indeed, undaunted by its absurdity, Barnes et al. embrace preciselysuch a paradoxical idea even in the case of arithmetical laws (Barnes, Bloor & Henry1996, p. 184). However, on their own account, given the underdetermination of theoryby evidence, the sociologists must be committed to the possibility of a consensus settlingon a vast range of possible laws via the contingent, “collective accomplishment” of “factproduction” by “local cultural traditions.” Unconvincingly, Barnes et al. suggest thatthe consensus on ‘2 + 2 = 4’ is due merely to “pragmatic reasons connected with theorganization of collective action” and the fact that “it is probably easier to organize”than a different convention such as ‘2 + 2 = 5.’ The fact that it might also be easier tobelieve is somehow not considered relevant.

Impartiality

Merton, like Mannheim, argued that theories judged to be correct and founded onrational considerations are not in need of sociological explanation in the way that falseand irrational theories are. In this sense, traditional conceptions relegated sociologyto the dross of science, to its residue of false and irrational beliefs. Bloor’s revival of


the Durkheimian view was explicitly rescuing sociology from this ignominious role byasserting the appropriateness of sociological explanations for all of science regardlessof evaluative judgements such as truth and falsity, rationality and irrationality, successor failure. Our own cosmology and science in general, like those of the Zuni, were to beshown as reflections of the social milieu.

Bloor’s complaint is directed at asymmetrical approaches such as Imre Lakatos’s“rational reconstruction” of episodes in the history of science which sought to explaincorrect scientific theories as products of reasoned thought and, therefore, not requiringresort to sociological explanations. Bloor regards this approach as having the effect ofrendering science “safe from the indignity of empirical explanation” (Bloor 1976, p. 7),but for Lakatos only sociology was to be excluded from accounts of successful sciencesince good reasons are a species of explanation themselves. Analogously, veridicalperception does not need explanation in the same way as misperception or illusion. Wedo not ordinarily seek explanatory causes in the case of normal veridical perception,not because we assume that there is no scientific explanation, but because we assumeit to be of a certain general sort. Thus, we don’t explain normal vision, but seek thecause of failure such as the influence of alcohol, disease and so on. In the same way,we do not seek to explain why the train stays on the tracks but only why it fails todo so. Again, this asymmetry does not mean that we believe there is no cause or noexplanation for the train staying on the tracks. However, this is the absurd view whichBloor imputes to rationalist philosophers such as Lakatos. Notice that Bloor takesLakatos to hold that a rational reconstruction of beliefs implies that they are therebyshown to lack empirical explanation altogether (Bloor 1976, p. 7). In his Knowledgeand Social Imagery (1976), Bloor characterized the ‘autonomy’ view he is opposing:

One important set of objections to the sociology of knowledge derives from the conviction thatsome beliefs do not stand in need of any explanation, or do not stand in need of a causalexplanation. This feeling is particularly strong when the beliefs in question are taken to betrue, rational, scientific or objective. (Bloor 1976, p. 5)

Elsewhere Bloor characterizes the opposing view as “the claim that nothing makespeople do things that are correct but something does make, or cause, them to go wrong”and that in the case of true beliefs “causes do not need to be invoked” (1976, p. 6). Bloorintends to make an absolute distinction between the ‘teleological’ view which inclinesits proponents to “reject causality” (1976, p. 10) on the one hand, and “the causalview”—that is, the sociological approach of the Strong Programme. On Bloor’s ownaccount, the viability of the Strong Programme rests on the tenability of this dichotomyand, in particular, the falsity of the ‘teleological model’. There could be no more crucialissue for the constructivist programme.

L. Laudan (1981) has characterized Bloor’s acausal attribution to philosophers asan absurd view which cannot plausibly be attributed to any philosopher at all. Inparticular, the approach of Lakatos does not deny the existence of causes in cases ofrationally held beliefs, but only assumes that reasons are themselves a species of cause(see Phillips 1997a). However, in a remarkable passage, Bloor (1981) responded toLaudan by attempting to deny these patent and quite explicit earlier intentions. Bloor’s

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discomfort was understandable, since the entire edifice of the Strong Programme restson this claimed opposition. Indeed in the second edition of his book, in the crucialsection on the ‘Autonomy of Knowledge’ dealing with the problem of causation, wediscover certain judicious changes to the original text whose rationale is clearly toavoid the criticisms made by Laudan (see Slezak 1994). It must be noted that thesealterations to the original text are somewhat difficult to reconcile with Bloor’s prefato-rial assertion that “attacks by critics have not convinced me of the need to give groundon any matter of substance” and, therefore, he says “I have resisted the temptation toalter the original presentation of the case for the sociology of knowledge” apart fromminor spelling and stylistic changes (Bloor 1991).

Bloor’s predicament, if not his tactic, is understandable since his statement of theconditions under which the programme retains its plausibility left no room for compro-mise and no way out. Bloor had declared forthrightly:

There is no doubt that if the teleological model is true then the Strong Programme is false.The teleological and causal models, then, represent programmatic alternatives which quiteexclude one another. (Bloor 1976, p. 9)

If the ‘rationalist’ ‘teleological’ ‘autonomy’ view is not the acausal, anti-empiricalstrawman that Bloor imagined, then its merits need to be confronted seriously. How-ever, this means finding a way to reconcile social constructivism with the full weightof considerations from cognitive science. This, in turn, means trying to downplay orexpunge the hostility to internal, mental or psychological accounts of rational beliefwhich was a central part of the social constructivist programme.

Social Constructivism as Born-again Behaviourism

The purported causal connection between ideas and social context is a version of stimulus-control theory akin to that of Skinnerian Behaviourism and, not suprisingly, in his laterwork Bloor (1983) explicitly endorses such notorious theories. In characterising oppos-ing rationalist or ‘teleological’ views, quoting Wittgenstein, Bloor refers to explanationswhich postulate mental states as infected by the ‘disease’ of ‘psychologism’ (1983, p. 6).Bloor’s frontal assault on the explanatory force of mental states is an intrinsic partof the defence of the radically alternative sociological approach to explaining science,but this bold stance left his programme vulnerable to a case on the other side whosestrength he had greviously underestimated. For example, Bloor’s programme dependson rejecting the reality of mental states such as images. However, this position is thirtyyears and a major scientific revolution too late (see Kosslyn 1980, 1994; Slezak 1995).

The pattern is consistent and instructive. Thus, Bloor has dismissed Chomsky’sreview of Skinner’s Verbal Behaviour with a passing footnote, and a reference to it asthe “fashionable,” “standard criticism” of behaviourism (Bloor 1983, p. 191). But thisreveals only a failure to comprehend its significance. One might have expected someindication of the weaknesses of the review and why this merely “fashionable” criticismis to be ignored—particularly since neither Skinner himself nor other behaviouristsreplied to it. In fact, the Chomsky review is generally regarded as having precip-itated the downfall of the tradition of behaviourism in psychology. Bloor’s cavalier


handwaving is rather more misleading than these comments suggest. Chomsky’s ideasforeshadowed in this review became the foundations of the dramatic developments ofthe ‘Cognitive Revolution’ (see Gardner 1987). Bloor’s failure to indicate the magnitudeand import of these developments is comparable to defending Creationism today bydimissing the Origin of Species as merely “fashionable” and failing to let one’s readersknow anything of modern biology founded on Darwin’s theory.

Newton’s Principia as Conditioned Response

Since behaviourism is a doctrine concerning psychology, it is at first sight suprisingthat it has been recruited to the cause of social constructivism. However, behaviourismserves Bloor as an ally, since it denies the explanatory role of internal mental statesand is thereby in diametrical opposition to the ‘rationalist’ or ‘teleological’ point of viewwhich the Strong Programme is also battling. If scientific beliefs are to be construedas the causal effects of an external stimulus, they are precisely analogous to Skinner-ian ‘respondents’ or ‘operants’ and, therefore, science is the result of conditioning orThorndike’s ‘Law of Effect’. In short, the deep insight of social constructivism is thatIsaac Newton’s Principia is to be explained as something like a rat’s bar-pressing inresponse to food pellets.

Bloor’s (1991) protest that his views are entirely consistent with cognitive sciencecannot be taken seriously and can be asserted at all only because Bloor now pretendsthat the sociological thesis at stake is merely whether or not there are social aspects toscience. This position is significantly different from the claim that knowledge is sociallyconstructed and constituted. This weak and uncontroversial thesis is not the originaldoctrine propounded whose inconsistency with cognitive science was evident from theaccompanying assault on the postulation of mental states. The very blandness of thisclaim for social influences testifies to the misrepresentation of the debate. The truismthat there are social dimensions to science would hardly have generated the oppositionand controversy evoked by the Strong Programme. Significantly, Bloor’s sociologicalcolleagues have reacted differently: their vehement attacks on cognitive science andartificial intelligence have been both telling and more ingenuous. Their strenuousattempts to discredit the claims of cognitive science in effect acknowledge the threatposed to the central sociological doctrines (see Slezak 1989). Indeed, H.M. Collins(1990) among others, has been explicit on this point, seeing the claims of artificialintelligence (AI) as a crucial test case for the sociology of scientific knowledge (Slezak1991a).

Revolt Against Reason

Recent social constructivism is essentially the same doctrine characterised in an earliergeneration by Karl Popper (1966) as the “revolt against reason”—a rejection of certainideals of truth and rationality which, however difficult to explicate, are nonethelesscentral to the Western heritage. Popper saw the same tendencies in Hegel which hebitterly denounced as “this despicable perversion of everything that is decent” (1966,p. 49). There can be little doubt about the close affinities between Hegel’s doctrines and

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those of social constructivism: Popper observes that for Hegel, “History is our judge.Since History and Providence have brought the existing powers into being, their mightmust be right . . . ” (1966, p. 49). The unmistakable parallel is seen in their essentiallysimilar answers to Popper’s fundamental question “who is to judge what is, and whatis not objective truth?” He reports Hegel’s reply that “The state has, in general—tomake up its own mind concerning what is to be considered as objective truth” andadds: “With this reply, freedom of thought, and the claims of science to set its ownstandards, give way, finally to their opposites” (1966, p. 43). Hegel’s doctrine expressedin terms of the ‘State’ is essentially the same idea that political success is ipso factothe criterion of truth. As we will see presently, precisely this idea is resuscitated inLatour and Woolgar, Pinch and Collins and the entire enterprise of contemporary socialconstructivism. The idea is a historical relativism according to which truth is merelypolitical and dependent on the Zeitgeist or spirit of the age. It is a view which Poppercharges with helping to destroy the tradition of respecting the truth (1966, p. 308, fn 30)and his discussion of Hegel’s “bombastic and mystifying cant” is striking in its aptnessto recent sociology of science, echoed by Gross and Levitt, Laudan and Stove, amongothers. Popper warns against the “magic of high-sounding words” and the “power ofjargon” to be found in doctrines which are

. . . full of logical mistakes and of tricks, presented with pretentious impressiveness. Thisundermined and eventually lowered the traditional standards of intellectual responsibility andhonesty. It also contributed to the rise of totalitarian philosophizing and, even more serious, tothe lack of any determined intellectual resistance to it. (1966, p. 395)

Laboratory Life Under the Microscope

Perhaps most obvious cause for such concern is another foundational classic of socialconstructivism, Laboratory Life by Latour and Woolgar (1979). This work is self-consciously subversive, rejecting the rules of logic and rationality as a merely “coerciveorthodoxy” (Woolgar 1988) and has the avowed goal of deflating the pretensions ofscience both in its knowledge claims and in its claims to the possession of a special“method.” Among its iconoclastic goals, the book professes to “penetrate the mystique,”(Latour & Woolgar 1979, p. 18) dissolve the appearances and reveal the hidden realitiesof science-in-the-making at the laboratory workbench. This study proposes to give anexpose of the “internal workings of scientific activity” (1979, p. 17).

Discovering certain puzzling questions concerning the nature of science, Latour andWoolgar conclude that there is no such thing. In their celebrated work they declare thatall of science is merely the “construction of fictions” (1979, p. 284). Latour explains theinsights emerging from the new discipline:

Now that field studies of laboratory practice are starting to pour in, we are beginning to have abetter picture of what scientists do inside the walls of these strange places called “laboratories”. . . The result, to summarize it in one sentence, was that nothing extraordinary and nothing‘scientific’ was happening inside the sacred walls of these temples. (Latour 1983, p. 141). . . the moment sociologists walked into laboratories and started checking all these theoriesabout the strength of science, they just disappeared. Nothing special, nothing extraordinary, infact nothing of any cognitive quality was occurring there. (Latour 1983, p. 160)


Needless to say, the implications of such insights must be revolutionary, not least of allfor science education, the foregoing remarks being approvingly quoted in a teachers’journal in an article recommending a radical new vision of “the reality of the scientificprocess” (Gough 1993).

For constructivists, science education is presumably only socialization into power,persuasion and propaganda. Rather than learning as a cognitive process involving rea-soning, logic and understanding, education involves merely the observance of arbitrarypractices and political interest. Although Latour and Woolgar do not explicitly addressthe questions of most direct interest to educators as such, their characterization ofscience clearly suggests the appropriate role of the teacher.

Each text, laboratory, author and discipline strives to establish a world in which itsown interpretation is made more likely by virtue of the increasing number of peoplefrom whom it extracts compliance. (Latour & Woolgar 1986, p. 285)

On this conception, presumably the function of science teacher is that of principalagent for the extraction of compliance—more like camp commandant than traditionalinstructor.

Constructing the World

The state government of Indiana in the last century considered a bill which would haveconveniently legislated the value of the mathematical constant π to be exactly 4. Thiseffort is a paradigm, if rather literal, example of negotiating or legislating the truth.Sociologists could only complain on the grounds that the bill did not gain a majorityamong legislators. As a facon de parler, the thesis of “constructing” facts has a sensiblereading according to which the theory or description of a substance, are settled uponand perhaps even “socially negotiated” in a certain sense. However, playing on thewords, one can also choose to construe such banalities as something more paradoxicaland seemingly profound—namely that objects and substances themselves did not havean independent existence and were socially constructed. In like manner, one might saythat Copernicus “removed the earth from the centre of the universe,” but asserting thisliterally would be an attempt at humour or evidence of derangement. Nevertheless, it isjust this sort of claim for which the work of Latour and Woolgar has been acclaimed—adefining text in the genre of ethnomethodology of science.

Witchcraft, Oracles and Magic Among the Azande/Academics

The authors’ own description of their project in Laboratory Life reads more like aparody than a serious inquiry. Upon entering the Salk Institute for a two-year study“Professor Latour’s knowledge of science was non-existent; his mastery of English wasvery poor; and he was completely unaware of the existence of the social studies ofscience” (1986, p. 273). It is from this auspicious beginning that the revolutionaryinsights into science were to emerge.

These apparent liabilities are portrayed as a unique advantage, since “he was thusin the classic position of the ethnographer sent to a completely foreign environment”(1986, p. 273). However, the idea that the inability to understand one’s human sub-

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jects is a positive methodological virtue is surely a bizarre conception. For Latourand Woolgar, however, it is intimately connected with their doctrine of “inscriptions.”The meaninglessness of the “traces, spots, points” and other recordings is a directconsequence of Latour’s admitted scientific illiteracy. Predictably enough, from the per-spective of complete ignorance, all these meaningful symbols are indiscriminable andmust, therefore, be placed in the category of unintelligible markings—“inscriptions.”Avoiding the possibility of understanding their subjects’ behaviour is justified on thegrounds that, just as the anthropologist does not wish to accept the witch-doctor’s ownexplanations, so one should remain uncommitted to the scientists’ rationalizations.The absurdity of such an attitude follows from the simple failure to appreciate thedifference between understanding the native and believing him.

Persuasion by Literary Inscription and Achieving Objects by Modalities

It is from a point of view of ignorance and incomprehension that Latour will rely on a“simple grammatical technique” in order to discern the true significance of the papers:“Activity in the laboratory had the effect of transforming statements from one typeto another” (1986, p. 81). Specifically, the rationale of the laboratory activities wasthe linguistic exercise of transforming statements in various ways in order to enhancetheir “facticity.” Thus, we see how Latour and Woolgar arrive at their constructivistconclusions. They explain “a laboratory is constantly performing operations on state-ments” (1986, p. 86) and it is through this process that “a fact has then been consti-tuted” (1986, p. 87) by social negotiation and construction. In short, the laboratorymust be understood “as the organisation of persuasion through literary inscription”(1986, p. 88). These are the grounds on which we must understand their claims thatsubstances studied in the lab “did not exist” prior to operations on statements (1986,pp. 110, 121). “An object can be said to exist solely in terms of the difference betweentwo inscriptions” (1986, p. 127).

Poison Oracles and Other Laboratory Experiments

From the meaninglessness of the “inscriptions” and his revelation that “the ‘scien-tificity’ of science has disappeared” (Latour 1983, p. 142). Latour is led inexorablyto a “naıve but nagging question”—namely, “if nothing scientific is happening in lab-oratories, why are there laboratories to begin with and why, strangely enough, is thesociety surrounding them paying for these places where nothing special is produced?”(1983, pp. 141-2).

. . . in the back of his mind there remains a nagging question. How can we account for the factthat in any one year, approximately one and a half million dollars is spent to enable twenty-fivepeople to produce forty papers? (Latour & Woolgar 1979, p. 70)

This question is undoubtedly a deep mystery if one systematically refuses to un-derstand the meaningfulness of the “inscriptions” on these papers. From this vantagepoint, Isaac Newton’s notebooks would be indiscriminable from random fly droppings—undoubtedly an important lesson for the science classroom.


On the analogy of “anthropologist’s refusal to bow before the knowledge of a prim-itive sorcerer” (1979, p. 29). Latour and Woolgar refuse to accept the authority of ourbest science, saying “We take the apparent superiority of the members of our labora-tory in technical matters to be insignificant, in the sense that we do not regard priorcognition . . . as a necessary prerequisite for understanding scientists’ work” (1979,p. 29). Ironically, though rejecting our best science in this way, they happily counte-nance the magical transformation of physical substances into inscriptions. However,more than being an absurd affectation, their “irreverent” approach amounts to anarrogance that elevates ignorance to a methodology. Since “prior cognition,” is notnecessary for understanding a scientist’s work, Latour and Woolgar see themselves ascompetent to adjudicate the merits of advanced scientific theories. These astonishinganti-intellectual ideas defy comment and should not require serious response. Equally,the corrosive educational values implied in such an outlook should be obvious.

This affectation of an Evans-Pritchard among the Azande is “anthropological strangeness”in a rather different sense of the term: no anthropologist was ever so strange. Givenhis method, Latour naturally finds the activities in the laboratory incomprehensible.Unwilling to allow his incomprehension to become a liability, it becomes the deepinsight of Laboratory Life. The behaviour of the scientists not only appears mean-ingless, it is meaningless. In their conclusion, Latour and Woolgar reveal that “Alaboratory is constantly performing operations on statements . . . ,” (1979, p. 86) andthe activities of the laboratory consist in manufacturing “traces, spots and points” withtheir “inscription devices.” The production of papers with such meaningless marks istaken to be the main objective of the participants in essentially the same way that theproduction of manufactured goods is the goal of any industrial process. This is the viewof science as sausage factory.

There is some unintended irony where Latour and Woolgar take their own confusionto be typical and presumptuously extrapolate their own predicament asking “Is thereany essential distinction between the nature of our own construction and that used byour subjects?” (1979, p. 254). To their rhetorical question they say: “Emphatically, theanswer must be no” (1979, p. 254). Based on their own experience, it is not difficultto see why Latour and Woolgar might arrive at the conclusion that science is a moreor less arbitrary construction and negotiation with fictions and that “nothing of anycognitive quality was occurring” in scientific laboratories.

“Derridadaism”: Readers as Writers of the Text

A measure of the perversity of this work is the fact that in the new edition of theirbook, Latour and Woolgar tell us that laboratory studies such as their own should,after all, not be understood as providing a closer look at the actual production ofscience at the workbench, as everyone had thought, since this view would be “botharrogant and misleading,” (1986, p. 282) by presuming some “privileged access to the‘real truth’ about science” that will emerge from a more detailed observation of thetechnical practices. Instead, Latour and Woolgar explain that their work “recognizesitself as the construction of fictions about fiction constructions” (1986, p. 282). This isthe textualism of Derrida combined with a much-vaunted ‘reflexivity.’ They continue:

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“. . . all texts are stories. This applies as much to the facts of our scientists as to thefictions ‘through which’ we display their work” (1986, p.284). Their own work, then,just like all of science, has no determinate meaning since “It is the reader who writesthe text” (1986, p. 273).

Here we see a deconstructionist affectation that conveniently serves to protect La-tour and Woolgar against any criticism. Where Bloor professes to adhere to the usualprinciples of scientific inquiry, Latour and Woolgar engage in a game which Lehman(1991) has aptly called “Derridadaism”. They evade criticism by adopting deconstruc-tionist double-talk and affecting a nihilistic indifference to the cogency of their ownthesis. In keeping with the principle of reflexivity, they embrace the notion that theirown text (like the science they describe) has no “real” meaning, being “an illusory, orat least, infinitely renegotiable concept” (Latour & Woolgar 1986, p. 273). Reflecting onthe controversies surrounding their work, Latour and Woolgar observe that defendersand critics alike have engaged in this futile “spectacle” in which they have debatedthe presumed intentions of the authors. This “spectacle” is, of course, just the exerciseof scholarly criticism. Latour and Woolgar now reveal that the ‘real’ meaning of atext must be recognised as illusory and indeterminate. The question of what theauthors intended or what is reported to have happened “are now very much up to thereader.” This Rorschach inkblot view of their own work is undoubtedly correct in onesense, if only because Laboratory Life is in many respects incoherent and unintelligible.For example, some of the diagrams offered as explanatory schemas are impossibleto decipher. It is sobering to consider how science teaching might be conducted inaccordance with this model of scholarship.

Balance of Forces

Though implications of social constructivism are not drawn out by the authors, they areclose to the surface and not difficult to discern. Thus, once Latour and Woolgar reject“the intrinsic existence of accurate and fictitious accounts per se,” the only remainingcriterion for judgement is judgement itself. “. . . the degree of accuracy (or fiction) ofan account depends on what is subsequently made of the story, not on the story itself”(1986, p. 284). There are no grounds for judging the merits of any claim besides the“modalizing and demodalising of statements,” a purely political question of persuasion,propaganda and power. Thus they suggest that the very idea of “plausibility” of anywork, including their own, is not an intellectual or cognitive question, but simply amatter of political redefinition of the field and other such transformations involvingshift in the “balance of forces”. In particular, the current implausibility of their owntheory is only due to its relative political disadvantages rather than the lack of anyintellectual merits (1986, p. 285). One could hardly find a more open endorsement ofthe doctrine that ‘Might is right.’

Education: Truth as Power

There could be no more fundamental challenge to education than the one posed bythese approaches, since their radical claims purport to overturn the entire edifice and


foundations of our scientific knowledge. Thus, a leading partisan of the sociologyof scientific knowledge has suggested that no less than “The foundations of modernthought are at stake here” (Pickering 1992, p. 22). All sides of the dispute may agreeon this, at least.

Social constructivist writings exemplify discourse that George Orwell (1946) desribedas giving “an appearance of solidity to pure wind” and that is “largely the defence ofthe indefensible.” Orwell’s essay ‘Politics and the English Language’ warned that suchlanguage is “like a cuttlefish squirting out ink” prevents clear, critical thinking and,thereby, the capacity to see through ideological mystification. Orwell sees the properuse of language as “an instrument for expressing and not for concealing or preventingthought,” and he argued that subverting this function will have a deleterious effectby producing a “reduced state of consciousness,” the anaesthesia of a portion of one’sbrain.

The bearing of social constructivist doctrines on these educational questions is starklybrought out in Chomsky’s remarks:

It is the responsibility of intellectuals to speak the truth and to expose lies. This, at least,may seem enough of a truism to pass without comment. Not so, however. For the modernintellectual, it is not at all obvious . . .. (Chomsky 1969, p. 257)

Chomsky goes on to quote Martin Heidegger who remained a card-carrying Nazieven after the Second World War. In a pro-Hitler declaration, echoing social construc-tivist ideas, Heidegger asserted “truth is the revelation of that which makes a peoplecertain, clear and strong in its action and knowledge.” Chomsky remarks ironicallythat it seems for Heidegger it is only this kind of “truth” that one has a responsibility tospeak—the “truth” which comes from power. In the same vein, we have seen Latour andWoolgar assert that the success of any theory is entirely a matter of, not persuasion,but politics and power, extracting compliance. On this theory a repressive totalitarianregime must count as a model of scientific success.

Concerns with the ‘revolt against reason’ are also seen expressed by ChristopherNorris (1992) who writes of Baudrillard as among those located in the “wider fashionfor pragmatist, anti-foundationalist or consensus-based theories of knowledge” (1992,p. 16). Baudrillard appllies the constructivist, contextualist, inscriptionalist approachand concludes that the 1991 Gulf War did not happen: “There is no reality behind thediscourse concerning the Gulf War. History, like science, is a fictive construct.” Norriswrites of the “intellectual and political bankruptcy” of doctrines which lead to suchconclusions.

Mertonian Norms: The Ethos of Science

On such a theory, it is impossible to distinguish fairness from fraud in science, since,after all, both are ways of constructing fiction. In the absence of the usual distinc-tions, the scientist who fraudulently manufactures his evidence cannot be meaningfullydistinguished from the honest researcher whose data are also “constructed,” albeit indifferent ways. The problem arises from social constructivists’ rejection of the famous

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Mertonian norms of universalism, communism, disinteredness and organized skepti-cism which constitute the “ethos of science” (Merton 1942). Merton described theseas institutional imperatives, being “moral as well as technical prescriptions,”—“thataffectively toned complex of values and norms which is held to be binding” on thescientist. As Merton observes, these institutional values are transmitted by preceptand example, presumably in the course of the scientists’ education. It is difficult to seehow someone committed to the social constructivist view can either teach or conductscience according to the usual rules in which truth, honesty and other intellectual andethical measures of worth are taken seriously.

Facticity and Maintaining One’s Position

In articulating the same political view of scientific claims, constructivist authors stopshort of openly encouraging cheating and other forms of dishonesty in science, but therecan be no mistake about the clear entailments of their theory. Thus, when examininga dispute concerning the claims of parapsychology or astrology, Pinch and Collins(1984) draw attention to symmetries in the attempts of opponents to maintain theircommitments—in one case to orthodox science and, in the other, to the paranormal.However, from the standpoint of scrupulous sociological “neutrality” or “impartiality”regarding the intellectual merits of the case on each side, there can be no way todiscriminate the relative merits of the arguments and evidence itself.

In the case study, both sides make questionable attempts to protect their favouredtheory against contrary evidence and, indeed, the scientists apear to have been lessthan completely forthright about some disconfirming evidence. Pinch and Collins wishto generalise from this example to a thesis about science as a whole by construing itas a typical case, that is, as evidence of the way in which public scrutiny removes themystique of science and exposes its socially constructed, negotiated character. Suchexpose serves to “dissolve the facticity of the claims.”

Pinch and Collins are unwilling to see such episodes as anything other than theway science always operates—not because all scientists are dishonest, but becausethe very distinction relies on being able to discriminate fact from fiction. When thescientists finally admit their error and revise their earlier stance in the light of falsi-fying evidence, they are ridiculed by Pinch and Collins for their grandiose, mythicalpretensions and for appearing to adopt “a mantle of almost Olympian magnanimity”(1984, p. 536). The scientists are reproached for failing to “re-appraise their under-stading of scientific method” and to learn about its “active” character—that is, the wayin which “facts, previously established by their presentation in the formal literature[sic], can be deconstructed” (1984, p. 538) by public scrutiny of the informal, behind-the-scenes reality of science. Remarkably, however, Pinch and Collins suggest that theright lesson about science was that, “provided they had been prepared to endorse thecanonical model in public while operating in a rather different way in private, theycould have maintained their position” (1984, p. 539). In other words, if they had beeneven more dishonest, they would have been right—in the only sense of “right” possible,that is, they would have “maintained their position.” The status or “facticity” of a claimis just a matter of how the claim is publicly presented (1984, p. 523) and the literature


can either construct or “dissolve the facticity of the claims.” If we drop the jargon,their point is simply that truth is what you can get away with. Heidegger would beimpressed.

Altering the Grounds of Consensus: Affirmative Action?

In practice, through the feigned suspension of judgement, social constructivism has ledto a tacit, or even explicit, advocacy of discredited or disreputable pseudo-science. Pinch(1993) and Ashmore (1993) go so far as to defend the supposed “merits” of unorthodoxand rejected theories on the grounds of equity. Not least, this policy includes the case offraud since it “is to be seen as an attributed category, something made in a particularcontext which may become unmade later” (Pinch 1993, p. 368). Ashmore proposes aradical skepticism concerning the expose of notorious cases of misguided science suchas that of Blondlot’s N-rays. Amid the usual jargon-laden pseudo-technicality, suchan approach amounts to promoting the alleged scientific merits or deserts of suchdiscredited cases. Thus, Pinch writes of “making plausible the rejected view” (Pinch1993, p. 371) and Ashmore is prefectly explicit: “To put it very starkly, I am lookingfor justice!—in a rhetorically self-conscious effort to alter the grounds of consensus”(1993, p. 71). Again, the educational implications for the curriculumshould hardlyneed drawing out. The “impartiality” defended by social constructivism has come tomean something like affirmative action for bullshit (in H. Frankfurt’s (1988) technicaluse of this philosophical term).

Writing on the ‘Science Wars in India,’ Meera Nanda (1997) discusses the directpolitical consequences of such “epistemological egalitarianism”. Specifically, she is con-cerned with the way in which social constructivist doctrines give legitimacy to various“ethno-sciences” such as “Hindu ways of knowing” in opposition to Western, Euro-centric, Northern science. Nanda expresses “increasing unease [with] the transna-tional alliance that has emerged around the idea that the rationality of modern scienceencodes Western and imperialistic social-cultural values.” She echoes the concerns wehave already seen expressed by Popper, Chomsky and Norris:

But when science is joined to culture at the hip in the constructivist fashion, it also opens thedoor to the so-called “enthno-science”—“Hindu science,” “Islamic science,” “third world women’sscience”—wherein scientific rationality is subordinated to the “forms of life” of different com-munities. When the existing social values are allowed to decide the validity of knowledge,knowledge loses whatever power it has to critique these often oppressive values.. . . The oppressed Others do not need patronizing affirmations of their ways of knowing, asmuch as they need ways to challenge these ways of knowing. They do not need to be told thatmodern science is no less of a cultural narrative than their local knowledges, for they need thefindings of modern science, understood as transcultural truths, in order to expose and challengelocal knowledges. (Nanda 1997)

Conclusion: Education as Intellectual Self Defence

To the extent that the doctrines we have seen encourage the anaesthesia and reducedstate of consciousness of which Orwell spoke, teachers have a special responsibilityto foster clear thinking. The extent to which citizens can think independently andcritically has immense consequences for our lives and very survival. In the spirit of

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Orwell’s concerns, Chomsky (1969) has documented the extent to which elite culture,the so-called ‘intellectuals’ and the education system, perform a crucial propagandafunction fostering ‘necessary illusions’ and, thereby, serving the interests of privilegeand power. In the face of such forces, he suggests that what is needed is the kind ofintellectual self-defence that has always been the ideal of a liberal education.

. . . Traditionally the role of the intellectual, or at least his self image, has been that of adispassionate critic. Insofar as that role has been lost, the relation of the schools to intellectualsshould, in fact be one of self-defence. (Chomsky 1969, p. 251)

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Re-examining the Image of Science in the School ScienceCurriculum

William W. CobernWestern Michigan University, USA. Email: [email protected]

Introductory Remarks

My task is to address the question of how the scientific community views the publicunderstanding of science and whether there needs to be a re-conceptualization of thechallenge to foster the public understanding of science, and also whether there is aneed to re-examine assumptions. I am compelled to begin by acknowledging a debt toan important book, Inarticulate Science, written by Edgar Jenkins and his colleaguesat Leeds. Inarticulate Science is an outstanding contribution on the concept of thepublic understanding of science and I think of my contribution today on this topic as afootnote. My perspective is somewhat different in that I have school settings in mindrather than adult learning (also see Lewenstein, 1992). I want to address the questionof how the science community should think about the public understanding of sciencewith respect to what happens in schools; and by school I mean K-12 school plus theundergraduate science education of non-science university majors. Also, I make myremarks from a cultural perspective in that I think it is important to think about howscientific ideas contribute to and influence the worldviews we construct for ourselves.Specifically, I am interested in science as an aspect of different systems of meaningthat people construct for making sense of their worlds: “An aspect” of meaning becausescience is not the entire ball game except for a few people who chose to elevate scienceto the level of metaphysics; “different systems” because even among scientists thereare differences as to how science is used in the construction of meaning.

I also want to preface my remarks by noting that I am of course speaking frommy experiences as an American science educator. What is happening in the USA,however, does not appear to be unique (see Gaskell, 1996; Sjφberg, 1996). For example,several industrial nations including Norway are involved in the Third InternationalMathematics and Science Study (National Research Council, 1996) for what appear tobe the same reasons. UNESCO is promoting Project 2000+ which has a parallel formin the USA. The slogan “Science for All” can be heard worldwide; but, I also think thatgiven the enormous size of the American scientific and education establishments alongwith publishing interests that what happens in the USA can hardly go unnoticed orunfelt. Nonetheless I will be at pains not to appear overtly Yankee-centric.

The structure of my remarks will be as follows. I begin with a celebration of sciencebut then move on to discuss what concerns the scientific community has about the pub-lic. From here I address the key problematic element within the scientific communityitself, the epistemology of scientific positivism. This epistemology creates considerable

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difficulties for the community of science within the public square.1Finally, I begin with the end. Let me say at the onset where I am headed. Yes,

the science community does need to re-conceptualize the challenge and re-examineits assumptions about the public understanding of science. The science community’shistoric perspective on the public is grounded in the legitimate interests of science;but, the promotion of the public understanding of science needs to be grounded inthe public’s legitimate interests in science. The distinction between the prepositions“of” and “in” is crucial and I owe this insight to physicist Martin Eger (1989). Eger’sdistinction is similar to Ziman’s (1984, 1991, 1992) science insiders and outsiders,which was also adopted by Jenkins (1992) and Layton et. al. (1993).

A Celebration of Science

What is the “scientific community?” Ask a scientist and he or she is likely to saythat the community of science is composed of the science departments and sciencelaboratories at universities and research institutions. This community surely includesscientific journals and professional societies and meetings. We might also be ableto agree that university science textbooks serve as a kind of unofficial canon for thescientific community. Above all these, the people we call scientists form the scientificcommunity. I do not think it is helpful to think of science as something separate fromthe people who construct, write about, teach or learn scientific knowledge. Regardingthe scientific community, we live at a time when that community finds itself in thethroes of considerable angst. It is an angst not only about the public’s apparent lackof scientific understanding but also about an apparent lack of public esteem for scienceand scientific ways of thinking.

Paradoxically this angst is being endured at the same time that government agen-cies are pursuing another round of science education reforms for the improvementof science learning. In the USA, the National Science Teachers Association (NSTA)and the American Association for the Advancement of Science (AAAS) have proposednew science curriculum frameworks. There is a new set of national science standardspromoted by the National Academy of Science (NAS) and endorsed by both NSTA andAAAS. NAS and AAAS are organizations clearly within the boundaries of the scientificcommunity and though NSTA is a teachers organization, it is an organization closelyrelated to the community of science. Hence the efforts of these organizations stronglyreflect the interests of the scientific community. Yet there is this angst evident bythe recent spate of literature scientists and fellow travelers have written to explorethe problem of “anti science” (e.g., Bishop, 1995; Crease, 1089; Durant, 1990; Dyson,1993; Gross & Levitt, 1993; Holton, 1993; Ruse, 1994; Theocharis & Psimopoulos,1987). That this literature strikes a resonant chord within the community of science isevident from the laudatory reviews and letters to the editor published in the mainlinescientific press. My position will be that the angst is well founded but the descriptionof the problem is wholly wrong headed. To paraphrase the words of Pogo, a famous

1The term “public square” is a metaphor based on the concept on a town square and was coined byNeuhaus (1984).

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cartoon character, the science community should be saying “we have met the enemy andhe is us!”

This seems a very negative remark but I am not launching another round of sciencebashing. In fact I want to move quickly now to a celebratory stance. There is much inscience to celebrate. I personally cannot think of a time when I was not interested inscience. Typical of many students I do not remember much science being taught in myelementary grade classrooms. What I remember is the power and the wonder of thePacific Ocean to the west of our home and the majesty of the Sierra Nevada mountainsto the east. I recall the fascination of flight whether the flight of birds or of airplanes.I remember being glued to the television set through the great events of the Apollomissions. From junior high school on I do remember my science classes. Not becausemy science teachers were exceptional. They were not. I do not recall ever havinga science teacher I would call an exceptional teacher whereas I clearly recall a highschool English teacher who was a superb teacher. As research has shown, there arestudents who seem almost naturally drawn to science; and it appears to matter littlewhat happens in school science, these science enthusiasts continue inexorably alongthe scientific pathway (see Costa, 1993, 1995). School science is a de facto naturalselection device for screening the majority of students out of science (West, 1996).

I admit to having mixed feelings about my experiences as a university student butmore than anything else that has to do with the time period. It was the late sixties—the height of the Vietnam War—and it was difficult to be a university student at atime of national crisis. But if I think only of my science studies I have to say it was aheady experience. Take for example the long laborious and grueling hours spent in aDrosophila laboratory working out genetic arrangements and chromosomal structuresfor fruit flies. To my friends in other disciplines this was certainly the best example ofa silly and boring use of one’s time. I can only describe the experience as heady becausewe were actually working out the physical mechanisms that made the particular fruitfly look the way it did. And then to actually photograph the chromosomes, what athrilling experience! A year later we took the next step and actually extracted DNA.Again, what a thrilling experience not only to know nature at such a fundamental level,but to touch nature at such a fundamental level. At the time of these experiences wealso met some of the great stars of scientific research. I had the honor of studyingbiology with Paul Saltman and physical chemistry with Stanley Miller. We had guestlectures by Gunther Stent and Max Delbrock. Who needs Mel Gibson when you havejust been to a lecture by Linus Pauling? Perhaps this is hyperbole but these experienceslend themselves to positive exaggeration—at least for the science enthusiast.

Indeed, the heroic stories of scientific investigations were almost as good as anyfilm. One story that has long fascinated me is the story of identifying the DNA syn-thesis enzyme because it seemed the perfect example of Karl Popper’s conjectures andrefutations. In 1957 Arthur Kornberg isolated a polymerase enzyme from Escherichiacoli bacteria that would synthesize DNA in vitro—conjectured and confirmed. Well,confirmed yes; but was the conjecture true? John Cairns was a doubter and he setabout searching countless quantities of E. coli bacteria attempting to find a mutantstrain of E. coli lacking Kornberg’s enzyme but still capable of reproducing itself—that


is, replicating its own DNA. His attempt at refutation was successful and Kornberg’senzyme though originally confirmed as a DNA synthesis enzyme turned out to havea different function in the natural setting of a cell. Perhaps this a minor story inthe history of biology but the broader history of molecular genetics can take on epicproportions. One of the best accounts of this history is suggestively titled, The EighthDay of Creation (Judson, 1979). The less than subtle allusion is of course to the Bible’saccount of the seven days of creation.

The stories of scientific success were important beyond their explicit purpose ofteaching scientific concepts. The stories bolstered student confidence in science. Forexample, when we did those DNA extraction experiments, the truth is that we studentsonly understood portions of what was being done. If any of us had been vigorouslypressed to answer how we knew that sticky stuff on the glass rod was really DNA,we would have struggled to answer. We knew in part but much else we accepted onthe basis of scientific authority vested in the professor and laboratory instructor. Whywouldn’t we? We had heard the stories. It never occurred to us that we had faith inscience and scientists. Several years later the basis for that faith was dramaticallyreaffirmed for me. My wife and I were expecting our first child. As it happened,Alex was born several weeks pre-mature and suffered from fetal respiratory distresssyndrome. Upon birth his lungs had not opened fully and the fetal duct that allowsblood to bypass the lungs of an unborn baby had failed to close at birth. We were livingin San Diego at the time and Alex was immediately transferred from the hospital of hisbirth to the University of California—San Diego teaching hospital. This hospital had aneonatal research ward where one of the specialty interests by God’s grace happened tobe fetal respiratory distress syndrome. Perilous days followed but Alex pulled throughwith no lasting ill effects. Had he been born only a few years earlier and with thissyndrome, he would not have lived through his first twenty-four hours. Why wouldn’tI acknowledge the authority of science?

The excitement I felt as a student of science and the power I witnessed with my son’sfull recovery are grounded in the powerful ideas and methods that science has uniquelycontributed to our culture in the 20th century. Cultural historian O.B. Hardison re-marked that “no examination of modern culture can exclude the influence of scienceand technology, and one that underestimated their influence would be irresponsible”(1989, p. xi). There is cultural capital in science that properly belongs to everyone.The science community will endorse this perspective and this is what “science for all”should at the least be about. The science community, however, is not always so noble.For example, the National Academy of Science in its attempt to ward off religiousincursions in the public square told American science teachers:

In a nation whose people depend on scientific progress for their health, economic gains, andnational security, it is of utmost importance that our students understand science as a systemof study, so that by building on past achievements they can maintain the pace of scientificprogress and ensure the continued emergence of results that can benefit mankind. (1984, p. 6)

The fact that this statement so blithely ignores the complex and ambiguous relation-ship between science and technology and between science and economic development

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(Drori, 1996), casts doubt on the Academy’s sincerity. Indeed some would see in thisstatement an attempt by the science community to protect its privileged status tocontrol the discourse in certain segments of the public square, particularly the schools.Lynda Birke (1990) asks whether the drive to educate the public about science is merelyan exercise in public relations and labor recruitment. Who will really benefit? For aprofitable discussion of these questions see Bishop (1995), Goodstein (1995), and Kevles(1995).

Anti Science Sentiment

Setting aside the contentious question of motive, the science community in its desirethat the public understand and esteem science finds itself concerned with the allegedlow levels of public scientific literacy. There is no point in once again rehearsing wellknown statistics (see Yager et. al., 1996) except to say that Science & EngineeringIndicators-1996 has very recent American data and the 1996 National Research Coun-cil report has comparative data on industrial nations. Suffice it to say, the scientificcommunity which is largely responsible for financing surveys of public scientific liter-acy is not very happy with the figures. Nor has it been for a very long time. Laytonet. al. (1993, p. 8) report that, “by the opening of the twentieth century laments werecommon about the failure of science to be assimilated into the common understanding.”What distinguishes the last twenty years is a slow rise in what the scientific communityhas called anti-science and irrationality.

Science & Engineering Indicators-1996, funded by the National Science Foundation(USA), is an important document on the current status of American science and engi-neering. The writers chose to highlight the fact that about 40% of Americans expressmuch confidence in the science community which is higher than confidence placed inthe US Supreme Court. The other side of this fact, however, is that 60% of Americansare less than confident in the science community. Some 30% are less than sure thatthe benefits of scientific research outweigh the harmful results and a full 10% viewscience as more harmful than beneficial. These statistics, strikingly inconsistent withAmerica’s status as a scientific giant, have been fairly steady since the late 1970s whenthe eminent historian of science Lynn White (1979, p. 73, emphasis added) asked:

Why has the level of antagonism toward science so clearly risen in our society during the pastdecade or so, to a point where many professionals feel not only angered at the mixed publicappreciation of their efforts but also threatened by declining support of their researches?

To which he answered,

The problem is public alienation. For a variety of reasons a significant part of the general publichas become distrustful of those goals, values and methods [of science].

White’s article appeared in the inaugural issue Science 80 which was a magazinepublished by the American Association for the Advancement of Science (AAAS) for thespecific purpose of improving the American public’s understanding of science.

Through the 1980s, however, the science community perceived continued outbreaksof dissatisfaction with science in the form of anti-evolutionism and spiritualism (Holton,


1992). In the 1990s scientists found that anti-science was no longer confined to K-12 schools and unscientific parents. Anti-science had infected the very institutions ofrationality, the universities. This perception motivated Gross and Levitt to write theirbook, Higher superstition: The Academic Left and its Quarrels with Science, publishedin 1993. Two years later, Gross and Levitt working with the New York Academy ofSciences brought together,

about 200 worried scientists, doctors, philosophers, educators, and thinkers. . . [because] thereis a growing danger, many said, that the fabric of reason is being ripped as under, and thatif scientists and other thinkers continue to acquiesce in the process, the hobbling of scienceand its handmaidens—medicine and technology among them—seems assured. (Browne, 1995,p. E2, emphasis added)

The meeting was titled, “The Flight from Science and Reason.” Those committed toripping reason asunder included feminists such as Sandra Harding (1993) who raisesquestions about the nature of objectivity in science. They include Molefi Asante (1992)and Ivan Sertima (1987) who are proponents of Afrocentrism and concepts of Africanrationality. There are multiculturalists in general (e.g., Grant, Sleeter, & Anderson,1986). Still worse are the strong proponents of the social study of science such asBruno Latour (1987) and Steve Fuller (1991) who advocate a social constructivist viewof scientific knowledge. Worst of all the offending academics are the critical theoristssuch as Henry Giroux who writes about critical pedagogy (e.g., Giroux & McLaren,1989) and the literary critic Stanley Fish who is the editor of the radical culturalstudies journal, Social Text.

“Can science get any respect?” asked Kevin Finneran (1996, p. 95), editor of Issuesin Science and Technology. One would hope so but in the same year that HigherSuperstitions was published, the eminent physicist Freeman Dyson published, “Sciencein Trouble,” in which he commented that “attacks against science are likely to becomemore bitter and more widespread in the future. . . ” (1993, p. 524, emphasis added).Perhaps with that ominous prediction in mind, one scientist recently attempted todeliver a “knock out” punch to the radical social constructivists. Alan Sokal is a physi-cist at New York University and he wrote a manuscript titled, “Transgressing TheBoundaries: Towards A Transformative Hermeneutics Of Quantum Gravity” (1996b),which he submitted to Social Text for review and possible publication. SubsequentlySocial Text published the article only to have Sokal within days of the publicationannounce that the article was a hoax. Sokal had submitted a nonsense manuscriptwhich by its acceptance for publication exposed the radicals as academic charlatans, inhis opinion of course. In his own words:

For some years I’ve been troubled by an apparent decline in the standards of intellectual rigorin certain precincts of the American academic humanities. But I’m a mere physicist: if I findmyself unable to make head or tail of jouissance and differance, perhaps that just reflects myown inadequacy. So, to test the prevailing intellectual standards, I decided to try a modest(though admittedly uncontrolled) experiment: Would a leading North American journal ofcultural studies—whose editorial collective includes such luminaries as Fredric Jameson andAndrew Ross—publish an article liberally salted with nonsense if (a) it sounded good and (b)it flattered the editors’ ideological preconceptions? The answer, unfortunately, is yes. (Sokal,1996a, p. 1)

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I doubt that Sokal landed a knock out punch but there is no doubt about the ruckusthat ensued.2 Moreover, Sokal may not respect the people at Social Text but he mustworry about them and other radical social constructivists. Why else would he even givethem a second thought? Indeed, what has happened to the scientific community thatone of its distinguished members finds enemies in academe that must be combated insuch a non academic fashion? This is a question that will surely occupy the sociologistsof science for sometime to come.

Scientific Positivism

I do not disagree that there are extremes of social constructivism antithetical to scienceand to the celebration of science that I have offered. To some extent Alan Sokal hasdone all scholarship a favor by exposing the excesses of extremist social constructivism.One should also be concerned that legitimate criticism of the scientific community notbe lost in these intellectual skirmishes involving extreme positions. It is in the scientificcommunity’s best interests to heed legitimate criticism. “If scientists willingly join thecultural debate about science, science can grow in stature” (Finneran, 1996, p. 96). Ifthey do not, the scientific community will by default affirm Martin Heidegger’s quipthat scientists do not think.

As I tried to convey in my celebration of science, science can be exhilarating. It isexhilarating to realize that one can know so much about the natural world and to feelthat one can discover so much more. Earlier I also hinted that the scientific communityshould look within itself as the community considers the current problems with thepublic and science. Along with being exhilarating, science is also seductive. It canseduce one to the naıve materialism that what one knows by science is fundamentalreality, when in fact the debates over the nature of scientific knowledge with respectto ontological realism are as current today as they ever were (see, e.g., Hawking &Penrose, 1996). Science can also be deceptive. It can deceive one into thinking that onehas privileged knowledge. Indeed, the cultural point of discussion that I think is mostcrucial is the point of epistemological position. How should the scientific communityseek to position science with respect to other domains of knowledge in the publicsquare? For the better part of the 20th century that question has been answered by aphilosophy of logical positivism which sought to “banish metaphysics from philosophy,because its theses cannot be rationally justified” (Holton, 1992, p. 45) leaving senseperceptions as the only admissible basis of human knowledge and precise thought. Inphilosophy, positivism is yesterday’s news, a failed project (Walsh, 1967), but whatmight be called scientific positivism (Gilmer, 1995) or colloquial positivism hangs on.Scientific positivism roughly represents a classical view of realism, philosophical ma-terialism, strict objectivity, and hypothetico-deductive method. Though recognizingthe tentative nature of all scientific knowledge, scientific positivism imbues scientificknowledge with a Laplacian certainty denied all other disciplines, thus allowing the

2Those interested in this strange affair should consult website <http://www.nyu.edu/gsas/dept/physics/faculty/sokal/index.html> for a full account including plus Sokal’s original article.Moreover, the University of Kansas held a conference in 1997 devoted to the topic of, “Science and its critics:A meeting to promote dialogue between the ‘two cultures,”’ where Sokal was the featured speaker.


Natural Sciences

Social Sciences

Other Knowledge Domains

Figure 1: Epistemological pyramid.

scientific community to make an a priori status claim with regard to knowledge. Thusthe scientific community projects in the public square a pyramid view of epistemology(figure 1) with the natural sciences, of course, occupying the top most position.

This view of scientific knowledge has long been endemic in the schools (Duschl,1985; Nadeau & Desautels, 1984; Settle, 1990; Smolicz & Nunan, 1975) and is whatgives rise to the cultural critics’ charge of hegemony (Cobern & Aikenhead, in press;Harding, 1993). Though philosopher of science Michael Ruse was speaking specificallyof evolutionary biologists, I think his remark is too often apropos of the general scien-tific community: Scientists “tend to treat evolution as a kind of religion. . . . Evolution-ists tend to be as fervent true Believers as Creationists. . . ” (Ruse, 1993, p. 353). Theterm “true believer” was made popular by the blue collar philosopher Eric Hoffer (1966)whose book titled, The True Believer, investigated the nature of mass movements.Science has the characteristics of a mass movement and:

It can be argued that technology and scientific positivism constitute the dominant ideology ofWestern civilization today. Technology has indeed become, as Heidegger noted, the metaphysicsof our age, a totalistic form of secular religion ultimately incompatible with the existence ofrival, nontechnological assumptions, beliefs, or thought systems. (Garrard & Wegierski, 1991,p. 611)

Unfortunately, this ideology couples the science community with what I call theFour Western Imperatives of the late 20th century:

1. The Imperative of Naturalism—All phenomena can ultimately and adequately beunderstood in naturalistic terms.

2. The Scientistic Imperative—Anything that can be studied, should be studied.

3. The Technocratic Imperative—Any device that can be made, should be made.

4. The Economic Imperative—Material well being is the highest good.

Further discussion of these statements is beyond the scope of my topic. What Iwant to point out is that these imperatives lead to a blinkered view of life that fosters

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a cynicism that soon gives way to longing. Moreover, with regard to science, the firsttwo imperatives cut the very ground from beneath science. Philosopher Hendrick Hart(1980, p. 6) observed that “the positing of the ultimacy of rationality unmasks itselfas a belief which cannot be rationally justified . . . Indeed, in our times belief in reasonis increasingly characterized as a commitment to reason which itself lacks rationalgrounds.” Similarly, in our times belief in science is increasingly characterized as acommitment to science which itself lacks rational grounds. And, that claim to epistemo-logical privilege has not gone unnoticed. The radical relativism that so severely vexespeople like Sokal, Gross, and Levitt is a classic case of having sown to the wind, onenow must reap the whirlwind. In other words, the radical social constructivists havesimply turned empiricism’s searing analysis back upon the scientific community itself;and the more the scientific community protests this ill treatment, the more vulnerableit looks.

The Deconstruction of Science

The problem of scientific positivism cannot fairly be attributed to the science commu-nity on the whole. Many scientists staunchly reject the notion that science can beproperly understood in the terms of scientific positivism. The proponents of scientificpositivism, however, such as Richard Dawkins and Francis Crick are a very vocalbunch. If we are to believe Dawkins then we need to understand that the universeis essentially pointless and we as mature adults better get used to the idea and geton with our lives. Crick offers his “astonishing hypothesis” as an explanation for thispointlessness:

The Astonishing Hypothesis is that ‘You,’ your joys and your sorrows, your memories and yourambitions, your sense of personal identity and free will, are in fact no more than the behaviorof a vast assembly of nerve cells and their associated molecules. (1994, p. 3)

These ideas resonate with the fashionable nihilism found in certain segments ofmodern western culture. Given this view of science, E.A. Burtt’s comments of 1967become prophetic:

The world that people thought themselves living in—a world rich with colour and sound, redo-lent with fragrance, filled with gladness, love and beauty, speaking everywhere of purposiveharmony and creative ideals—was crowded now into minute corners of the brains of scatteredorganic beings. The really important world was a world hard, cold, colourless, silent, and dead;a world of quantity, a world of mathematically computable motions in mechanical regularity.(1967, pp. 238-239)

To better understand the radical social constructivist critique of science, it is in-structive to take what has happened in science as an analogy of what has happened inliterary studies. Figure 2 depicts the traditional concept of hermeneutic interpretation.

A literary text is taken as the product of its author’s intentions. Thus, there is anobviously direct interaction between author and text. A reader of the text attempts tounderstand the author’s intent. This involves a direct interaction with the text (readingthe text) and an indirect interaction with the author. The interaction with the authormust be indirect because our interaction with the author is mediated by the text. In


Author (Melville)

Text (Moby Dick)

Reader of Text

Direct Interaction

Direct Interaction

Indirect Interaction

Figure 2: The deconstruction of text.

so far as we are able to assume that the author is sane, we can approach the textas something meaningful that can communicate to the reader ideas that the authorintended. Of course, authors with greater writing talent will be better communicators.Similarly, there is a tradition of hermeneutics in natural philosophy that is depicted infigure 3.

Nature may be taken as a meaningful whole either because there is a Creator ofthe whole (as in theistic traditions) or for other transcendent values one holds aboutNature. Nature understood holistically expresses itself in a myriad of natural phenom-ena. The Natural Philosopher—who is our modern day scientist—interacts directlywith natural phenomena through his or her studies and indirectly with Nature as awhole. The assurance that Nature transcends the experience of natural phenomenais as well the assurance that natural phenomena are deeply meaningful. They havemeaning that transcends the brute facts of experience.

But literary studies have changed. Many modern day literary critics will tell youthat the purpose in reading a text is not primarily to understand the author’s intentbut to deconstruct the text, as shown in figure 4. In modern literary interpretation,the text is considered the product of social forces that impinged upon the writer ofthe text. The reader of the text, thus, attempts to understand not the writer’s intent(as if there actually were an author), but to understand the social forces that actedupon the author (who is more writer than author). Rather than an indirect interactionwith an author who directly communicates intention through his or her text, there isan indirect interaction with the social forces. Hence, the text must be deconstructedrather than simply read—the words cannot be taken at face value (see figure 5).

Similarly, in recent years science has become an act of deconstruction as shown infigure 6, at least as science is portrayed by the scientific positivists. There is no Natureas Nature—that is, no holistic understanding of a meaningful Nature—hence all thatis available to humans are the brute observations of natural phenomena.

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Author of Nature/ Nature qua Nature

Natural Phenomena

Natural Philosopher

Direct Interaction

Direct Interaction


Figure 3: The hermeneutic circle of natural philosophy.

What we call Nature is merely the experience of natural phenomena. Scientificmeaning proceeds from the deconstruction of natural phenomena and the re-representationof our experiences of natural phenomena as a naturalistic conceptual system. Thearresting point about this is that Nature as an inherently meaningful concept is sepa-rated from any meaningful relationship with natural phenomena; hence, the situationis analogous to the separation of author and text in radical literary criticism. Hence,rather than looking to natural phenomena as a way to understand Nature and toNature as the guarantor for the essential rationality of our endeavors to understandNature—which would be the traditional scientific perspective—we are left with onlythe scientific re-representation of our experiences of natural phenomena. WithoutNature as our guarantor, science itself is open to deconstruction as depicted in figure 7.The radical sociologist of scientific knowledge thus attempts to understand not theintent of scientific knowledge as written by an author (author as scientist), but tounderstand the social forces that acted upon the scientist (as a writer) resulting inthe scientific text.

It is my assertion that the reasons that have brought us to the deconstruction ofscience have to do with the inordinate influence of scientific positivism on the academicand public perception of science. What is needed at the school level, is an alternativeunderstanding of science.

An Alternative View of Science and the Public

Yes, the science community does need to revamp its conceptualization of the public’sunderstanding of science if the public is to be well served and if science is to prosper.We can begin, however, with a celebration.

1. We can affirm that science is part of the cultural heritage that belongs to allpeople. The exhilaration that I felt as a student of science should be available to


Author (Melville)

Text (Moby Dick)

Reader of TextDirect

Interaction


all who wish to avail themselves of it. The benefits to my family should be benefitsavailable to all; that is, all who wish to avail themselves of these benefits.

2. Science is part of the cultural heritage that belongs to all people, but it is notthe sole constituent of that heritage, neither is there any consensus on its rankordered position in that heritage. Historian O.B. Hardison (1989, p. 70-71) notedthat, “The science of the late twentieth century asks man to understand himself inthe light of his own reason detached from history, geography, and nature, and alsofrom myth, religion, tradition, the idols of the tribe, and the dogmas of the father.”This request is an invitation to alienation. Doing this not only places science atthe top of the epistemological pyramid (figure 1), it removes science from the pyra-mid. Science has powerful ideas such as the conservation of energy, homeostasis,ecological systems, change through time, uniformity, and empirical-experimentalinquiry. There are also other powerful ideas such as freedom, democracy, rule oflaw, human dignity, moral rectitude, social solidarity, and transcendence. Whatthe scientific community must understand about people, is that science along withhistory, art, language, technology, and religion are pendants on a wonderfullyintricate mobile of everyday thought, “touch one and the rest tremble and changeposition in sympathy” (Hardison, 1989, p. xiv).

3. There are legitimate differences between the interests of science and public’s in-terest in science. These differences will preclude any consensus on science’s rankordered position in our cultural heritage. The template for school science throughundergraduate education, however, has traditionally served the interests of sci-ence. In science education it is common to hear of the scientific “pipeline” (fig-ure 8). This is a metaphor for a flow system that delivers scientists and science re-

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Socio-cultural Forces on Melville

Text (Moby Dick)

Reader of Text

Direct Interaction

Direct Interaction



lated graduates; and, as such, this is a system where the educational experiencesof the many are dictated by the needs of a very few. Even when interdisciplinaryscience curricula are adopted, they often continue to serve the interests of science.These curricula acknowledge that students have other disciplinary interests butdo so for the purpose of manipulating those interests to meet the traditionalobjectives of science education. Thus, these other disciplinary interests becomepaths to science and the paths are clearly secondary to the destination, which isscience. Moreover, one is likely to find that the destination, science, will occa-sionally critique those other disciplinary paths and starting points. For example,we may hear that the starting point is very distant from science and it will bedifficult to build this path but the community of science and science teachersmust try for the good of the learners and for the public. What is not an option isthe critique of science by those other disciplinary interests that science educationis manipulating. This is a problem against which the Science-Technology-Societycurricula are making some inroads.

4. Moreover, the public’s variable interests in science will inevitably lead to differentconceptualizations and valuations of science. Earlier I mentioned that beinga student during the height of the Vietnam war. Many of my friends had avery different valuation of science because of what they perceived as an unholyalliance between the community of science and a military-industrial complexthat developed and produced weapons. The rhetoric of value neutrality was nottenable when the science community having taken credit for such things as the“Green Revolution” now denied any responsibility for “Agent Orange” and the like.Thus they place a low value on science and sometimes a negative value.There are, however, more common examples than this one. In a recent studyresearchers talked with ninth graders about their views on nature. The objective



Natural Phenomena

Modern ScientistDirect

Interaction

Figure 6: Science as deconstruction.

was to gain insight on the extent to which science was used in everyday thinking(Cobern, Gibson & Underwood, 1995).3 One of the students, Ann, spoke of natureas something one can know about through science.

Ann: Nature is knowable. . . We can learn to understand many things about nature throughpersonal experience, school and science. Science itself provides us with technology whichin turn increases our scientific knowledge. Technology helps provide us with many wantswhich, of course, increases our pleasure. It also uses resources. (ATG.n6, Narrative inCobern et al., 1995, p. 24)

This appreciation of science, however, is not where her discussion with the re-searchers began. Note the emphasized words.

Ann: To me, nature is beautiful and pure because it is God’s creation. Nature providesboth aesthetic and emotional pleasure and I need it for self renewal. I like to go where youcan’t see any influence by man. When I’m out in nature I feel calm and peaceful. It is aspiritual feeling and it helps me understand myself . . . This leads me to ask questions thatI’d like to find answers to. The pleasure I get from nature is enhanced by the mysteries Isee in it. (ATG.n6, Narrative in Cobern et al., 1995, p. 24, emphasis added)

Ann’s conceptualization of the natural world has significant aesthetic and reli-gious elements. Nature in her view is something friendly that you can joyouslybe part of.Now consider Mr. Hess. He is Ann’s physical science teacher and he who satfor the same research interview as did Ann. He began his discussion in markedcontrast to Ann.

3The research was funded by a National Science Foundation grant (RED # 9055834)

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Text Sociologist of Science

(Edinburgh School!)Direct Interaction

Figure 7: The deconstruction of science.

Mr. Hess: Nature is orderly and understandable. The tides and the rotation of the earth,the seasons and so forth are examples of order in nature. That the planets and the starsare governed by physical forces and any deviations are simply because we have not yetdiscovered the other part of nature’s orderliness. According to chaos theory even thingsthat appear to happen randomly have patterns. I think that everything has patterns. . . .

As a science teacher I feel that with enough scientific knowledge all things are understand-able . . . . I think that the more we understand about matter itself, and the more we knowabout how to make things, the more predictable nature will be. Scientific or reductionisticthinking is very powerful. I feel that once we know enough about the minutia of the world,breaking it down by using the scientific method, scientists tearing it apart and analyzingthe parts of nature and seeing how they interact, that we will be able to predict just aboutanything about nature. (WWC.t6, Narrative in Cobern et al., 1996, emphasis added)

In contrast to Ann, her science teacher’s conceptualization of nature showingthe integration of scientific themes is essentially monothematic. It is classicalscientific positivism and could hardly differ more from his student, Ann. Fig-ure 9 is a generalized concept map of Nature drawn from interviews with highschool science teachers and college science professors. Although our studies showmarked differences between biologists and physicists (Cobern et al., 1996), theyare consistent with respect to the centrality of science in their thinking. Theninth grade students of our studies and the non science college majors showedsubstantial variability in their conceptualizations of nature and integration ofscientific themes and concepts. Figure 10 is a generalized concept map of Naturedrawn from interviews with students and shows the extent of variation.Occasionally one finds a student who talks very much like a science teacher orprofessor. Most do not, but this does not mean that the students are unscientific.For example, it is possible to have an aesthetically oriented view of life thatincorporates scientific thinking. Not aesthetics manipulated for the purposesof science, however. I have in mind Pythagorean viewpoint where the artistic


Elementary School Leavers

High School

Graduates

General College

Graduates

Elementary Teachers

Secondary Teachers

Science and Science related Graduates

Figure 8: The science education pipeline.

person would value learning science because of the beauty and elegance of itsrepresentations. Near the end of Kepler’s Harmony of the World (1619) he wrote,“I thank thee, Lord God and Creator, that you have permitted me to see the beautyof your work and creation.” J.B.S. Haldane in this century wrote:

As a result of Faraday’s work you are able to listen to a wireless. But more than that,as a result of Faraday’s work, scientifically educated men and women have an altogetherricher view of the world. For them, apparently empty space is full of the most intricateand beautiful patterns. So Faraday gave the world not only fresh wealth but fresh beauty.

Benoit Mendelbrot’s pioneering work with fractal geometry is another area ofscience and mathematics where aesthetic elements have blurred traditional dis-ciplinary boundaries. My own view is that the different conceptualizations ofscience should be encouraged; and in addition to the aesthetic, these could beeconomic, religious, contemplative, environmentalist and others.

5. The community of science can help itself by engaging the public in good-faithdiscussions about these different conceptualizations and valuations of science. Bygood-faith I mean that the scientific community does not presume that it holds aprivileged position in the discussion. For example, a typical scientist to use aKuhnian term is a puzzle-solver who looks at a scientific solution with the prideof mastery as if to say, “Here is an important natural phenomenon and I knowhow it works!” The scientist should not assume, however, the moral neutrality ofhis or her discovery. During the Vietnam era, and I think this continues today, thepublic is very interested in the moral implications of scientific work. The HumanGenome Project or fetal tissue research are only two of many examples. In a veryinformative study Tobias (1990) found that for some well educated people, sciencelacks interest because it appears to them that scientists do not ask importantquestions such as about the morality of what they do.

6. An important point of discussion especially with respect to school science, isthe compatibility of science with very different perspectives. It is important to

Cobern 125

Nature

Science Environment

Other Ideas

for example

for example

aesthetic religious recreational contempative/emotional relational economic�

Philosophy of Nature

leading to

Questions to ask about Nature

of secondaryimportance

primarily understood via

conceptualized as

understoodvia

which provides

requires provides

Conservation Essential Resources

tosustain

Discovery Development Extraction Utilization Management

Acceptable explanations of natural phenomena

Acceptable methods of investigation

Order in Nature

Comprehensibility of Nature

which facilitate

togive

and

Figure 9: A scientist’s view of nature.

acknowledge that not all ideas and worldviews that people hold will be compatiblewith science. It is also important to recognize that learning science in even themost enlightened of settings will bring about change. The important question isabout when change is warranted and when it is not.

Concluding Remarks

So, yes, the scientific community does need to re-conceptualize the challenge and re-examine its assumptions about the public understanding of science. The scientificcommunity’s historic perspective on the public is grounded in the legitimate interests ofscience; but, the promotion of the public understanding of science needs to be groundedin the public’s legitimate interests in science. Professor John Polkinghorne, presidentof Queens College, Cambridge, who is a physicist and Anglican priest, recently madethe following remarks in Scientific American:

Everyone has a metaphysics—a worldview—just as all people speak prose, whether they areaware of it or not. Science can and should contribute to that worldview, but it should by nomeans monopolize it. Unless you are one of those biologists so flushed with the recent success ofyour discipline that you are moved to claim that ‘science is all,’ you will want to locate scientificunderstanding within a wider view of knowledge that gives equally serious consideration toother forms of human insight and experience. (Polkinghorne, 1996, p. 121, emphasis added)

It is time that the science community and school science education began to do justthis: to locate science within a broader view of knowledge.


Philosophical Orientation

Naturalistic Religious

Atheism�

DeismClassical Theism Fundamentalism

Nature

Status� Changeable Orderly Knowable Mysterious

Mundane SpecialDynamic Expansion

TypeDiscipline

Type

Teleonomic Teleologic Science Unspecified

Complementarily Environment

Aesthetically Religious Emotionally

PrimarilyPrimarilyToward

RangeRange

Has Can be

or

Balance of BothCan beor

or or

or

or

Types Can be Can be

Can be

By

Focus on�

Majority view

Figure 10: Non-scientists’ views of nature.

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Linking Science Pedagogy with History and Philosophy of ScienceThrough Cognitive Science: A Proposal

Amitabha GuptaIndian Institute of Technology, Bombay, India. Email: [email protected]

Introduction

The curriculum for science education at present both at the school and the post-schoollevels emphasizes narrow specialization of only technical material. All the cognatesubjects in the curriculum are arranged horizontally and the students move throughschools and colleges vertically from level to level of successive stages of specialization.The teaching materials of the program are structured in a hierarchical order mainlyaround narrower and still narrower technical content as the student moves up athigher levels. This is considered to be undesirable. In what follows I would like tofirst argue for integrating science education with philosophy, history and sociology ofscience with the help of cognitive science, secondly, suggest a model of integration, andfinally, illustrate the model with two examples.

Section 1 deals with issues relating to narrow science education programmes thatcurrently exist, the misconceptions about science that may arise from such scienceeducation programmes, and a possible model for science studies that may remedy it.Section 2 suggests that science studies based on a straight forward Philosophy andHistory of Science may get entangled in unnecessary controversies/debates and fail tointegrate the technical content and the insights into scientific practices. The sectionfirst identifies two such conventional debates in science studies and discusses onedebate, viz., whether scientific knowledge is the creation of the individual scientist ora product of society, and offers a possible resolution by adopting the cognitive-historicalapproach. In Section 3 the same is done for another debate, viz., whether scientificknowledge is objective or subjective. The discussions on both the debates shows howCognitive Science and Case Study based approach can act as unifying factors. This isillustrated with the help of examples of scientific work illustrated with two case studies:one on scientific experiment and the other on introduction of new concepts and ascientific law.

1 The Paradoxical Nature of the Conventional Science Education Programme

The consequences of this narrow, isolated, fact-oriented science education are as fol-lows:

i. Although the teachers and the textbooks of science mostly claim to stick to ‘facts’and to exclude ‘idle philosophic talk’, they end up creating misconceptions pre-cisely about these facts, may be not by deliberate instruction but by implication.

132 Science Pedagogy through Cognitive Science

Philipp Frank4 has given examples of textbook formulation of laws of physics,e.g., the law of inertia, and shown that in that formulation no physical factswhatsoever can be logically derived from the law, and the law is inapplicable toany actual situation in the physical world. This means that textbook formulationoften is not physical but purely metaphysical.

ii. It is true that valid scientific knowledge is often intuitive, the acquisition orassessment of which is based on practical experience in learning science, research,and active participation in scientific work and scientific community. It has beensaid that ‘valid’ science is what is recognised as ‘valid’ by scientists and can sel-dom be identified as a formal logical property of scientific discourse. And yet thosewho enter into a scientific career in which their earlier fact-oriented training isnot derived from any exposure to the actual processes of creative scientific workand research, may have no personal experience of the fundamental importanceof the mistakes, groping and criticisms in the generation of new and reliableknowledge or the importance of inventive imagination or of the limitations anduncertainties of the so-called ‘scientific methods’. The reason for this is that ourfact-oriented science education program has lost contact with living experienceof scientific work and research, since it has been turned into a ’banking system’,in which the teachers deposit a certain amount of factual knowledge with thestudents and retrieve it during the examination essentially treating the studentas no more than a memory bank.

iii. Finally, as a consequence of increasingly narrowing hierarchical arrangementof factual content and rigid standards of valid scientific knowledge or proof, astudent of science forms the opinion that the scientific view is the only legitimateview, ignoring all questions concerning its scope and the legitimacy of other al-ternatives. Since in his narrow and exclusive science education the student istaught to treat only science as valid he naturally makes an inference that it mustbe valid in other regions as well.

The irony of the present science education program is that whereas it really intendsto impart “nothing but facts” and to remain neutral regarding any attempts to incor-porate discussions about science, it creates, in the process of teaching, a vacuum. Theinfluence of the isolated technical scientific content on the total attitude of the studenttowards science forces him to fill up this vacuum. In the absence of any consciousprovision for providing an over-view of science and thereby protecting students fromnarrow blinkers or nave euphoria just as much as from the false and hostile ideasabout science, this vacuum is filled up by many misconceptions. As a result, mythsabout science abound and a mystique of science prevails.

4Frank, P.: 1961, The Place of the Philosophy of Science in the Curriculum of the Physics Students, inModern Science and Its Philosophy, Collier Books, New York, 224-252.

Gupta 133

1.1 Misconceptions about Science Implicit in Conventional Science EducationProgramme

What are some of these misconceptions? First, science is claimed to provide absolutetruth, completely objective and pure description, and, therefore, should be consideredthe only authority for belief and the only source of reliable knowledge. The overempha-sis on mathematical and formal aspect of science, the authoritarian manner in whichscientific knowledge is imparted, and the total absence in science education of initialdoubt, the element of surprise, inventive imagination, creative criticism lend credenceto the belief that scientific knowledge is absolute. The manner in which scientific exper-iments are conducted in a school or college laboratory shows that an experiment on, say,Boyle’s law, amounts merely to observe a series of values of the pressure and volumeof the gas, which can be plotted on a nice smooth curve confirming a mathematicalrelationship between relevant variables. Accounts of Boyle’s own experiment could givea contrary picture. Besides, the absolute knowledge view of science has been reinforcedby another widespread misconception that there exists a master procedure or methodunderlying all scientific work and the successful application of this unique infalliblemethod is what validates scientific knowledge. P.W. Bridgman, J.B. Conant and manyother practicing scientists have claimed that ‘science is what scientists do’ and thesearch for ‘the Method’ is futile as there are not one but many methods.

Secondly, science education conveys the impression that science is ‘hard’, objective,and value free as opposed to humanistic studies that are ‘soft’, subjective, and value-laden. Reacting to this many have argued that science dehumanises, that the conse-quences flowing from science are preponderantly evil, trivial or false by comparisonwith what can be derived from other sources, such as poetic insight, religious revela-tion, mystical experience or self-knowledge. This polarization of attitudes is the basisof C.P. Snow’s ‘two cultures’ and Holton’s Distinction between the New Apolloniansand the new Dionysians. There are two aspects of this: (a) this polarization is simpleminded and misconceived, augmented, on the one hand, by the way science is taughtobstinately, scornfully, neglectful of all the humanistic issues that arises within theirdomain and humanists, on the one other hand, exhibit corresponding scorn and neglectfor science; and (b) the myth of value-freedom and objectivity of scientific knowledgehas been questioned by the sociologists of knowledge. The works of Kuhn, Merton,Bloor, Barnes and others have emphasised the role the scientific community plays inthe production of scientific knowledge: the ‘invisible colleges’, the peer review, author-ity, consensus, norms and recognition of the scientific community.

Thirdly, a widespread impression, which prevails among many students and prac-titioners of science, is that science possesses a unique world picture, an overall sci-entific representation, such as the mechanistic world picture or materialism, i.e., theworld picture that all phenomena are by-products or epiphenomena of the ultimateconstituents of matter. The belief in such a world picture makes the scientist confidentthat science can provide valid answers to all questions since they follow from the samesource, i.e., a single, unique world picture. History of science has exploded the myth ofsuch a world picture. Moreover, we know that even if it exists it does not show up in


our science education since it is totally fragmented to provide such a unified view.Fourthly, since Bacon in 16th century the view that knowledge is power has turned

science into a means to gain control over nature. Consequently, many subscribe tothe naıve eupheria that all our problems—disease, poverty, and hunger—can be doneaway with by the deliberate application of scientific knowledge. This belief is the basisfor massive investment in science and technology. However, this faith is somewhatmisplaced as it is impossible to calculate the relevance of any particular fundamentalresearch to any particular human need, e.g., the work of Faraday and Maxwell onelectromagnetism could hardly have been predicted to lead to phenomenal developmentof electrical and electronic industries. Therefore, the whole question of how to guidescience towards solution of practical problems will remain open and quite unanswer-able.

These influential myths about science, direct products of the narrow, isolated, andover-specialised science education, may be given a common name, i.e., ‘scientism’. Ofcourse, the origins of scientism can be traced back to the rise of modern science inthe 17th century with its fundamental insistence on the value of scientific methods ofinvestigation and argument. Based on it, the pioneers of modern science were ableto make a break-through in their attempts to understand nature, when approachesother than science were dominant. In recent times, however, science has taken amore dominant place in every sphere and scientism has assumed a more extreme,threatening and doctrinaire form with blind belief in the success of technical scientificknowledge and an ‘addiction’ to science.

1.2 Empirical Evidences and the Need for Removing the Misconceptions

There is some evidence, based on at least two empirical studies5, that the current sci-ence education programs, by concentrating on objectivity and validity of science, by itsdisciplinary specialization and fragmentation, by glorifying the rational, mathematicaland analytic aspects without any reference to intuitive, imaginative, subjective aspects,do project the doctrine of ‘scientism’ as the official image of science.

The fact of the matter is that while designing science curricula, the influence of thetechnical scientific content on the total attitude of the student towards science itselfcannot be ignored. From the point of view of a good educational strategy, it is importantto make sure that students and those concerned with the promotion of science doacquire the appropriate standards and norms of scientific practice, and not wrongintellectual habits and false standards of scientific proof. Moreover, whenever scientificknowledge and technology are hoped to be twin pillars of social transformation, thebase for science is dangerously weak if the vision concerning the place and scope ofscience among students and practitioners of science is narrow. Yet, it is not clear howit can be achieved without some ‘self understanding’ of science, i.e., without makinga conscious and deliberate effort to critically discuss science, rather than learning it

5(i) Mead, M. & Metraux, R.: 1956, Image of the Scientist among High-School, Students, Science, 126,384-390.

(ii) Ahlgren, A. & Walbery, M.J.: 1973, Changing Attitudes Towards Science Among Adolescents, Nature,254, 187-190.

Gupta 135

merely by rote. Current science education program stubbornly repudiates any suchresponsibility leaving it totally to chance and intuition. As a result some have pleadedforcefully that science education programs will produce better educated science stu-dents if they are taught “a little less science as such, and a little more about science”.

Thus the main objective of integrating teaching and learning of science with teach-ing about science or understanding science will be (i) to display the developing char-acter of scientific endeavour by incorporating historical awareness, and (ii) to foster acritical attitude on the part of the learner.

1.3 Current Approaches to Science Studies

In the recent past systematic and rigorous disciplines have evolved with a view tocreate understanding of science, such as History of Science, Philosophy of Science,Sociology of Science. Here one must guard oneself against the possibility of fallinginto the trap of any of the exclusive disciplinary approaches.

Integration of understanding science with science education program will be effec-tive only if the starting point is living science itself. The philosophical and historicaldiscourse must emanate from this source. Understanding of science will continueto remain poor if we add to the traditional presentation of science some philosophicspice or ice topping, rather than giving to the presentation of a given scientific topicitself a philosophic or historical or sociological orientation. We have to make use ofthe philosophic, historical and sociological insights that have grown up on the soil ofscience.

Constituent disciplines of the Science Studies, such as Philosophy of Science, His-tory of Science and Sociology of Science, themselves have grown into vast disciplinesand many issues in them are unresolved.

1.4 A proposal: Cognitive Science Based Model for Integration

The task will be to argue our way to a provisional model for analyzing the process ofscientific development such that the model will facilitate integration of the traditionallyconflicting tasks of teaching science and understanding of science.

The model for analyzing the process of scientific development that I would liketo propose is based on the evolutionary growth of knowledge approach of Toulmin,Shapere, Lakatos and Laudan. It is a model in the sense of developing a theoretical pat-tern showing the interrelations of different questions and concepts based on cognitive,historical and critical awareness. This approach is often called cognitive-historical.

The model requires that for an improved understanding of scientific ideas one mustknow the conditions under which it originated, the questions, which it answered, andthe functions it was created to serve. The model will present the world of science, as ascientist knows it by enabling the student of science to put appropriate kind of ‘thinkingcap’, to use Butterfield’s expression, so that the student becomes a participant in thescientist’s quest for understanding nature. In order to do this the model will retracethe steps and describe the processes by which certain end results or finished ideas inscience are seen to emerge. However, while retracing the steps the model will combine


intellectual-social-historical and technical material. The continuity and change thatare characteristic of an evolving intellectual tradition must be related to the processesof transmission by which scientific ideas in question are passed from one generation ofscientists to the next.

The starting point of this enterprise must be scientific concepts, activities (such asobservation, experiment etc.), or actual problems that the scientist encounters. BothConant and Toulmin have shown how the process of scientific development can beseen as an organic (not so much as a quantitative) growth process of investigationsyielding ideas, which in turn provide material for new investigations, out of whichemerge further ideas. Problems leading to introduction of new concepts and solutions,which in turn giving rise to new problems, whose solutions pose new problems againand lead to the generation of further concepts, and so on.

The most distinctive feature of this ‘dialectic’ sequence of observation and ideas/conceptsin the ‘scientific’ tradition/domain is that the men who carry it in any particular gen-eration regard the ideas to which their training exposes them in a sufficiently ‘criticalspirit’, i.e., in a spirit of innovation by a desire to build up a more adequate, detailed,and/or elegant synthesis of the knowledge transmitted to them, in a spirit of genuine,first hand curiosity. Thus the critical question that will be raised, according to Toulmin,at a specific time in the course of scientific development will take the form:

. . . given that concepts c1, c2, . . ., are in some respect inadequate to the explanatory needs ofthe discipline, how can we modify/extend/ qualify them, so as to give us the means of askingmore fruitful empirical or mathematical questions in this domain?6

The model of scientific development, i.e., the pattern of responses given to the abovequestion if one examines the history of a scientific discipline, can be specified by theDarwinian Theory of evolution, Toulmin7 draws the following analogy as described bythe Table 1 below:

6Toulmin, S.: 1974, Rationality and Scientific Discovery Boston Studies in the Philosophy of Science, K.Schaffner & R. Cohen (eds.), D. Reidel, Dordrecht, 394.

7Toulmin, S.: 1972, Human Understanding, Clarendon Press, Oxford, 1, 121-123, 135-144

Gupta 137

Organic Evolution Conceptual ChangeUnit of study comprised of Species Scientific discipline

Individual organisms Concepts, methods, aims

Units of variation Mutant forms within the Conceptual variants withinpopulation at t1 the discipline at t1

Units of effective These t1 variants dominant Those t1 variants dominantmodification within the population at t2 within the discipline at t2

Mechanism of selection Differential reproductive Need for deeperpressure understanding

Table 1: Evolution: Organic and Conceptual

Following the above analogy Toulmin maintains that conceptual development withina scientific discipline is a ‘natural selection’ imposed by disciplinary pressure on a setof ‘conceptual variants’. Understanding science or scientific concepts will result fromseeing the conceptual evolution in the analogy of the question and answers regardingthe phylogeny and ecology of biological evolution. This is exhibited in the followingTable 28:

Evolution of species Conceptual evolutionPhylogeny Ecology HS PS

Question From what By what From what By whatsuccession of sequence of succession of sequence ofprecursors has responses to precursor responses tothis species environmental concepts has disciplinarydescended? pressures did the this set of pressure did

species acquire concepts this set ofits present form? descended? concepts arise?

Answer A tree Application of A History of A rationalof descent theory of a scientific reconstruction of

natural selection discipline scientific growth

Table 2: Conceptual evolution

Thus, understanding of science, in the sense of adequacy or ’fruitfulness’ of scientificideas, can be obtained, according to Toulmin’s evolutionary model, by seeing in how

8Toulmin, S.: 1974, Rationality and Scientific Discovery, Boston Studies in the Philosophy of Science, K.Schaffner & R. Cohen (eds.), D. Reidel, Dordrecht, 402-3.


many ways novel scientific ideas or concepts may, in conditions of its introduction,be ‘better adapted’ than its predecessors or rivals. For example, the merits of theCopernican revolution can be understood precisely in this way. Its merits did not liein its simplicity in comparison with the Ptolemaic system. According to Toulmin theCopernican system was ’better adapted’ to the new conceptual framework that wasemerging i.e. the celestial dynamics of Kepler, Brahe and finally Newton.

The attempts to create understanding of science by Conant, (in terms of tacticsand strategies of science), by Lakatos, (in terms of Methodology of Scientific ResearchProgramme (MSRP)), and by Laudan (in terms of judgements embodying ‘preferredintuition’), are similar, for all to invoke the notion of evolution and its variants (such as‘change’, ‘growth’, ‘progress’) without explicit reference to biological evolution. Never-theless, the evolutionary model may provide a basis for integrating teaching of scienceand understanding science/teaching about science without falling into the trap of anyof the exclusive disciplinary approach.

2 Two Debates

There are two basic debates in the current literature in Philosophy of Science andSocio-Historical studies in science:

• the first debate concerns the agency responsible for the construction of scientificknowledge: whether it is the creation of the individual scientist or a product ofsociety.

• the second debate relates to the nature of scientific knowledge: whether it isobjective or relative to a conceptual perspective, and

I shall review these debates and show that a closer attention to the underlyingcognitive issues help us to resolve them.

2.1 Debate 1: Construction of Scientific Knowledge—Individual or the Social

The debate centers around the issue regarding the agency that is responsible for theproduction of scientific knowledge: whether it is a product of society or the creationof the individual scientist. Many researchers in science studies have viewed, mistak-enly I believe, that the rise of cognitive science is a vindication of the individualisticexplanations of scientific knowledge and an attempt to reduce social to the individual.

2.1.1 Sociology of Knowledge

The proponents of sociology of knowledge (e.g. Bloor 1976, 19839, Brown 1984, 1989,Barnes 198210, Collins 198511,) have eschewed the psychological and cognitive studies

9Bloor, D.: 1976, Knowledge and Social Imagery, Routledge and Kegan Paul, London,Bloor, D.: 1983, Wittgenstein: A Social Theory of Knowledge, Columbia University Press, New York.10Barnes, B.: 1982, T.S. Kuhn and Social Science, Macmillan, London.11Collins, H.M.: 1985, Changing Order: Replication and Induction in Scientific Practice, Sage, Beverley

Hills.

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of science and claimed that scientific knowledge is entirely a product of social interac-tions and influence.

Latour and Woolgar (1986) have proposed a ten-year moratorium on cognitive ex-planations of science. For them what matters is the communication and interrelationsamong the scientists based on public documents. These documents clearly exist outsidethe mental representation of individual scientists. They are the shared property of thescientific community and public embodiment of scientific theories. Latour and Woolgarshowed how in the laboratory the inscription devices (i.e. initial records that areharder to read and more open to attack are transformed by the experimenter later intopublished transcripts that become powerful weapons in arguments) and external repre-sentations or documents exert influence on other scientists. Latour (1987)12 examinesthe function scientific texts, diagrams, schematic representations etc. fulfill in creatingunderstanding within a scientific community. He calls these public embodiments “im-mutable and combinable mobiles” that in the process of scientific communication oftenmutate and facilitate an improved or different understanding.

The anti-cognitivism of Latour and Woolgar (1979)13 and Collins is shared by Downes(1993). He accuses the cognitivists of cognitive individualism and claims that theysubscribe to “the thesis that a sufficient explanation for all cognitive activities can beprovided by an account of autonomous individual cognitive agents”. He finds that thecognitivists are guilty of reducing social explanations to psychological explanations.

According to the sociologists of scientific knowledge, the reductionism of the socialto psychological is not possible for various reasons:

i. Durkheim showed that social facts are irreducible and have an existence of theirown. Following this idea, Downes distinguishes three levels of the social aspectsof science and claims that each has an independent existence and none can bereduced to psychology: (a) scientific documents, particularly classics, as Kuhn,Latour and Woolgar showed, have an independent, external existence, provide aparadigm for the individual scientist and influence his problem solving approach.(b) social interactions among scientists, as can be found in complex laboratories,are based on cooperation where individual scientist is not entirely responsible forthe final scientific outcome, and (c) much of the decision making processes of theindividual scientist are guided by external social considerations and influences,e.g., decisions regarding what funding agency to approach, how to formulatethe research proposal so that it would be acceptable, the choice of the researchproject, the journal and conference where the research paper is to be published orpresented.

ii. Collins (1990) gives the following reasons for which he claims that science issocial: (a) the routine servicing of scientific belief reveals that it is the scien-tific group which determines how an individual scientist checks the validity of

12Latour, B.: 1987, Science in Action: How to Follow Scientists and Engineers through Society, OpenUniversity Press, Milton Keynes.

13Latour, B. & Woolgar, S.: 1979, Laboratory Life, Sage, Beverly Hills and London.


beliefs. The hypothesis formulated by an individual scientist is communicated toanother who may reply by communicating additional evidence, counter-evidence,alternative hypothesis or rebuttal. This may help in assessing the validity of thehypothesis, (b) the assessment of the validity of the hypothesis may result fromcommunication, debate and finally in the form of social consensus arrived at by ascientific community that no further change is necessary, and (c) transmission ofnew experimental skills require apprenticing with an experienced researcher, aface-to-face interaction, some form of social exchange and communication basedoften on visual representations. This mode of communication is radically differentfrom transmission of information by simply reading text-books or journal articles.Thus, according to Collins the persuasive force of experiments resides outside theconduct of the experiment itself. It resides in the judgements made by otherscientists about the quality of the experiment. Of course, any experiment canbe challenged because of technical competence with instruments and data analy-sis, theories of instrumentation, correctness of computation and interpretations,theoretical plausibility. However, acceptance or rejection of a result ultimatelyrests outside the experiment itself in the evaluative judgements made by groupsof experts.

iii. Social phenomena are far too complex and the reduction of sociology to psychologydoes not seem to be tractable. No reduction has been carried out fully.

2.1.2 The Cognitive Turn in Science Studies

The so-called cognitive turn in science studies has resulted due to the following impor-tant realizations:

i. that both the words science (which comes from the Latin word sciencea meaningknowledge) and the word cognition (co = together, gnocere = knowledge) haveknowledge in common. Science is taken to be a major paradigm of a knowledge-producing enterprise and Cognitive Science studies the underlying mechanismsresponsible for the production, acquisition and deployment of knowledge, includ-ing scientific knowledge.

ii. that the exclusively a priori, speculative and normative approach to traditionalepistemology is to be replaced by an empirical and naturalistic approach treatingcognitive activities and phenomena as natural phenomena. The traditional epis-temology has undergone radical changes as it became apparent that an importantresource for a naturalistic account of knowledge is Cognitive Science.

iii. these mechanisms presuppose that the human mind or artificial intelligent de-vices can function based only on representational structures and processes thatoperate on them to produce new structures. These structures may include linguis-tic expressions, concept trees, schemas, cognitive maps, mental models, diagrams,visual images etc.

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In the traditional epistemology, Kant for example, provided such an account of theunderlying mechanism for the possibility of scientific knowledge by adopting a specula-tive and apriori approach. Kant asked the question as to what sort of mechanism wouldmake mathematical and natural scientific knowledge possible and gave a descriptionof such a mechanism.

In the 1950s, Kuhn and Hanson used psychological ideas, particularly from theGestalt school, in order to explain certain phenomena in scientific observation. How-ever, due to the progress made in Cognitive Science since 1950s there is a betterunderstanding of the cognitive mechanisms involved in many scientific activities andpractices.

A survey of the relevant literature shows that the Cognitive Science based ap-proach complements the traditional historical approach (both internal and external),the sociological approach, and the philosophical concern for the epistemology of sci-ence, by providing an enriched understanding of how scientists generate and evaluatescientific ideas. For example, the volume, (No. XV), entitled Cognitive Models ofScience, published in 1992 by R.N. Giere14 in the series “Minnesota Studies in thePhilosophy of Science” presented the work of psychologists, historians, researchers inArtificial Intelligence and philosophers who had employed ideas and methodologiesfrom Cognitive Science in order to study the underlying cognitive mechanisms forexplaining and understanding scientific practices.

Moreover, there are major studies on scientists and scientific theories from thecognitive point of view. A few examples of such studies may be mentioned here. Dar-den has identified the cognitive strategies that contributed toward the development ofMandelian genetics. Giere has used psychological and sociological ideas to improve ourunderstanding of the recent developments in geology and physics. Based on the casestudy on plate tectonics, Solomon shows how certain cognitive heuristics play a crucialrole in scientific decision making. Nersessian has drawn on ideas from cognitive psy-chology to help understand the developments in electro-magnetic theories made possi-ble by the contributions of Faraday, Maxwell and Einstein. Churchland has discussedthe nature of theories and explanations from the perspective of computational neuro-science. Thagard has used computational and cognitive theories to help understandthe structure and growth of scientific knowledge.

2.1.3 A False Dichotomy

Many historians and researchers of science studies feel that the dichotomy betweencognitive and sociological, or the internal and the external history is a false one. Shapin(1982) and Nersessian argue that undoubtedly sociological insights and methods haveenriched our understanding of science, but the concern of science studies is not tofigure out what discipline in science studies is most fundamental and support thereductionist position. The concern rather is to provide a better understanding of thenature of scientific thinking by integrating the individual and group level of knowledgeproduction practices. Nersessian says:

14Giere, R.N., (ed.): 1992, Cognitive Models of Science, Univserity of Minnesota Press, Minneapolis.


As to the question of what factors are or are not pertinent to historical explanation, we needto keep in mind that history is an empirical subject. It should not adopt a priori a positionon what is the essential level of analysis for an historical understanding of science.. . . Whatfactors are or are not salient in specific historical cases remains an open and largely empiricalquestion

The understanding of the complexities and the limitations of cognitive activities ofthe individual scientist is as important in our historical understanding of the processesand products of science as the constraints imposed on them by society. We must admitthat after all science is a product of the interaction of the human mind with the worldas well as with other humans and also the most cerebral among other human activitiesand enterprises. We need an account of how and what cognitive activities of theindividual scientists contribute to the construction of scientific knowledge as well asthe manner in which such constructions are constrained by society. Hence, cognitiveand social-historical analyses are reciprocal. There is no need for sacrificing one for theother.

An integrated approach to the understanding of certain scientific practices candemonstrate that the dichotomy between individual and the social is false and need tobe corrected. The scientific practices that can illustrate the integrative approach are:scientific experiment (including thought experiment), scientific reasoning (includinganalogical reasoning), model building and representation (imagery and visual repre-sentation), theory change. We will discuss only one example of the scientific practice interms of this integrative approach, viz., scientific experiment.

2.1.4 Scientific Experiments

Although the final products of scientific experiments, viz., the observational data andthe generalization or law are universally acknowledged as important, the process ofexperimentation by which new interpretation is given, meaning is made and the ex-perimenter’s practices are revealed, is a largely neglected aspect of science. Studieson scientific experiments collected by J.B. Conant in Harvard Case Histories in Exper-imental Science (1984), Rom Harre in Great Scientific Experiments (1981), and DavidGooding, Trevor Pinch and Simon Schaffer (eds.) in The Uses of Experiment - Studiesin the Natural Sciences (1989) have somewhat mitigated this neglect.

Examples of experiment can be cited in the science of antiquity. Empedocles ofAkragas in Sicily (c. 450 BC) is said to have made an experiment with clepsydra todemonstrate the effect of “air pressure”. Duhem, Randal and Crombie have isolatedand studied an important medieval methodological tradition, from the 13th into 17thcentury, elaborated rules for drawing sound conclusions from experiment and observa-tion. Jean Buridan and Nicole Oresme belonged to this tradition.

Another tradition of experiment views the experimenter as a reader of theBook of Nature. According to this tradition experiments should be looked upon asscriptural interpretation provided the experimenter hits upon the appropriate languageand technique of reading. This tradition found its most celebrated articulation inGalileo who regarded Nature as a divinely authored book written in the languageof mathematics. This tradition often takes experiments as premediated and is also

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identified with what is known as the Platonic-Pythagorean tradition or the deductive,or sometimes the mathematico-experimental (according to a 17th century tradition) orthe hypothetico-deductive tradition.

However, there is an essential and qualitative difference between the older formsof experiment and those carried out in science since 17th century. This is due tothe emergence of the so-called Baconian sciences. For Bacon knowledge is not an endin itself and it provides us power over nature. However, nature does not voluntarilyreveals its secrets. We can gain knowledge by coercing nature to answer our questions.The role of experiment is essentially to constrain nature and force nature due to theforceful intervention of the experimenter to show how it behaves under previouslyunobserved, often non-existent, conditions. Bacon’s book Novum Organum gives asystematic account and his attitude towards experiment. This influenced The NewPhilosophy or Experimental Philosophy enshrined in the Charter and advocated by theRoyal Society. This tradition is often identified with the inductive tradition.

The social aspect of experiment relates to the fact that experiments are powerfulresources for persuasion, argumentation and conviction. The experimenter is alwaysconscious of the third party, other than nature and himself, and directs his efforts toestablish a particular reading of nature and its behaviour as more valid than others.

The cognitive aspects of experiment include the active, rather than the passiverole, the experimenter plays in realizing the phenomena or producing a novel phe-nomenon by instrumental manipulation. However, this cognitive role of experiment,which was used to learn how to manipulate and represent new aspects of nature,gradually changed to the epistemologically significant role in which experiment wasused to defend theoretical claims about nature. The relation between the experimentand epistemology is quite close and can be seen clearly when we raise the questionas to what makes an experiment, or a set of experiments, believable. Franklin (1989)enumerates a number of experimental strategies or arguments designed to establish thevalidity of an experimental result or observation. They are:

i. looking at the same phenomena with different pieces of apparatus,

ii. prediction of what will be observed under specified circumstances,

iii. regularities and properties of the phenomena themselves which suggest theyare not artifacts. Hacking (1983) calls this intervention where the predictedobservation increases our belief in both the proper operation of the apparatusand in its results,

iv. properties of the phenomena as validitions of an existing theory,

v. explanation of observations with an existing accepted theory of the phenomena,

vi. elimination of alternative explanations,

vii. calibration and experimental checks for validating results and providing a nu-merical scale for the measurement of the quantity involved,


viii. statistical validation (combined with theoretical predication).

Nickles (1989) demonstrates how experiment enables the empirical justification oftheory. In the received view in philosophy of science the context of discovery and discov-ery arguments were eliminated from the logicality of justification. Nickles introducesand makes a case for generative justification, i.e., the use of empirical knowledge tosupport theories, which include that knowledge, or using what is known to constructnew experimental trials. He argues that the generative justification is different fromthe consequentialist or hypothetico-deductive methodologies. Nickles claims that thebody of taken-for-granted knowledge, embodied in skills, instruments etc. is necessaryto the construction of evidential arguments. The received view also claims thatknowing how to produce a phenomenon or datum is irrelevant to showing that it isthe case. Nickles concept of generative justification closes the gap between knowinghow and knowing that.

Gooding (1990) enriches our understanding of how representations the scientistsconstruct, often with the help of experiments, correspond to the way things reallyare. Gooding, in a series of articles since 1980, grapples with the problem of how toaccess and unravel the procedural knowledge a scientist has which may shed lighton his experimental practices. This leads him to investigate the role of experimentalpractice in conceptual innovation. Gooding’s concept of experimental map is an effort toconstruct graphical representations that depict sequences of experimental proceduresacting on physical and conceptual objects. The maps display how experimentation pro-vides multiple possible pathways between goals and solutions of the scientist. Goodinghas applied the mapping technique to uncover the procedural knowledge Faraday hadfrom Faraday’s experimental practices, laboratory records, which revealed the cognitiveand social dimensions of Faraday’s experimental practices. Gooding’s experimentalmaps are similar to the analytical tools used by the cognitive scientists known asthink-aloud protocols. These are the records of every verbalizable thought a subjecthad during a problem-solving task. Faraday’s record keeping and his diaries andthe detailed autobiographical narration in Kepler’s Astronomia Nova approximate tothink-aloud protocols.

2.1.5 A Case Study: Galileo’s Experiment with Freely Falling Bodies

The Case Study of Galileo’s experiment on freely falling motion illustrates the follow-ing:

i. what were the generative justifications provided by Galileo for his claim (the so-called Distance Theorem) that

. . . the distances traversed during equal intervals of time by a body falling from rest, standto one another in the same ratio as the odd numbers beginning with unity?

ii. Galileo was aware of the fact that observation of vertically falling bodies involveddifficulties, as the motion would be very fast. Hence for the purpose of under-standing the nature of vertical motion based on experiment, it would be necessary

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to slow down the motion on an inclined plane. However, Galileo felt the necessityof justifying as to whether the slowed down motion on the inclined plane and thevertical motion of freely falling bodies are the same and whether the same lawwould hold for both the motions.

iii. the question of the reliability of the experiment allegedly performed by Galileoand Galileo’s resolution of the problem of the reliability and epistemic justifica-tion of the knowledge claim regarding the law of freely falling bodies.

2.1.5.1 Controversy about Galileo as an “Experimentalist”Controversy about Galileo as an “Experimentalist”

Galileo’s so-called inclined plain experiment construed as providing generative justifi-cation for the law of freely falling bodies shows that Galileo was not an inductivist. Hewas not what Ernst Mach represents him to be, i.e., Galileo as a strict experimentalist.Mach claims that modern experimental science was born with Galileo as he

. . . did not stop with the mere philosophical and logical discussions, but tested it by comparisonwith experience15

Thus Galileo was considered the father of modern observational and experimentalmethods. As opposed to this Aristotle saw the experiments performed, but would notbelieve the evidence of experience, although in Biology Aristotle was a down-to-earth,hard-boiled realist.

Galileo himself seems to be responsible for this impression as he sometimes usesthe word “experience”/“experiment” (e.g. in the statement at the beginning of Two NewSciences) in a way that one would be led to the “traditional” picture of Galileo that hewas the founder and earliest successful practitioner of modern experimental science.Or Galileo was the man who relied on experiment and Aristotle was one who deniedthe validity of experience. This is bolstered by the image of Galileo confounding hisAristotelian adversaries at Pisa and experimentally disproving Aristotelian dynamicsby dropping weights of various sizes from the Leaning Tower.

History of Science, however, dispels these misconceptions based on anecdotes/traditionalpictures/historically nave attitudes. It instills a sense of historical skepticism, makesus more cautious about relying on facts as one has not yet the time to check some ofthese episodes closely. It also urges the need for more accuracy in the description of thecreative part of the scientific work/intellectual development and growth of science/thepart relating to the process rather than the final product.

2.1.5.2 Historically Sensitive AccountHistorically Sensitive Account

Historically sensitive account Galileo’s role as an observational/experimental scientistreveals that

a. Galileo was hardly an extreme empiricist; he was much addicted to15Mach, E.: 1960, The Science of Mechanics, translated by T.J. McCormack, Open Court, La Salle, 135.


. . . thought experiment in which he imagined what the consequences would be if one didso and so16.

The thought experiments of Galileo are particularly well described by Butterfieldin his book. Within the ancient and medieval traditions many experiments onclose scrutiny turn out to be thought experiments. A thought experiment is theconstruction in mind of potential experimental situations the outcome of whichcould safely be foretold from previous knowledge or everyday experience.

b. the so-called experiments taken as generative justification would provide an al-together different view of Galileo as an experimentalist. Generative justificationincludes (i) the body of taken-for-granted knowledge which is embodied in theprevailing instrumentations, skills, etc. necessary for the epistemological warrantof the experiment and (ii) the persuasive force which often resides outside theconduct of the experiment.

c. Some of Galileo’s experiments were re-enacted by his contemporaries. In thecase of the ball on the inclined plane, Galileo’s contemporary, Father Mersenne,actually tried it in the hope of duplicating Galileo’s confirmation of the supposedexact direct proportion between the square of the time and the displacement inthe uniformly accelerated motion. But he failed to find such a fit. Mersennecontradicts the accuracy of Galileo’s claim that

. . . the times of descent, for various inclinations of the plane, bore to one another preciselythe ratio which . . . had been predicted . . . Also . . . there was no appreciable discrepancyin the results. (Two New Sciences, p. 179)

Galileo also claimed that the measurement of time was so accurate

that the deviation between two observations never exceeded one-tenth of a pulse-beat

Such accuracy was not possible because of (i) the difficulties in the synchronizationof the rolling ball and the timing device, especially when time is being measured bycertain crude devices used at that time such as water-clock or pulse-beat, and (ii)friction and rotational inertia.

Lane Cooper17 also casts doubt about Leaning Tower experiment. To be sure, Galileodid make observations and performed rough checks of his results, but the experimentalmethod and inductive method of the new science was really, from the historical point ofview, the creation of the new generation of scientists, including such heroic experimen-talists as Robert Boyle, Robert Hook and Isaac Newton (especially his work on Optics)and the members of the Royal Society.

16Butterfield, H.: 1949, Origins of Modern Science, Macmillan, 71.17Cooper, L.: 1935, Aristotle, Galileo and the Tower of Pisa.

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2.1.5.3 Galileo’s Lineage to the Platonic-Pythagorean TraditionGalileo’s Lineage to the Platonic-Pythagorean Tradition

Instead, Galileo belonged to the Platonic-Pythagorean (Idealist) Tradition: This tra-dition is associated with the assumption that (a) the underlying reality is that ofnumber, (b) abstraction and idealization is inevitable in understanding Nature, and (c)mathematics must be applied to the understanding of the physical phenomena. This isin clear opposition to the Aristotelian tradition, which created a clear cleavage betweenmathematics and physics.

Galileo’s adherence to the Platonic-Pythagorean tradition is evidenced by his ownstatement that the Book of Nature is written in the language of mathematics. To thequestion whether the ship experiment was really been done, Salviati (the spokesmanof Galileo) replied

I without experiment [experience] am certain that the effect will follow as I tell you, because itis necessary that it should, (Dialogue concerning Two Chief World Systems)

Alexaneder Koyre18 emphasized Galileo’s mathematical as opposed to his experi-mental method. Koyre attacked the traditional empiricist interpretation of Galileo andsubscribed to Galileo’s ‘modified empiricism’ or ‘tempered rationalism’, i.e., Galileo didthought-experiment in the course of developing his theories, and referred to experienceprimarily a final check in order to be sure that he hadn’t gone wildly astray. “For itis thought pure unadulterated thought, and not experience sense-perception, as untilthen, that gives the basis for the ‘new science’ of Galileo Galilie” (M & M, p. 13). Giorgiode Santillana also supports the same view. He says19: “Galileo uses facts only as acheck, as discriminator between necessary and wishful arrangement.” According toWilliam R. Shea20:

Galileo’s Platonic conception of scientific procedure implies a predominance of reason over mereexperience. While Colombo and Lagalla constantly appeal to untutored experience, Galileocalls upon mathematics to interpret nature. The crucial distinction no longer lies betweenmental and factual, but between mathematical and crudely empirical. Experiments—be theymathematical or real—are equally valid if they are set up in accordance with the requirementsof mathematics

2.1.5.4 Galileo’s Technique of Geometric Representation and ModelingGalileo’s Technique of Geometric Representation and Modeling

The mathematics Galileo used consisted of Euclid’s geometry and Eudoxus’ equality ofratio. Galileo did not use the notation “v as s/t” since be believed that no arithmeticaloperation, such as division, can be performed between two inhomogeneous physicalquantities. Galileo represented both time and distance in terms of line segments.For him it did not make any sense to divide one line segment by another. Moreover,following his precursors Galileo represented uniform and uniformly accelerated motionin terms of rectangle and triangle respectively.

18Koyre Alexaneder, Etudes Galieenes (1938), Metaphysics and Measurement, (1968)19de Santillana, G.: 1968, Reflections on Men and Ideas, 175.20Shea, W.R.: 1972, Galileo’s Intellectual Revolution, 155


Nor could Galileo have formulated the equations s = v0t + 1/2at2. This is becauseof the fact that he did not have the advantage of using the concept of “instantaneousmotion” as calculus was not available to him. Instead Galileo went on to show thatratios of displacement from rest vary as the ratios of squares of the corresponding timeintervals. He states this in the form of a Theorem. The geometrical representationof the Theorem is as follows: HL : HM :: AD2 : AE2 (where HL and HM are linesegments representing distance and AD and AE representing time). He proves thetheorem geometrically using results of similarity of triangle and equality of ratios.

Galileo’s lineage to the Platonic-Pythagorean tradition is evident in his attempt(a) to represent physical problems in terms of geometry and resorting to arithmeticalmodeling in terms of ratios, (b) deduce the results in the form of proof in the frameworkof Euclid’s geometry and Eudoxus’ equality of ratio, and (c) interpret the conclusionsthus arrived at back to the physical world.

2.1.5.5 Galileo’s Brand of EmpiricismGalileo’s Brand of Empiricism

Nevertheless there has been a resurgence of interest in Galileo’s empiricism based ondiscovery of historical evidence in Galileo’s manuscript S. Drake, R.H. Naylor, ThomasSettle21, showing that he did, in fact, perform some experiments.

These reports of what Galileo actually says he did are attempts to comprehend themethodology he is reputedly so famous for having developed. One important aspect ofthis methodology has to do with experiments and what Galileo thought they accom-plished and what they actually mean. It is one thing to ask whether or not he droppedthe steel balls from the Tower of Pisa, it is quite another to ask why he would havethought it important to do so just in case he ever did22.

2.1.5.6 Abstraction & Idealization in GalileoAbstraction & Idealization in Galileo

Without any shred of doubt Galileo resorted to abstraction and idealization. In “think-ing away” the resistance of air to the motion of the falling body, Galileo explicitlyintroduces idealization into scientific thought. He recognizes that progress can be madein understanding nature without immediately dealing with natural phenomenon in alltheir actual detail and complexity; that refinements can be developed subsequentlythrough successive approximation. The bulk of our study of in physics is confined tosuch simplified and idealized situations. One can hardly put the justification in clearerterms than Galileo himself did:

21Drake, S., Galileo’s Experimental Confirmation of Horizontal Intertia: Unpublished Manuscripts, ISISNaylor, R.H., Galileo’s Simple PendulumNaylor, R.H., Galileo: The search for the Parabolic Trajectory;Naylor, R.H., Galileo: Real Experiment & Dialectic Demonstration.Settle, T., Galileo’s use of Experiment as a tool of Investigation, A Experiment in the History of Science22Shea, W.R.: 1972, Galileo’s Intellectual Revolution

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As to perturbations arising from the resistance of the medium, this is . . .. Considerable anddoes not, on account of its manifold forms, submit to fixed laws and exact description. Thus ifwe consider only the resistance which the air offers to motions studied by us, we shall see that itdisturbs them all and disturbs them in an infinite variety of ways corresponding to the infinitevariety in form, weight, and velocity of the projectiles . . .. Of these properties . . . infinite innumber . . .. It is not possible to give any exact description; hence in order to handle this matterin a scientific way, it is necessary to cut loose from these difficulties; and having discovered anddemonstrated the theorems in the case of no resistance, to use them and apply them with suchlimitations as experience will teach.. . . Just as the computer who wants his calculations to deal with sugar, silk and wool mustdiscount the boxes, bales and other packing, so the mathematical scientist, when he wantsto recognize in the concrete the effects which he has proved in the abstract, must deduct thematerial hindrance, and if he is able to do so, I assure you that things are in no less agreementthan arithmetical computations. The errors, then lie not in the abstractness, not in geometryor physics, but in a calculator who does not know how to make a true accounting.

2.1.5.7 The Role of Experiment & Observation in Galileo’s ScienceThe Role of Experiment & Observation in Galileo’s Science

Galileo, carrying forward the work of the medieval thinkers, constructed a kinematicaltheory in his Discourses and Mathematical Demonstrations Concerning Two New Sci-ences Pertaining to Mechanics and Local Motion (1638), which bears similarity to thatof the Axiomatic structure in Euclidean geometry. The central question in the rivalrybetween Aristotelian and Platonic-Pythagorean traditions in Galileo’s thought is therole of the abstract mathematics and idealization, and its relation to the role of senseperception and practical experience.

Galileo’s thought on this issue has led many scholars (e.g. Koyre, Burtt, Drake,Settle) to debate his affiliation either to Platonism or to empiricism and experimentalscience:

i. Galileo did not belong to the experimental tradition in which (a) conditions wouldbe artificially created to show how nature would behave under previously unob-served, often previously non-existent circumstances, e.g., vacuum created by airpump, (b) the experimental conditions could be manipulated to coerce nature toanswer questions; what Francis Bacon described as “twisting the lion’s tail”.

ii. Galileo also differed from the Greeks who performed experiments with inflatedpig’s bladder that resist compression or experiment with clepsydra and pipette asdirect evidence for the corporeality of air.

iii. For Galileo experiments are designed to test already formulated hypothesis inorder to make it “more evident”, rather than deriving the hypothesis on the basisof experimental data. Thus, for Galileo, the job of observation/experience andexperiment is to render his basic mathematical principles immediately evident.

2.1.5.8 Quotations from Galileo on his Views on ExperimentQuotations from Galileo on his Views on Experiment

• Ex Suppositione: Conditions under which a mathematical definition will be veri-fied in nature to a determinate degree of approximation


Believe me, if I were again beginning my studies, I should follow the advice of Plato andstart with mathematics, a science which proceeds very cautiously and admits nothing isestablished until it has been rigidly demonstrated.

• Starting with Definitions, Axioms Galileo proved two Theorems which were es-sentially numerical:

(a) In Uniformly Accelerated Motion the spaces D1, D2, D3 . . . which are traversed insuccessive time interval bear to one another the ratio 1,3,5,7,. . . i.e. odd numbers. (TheDistance Theorem),(b) The spaces described by a body falling from rest with Uniformly Accelerated Motionare to each other as the squares of the time intervals. (Time Square Law).

Galileo, then, claims that without experiment this formulation is correct andsays:

No, and I do not need it, as without any experience I can affirm that it is so, because itcannot be otherwise, it is necessary that it should.

• Then goes on to show that the law thus obtained yield, on interpretation, empiri-cally testable predictions in terms of direct measurement.

The request which you as a man of science, make, is a very reasonable one; for this isa custom—and properly so—in those sciences where mathematical demonstrations areapplied to natural phenomena, as is seen in the case of perspective (optics) astronomy,mechanics, music, and others where the principles, once established by well-chosen ex-periments, become the foundations of the entire superstructure. I hope therefore it willnot appear to be a waste of time if we discuss at considerable length this first and mostfundamental question upon which hinge numerous consequences of which we have in thisbook only a small number placed by the Author, who has done so much to open a pathwayhitherto close to minds of speculative turn. So far as experiments go they have not beenneglected by the Author; and often, in his company, I have attempted in the followingmanner to assure myself that the acceleration actually experienced by falling bodies isthat above described.

2.1.5.9 Conclusions Regarding Galileo’s Attitude to Experiments and their Implica-tions for Science Education

Conclusions Regarding Galileo’s Attitude to Experiments and their Implications forScience Education

Since antiquity experiments formed an integral part of scientific activities. However,our notion of experiment during this period underwent radical changes (Section 2.1.4above). Galileo adopted a very special approach to experiment. According to theReceived View Galileo was the father of modern experimental science. The specificnature of his approach to experiment is not clearly spelled out in our discussion ofGalileo in the text books.

The Case Study here removes some of these misconceptions and enables us to geta better understanding of Galileo’s attitude towards experiment based on Toulmin’s

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notion of conceptual evolution and Nickles’ notion of generative justification. ForGalileo the purpose experiment, such as the incline plane experiment, was not tofind the law in its original discovery, but simply to make certain that in fact uniformacceleration as Galileo described may actually occur in nature. So far as Galileo wasconcerned, the truth of his law of falling bodies (i.e., V ∝ t) was guaranteed by itsexemplification of the simplicity of nature (what Holton calls a Thematic Presup-position) and the relations of integers, and not merely by a series of experiments orobservations. Galileo used empirical knowledge to support theories already arrived atand justified through some other means).

The Case Study also demonstrates that the notion of generative justification re-solves the conflict between individual versus social origin of ideas and effectsunification by looking at both the sources. It is also cognitive-historical as the Table3 below shows:

History of Science: Succession of precursor concepts & techniques and social determinants

Philosophy of Science: Responses to disciplinary pressure---a rational reconstruction

Concept Formation Techniques Epistemic Justification & Reality

Rational: Platonic- Pythagorianism

Metaphysical Empirical/ experimental

Galileo's experiment was designed to test already formulated hypothesis

Justifying the definitions & hypothesis on the principle of simplicity

Organizing the concepts inherited in an axiomatic framework & constructing proofs therein Geometric representation & Modeling

Individual: Concepts & techniques developed by Galileo

Social: Inheritance of concepts & techniques from the precursors of Galileo

Classification of Motion

Definition of Uniform & Non- uniform motion

Geometric representation & shift from Aristotelian qualitative to quantitative analysis

Discovery & Proofs of Mean-Speed & Distance Theorems

Hypothesis: V t Incline Plane

Experiment

Table 3: Generative Justification Account of Galileo’s Experiment on Freely FallingBodies

The cognitive-historical Case Study based on generative justification accountof Galileo’s experiment on freely falling bodies has the following implications forscience education. The Case Study

i. provides the students a more accurate view about the role Galileo assigned toexperiment in his scientific work by removing some of the misconceptions aboutGalileo’s notion of experiment,

ii. emphasizes the importance of modeling and representation in science education.Piaget and his followers (e.g. McKinson and Renner (1971), A.B. Arons (1990))


observed the gap in the early education in mastering reasoning involving ratiosthat poses serious impediments to learning science. This gap is especially evidentwhile dealing with comparisons of inhomogeneous physical quantities, such asdistance and time, acceleration and time or mass and volume. The Case Studyshows that Galileo’s analysis of uniformly accelerated motion in terms of ratioand its geometric representation was more natural than sudden introduction ofthe relevant algebraic formula, and

iii. attempts to resolve the conflict between individual versus social origin of sci-entific ideas with the help of Toulmin’s notion of conceptual evolution and Nickles’notion of generative justification.

3 Debate 2

3.1 The Debate Relating to the Nature of Scientific Knowledge: Whether it is ob-jective or relative to a conceptual perspective

It is said that before philosophy of science took what is sometimes called the cognitiveturn (mentioned in 2.1.2 above), it was preceded by two phases, viz.,

• the so-called linguistic turn emphasizing on objectivity and rationality of scientificknowledge and

• the socio-historical turn (mentioned in 2.1.1 above) highlighting the relativis-tic socio-historical nature of scientific knowledge (also called the conceptualperspective approach)

3.1.1 Linguistic Turn

For several decades Philosophy of Science was dominated by the logical empiricistapproach, which had two main aspects: (i) the claim that scientific theory involvesa “double language”, i.e., an observation language and a theoretical language, and thelater could be translated completely in terms of the former by reducing the theoreticalterms contained in the theoretical language to the observational terms of the formerlanguage denoting sensations. (ii) the main problem in philosophy of science is tosearch for an appropriate method and logic of justification and confirmation of scientificlaws and theories and not how they are arrived at in the first place. The main objectiveof the logical empiricists was to investigate how, using only the techniques of formallogic, scientific knowledge could be linked with sense experience.

The epistemological underpinning of the logical positivistic view was to provide astrong foundation to science by claiming that the observation sentences are the oneswhich precisely provide this foundation as they are the direct expressions of givenexperience, and hence, are certain, indubitable, incorrigible reports of the empiricalworld. All other knowledge is logically derived from them. The item (i) above explainsthe objectivity and realism of scientific theory and knowledge and (ii) accounts forscientific rationality.

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3.1.2 Socio-historical Turn: Relativistic Conceptual Perspective Approach to Phi-losophy of Science:

The relativistic socio-historical view was advocated very forcefully by Hanson, Kuhnand Feyerabend. The role of the conceptual perspective on the epistemology ofscience is significant as it determines the class of legitimate problems, delimits thestandards for their acceptable solution, and specifies the epistemic grounds involvedin the historical and sociological factors responsible for the discovery, development andacceptance or rejection of scientific theories. The main emphasis within the relativisticsocio-historical view on Philosophy of Science was to study of the internal and externalhistorical factors responsible for theory change and the epistemological and ontologicaltheories that provide justification for such changes.

Thus, Philosophers of Science began to pay more attention to historical and psy-chological factors that influence scientific work and practices. On the other hand, thehistorians of science derived more inspirations from the work of the sociologists, sub-scribing to the claim that scientific knowledge is a social product. Their investigationof the social context of science for the proper understanding of scientific practices gavethe discipline of historiography of science a sociological turn.

However, in contrast with a static model of human knowledge of the logical posi-tivists the proponents of the conceptual perspective and the socio-historical view ofscience provided a dynamic account of scientific knowledge.

3.1.3 False Dichotomy Again: Unending Controversies

The socio-historical approach to the evolving nature of scientific knowledge takes thecanons for evaluating what to admit as scientific knowledge not only as relative to agiven conceptual perspective, but also as variable from one historical period to another.Although the canons of rationality and justification change and are relative, but theconditions characterizing the nature of knowledge, as spelled out in the Logical Posi-tivistic view on Knowledge, i.e., construing knowledge as justified true belief, remainthe same.

In spite of its role in exposing the deficiencies of a static, ahistorical and extremeempirical nature of scientific knowledge of the Logical Positivists and replacing itby a more historically sensitive account of scientific knowledge based on an analysisof actual scientific practices, the conceptual perspective approach led to an extremeepistemic relativism. The epistemic view turned out to be so permissible as to acceptanything as knowledge as long as any science permits it to enter into its domain andto take any change in the canons leading to corresponding change in what counts asknowledge. This goes against the very basic notion of science as an enterpriseproviding objective knowledge where the central aim of science is to find outhow the world really is.


3.2 Epistemic Norms and the role of the Cognitive-ecological Factors in the Ac-quisition of Knowledge: Naturalization of Epistemology and the Demise of theInferential Justificatory Account of Knowledge

The recent developments indicate that a viable epistemology of science not only needsto take into account the actual scientific practices as revealed by socio-historical stud-ies, but also establish linkages with Cognitive Science and its programme of natural-ization of epistemology. This may provide a way out of the impasse due to subjectivismand relativism to which the Conceptual Perspective analysis reduced the contemporaryphilosophy of science and its epistemology.

The historical account of the development of science show that despite scepticalwarnings the success of scientific investigations enabled us to gather much usefulknowledge about the universe. This is what impressed our philosophical forebears,such as Locke and Kant, who were concerned with the task of understanding thenature of science as a paradigmatic knowledge-yielding enterprise that is concernedwith employing conceptual devices aimed at discovering how the world really is and thecharacteristic regularities of the real world. In view of the new sceptical onslaughts,such as Gettier type paradoxes and riddles of induction this task has assumed newimportance.

3.2.1 Cognitive Processes and Ecological Factors

If one of the goals of epistemology is to account for the way science comes to haveknowledge of how the world really is, then one must pay more attention to the cognitiveprocesses, including the ecological factors, involved in acquiring this knowledge. Anunderstanding of the nature of epistemic norms will remain incomplete as long as itis not integrated into a more comprehensive account of the cognitive and ecologicalfactors and their interactions that form part of the functioning of the epistemic agent.Only in the recent past more attention is being paid to the role of the cognitive andecological factors in such important issues in philosophy of science as scientific observa-tion/experiment, formation of concepts and categorization, model building and theorychange. This section attempts to provide an outline of this approach and its relevanceto the formulation of epistemic norm.

3.2.2 Scientific Knowledge and Naturalization of Belief and Knowledge: The Interaction-Information Theoretic Account of Observation and Belief/Knowledge

The cognitive, ecological, interactive and information theoretic approach, advocated,among others, by Goldman23, Dretske24, Barwise and Perry25, J.R. Anderson26, J.J. Gib-son, may be construed as denial of the justificatory account of knowledge (involving the

23Goldman, A.I.: 1986, Epistemology and Cognition, Harvard University Press, Cambridge, MA.24Dretske, Fred: 1981, Knowledge and the Flow of Information, MIT Press/Bradford, Cambridge, Mass.25Barwise, J. & Perry, J.: 1983, Situations and Attitudes, MIT Press, Cambridge, MA.26Anderson, J.R.: 1990, The Adaptive Character of Thought, Hillsdale, Erlbaum, NJ.Anderson, J.R.: 1991, The adaptive nature of human categorization, Psychological Review, 98, 409-429Anderson, J.R.: 1991, Is human cognition adaptive?, Behavioral and Brain Sciences, 14, 471-517

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base statement and inductive inferential view).Epistemic acts, such as observation, according to this view, is said to involve suc-

cessive type of states or situations where information flows from one type of state orsituation to another. Thus, in observation the information that “x is P”, where x andP are features of the physical world is carried from the object to the sense organs orreceptors through a process of interaction between the two. This interaction relationleading to information flow is based on a nomic regularity/constraint holding betweenstate or situation type where one involves the other, e.g. the fact that the X-ray hassuch and such a pattern carries information about/involves/indicates that Jackie hasa broken leg.

3.3 The Issue of Appropriate Framework for Representing Information

The dominating view on representing information, belief and knowledge has been var-iously called the language centered, propositional or symbolic/syntactic view.In the context of Cognitive Science and AI, this view has been endorsed by Fodor27,Pylyshyn28 and Newell and Simon29. The theses of language of thought or mentaleseand physical symbol system hypothesis forcefully articulated the language centered,propositional or symbolic syntactic view on representing information, belief andknowledge.

This language centered, propositional or symbolic/syntactic view is facedwith several difficulties :

i. the symbol grounding problem: How can the meanings of the meaningless symboltokens, manipulated solely on the basis of their arbitrary shapes be grounded orconnected up with the world in the right way?

ii. the frame problem: Assuming that an intelligent agent is capable of planning andproblem solving and given the fact that she is acting, can we specify in symbolicformalism what changes and what remains constant in the particular domain?Classical symbolic systems are monotonic, whereas planning and problem solvinginvariably involve new experience and change.

iii. the problem of induction: Mere symbolic representation does not lend itself eas-ily to model judgements of similarity and to identify projectible predicates thatdenote natural kinds. Both Goodman and Quine taught us that these issues areintimately related to the problem of induction.

The basic problem with systems using propositional and symbolic representation isthat they are disjoint from non-symbolic system (i.e. the world). Hence, there must besome point where the information from the world is presented in symbolic form.

27Fodor, J.A.: 1981, Representations, MIT Press, Cambridge, MA.28Pylyshyn, Z.: 1984, Computation and Cognition, Bradford/MIT Press, Cambridge,MA.29Newell, A. & Simon, H.: 1976, Computer Science as Empirical Inquiry: Symbols and Search, CACM, 19,

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3.3.1 Two Important Issues

There are two important issues here:

i. how a system using propositional or symbolic representation takes in informa-tion from a non-symbolic world? This is what S. Harnad30 called the SymbolGrounding Problem.

ii. how does a cognitive system distinguish and grasp non-logically the predicatesthat denote natural kinds or natural properties, which represent things that existin reality, make the scientific laws describe the processes that actually take placein nature or scientific induction possible?

3.3.2 Conceptual Space Approach as a Framework for Representing Information:An Information Theoretic Approach to Observation and Concept Formation

Many cognitive scientists31 claim that symbolic and cognitive structures are percep-tually grounded. This, however, involves an analysis of (a) what role the informationat the sub-symbolic level play in the explanation of in various epistemic, knowledgeacquisitive and cognitive acts, such as observation, and (b) how (a) lead to formationof concepts and categories, which finally give rise to formulation of knowledge at thelinguistic level.

J.J. Gibson32 and David Marr33 (especially while dwelling on his first two modules,viz., Primal Sketch and 2 1/2 D) provided an analysis of 3.3.2. (a) mentioned abovewith specific reference to visual information.

Gibson offers an analysis of optical information in which appearance in the sense ofthe way things are is directly given in visual information and not inferred. Therefore,his view is sometimes called Theory of Direct Perception (TDP). TDP comprises oftwo separate investigations:

• one involves examining the perceiving organism,

• the other concentrates on the what of perception, examining the visible worldexternal to the organism.

Gibson terms the latter inquiry Ecological optics, which involves finding envi-ronmental properties that can be uniquely and invariantly specified in the structure ofthe reflected ambient light in the form of an optic array. The structure of the reflectedambient light depends upon the structure of the surface of the perceived object. Unlike

30Harnad, S.: 1990, The Symbol Grounding Problem, Phisica D 42, 335-346.31Johnson, B.: 1987, The Body in the Mind: The Bodily Basis of Cognition, University of Chicago Press,

Chicago, Ill.Lakoff, G.: 1987, Women, Fire, and Dangerous Things, University of Chicago Press, Chicago, Ill.Langacker, R.W.: 1987, Foundations of Cognitive Grammar, 1, Stanford University Press, Stanford, CA.32Gibson, J.J.: 1950, The Perception of the Visual World, Houghton Mifflin, BostonGibson, J.J.: (1966), The Senses Considered as Perceptual System, Houghton Mifflin, BostonGibson, J.J.: 1979, The Ecological Approach to Visual Perception, Houghton Mifflin, Boston33Marr, David: 1982, Vision, Freeman, San Francisco

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the radiant light from a light source, the structure of the reflected ambient light isresponsible for the perception of distance, depth, motion etc. For Gibson the structureof the reflected ambient light does not carry/convey information, it is information.The job of the perceptual system is merely to pick up the information by orienting,adjusting, resonating and tuning to the light input. Thus Gibson treated the problemof perception as that of recovering from sensory information valid properties of theexternal world.

However, as Marr points out, Gibson’s analysis is incomplete. Gibson failed to real-ize the fact that the detection of physical invariant, like image surfaces, is exactly andprecisely an information-processing and cognitive problem. Secondly, Gibson vastlyunderrated the sheer difficulties of such detection.

Marr, then, goes on to provide an elaborate analysis of how the information providedat the Primal Sketch and 2 1/2D levels lead to identification and categorization of 3-Dobjects as we ordinarily recognize them.

3.3.3 Gardenfors’ Notion of Conceptual Space

The analyses of Marr and Gardenfors appear to be complementary to each other andare relevant to 3.3.2. (b) mentioned above.

Peter Gardenfors34 offers an answer to the second issue by suggesting a hybrid threetier cognitive system with (a) sub-conceptual, (b) conceptual and (c) higher symboliclevel. For the traditional empiricist thinkers, such as Locke and Hume, the bridge be-tween the external world and mind was provided by impressions, ideas and associationsbetween them. Marr also accepts a three level analysis in which sub-conceptual levelof primal sketch and 2 1/2D plays an important role in modeling perceptual knowledge.

Gardenfors, however, introduces a nonlinguistic and non-logical way of representinginformation and knowledge in terms of his theory of Conceptual Space in which theobjects of the representation no longer form a language or have even a propositionalstructure. Gardenfors treats his knowledge representation framework as “cognitive”and bases it on analogical representation. He treats this as an alternative to linguistic,propositional or Fregean representation and shows its drawbacks.

For Gardenfors conceptual space is “a cognitive entity”, which he claims is “ontologi-cally prior to any form of language”. A conceptual space is a set of pre-linguistic qualitydimensions that are closely connected to what is produced by our sensory receptors.Typical example of quality dimensions is color, length, weight, temperature, time etc.,which represent various qualities of objects by assigning properties to them and speci-fying relations between them. Each quality dimension has a geometrical, topological ormetrical or just an ordering structure, rather than syntactic or logical structure, as insymbolic models, or associations, as in connectionist model.

Gardenfors’ quality dimensions are psychological dimensions and not scientific ortheoretical ones. For example, he distinguishes the psychological interpretation of hue

34Gardenfors, P.: 1990, Induction, conceptual spaces and AI, Philosophy of Science, 57, 78-95Gardenfors, P.: 1991, Framework for Properties: Possible World vs. Conceptual Spaces, Acta Philosphica

Fennica, 49, 383-407Gardenfors, P.: 1992, Three Levels of Inductive Inference Lund University Cognitive Studies, 9


in terms of the color wheel and the scientific or theoretical interpretation in terms ofwavelengths of light. However, for him the quality dimension precedes and providesthe basis for symbolic and conceptual representation.

How does Gardenfors notion of conceptual space grasp non-logically the predicatesthat denote natural kinds or natural properties, which represent things that exist inreality and also make induction possible and distinguish them from other properties?

3.3.4 How are the Basic Projectible Predicates get Established?

Gardenfors makes a constructive use of his notion of conceptual space and uses it asa basis for formulating a new criterion of what a property is. He goes on to representa property as a region in a conceptual space. And defines a natural property as repre-senting a space which is convex in the following sense: if a pair of points a and b are inthe region, then all points between a and b are also in the region.

This definition of natural properties makes them perceptually grounded, i.e., forthese properties there is a direct link between the convex region of the conceptual spacewith its quality dimensions and perception.

According to Gardenfors the predicates green and grue differ from each other, be-cause green designates a property that can be represented in a convex region, whilegrue cannot be represented by a convex region, because the predicate grue involvesboth color as well as time dimensions (i.e. an object has the property grue, if it isexamined before time t and determined to be green, or it is not examined before time tand it is blue).

3.3.5 Natural Properties, Similarities and Induction

Gardenfors contends that the projectible predicates are the predicates, which designatenatural properties and that only these predicates make inductive inferences possible.He also goes on to define a relation of comparative similarity in terms of a conceptualspace by letting two objects count as “more similar to each other the closer their set ofproperties is located in the underlying conceptual space”.

Gardenfors claims that humans generally agree as to which properties are theprojectible ones. This suggests that humans have close to identical psychological con-ceptual spaces. The evolutionary theory and natural selection explain why “our way ofidentifying natural properties accords so well with the external world as to make ourinductions tend to come out right” and demonstrate that our inductive capacities aredependent on the “ecological circumstances under which they have evolved”.

3.4 Case Study on Galileo: The Cognitive-historical Aspects of Science

My intention in the Case Study on Galileo is not to demonstrate that the current ideason properties, projectible predicates and concept formation are present in Galileo’swork. That would amount to doing, what Butterfield called, whig history.

What I would, however, like to show is that Galileo was concerned with the prob-lem of the fit between his law abstractly arrived at within an axiomatic framework

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by providing a geometric representation of the physical problem and the physical phe-nomenon he was investigating. He resolved this by

• making a distinction between primary and secondary qualities and insisting thatthe law must be couched only in terms of primary qualities, and

• appealing to certain thematic presuppositions, e.g. simplicity, while justifying hischoice of a hypothesis or law.

The new science Galileo Galilei (1564-1642) was involved in developing was con-fronted with many methodological, epistemological and metaphysical issues. He says:

My purpose is to set forth a very new science dealing with a very ancient subject. There is, innature, perhaps nothing older than motion, concerning which the books written by philosophersare neither few nor small; nevertheless I have discovered by experienza some properties of itwhich are worth knowing and which have hitherto not been either observed nor demonstrated.Some superficial observations have been made, as, for instance, that the free motion [natu-ralem motum] of a heavy falling body is continuously accelerated;∗ but to just what extent thisacceleration occurs has not yet been announced . . . (Italics mine)

In relationship with Galileo’s scientific claim contained in the last sentence in thequote there are several cognitive/epistemological questions “How do we know?, Whydo we believe in something?, What is the evidence for?”, How did Galileo developthe scientific concepts?”, “How did he go on to justify the introduction of a concept?” Another set of partly scientific, partly sociological problems arises with regard thevalidation and acceptance of scientific theories. Moreover, there are the metaphysicalproblems concerning “reality” of entities that transcend our senses or the assumptionof certain properties that can form the basis for doing science, e.g. in Galileo’s case, theprimary qualities.

Understanding what Galileo contributed goes much beyond the law of freely fallingmotion and the concept of uniformly accelerated motion he formulated or being able tocalculate how fast the stone falls when we drop it from a certain height. Understandingthe ingredients of his scientific inquiry and imagination must form an integral part,not as additional material to the calculation, but as issues intrinsically arising out ofthe understanding and presentation of the technical material in order to develop thecapacity for abstract reasoning based on practice and experience, problems relatingto relevant concept formation, modes of appropriate reasoning/thinking, perceivingrelationships. This effort may include removing certain misconceptions.

From this point of view Galileo’s main achievements were

• welding together the works of the anti-Aristotelian’s of the past two centuriesor so and develop a Philosophy of Science by raising certain methodologicalissues.

• presenting a consistent, reasonable conceptual scheme that was descriptive ratherthan teleological, i.e. he was not concerned with final causes.


3.4.1 The Methodological Issues Raised by Galileo

Galileo’s concern with the fit between an abstract mathematical theory and its ap-parently arbitrary definitions and facts that they are designed to explain. He asksthe question: How does an abstract mathematical theory and its apparently arbitrarydefinitions fit the facts? Fruitful insight as to what was Galileo’s answer can be derivedfrom what Galileo himself emphasizes in his approach:

Galileo was acutely conscious about the fact that he was defining new conceptsand not “discovering” objects. He was concerned that the definition should best fit thenatural phenomena. In the Discourses and Mathematical Demonstrations ConcerningTwo New Sciences he says:

Since all definitions are arbitrary, I may . . . be allowed to doubt whether such a definition asabove, established in an abstract manner, correspond to and describe that kind of acceleratedmotion which we meet in the nature in the case of freely falling bodies.. . . some have imagined helices and conchoids as described by certain motions which are notmet within nature and have very commendably established the properties which these curvespossess in virtue of their definitions, but we have decided to consider the phenomena of bodiesfalling with an acceleration such as actually occurs in nature and to make this definition ofaccelerated motion exhibit the essential features of observed accelerated motions.

Galileo formulates his hypotheses regarding the nature of motion first and thengoes on check them in terms of experiments and not the other way around.

3.4.2 Galileo’s Solution

Galileo was looking for an answer to the same problem we discussed in the Section 3.3above. Galileo’s solution to this problem is based on

i. his belief in one of the metaphysical/thematic Presuppositions, viz., simplicity ofnature. Galileo invokes this in the following way:

. . . in the investigation of naturally accelerated motion we were led, by hand as itwere, in following the habit and custom of nature herself, in all her variousother processes, to employ only those means which are most common, simpleand easy. For I think no one believes that swimming or flying can be accomplished in amanner simpler or easier than that instinctively employed by fishes and birds.When . . . I observe a stone initially at rest falling from an elevated position and con-tinually acquiring new increments of speed, why should I not believe that such in-creases occur in a manner, which is exceedingly simple and rather obviousto everybody? If now we examine the matter carefully, we find no additionor increment more simple than that which repeats itself always in the samemanner. (Emphasis mine)

Proceeding on this principle of simplicity in nature Galileo considers two hypothe-ses which are both simple, viz.

(1) V ∝ T (2) V ∝ D: speed increase in proportion to distance traveled.

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He rejects (2) on grounds that are not completely sound (as he thinks that thissimple assumption leads to an inconsistency, while the other does not) and adopts(1), largely because he has the deeply rooted hunch that it is correct.

ii. Galileo’s distinction of qualities: Galileo makes a distinction between:

• Primary qualities: those qualities which admit of systematic quantitativedescription relative to a scale, e.g. distance, length, shape, size, time, position. . ..

• Secondary qualities: those qualities, which exist only in the mind of theperceiver, e.g. taste, odour, sound, colour, etc.

In IL SAGGIATORE Galileo writes:I think that these tastes, odors, colors, etc., on the side of the object in which they seem toexist, are nothing else than mere names, and hold their residence solely in the sensitive body;so that if the animal were removed, every such quality would be abolished and annihilated.Nevertheless, as soon as we have imposed names on them, particular and different from thoseof the other primary and real accidents, we induce our selves to believe that they also exist justas truly and really as the latter.

Galileo’s criterion of demarcation and the criterion of acceptability. Galileo

• withdraws the attention of science from the realm of unquantifiable secondaryqualities, i.e., he restricts the scope of science to assertions about primary quali-ties and their relation alone, and

• excludes taleological explanation from the range of permissible discourse in Sci-ence.

Consequently, Aristotelian explanation of freely falling bodies in terms of naturalmotion towards natural place does not qualify as scientific explanation, because itfails to explain the phenomenon. According to Galileo, it is not a bona fide sceintificexplanation to claim that a motion takes place in order that some future state may berealized.

3.4.3 Conclusion

A review of the second debate, the survey of the recent work on concept formation inCognitive Science and the Case Study of Galileo provide evidence that go on to showthat the information about the way the world is and theorizing about it may lead toobjective claims regarding the world provided the processes of the formation of conceptsinvolve an account of (a) the interaction between the features of the physical world andthe cognizer, and (b) the information about the features of the world is represented andrevised in a frameworks which also includes the sub-symbolic level.

Galileo’s answer to the problem was based on (i) his belief in one of the ThematicPresuppositions, viz., simplicity of nature, (ii) his classification of properties in terms ofprimary (quantifiable) and secondary qualities, and his demand that scientific conceptsare articulated in terms of primary qualities alone, and (iii) his abandonment of thesecondary qualities as well as teleological explanations.


3.5 Final Remarks on the Implications of the Case Studies for Science EducationProgramme

The Case Studies on Galileo that I have chosen may appear to be antiquirian. Thisis deliberate. Galileo’s scientific writings and scientific work are instructive in moresense than one. It provides a rich context for many important pedagogical issue, suchas introduction and proper understanding of new concepts, distinction between obser-vation and inference, model building and mathematical representation, formulation ofhypothesis, laws and their linkages to observation and thematic presuppositions, thequestion of justification, etc. The standard textbook presentation of Galileo’s kine-matics suppresses the intellectual history, the context and the process of scientificinquiry by hurrying through the final product in the form of the laws he formulated.As a result it fails to use this significant episode at an early stage of science withrelatively simple subject matter as an illustration of various facets of modern scientificthought and inquiry. Our science pedagogy would be immensely richer by incorporatingan examination of such intellectual dimensions and putting a little less emphasis ontechnical science.

Pedagogy of science ostensibly enables the students to also learn “strategies andtactics” of problem solving and generating representations of scientific knowledge. TheReceived View on the cognitive processes involved in such procedures, such as inductionor linear conception of experimental discovery, appears to be highly deficient (Nerses-sian, 1989 and Gooding, 1989). The Cognitive-historical and generative justificationapproaches discussed above in the case studies can provide different realistic exem-plars of scientific problem solving. Thus, the standard laboratory experience can besupplemented by incorporating such exemplars, which will give students an opportu-nity to examine other problem solving procedures or to develop their own insights intoconstructing or changing representations of conceptual structures in science.

Conceptual Change in the Learning of Science

Stella VosniadouUniversity of Athens, Greece. Email: [email protected]

Why is Science Learning Difficult?

Cognitive science and science education research has shown that students have a greatdeal of difficulty understanding science concepts. This applies even to students whoperform above average in terms of test scores and teacher evaluations, and even aftermany years of science instruction (e.g., diSessa, 1993). In addition to the difficultyof understanding, science learning seems to be accompanied by misconceptions. Mis-conceptions have been noted in practically all subject areas of science. Hundreds ofmisconceptions enough to fill out tens of volumes have been reported in the literature.1How can we find out why science learning is so difficult?

For many years now, researchers in this area have realized the need to pay moreattention to the actual content of the pupils ideas, and to understand how these ideasdevelop in order to formulate a coherent theoretical framework for guiding researchin science education (see for example, Driver and Easley, 1978, Novak, 1977). It isonly on the basis of such a developmental theory that we can make informed decisionsabout the design of science curricula as well as about instruction. In this paper I willargue that cognitive developmental research can provide rich descriptions of the knowl-edge that students have about science at different ages and about how this knowledgechanges. I will describe some of the findings regarding the processes of conceptualchange in science derived from research in my lab and will draw their implicationsfor instruction. I hope that in the process the readers will find some answers to thequestion: “Why is science learning difficult?”

The Conceptual Change Approach

A few years ago I attended a workshop on the topic of learning and teaching science.The workshop was composed mostly of researchers and teachers in science educationand a few developmental psychologists who did research on the development of scienceconcepts. I was very surprised to discover that main theoretical framework that guidedthe science educators’ teaching and research was basically an empiricist framework.What I mean by an empiricist framework is the idea that learning science involvesmainly the enrichment of prior experiences. According to this framework, knowledgeis continuous, it develops from concrete to abstract, and is mainly characterized byenrichment. What we need to do when we teach science is expose children to richhands-on experiences. Through these experiences they are going to eventually learnscience.

1See the Proceedings of the First and Second International Seminars on “Misconceptions in Science andMathematics” edited by J.D. Novak (1987) and Helm, Hugh and Novak (1983).

164 Conceptual Change in the Learning of Science

In this framework there is no realization that childrens’ initial knowledge, basedon their every day experiences may stand in the way of understanding the currentlyaccepted scientific ideas. The conceptual change approach to be described below is avery different approach. More specifically, the following claims are being made aboutthe process of learning science.

i. The human mind has developed, through evolution, specialized mechanisms topick up information from the physical and social world. This results in very quickand efficient learning that starts immediately after birth. Some kinds of thingsare easy to learn, not because what is learned is less complex but because humanbeings are prepared through evolution for this kind of learning. This seems toapply to the learning of language and to intuitive physics. Intuitive physics isthe knowledge about the physical world that develops early in infancy and allowschildren to function in the physical environment.

ii. Learning which is acquired early in life and which is not subject to consciousawareness and hypothesis testing can stand in the way of learning science. Thishappens because scientific explanations of physical phenomena often violate fun-damental principles of intuitive physics, constantly confirmed by everyday expe-rience. After all, the currently accepted scientific explanations are the productof a long historical development of science characterized by revolutionary theorychanges that have totally restructured our representations of the physical world.

iii. Conceptual change is required in the learning of many science concepts (andnot only science). This is because the initial explanations of phenomena in thephysical world are not unrelated and fragmented but are organized in an intuitiveframework theory.2 That constrains the process of acquiring further knowledgeabout the physical world and can cause misconceptions. Many misconceptionscan be explained as synthetic models formed by individuals in their effort toassimilate new scientific information into their framework theory. The changeof the framework theory is difficult because it represents a coherent explanatorysystem based on everyday experience and is tied to years of confirmation.

From a conceptual change point of view the questions that are important to answerare questions such as the following: What is the nature of initial conceptual structures?Are they actually organized in a coherent theoretical framework? If so, how do thesetheoretical frameworks change? How is conceptual change achieved?

In the pages that follow I will argue that children do have an initial, intuitive,framework theory about the physical world. I will argue that this theory has content.I will describe this content in terms of presuppositions, beliefs, and mental models. Iwill also argue that this framework theory has a structure and I would describe thisstructure in terms of framework theories and specific theories. Another issue I would

2The term theory is used to denote a causal explanatory framework. We do not claim that frameworktheories are similar to those of scientists and we further assume that they are not available to consciousawareness and hypothesis testing.

Vosniadou 165

like to raise here is the issue of metaconceptual awareness. It appears that youngchildren have conceptual structures that are relatively well organized but they are notmetaconceptually aware of the knowledge that they have. By that I mean that theyare not aware of the actual beliefs and presuppositions that constrain the knowledgeacquisition process, neither do they recognize that these beliefs are hypotheses subjectto falsification. This is a very important difference between children’s theories (tothe extend that we can call them theories) and scientific theories. When we come toconceptual change, I will tell you about synthetic models and what they are. Finally, Iwill pay a lot of importance to the sequence in which concepts are acquired in a givensubject-matter area.

The Observational Astronomy Research Project

Let me give you a general description of the kind of research that my colleagues andI have been doing. We started this research when I was in the United States, atthe University of Illinois, with William Brewer. We investigated elementary schoolchildren’s understanding of observational astronomy. The studies that we did wereabout the shape of the earth, about the day and night cycle, explanations of the seasonsand of the weather, and of the phases of the moon/explanations of the phases of themoon. We tried to understand how children’s knowledge in this area changes during theelementary school years (Vosniadou & Brewer, 1992, 1994). We also conducted a greatdeal of cross-cultural research. I had a student, at that time, Ala Samarapungavan,who came to India to do a study of Indian children (Samarapungavan, Vosniadou, &Brewer, 1997). I did several studies in Greece, while a student in anthropology from theUniversity of Illinois went to Samoa and collected data from children there (Vosniadou,1994). Other people took our questionnaire and did studies in Australia, England,Germany, etc.

The methodology we use is that of a clinical interview in which children are askedquestions from a pre-designed questionnaire. The children are also asked to makedrawings and/or play dough models, or select among ready made physical models. Wepay a lot of attention to the distinction between factual and generative questions. Afactual question is a question like “What is the shape of the earth?” and a generativequestion is a question like “If you were able to walk for many days would you be ableto reach the end of the earth? Is there an end to the earth?”

The difference between the two types of questions is the following. Factual questionscan be answered if the children have memorized in a superficial way information taughtat school. It is possible however that children do not really understand the informationtaught at school. When children say that the day/night cycle happens because the earthturns around its axis, do they really understand this explanation? Do they know whatits implications are? Or is it the case that they have memorized the explanations givenin school without really understanding them. The generative questions try to find thisout.

Generative questions ask children to think about situations to which they have notbeen exposed in the regular school. We present them with a new, productive problemthat they have to solve. If they have really understood the scientific explanation, then


they can give a scientific answer. For example, if they have understood how the dayand night cycle happens through the earth’s rotation, they can provide scientificallycorrect answers to questions like “What do we need to do in order to make it day timealways in Bombay?” It is possible, however, that when we ask children the generativequestion mentioned above they say things like the following: “you need to make themoon disappear” or “you must have the sun in the sky all the time.” The kinds ofanswers we get from the factual questions are very different from the kinds of answerswe get from the generative questions.

On the basis of children’s responses we try to understand children’s representations,or their mental models. We are interested in finding out whether children use the samemental representation to answer all the questions in a consistent fashion. Indeed wehave found that it was possible to account for approximately 85% of the children’sresponses on the basis of the consistent use of one of a small class of mental models ofthe earth (Vosniadou & Brewer, 1992) and of the day/night cycle (Vosniadou & Brewer,1994).

In the case of the shape of the earth we have identified six different kinds of mentalmodels held by elementary school children (in our American sample). These modelsrepresent the intuitive view of the earth as a flat, supported rectangularly-shapedphysical object, the scientific view of the earth as a physical unsupported, astronomicalobject, as well as a number of intermediate views (see figure 1). Most of the childrenin our sample used mental models of the earth that showed a combination of intuitiveand scientific views. We have identified four such mental models: the disc earth, thedual earth, the hollow sphere and the flattened sphere. According to the disc earth, theearth is both round and flat and has an end or edge from which people can potentiallyfall. In the dual earth, children think that there are two earths: a flat one on which welive and a spherical one which is a planet in the sky. The children who believe in thehollow sphere model think that the earth is spherical outside but the people live on flatground inside the earth. Finally, according to the flattened sphere, the people live onthe outside of the earth but on flattened pieces of ground.

If we examine all these representations, we see that they have some things incommon. What they have in common is that they all try to incorporate on the onehand the information that the earth is spherical, coming from instruction, and on theother hand, the information they receive from everyday observation that the earth isflat and people live on top of this flat earth. They represent an attempt to synthesizeinitial, intuitive beliefs about the earth with currently accepted scientific information.For this reason we have called them synthetic models.

We have explained the formation of synthetic models by assuming that children’sunderstanding of the scientific concept is constrained by certain beliefs or presupposi-tions that have their origins in their intuitive framework theory. One is the belief thatthe earth is basically flat, and the other is the belief that the objects on the earth needto be supported, otherwise they will fall down. We know from psychological studiesthat even 6-7 month old infants understand that when you drop an object it will fall onthe ground. This evidence has been interpreted to indicate that young infants form anelementary up-down gravity concept.

Vosniadou 167

Scientific Model

Synthetic Models

Initial Models

Sphere

Flattened Sphere

Hollow Sphere

Dual Earth

Disc Earth

Rectangular Earth

(a) (b)

Figure 1: Mental models of the earth.

If it is indeed the case that children hold a belief in up-down gravity then we wonderhow this belief can make it difficult for them to understand how people on the outsideof a spherical earth live without falling down! I have looked at the curricula usedto teach astronomy in Greece and in the United States and I have never found anyattempt to explain to young children how it is possible for people to live on the sphericalearth without falling, or how it is possible for the earth to be spherical and flat at thesame time. Information regarding the spherical shape of the earth is introduced bythe teachers in the classroom in a straightforward, factual manner. Often, a globe isused, or sometimes the teachers show a picture of the globe in a book, or a picture ofthe earth as we see it from the moon. Teachers usually believe that it is very easy tounderstand that the earth is spherical and that the concept of a spherical earth doesnot really require any explication.

So there is no explanation provided to children of how it is possible for the earth tobe spherical and flat at the same time, despite the fact that our everyday perception isof a flat earth. And there is no attempt to say anything about gravity and to explainhow it is possible for people to live on the spherical earth without falling down. Gravityis a concept addressed later on when children are taught about mechanics, not in the


context of observational astronomy.What I am trying to say is that the kind of instruction we give to children is

inadequate. It does not provide explanations to the legitimate questions that thechildren may have, assuming that they have formed a representation of the earth onthe basis of their everyday experience. Teachers of science and curricular designersdo not take into consideration that children may have formed such possible initialrepresentations of the earth. They think (based on the empiricist framework describedearlier) that since children have not been instructed in science, they do not knowanything about the earth. They also think that the concept of a spherical earth issuch a simple and easy to understand concept. I remember that when we started thesestudies we actually wondered whether we would find any children who will have aconception of the earth different from the spherical one. We were so immersed in thistradition ourselves and I remember we had to go to preschoolers to find out that theyindeed believed the earth to be flat.

In an attempt to explain these findings we came to the idea of an intuitive frame-work theory of physics. The idea is that from very early on children construct aframework theory of physics that contains the ontological presuppositions that definewhat is a physical object and how physical objects move in space. So you would find herethe information that physical objects are solid and stable, that the space is organisedin the direction of up and down, and that physical objects fall down when we dropthem. The framework theory also contains some epistemological presuppositions likethe presupposition that things are as they appear to be (appearance is reality).

So the idea is that such a framework theory of physics is formed very early on andforms the basis of our physical knowledge. Obviously, we have a great deal of physicalknowledge, otherwise we would not be able to move around in the physical world.

It is further assumed that the framework theory constrains the way we interpretobservations such as that the ground extends along the same plane over a great dis-tance, that the sky is located above the ground, that the sun, the moon, and the starsare in the sky, and that there is ground or water below the ground. The interpretationsof such observations are used to form intuitive theories, about the earth, the day/nightcycle, the seasons, etc.

We make a distinction between presuppositions that belong to the framework theoryand beliefs that belong to more specific-theories. We think this distinction is importantbecause it can explain why some beliefs are easier to change than others. For example,it is not very difficult to change the belief that the earth is supported by ground, or thatthe earth does not move, or even that the earth is flat. But, it appears that it is verydifficult to change the up/down gravity presupposition and the organization of spacein terms of the direction of up and down. These presuppositions constrain childrens’understanding and explain synthetic models in which the earth is represented as roundor spherical but where the people live on its top or inside it.

To summarize, the results of our experiments showed a relatively small numberof the mental models of the earth, that could be grouped into initial, synthetic andscientific. The synthetic models are constrained by certain underlying presuppositions,such as that the organization of space is in terms of the direction of up and down

Vosniadou 169

1. The sun goes down, on the ground, behind mountains, and the moon comes up.

2. The sun goes down, to the other side of the earth, and the moon comes up.

3. The earth rotates in an up/down direction. The moon and sun are located at opposite sides.

4. The earth rotates in an east/west rotation. The sun and moon are located at opposite sides.

Figure 2: Mental models of the day/night cycle.

and that gravity pulls physical objects down to the ground. These two presuppositionsseem to be the main barriers to children’s understanding of the spherical shape of theearth. If our hypotheses are correct, it means we need to pay particular attention tosuch presuppositions, when we teach the shape of the earth. If we deal with thesepresuppositions we have a better chance of being more successful in teaching childrenthe spherical shape of the earth.

Before finishing I would like to say that teachers are not aware of the ideas andmisconceptions that students have. Usually science is taught in a factual way, whereteachers explain the scientific view and then ask a few questions to see if the scientificexplanation can be repeated. Sometimes teachers are really afraid to ask too much.Because in some areas like science they feel themselves insecure about their knowledgeof science. They do not want to raise any questions because they feel they might not beable to answer. The communication that goes on in the classroom is very superficial. Itis a big problem in science education that the teachers are not well trained in sciencethemselves and this affects their ability to teach science.

There is an additional point I would like to make here. I would like to show you theimportance not only of presuppositions, like the up/down gravity or the organization ofspace in terms of up/down, but also of the particular representations or mental modelsthat the students have. When new information comes in, it is often interpreted in termsof some kind of a situation model, a mental representation which is formed at the time(based on prior knowledge) to help the individual incorporate the new information tothe knowledge base. These mental representations can exert important influence onlearning of science.

The figure 2 shows various explanations of the day/night cycle. The first explanation(1) is in terms of the sun going down, hiding behind the mountains, and the moon


going up. When you look at this explanation of the day and night cycle, usually nightis interpreted by the sun either going down, or hiding behind the mountains or cloudsand at the same time the moon coming up or getting out of the clouds. The sun and themoon are associated. The sun creates the day and the moon creates the night. So thesun goes down when the moon comes up. If the child’s representation of the earth isthat it is a flat earth supported by ground, then of course they cannot understand theexplanation of the day/night cycle in terms of the earth’s rotation. Sometimes we tellthem that the earth moves but the way they understand the earth’s movement is likean up/down motion similar to what you get in an earthquake. They cannot understandthe rotational movement if they do not have representation of the earth as a sphere inspace.

As we can see here, the representation of the earth, constrains the kinds of explana-tions of the day/night cycle that can be formed. We have not found even a single childwho had a flat representation of the earth and also gave a scientific representation ofthe day/night cycle.

Children who had flat representation of the earth gave us initial, non-scientific,explanations of the day and night cycle. But some of the children who had formedspherical representations of the earth also gave us initial explanations. We have in-terpreted this evidence as indicating that the change from a flat to a spherical earthshape is a necessary, but not sufficient condition for the scientific explanation of theday/night cycle. It is only when you have spherical types of representations of theearth that more advanced scientific explanations of the day/night cycle, that assumethe earth to be rotating or the sun to be revolving round the earth, can take place.

As I said, the representation of the earth imposes additional constraints on how oneunderstands the day/night cycle. Let us now see how the two different representationsof the earth as a sphere and as a hollow sphere affect explanations of the day/nightcycle. When children have formed a spherical representation of the earth, then theycan understand that the earth can rotate. However, they usually interpret rotation asan up/down rotation rather than a left/right rotation around the earth’s axis.

So the usual explanation of the day/night cycle, even in the children who haveunderstood that the earth rotates, assumes that the earth rotates in a up/down fashion.Usually, the sun is supposed to be located at the top and the moon is located at thebottom of the earth. You can understand that this is a very easy transition from theprevious representation where the sun and moon went up and down. All you have todo is to make the earth’s movement circular. You can see how easy it is to go from theprevious representation to this representation once your idea of the shape of the earthchanges. So the sun is now up there, and the moon down below the earth, and it is notthat the sun and the moon that go up and down, but it is the earth that moves in acircle. When we are up here it is day and when we go down it is night and when it isnight it is always dark in the sky where the moon is present. This is a nice syntheticmodel. This is a prevalent explanation of the day and night cycle by the children whosuppose to understand the scientific explanation.

Now let us examine the children who have a hollow sphere model of the earth.How do you explain the day and night cycle if you think that we are inside a hollow

Vosniadou 171

sphere and when the earth and the moon are supposed to be located on top of you?These children interpret the earth’s rotation to be an east/west rotation. Obviously,these children do not interpret the rotation as up/down, since they do not know aboutthe earth’s gravity and they think that people will fall down if they are outside theearth. So their model is one of sideways i.e. east/west rotation rather than up/downrotation. As the earth rotates, people go from the place that is day, where the sun islocated, to the place where is night, where the moon is located. This is the model of theday/night cycle found in many of the explanations of the children with a hollow spheremodel. They often try their best to take into consideration all the physical data thatthey have at their disposal. When we point out to them that their explanations areinconsistent, they try to repair the inconsistencies. They try to formulate explanationsthat are empirically adequate and they get disturbed by logical inconsistency. We seea lot of sensitivity to the issues of empirical adequacy and logical consistency even inelementary school children.

We also looked at the geocentric and heliocentric models of the solar system. Theyounger children think that the earth is located at the centre and the sun is revolvingaround the earth (when they understand ‘revolution’). The older children believe inheliocentric model. We have not found that there is particular difficulty in changingfrom a geocentric to a heliocentric model of the solar system. What we have found isthat children have a great deal of difficulty in understanding the shape of the earth.Once they understand the spherical shape of the earth and something about gravity,then they do not have a great deal of difficulty in creating heliocentric models of thesolar system.

To sum up: I started by telling you about science education research, and howresearch in science education is basically interested in instruction, how we cannothave a theory of instruction before we understand some of the more basic things aboutconceptual development, how concepts are organised, and how conceptual change takesplace. I mentioned some of the results from the studies on conceptual change inobservational astronomy. Still, developmental research focuses mainly on internalprocess and not on the environmental variables that promote activity and cognitivechange. In order to be able to have the theory of instruction, we need to bridge thedevelopmental and science education approaches, inorder to produce a theoretical basefor a theory of learning and of instruction. We need to understand what are theenvironmental variables that promote the kind conceptual change mentioned above.

References

diSessa, A.: 1993, Toward an epistemology of physics, Cognition and Instruction10, 105–225.

Driver, R. and Easley, J.: 1978, Pupils and Paradigms: A Review of literature related toconcept development in adolescent science students, Studies in Science Education5, 61–84.


Helm, H. and Novak, J.: 1983, Proceedings of the International Seminar: Misconcep-tions in Science and Mathematics, Department of Education, Cornell University,Ithaca, New York.

Novak, J.: 1977, An Alternative to Piagetian Psychology for Science and MathematicsEducation, Science Education 61, 453–477.

Novak, J.: 1987, Proceedings of the Second International Seminar: Misconceptionsand Educational Strategies and Mathematics, Vol. II, Department of Education,Cornell University, Ithaca, New York.

Samarapungavan, A. Vosniadou, S. and Brewer, W.: 1996, Thinking about the earth,the sun and the moon: Indian Children’s Cosmologies, Cognitive Development11, 491–521.

Vosniadou, S.: 1994, Capturing and Modeling the Process of Conceptual Change,Learning and Instruction 4, 45–69.

Vosniadou, S.: 1998, From Conceptual Development to Science Education: A Psycholog-ical Point of View, International Journal of Science Education 20(10), 1213–1230.

Vosniadou, S. and Brewer, W.: 1992, Mental Models of the Earth: A Study of ConceptualChange in Childhood, Cognitive Psychology 24, 535–585.

Vosniadou, S. and Brewer, W.: 1994, Mental Models of the Day/Night Cycle, CognitiveScience 18, 123–124.

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Introducing History of Science in Science Education: A Perspectivefrom Chemical Education

Prajit K. BasuUniversity of Hyderabad, Hyderabad, India. Email: [email protected]

In this paper I argue that it is as yet unclear whether history of science can play arole in science education. I argue that whether history of science may or may not berelevant for science education is a complex question and does not lend itself to an easyanswer. It is also an empirical issue whether history of science is effective in scienceeducation. I also point out that there are certain reasons to think that one cannot usehistory of science across the board to enhance science education.

What I am going to do is to first quickly enumerate the questions that arise in thecontext of science education. One of them is that science education is an umbrella termwhich means it is quite ambiguous and it needs to be sorted out. For my own edificationI have sorted it out for myself and I show that delineating various meanings of scienceeducation tends to show that the role of history of science in science education shouldbe questioned even more threadbare. Next, I look at the general argument that historyand philosophy of science play an important role in science education. Again, I tryto show that the argument is not very straight forward, and we do not have reallya knocked down argument in favour of the claim that history of science can play asignificant role in science education. Thirdly, I look at certain concepts in chemistry andexplore whether history and philosophy of science can play any role in the instructionof those concepts in the classroom situation.

1 Varieties of Science Education.

Straight forwardly science education will depend upon first answering the question:What should we include in science? Should we include both natural sciences and socialsciences? Can we include history? Because history used to be a part of sciences ornatural philosophical concerns long time ago. In fact, as E.H. Carr points out, historyis included in sciences in all European languages except in English.1 Lastly, shouldone include philosophy? After all natural sciences were known as philosophy a coupleof hundred years ago. Philosophy is supposed to be “mother of all sciences.” Now,this brings us to the question of demarcation that how will one decide what should beincluded in science? How does one separate out science part from the non-science part?And the question is can philosophy help? It is indeed a bit ironic that one has to takehelp of philosophy to settle the issue whether science can be separated out from theother non-science intellectual endeavours when one is wondering whether philosophyis a part of science or not. This attempt to disambiguate science from other non-scienceendeavours has been addressed by scholars, and there have been claims that it would

1Carr, E. H.: 1974, What is History? Penguin, London, p. 56.

174 Chemical Education

be possible to separate out science from the non-science in terms of method. Scienceis supposed to follow a method. It is this method which characterises science, anddisambiguates it from non-science. However, the last (almost) 50 years of work inphilosophy of science clearly brings out that it is remarkably difficult to really pindown a single method which informs science. This raises the possibility that there maybe various kinds of methods that are employed in science, by the scientists, and theremay even be a problem of plurality of methods based on discipline specificity.

Now this is so much for what to include in science and what to exclude, and theproblems in deciding, therefore, science from the non-science aspect. There is also theproblem that science is taught from secondary to high school, to college, to universityand so on. This implies that science is introduced slowly over a period of time and hencethere is some kind of gradation of content. This gradation of content, it seems to me, isindicative of certain demands. Keeping aside the issue about the specific scientific con-tent that is involved in this gradation and how to achieve it and what is to be introducedat what level of instruction, I think the demand at one level can be understood as: Dowe need science education for all school students, and do we need science education forall college students, and should methods of science or scientific investigation be part ofscience education? Finally, to put it a bit more contentiously, I shall use C.P. Snow’sexample that there exists an almost an unbridgeable gap between scientists and thenon-scientists. Snow used the example of second law of thermodynamics to make thepoint that the non-scientists have no idea whatsoever about this law. So, the questionthen is should we expect that all the non-scientists know the content of the second lawof thermodynamics, or, take the more recent example: What are Bucky balls?

The questions raised above highlight that there are problems regarding what weexpect the students at different levels to know. This, in turn, will have repercussionson how and what should be introduced in different stages of science education. The nextis the question about science being a cultural enterprise. Here there are two aspects.One is that of the scientific community (the smaller cultural group). The scientificcommunity has its own cultural norms regarding how to do science, what constitutesgood science, and what constitutes bad science and so on. I will outline some of theselater on when I come to chemical education. The second aspect is that science as acultural enterprise is embedded in the wider society or wider culture. To the extentit is a part of the wider culture it will interact with the larger society in various waysand the Science, Technology, and Society issues become important. The question thenis should these also be included in science education curriculum?

Last but not least, I think science education itself is a cultural enterprise. Itmight be seen in the wider society as a certain kind of cultural initiation. Besides,in the classroom situation, it is well known by now that students come with their ownconceptions and ideas. It is also equally well known how counter-intuitive some ofthe scientific ideas or concepts of science are. If there is a counter-intuitive aspectin scientific ideas, then, of course, these concepts will not match with the life worlddomain concepts that the students bring to the classroom. So, there is an attempt inscience education which needs to be perhaps sensitive to the fact that science educationis an attempt to replace the world view of the students, which they get from their

Basu 175

cultural milieu. These students come to the science classrooms with their own ideas,and there is an entirely different culture (of unintuitive scientific ideas) that she/hehas to confront. How will these two cultures match or interact? It is a question thatscience educators must worry about.2

2 Role of History and Philosophy of Science in Science Education

Having made these preliminary remarks, I now go on to the question about the roleof history and philosophy of science in science education. I wish to begin with a set ofarguments offered by both the protagonists and the antagonists because that will high-light the issue sharply. The protagonists’ point is that history and philosophy of sciencedoes give a better picture of science than what is given in the textbook. A textbook, atany level of science education, at present, often gives the students an erroneous pictureof scientists destroying all the irrational and old ideas and establishing new ideas. Itdoes not bring out the fact about science being a kind of human enterprise, or aboutscience being a social and cultural enterprise. But history and philosophy of sciencecan begin to give the students a better picture. The modern textbooks will not tellthe students about plurality of methods. It will almost indoctrinate the students thatthere is one and only one method that is employed in science. It is not surprising thatany undergraduate student who has gone through school education claims that thereis one and only one method called scientific method. All these ideas can be gotten ridof, at least the claim is, through introduction of history and philosophy of science inscience education. Students, through the help of historical episodes and philosophicalarguments, will be able to understand that some of these ideas about the method inscience are highly problematic.

Now once people have a better picture of what science is all about, then they candecide on their own what science can do and what science can not do. This meansthat they understand what the limitations of science are. They do not anymore expectscience to solve each and every problem of their lives or of the life of other individuals ofsociety at large. They know where to stop. This will indeed be a huge gain, if studentscome out of the classrooms with this realization although it is not clear that this willindeed be the major outcome of the instruction.

Secondly, introduction of history and philosophy of science will improve actual sci-ence education or science instruction in classroom and laboratory. And here the waythings are supposed to work is that students basically follow the scientists in theconceptual conflicts and within that course discover with them. Now I know thatdiscovery learning of certain sorts has been discredited long time ago. But here whatI have in mind is that the kind of discovery that students do with the scientists isto recognize that scientists of the olden times had faced a whole lot of difficulties intheir work. The difficulty could arise either in clarifying a concept, or having clarifiedthe concepts to an extent, how to design experiments. The difficulty could also arisefrom the open ended nature of the results of the experiments designed and the kind ofcultural conflicts the scientists had gone through as they had tried to see the bearing

2Solomon, J., and Addinell, S.: 1983, Science in Social Context, Hatfield, Oxford.


of the evidence on the hypothesis and so on. Sometimes, in this process, the scientistsmight have reached a blind alley. They had retracted their steps, had gone back andthought about it and so on. This process is a messy affair. As the students get toknow those, and follow the scientists in their footsteps to what might be called theappropriate or more correct theory or understanding the students discover as it werealong with the scientists. So, the students are in the position of the scientists takingsimilar steps and they are facing the problem that the scientists were facing. This wayof learning, if this is how students do actually learn, will, perhaps, undermine theirfaith in naıve inductivism, which means the students will recognize that scientists donot go out and make observations, and directly induce the results. Even if they take anot very complicated experiment, they look at the observation, and they may not seethat this must be the relation between the properties that they have been looking for.So this lack of obvious relation between the observations made during the course ofan experiment and the relation among properties they may be attempting to establishdoes undermine that the theories or hypotheses in science are directly induced fromthe observations.

I use the example of Antoine Lavoisier’s arguments to elaborate the above positiona little more. Lavoisier’s thesis about compound nature of some chemical substance isa sophisticated position and this position tells us something insightful when one has acomplicated argumentation or complicated experiment going on. A lot of things happenin science besides doing an experiment or thinking about the concepts. So, considerLavoisier’s four experiments which are supposed to establish the compound nature ofwater.3 It seems to me, as I went through the descriptions of these arguments, thatthese (were, and still) are difficult experiments to do. In fact, these were indeed verydifficult experiments to do in the eighteenth century and these were not unproblematicat that time. Very respectable scientists at that time, including Joseph Priestley, foundall kinds of problems with these experiments. Yet, there is something to be said aboutthe way Lavoisier presented his arguments and the way he presented the results of hisexperiments.

Let me dramatize it, before I show what was interesting about Lavoisier’s argument.It is well known that, according to Lavoisier, a compound is classified as acidic if it hadoxygen in it as a chemical constituent. This is because the word oxygen (more correctlyoxygene) means acidic principle. So, any compound, at least binary, that has oxygen isacidic. Yet Lavoisier failed to realize that water is not acidic. Water contains oxygenand it is not acidic and to top it all, if one looks ahistorically, Joseph Priestley overand over again pointed out that if water is synthesized, a little bit of acid could alwaysbe detected in it.4 Now, with the hindsight it can be explained why that acid is there.It is there simply because chemical substances, including elements, in the eighteenthcentury, could not be purified completely. So, since water was synthesized by Lavoisierby burning oxygen and hydrogen together in a vessel, and these gases could not bepurified completely there was always a bit of nitrogen and carbon dioxide in the vessel.Carbon dioxide continued to remain there and the nitrogen became nitric oxide and a

3Lavoisier, A.: 1965, Elements of Chemistry, trans. R. Kerr, Dover Publications, New York.4Priestley, J.: 1799, On the Phlogistic Theory, New York Medical Repository 2, 383-387.

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little bit of acid was also synthesized by dissolution of these oxides in the water thatwas synthesized by the combination of oxygen and hydrogen.

It is easy to see how the situation can become muddy. Lavoisier could have said thatthe presence of acid proved his case. Water is a bit acidic because it contains oxygen.Yet he is so driven by his own idea that water is a compound and if pure elements areused in the experiment of synthesizing water from its constituents, then the reactantswill contain only pure hydrogen and pure oxygen. If these are put together and heatedwater should be formed. He was more interested to point out that the acidity that onewould detect, in synthesized water, was because of impurity and not because waterby itself could be an acid. What he could have said that water was a very mild acid.Although scientists had not realized that water was an acid, but it indeed was. Anyway,the heart of the problem is that Lavoisier’s belief was that if pure elements (for himelements are like particles or made up of particles) were made to go through certainkinds of reactions then only a certain kinds of compounds would be produced. Thisis of course based on scientists’ accepting Lavoisier’s understanding of the principleof conservation of mass, principle of chemical elementarity, or principle of chemicalsimplicity. So, underlying Lavoisier’s arguments is the idealization of the reactionprotocols and this aspect of idealization is something that Michael Matthews brings outin his argument, where he talks about Galileo’s experiments with pendulum.5 Clearly,one can never get the kind of results that Galileo had reported. One really cannotget those kinds of pure results. One needs to idealize. And what Lavoisier did was toidealize and tried to show what an “ideal” chemical experiment would look like, anddrew conclusions from those experiments.

Now, if we go back to this question about science instruction and if we look at or ifwe follow let us say Lavoisier in his trails, we will realize what kind of arguments thatthe protagonists, for introducing history of science in science education, are employing.What we need to do in order to do good science like Lavoisier or Galileo is to be ableto idealize in the right kind of context. It seems to me that this is a bit too much toexpect from high school students. If the students are put in the kind of conflict thatLavoisier went through and are asked here you are at this stage: How will you proceedand should you not idealize now, should you not think that the atoms are pure thingsand when are they pure and you put them together will they behave in such and suchway. I think that is a bit too much to ask. For secondary science education at least at7-8th standard when the idea of water as a compound is introduced it is a tall orderat least or at best, and at worst it will not lead to the kind of expectations that historyand philosophy of science is supposed to bring out in science instruction.

There is another argument of the antagonists. This is a well known argument—(H)istory of science is an academic discipline. If we include in history of science whatacademic historians actually produce, the science students may not do justice to thematerial that the historians have produced. If they do justice to the material, no initia-tion to the paradigm based understanding and research is possible, where a paradigmis understood in the way Thomas Kuhn had employed the term in his book The Struc-

5Matthews, M. R.: 1992, History, Philosophy, and Science Teaching: The Present Rapprochement, Scienceand Education, 1, 11-47.


ture of Scientific Revolutions. This is basically the heart of the argument that Kuhn,6Martin Kline,7 or Steven Brush8 has given. So, they conclude from this that eitherhistory of science is not useful to train scientists or history of science will lead tosituation where it will not be possible to train scientists. So if someone is good ininterpreting history of science well, (s)he will not feel like doing science. The claim isthat to do science after having figured out that scientists do all kinds of stuff is a tallorder. At least it will begin to inhibit students from pursuing science, or it will notserve the purpose of introducing scientific concepts through history of science.

There is a reply of course. Michael Matthews, as a major protagonist, claims thatone needs to introduce history of science in moderation5. It is not advisable to take theresearch outputs of the historians of science and introduce that directly into high schoolscience curriculum. The point is well taken. However, it seems to me the counter replyinvolves a certain kind of pragmatism. This pragmatism implies that the question,“What should be the outcome of science learning?” needs to be first answered. Inscience instruction there are some expectations at the end of instruction, and whatthese expectations are need to be answered. It is not the same question as what wasactually the process of growth in science. If these two questions are different, then it isa completely and totally empirical question whether the answer to the second questionhas any bearing on the answer to the first. This is I think one point or one area wherethe pragmatists or the people who suggest moderation in introducing history of sciencein science education either fail to recognize or haven’t satisfactorily addressed.

3 History of Chemistry in Chemical Education

So much for general science education, and the role of history and philosophy of sciencein science education. Now, I address specific question about chemical education. Takingthe last concern in the section above first, I first look at the response to the question:What is the aim of chemical education? Here is what M. J. Frazer claims is the generalaim of chemistry should be like:9

• to prepare students for professional career in science especially in chemistry,

• to contribute to general education using chemistry as an instrument and

• to inform future citizens of the country of the nature and the role which chemistryplays in everyday life.

I shall dispose of the first aim with some preliminary remarks since I wish toenquire the role of history of chemistry/science in achieving the other two aims at this

6Kuhn, T. S.: 1977, The Essential Tension: Tradition and Innovation in Scientific Research, in his TheEssential Tension, University of Chicago Press, Chicago, pp. 225-239.

7Klein, M. J.: 1972, Use and Abuse of Historical Teaching in Physics, in, S.G. Brush and A.L. King, (eds.),History in the Teaching of Physics, University Press of New England, Hanover.

8Brush, S. G.: 1974, Should the History of Science be Rated X?, Science, 18, 1164-1172.9Frazer, M. J.: 1975, Up-to-date and Precise Learning Objectives in Chemistry, New Trends in Chemistry,

The UNESCO Press, Paris, IV, 43-53.

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stage. I shall take up the role of history of science in achieving the first aim in somedetail in the next section. It may be seen that the first point is related specifically tothose students who will become chemists and the last two to more like chemistry forcitizens. Before I make the preliminary remarks regarding the first aim, I introducetwo other lists that tend to document in more detail what are the expectations of acourse in chemistry. Some of these courses are under the rubric of chemistry forcitizens. One list is organized after taking a poll among chemistry educators, as towhat should a course of chemistry for citizens at the secondary school level aim toachieve.10 These aims include:

1. to assist the overall development and maturation of the student,

2. to show that science is a human activity and is a part of cultured person’s worldview,

3. to provide an indication of the way scientists work by seeing relations betweenconcepts and validating these by empirical tests,

4. to instil an awareness of the profound and far reaching consequences of the usesand abuses of science,

5. to show the historical continuity of the growth of science,

6. to generate a liking for science, and

7. to develop the facility for critical and unbiased observation.

It may be seen from the above list that there is not much emphasis in terms ofthe objectives which require introducing lessons in terms of introducing STS. There issomething in the 4th point which is aimed at achieving “an awareness of the profoundand far reaching consequences of uses and abuses of the science”. Otherwise thelist underscores that there is or should be some attempt to introduce what may becalled the nature and method of science. There is an attempt to show the continuityof growth of science and there by alerting them to science being a historical process.Then the 6th one is interesting in that it takes that chemical education should attemptto generate a liking for science and that is where the ideology for science educationcomes in. The 7th point says that chemical education should develop the facility forcritical and unbiased observation. I am not sure what kind of unbiased observationone will generate in chemical contexts. It is an aim which may be unattainable unlessan account of unacceptable biasedness is spelt out, argued for, and already in place.

I now take up the last list which is much more extensive and hence is more illumi-nating. This list is prepared from the information sought from the research chemistsin USA.11 I first enumerate the list before taking up some of these in the rest of mypaper.

10Idem.11Billing, D. E., Private Communication, referred in footnote 9 above, p. 52.


1. To develop and sustain an interest in science and in chemistry as a central,supporting and challenging area of study

2. To develop a working knowledge of, and favourable attitude towards, scientificmethods of investigation, using chemistry as an example

3. To encourage the exercise of curiosity and creative imagination, and an apprecia-tion of the role of such speculation in the selection and solution of problems, theconstruction of hypotheses, and the design of experiments

4. To develop the ability to see, and the habit of looking for, inter-relationshipsbetween individual phenomena, principles, theories, philosophies or problems

5. To develop an appreciation of scientific criteria and a concern for objectivity andprecision

6. To develop an understanding of the fundamental and unifying principles under-lying the behaviour of atoms, ions and molecules, and an ability to apply theseprinciples to real problems involving materials in various physical and biologicalconditions

7. To develop the skills, knowledge and habits required for the safe, efficient andthoughtful manipulation of chemicals and apparatus in common laboratory pro-cedures

8. To develop confidence and skill in the quantitative formulation of problems andin the treatment of data

9. To develop in the student the ability and predisposition to think logically, tocommunicate clearly by written and oral means, and to read critically and withunderstanding

10. To promote the student’s understanding of science, technology, economic and so-ciological factors in modern society, and of the contributions they can make toimprove material conditions and to widen man’s imaginative horizons and hisunderstanding of the universe

11. To encourage the applications of chemical knowledge and skills to problems whichare of importance to the community, in particular the optimum use of naturalresources

12. To provide an opportunity for the development of the student’s motivation andsocial maturity, including an appreciation of his own limitations in relation to acareer choice which will be fruitful to himself and to society

13. To develop the student’s understanding of the structure, values and procedures ofchemical industry, and the chemist’s professional role in such a situation

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14. To develop a knowledge of, and familiarity with the use of, important sources ofchemical information

15. To make the student aware of the limitations of his disciplines and their methodsand to provide opportunities for him to understand, make and criticize valuejudgements

16. To cope with individual differences in the abilities and interests of students,so as to ensure the optimum development of each student’s potentialities forachievement and satisfaction and

17. To draw upon staff interests and expertise in such ways that the teaching ischallenging and satisfying

This extensive list brings out some of the aims of chemistry courses and it is possibleto see that the list tries to achieve a range of expertise for chemistry learners. There areefforts to introduce students to aspects of philosophy of science, the idea(s) of methodin science in general and in chemistry in particular. The interdisciplinary nature ofchemistry is another objective that is supposed to be achieved through chemistry in-struction. There are a few which underscore the relations between science, technology,and society. The last two are more close to the problems of day to day learning ofteaching chemistry. One interesting aim included in the list is that the students mustbe able to understand the limitations of science in solving a wide ranging problems andmake value judgements. I think that goal is quite laudable although hardly satisfiedby any course in chemistry.

I wish to start with the first aim in the list above. It claims that one of the goalsof courses in chemistry should be to develop and sustain an interest in science and inchemistry as a central, supporting and challenging area of study. There have oftenbeen complaints that chemical education has fostered memorization of facts and verymany of them at that. As a result chemistry courses have been rather boring and havedriven good students away from chemistry. While responding to this challenge, variouscurricula reforms were brought about in all areas of science including chemistry. Thecourses developed by CHEM study, in USA, Nuffield Foundation, in UK, and the Scot-tish Education Department, in UK, were intended to improve learning through science.There were much more emphasis on understanding the principles of chemistry and lessemphasis on remembering facts. However, chemists began to complain soon that thestudents continue to have poor understanding of chemistry. An interesting and pio-neering article by R. J. Gillespie,12 written in 1977, and quoted somewhat approvinglyby M. Chastrette and C. N. R. Rao,13 in 1992, emphasized that chemistry trainingrequires remembering facts. Otherwise, there would be embarrassing response fromstudents, like “Silver Chloride (AgCl) is a green liquid.” More substantively, Gillespieargues that, the principles that are taught in introductory courses are not a part of

12Gillespie, R. J.: 1977, IUPAC International Newsletter on Chemical Education, (6)13Chastrette, M., and Rao, C. N. R.: 1992, New Trends in Chemistry Teaching: An Overview Giving

Examples of Innovative Projects, New Trends in Chemistry Teaching, The UNESCO Press, Paris, VI, 9-14.


chemistry.14 Thermodynamics, Kinetic Theory, and Quantum mechanics are areas ofphysics that have proved particularly useful in chemistry. These theories are usefulsince these explain chemical facts and help understand the phenomena in chemistry.This raises the question: What is chemistry? I now deal with this question brieflybefore I get on with my task to look at the aims of chemistry and whether history ofchemistry/science can fulfil these aims.

It has been argued that chemistry is a central science.15 Now it is unclear inwhat sense is it a central science. The notion of centrality has been viewed in morethan one way by chemists and scholars. Chemistry may be taken to be conceptuallycentral because it is conceptually networked with a variety of other disciplines. Oftenchemistry is viewed this way because of its strong links with physics and biology. This,however, does not mean that chemistry is foundationally central. In fact the presentwisdom is that (most of) chemistry is, in principle, reducible to physics. Yet anotherkind of centrality is possible. It has been argued that chemical change, or lack of it,is so much a part of everything with which we come in contact and everything we do,it is in a very real sense the central science. Besides this what are the interestingfeatures of chemistry? Gillespie argues that chemistry is the science of various formsand their transformations. In other words, it is the science of properties and reactionsof substances. He claims that

The preparations of new substances and their study of properties is one of the main activitiesof the chemist whether (s)he is an industrial chemist preparing new semiconductors or newdrugs or an academic chemist preparing new compounds simply to find out how a previouslyunexplored combination of element behaves.16

To quote Gillispie again,

The student who never goes into doing any more chemistry, never gets an opportunity to seethe application of the principles of any real chemistry. (S)he never learns what chemistry isabout. (S)he never learns anything about the fascination of making something new, somethingthat has been never made before: The synthetic aspect of chemistry. It is one of the aspects ofchemistry that distinguishes it from biology, from physics, and from other sciences.17

I shall return to the issue of synthesis in the next section. The second list enu-merated above subsumes the aims in the first list and is more akin to an elaborationof items and 2 and 3 in the more extended third list. As mentioned above, whenwe look at the list of aims mentioned against courses on Chemistry for Citizens, wesee that students are expected to internalize certain philosophical views about sci-ence. This is supposed to be part of the result of a good chemical/science education.A. J. Harrison points out quite appropriately that although research scientists thinknaıvely that whatever they produce in the laboratory are ready for market, “an array

14Gillespie, R. J.: 1981, Chemistry: Fact or Fiction?, New Trends in Chemistry Teaching, The UNESCOPress, Paris, V, 35-40.

15Newbold, B. T.: 1981, Chemical Education: The Current Challenging Scene, New Trends in ChemistryTeaching, The UNESCO Press, Paris, V, 22-28.

16Gillespie, R. J.: 1981, Chemistry: Fact or Fiction?, New Trends in Chemistry Teaching, The UNESCOPress, Paris, V, 36.

17ibid.

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of organizations mediate between the research scientists and the consumer.”18 Someof these organizations include political/planning establishments, industrial groups, ju-diciary, trade unions, consumer protection groups etc. A smooth liasion among thesevarious groups may as well depend upon persons with chemical/scientific training to bemembers of these organizations and recognize the role of chemistry/science in bringingabout material difference to the society.

In order to achieve these goals, the chemical education must have a social dimen-sion. This, however, may not mean that the general concepts of chemical systems andchemical change are not within the grasp of the public. It implies instead that thereis no reason why chemistry courses should be more difficult than a course in history.19

The success will be measured by the attitudes of the individuals towards themselves.Have they grown in their confidence to extend their knowledge at the level of publicmedia? The emphasis is not whether they have only learnt certain techniques. Thesocial dimension is also captured by recognizing that learning of chemistry shouldgo hand in hand with its social application. The third social dimension is the socialnature of chemical discovery. Here, one may try to introduce through the study ofchemistry and of discoveries within it, Mertonian social attributes attending the prac-tices of chemistry within a scientific community. A good way to achieve that will be tointroduce institutional history.20 A wider social history may also alert students to thenational, political, military, and industrial demands leading to orienting scientific workin specific directions. This is one reason why history of chemistry/science may becomeuseful to chemistry/science education.

It has been argued that science provides opportunities for students to practice or usesome of the more obvious processes such as hypothesizing, observing and recognizingpatterns. However, many other subjects can provide equally good opportunities. To thefuture citizens, the skills which are most important may be least specific to science.Thus the philosophy of science training is claimed to be possible without explicitlyintroducing philosophy of science.

4 History of Chemistry and Chemical Education

We can now get on with our attempts to answer the question about history of chemistryand how this history might help chemical/science education. As mentioned above,chemistry has been called a central science. Although the conceptual centrality isdoubtful, not much depends upon that one way or the other. Often chemical phenomenaare best understood or explained by appealing to chemical categories. This allows thechemists to get on with their jobs. The common chemical concepts are generally ofhigh complexity since object—phenomenon relations in chemistry are generally quiteintricate. Some of the examples of ‘basic’ chemical concepts include ‘chemical species,’‘reaction mechanism,’ ‘structure,’ ‘conformation,’ ‘stoichiometry’ or ‘non-stoichiometry,’

18Harrison, A. J.: 1981, Chemical Education and the Expectations of Society, New Trends in ChemistryTeaching, The UNESCO Press, Paris, V 19-21.

19Idem., p. 20.20Fensham, P.: 1981, Social Content in Chemistry Courses, New Trends in Chemistry Teaching, The

UNESCO Press, Paris, V, 31-34.


and ‘chemical equilibrium’. Equally basic and fundamental concepts in chemistry arethose of ‘element,’ ‘mixture,’ and ‘compound’. It is worth exploring whether history ofchemistry can help understand these three basic concepts easily and accurately. And Iturn to that question next.

6-7 standard students are introduced this very elementary notion of distinctionbetween element, mixture and compound. Anyone who has gone through 6-7 standardbooks developed by the National Council of Educational Research and Training, India,is expected to understand what these concepts are. Yet it turns out that students haveremarkable difficulty in understanding the distinction and in applying the same in notso straightforward instances. This I figured out only two days ago in this workshop. Iam thankful to the two teachers who have pointed this to me that the teachers or thestudents who will become teachers and are enrolled in the B.Ed. program have shown aremarkable inability to distinguish between a mixture and a compound, or an elementand a compound.

Suppose we wish to look at the distinction between the three concepts mentionedabove. The modern definition of a chemical element is that its atoms are of the samekind. A mixture is defined by a sleight of hand as that which is neither an elementnor a compound. A compound is a result of a combination of at least two atoms, oneeach belonging to two disparate elements. This seems to be one place where history ofchemistry may be expected to intervene since the history of the seventeenth and theeighteenth century chemistry is rich with attempts made by the chemical philosophers,of those days, to develop a set of criteria to disambiguate these concepts from each otherwhile attempting to disambiguate these objects of chemical investigation from thoseof mechanical investigations. That gets to me thinking, that can I use the historicalattempts by the chemists of the 17th and the 18th centuries starting from RobertBoyle up until Pierre Macquare when they tried to establish disciplinary autonomy ofwhat might be called chemical philosophy from mechanical philosophy? Basically theattempt is to demarcate chemistry from physics. Because physics was in some sensemore professionalised at that time and chemistry was not, and because the chemicalphilosophers felt that they did chemical philosophy in its own terms and they were verygood at it, and hence could as well claim some kind of disciplinary autonomy. But if onewants to claim some kind of disciplinary autonomy, then (s)he must show that chemicalelements, chemical composites like mixtures, and chemical composites like compoundsare different from what might be called physical particles or mechanical particles,and mechanical composites. Now how do we go about doing it. About 150 years of“philosophical and theoretical” analyses were pressed into service starting form Boyleand until Macquare.21 These attempts by the European chemical philosophers showthat these distinctions are tied to the notion of chemical and physical (mechanical)properties and the distinction between them, and to the notions of chemical and phys-ical (mechanical) operations and the distinctions between them. And these attemptswere circular, and the chemists had to get on with their jobs in spite of the lack of this

21Basu, P. K.: 1996, Disciplinary Autonomy of Chemical Philosophy: A Philosophical Dilemma of the 17thand the 18th Century Chemical Philosophers, Presented in Annual Australasian Association of History,Philosophy, and Sociology of Science Meeting, Auckland.

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resolution. The picture hence is not pretty. It does not help to introduce the historicaldebate to clarify the distinction among the concepts. The history of chemistry hereis not much of help. This shows that if we want to bring to bear this 150 years ofdebate into the classroom, no matter how much we want to impose on the historyit will not lead to a very pretty learning/instruction situation. It will rather be amurky event for the teachers as well as for the students. The debate, however, willbe of enormous help for junior college or undergraduate college level students in adifferent sense. It can show very clearly how scientists attempt to develop analyticalarguments to clarify the concepts they use. The sophisticated use of reasoning, appealto empirical observations relevant for the case in hand are examples which can helptrain students to develop a critical and analytical inclination. But given that the abovechemical concepts are introduced at the 7th standard science curriculum, situation isnot conducive to introduce these philosophical and methodological intricacies.

I now come to another example which seems to resist introduction of history ofscience by the very nature of the endeavour itself. It may be remembered that chemistsagree that synthesis of materials constitute an important aspect of chemistry. If chem-ical synthesis is a part of chemical education, then one needs to ask whether it canbe historically packaged for teaching. The reasons for apprehension or question maybe because of the nature of the enterprise itself. Chemical synthesis, be it organicor inorganic, in liquid state, gaseous state, or solid state, requires that materials ofcertain kind are made to react to make a desired product. Of course, there are situa-tions where scientists start a reaction without a specific product in mind. Historicallythere have been various synthetic routes developed to arrive at a desired end. Thesedevelopments occurred through the application of specific knowledge—thermodynamic,reaction rates, stereochemistry or geometry of the starting materials or of product(s),modes of interaction among the reactants. Yet these knowledge claims are in somesense a reasonable guide at best. Their status is not that of a theory or a law explainingor predicting phenomena. That much is obvious since failure of a synthesis process ina new situation is not a serious evidence against these laws. I think that the logic ofthe situation is somewhat different.

I am going to rely on Ian Hacking’s argument that experimenting or synthesisingis a kind of intervening.22 New phenomena or materials are created in laboratoryunder carefully controlled conditions. Control of initial and boundary conditions (main-tenance of relatively closed systems) is crucial to the emergence of the regularitiesunderlying various synthetic processes. However, this practical mediation makes thepractical application of the regularities problematic. The chemists design a syntheticcompound for it to perform a desired function. They want to be assured that thecompound will perform that function. But this can happen if the boundaries of thesystem can be defined and fixed. But in a new synthesis that is rarely the case.

Now I want to begin to answer why that is so. If we remember that at times theregularities arrived at or the laws cannot be expressed in a straight forward fashionin terms of a universal generalization, then we realize that these statements of reg-

22Hacking, I.: 1983 Representing and Intervening, Cambridge University Press, Cambridge.


ularities may contain a ceteris paribus clause. These are like “P is a Q,”other thingsbeing equal. The explanations and predictions using these laws are somewhat shaky.This is because the condition, other things being equal, may not obtain. This is what isunderscored, in the case of synthesis, by pointing out that the boundaries of the systemare not defined and fixed. The real world is complex and hence the conditions involvingthe occurrence of P may be complex enough not to let Q happen. There are two waysof getting around this. One way is to modify the real world environment to the extentthat it mimics the environment of the laboratory with the defined boundary conditionswhich result in the regularity of if P then Q. So, basically what we do is, if we have asynthetic route and we want to apply it to a new context, then what we need to be ableto do is as simple as change and modify the context in such a way that we can run oursynthesis. The other is to mimic the environment of the world in the laboratory, whichmeans to be able to say that here we have a complex situation and we need to mimicthis in the context of our synthetic route.23 That may be an expensive affair since theworld would keep changing and mimicking these variations in the laboratory may notbe viable. So the option in this case is then to take the law of nature or the regularityof the world and attempt to modify the world. This attempt to modify the world maynot always be possible and given that seldom it is one law of nature or regularitythat is involved in the synthetic procedure, the open ended nature of synthesis andthe lack of viability and efficacy of various laws or regularities in various situationsbecomes apparent. This open ended nature of chemical synthesis is apparent whenyou look at the synthesis of some of the recent materials specially the superconductingmaterials like one, two, three super conductors (Y Ba2Cu3O7), and Bucky ball, the C-60molecule. Although both are designer materials, the actual synthesis of which requiredextraordinary manipulations of the environment, and was assisted by a certain degreeof chance. If the expectation is that these ideas of chemical synthesis may be introducedhistorically in science instruction, and these ideas will help in conceptual learning ofstudents regarding the nature of synthesis, it is not clear how that will be possible.In the context of actual instruction in chemical synthesis through history, it is unclearwhether the instruction will give the students the correct picture. This is becauseeven if we learn how a certain kind of compound can be transformed into anotherkind of compound, the next time a student wants to make anything new, and chemicalsynthesis is all about making something new, the old information is never enough.One has to be much more innovative to realize that one has to keep changing theenvironment of the world such that the new synthetic law or new synthetic regularitiescan play out their role and it is here I claim that historical lessons might not be of help.However, there are some methodological lessons that one can draw from discussingthe history of synthesis of chemical compounds. One of these is to make the studentsrealize that synthesis is an open ended endeavor and whenever it comes to employingchemical synthesis ideas in a new context one needs to be able to control the world ina new environment. These are some of the tips that one can give. Chemical synthesisis something that is taught at 11th or 12th standard. And it is unclear whether at that

23Latour, B.: 1987, Science in Action, Harvard University Press, Cambridge, MA.

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level history of chemical synthesis can be employed to help science instruction in thisarea.

In general conclusion, I become a bit more provocative by pointing out that scienceeducation has a very strong cultural aspect. I come to that conclusion to an extent dueto the fact that when you look at the way the colonial science was introduced into theIndian context it was to train the natives “in moral” issues. For the British, nativeswere immoral. For those natives the colonizers needed to teach certain kinds of sciencelike arithmetic or geography and not anything else.24 The understanding was that thenatives would become morally equipped having gone through the training. This is notto blame the British as such. Because the British tried to do on a similar line somethingto themselves. In the 19th century BAAS introduced chemical analysis as part of thechemical curriculum so as to give students some kind of mental training so that theybecome “logical”.25 Now, the idea of introducing chemical analysis is because one canuse that method of chemical analysis to introduce what might be called a hypothetico-deductive mode of reasoning. So, if one has a hypothesis that sodium metal burnswith a yellow flame, then one can predict that a salt containing sodium atom will testpositive in a flame test. Now one can do a qualitative test. If the colour of the flame isyellow, hypothesis is confirmed and if the colour is something else, then the hypothesisis disconfirmed. Since scientific knowledge is acquired and justified by this method,people at large will be better off using this method in their daily life since they can allbe scientific in their outlook. And a citizen who is scientific is an asset to a country’swell being. Thus, mental training is a part of a larger game plan to have people withsuperior ability. So what one has to realize is that science education has this kind ofgame plan in some form or the other.

24Kumar, K.: 1997, Political Ideology of Education, Sage Publications, New Delhi, 42.25Layton, D., Davey, A., and Jenkins, E. W.: 1986, Science for Specific Social Purposes (SSSP): Perspectives

on Adult Literacy, Studies in Science Education, 13, 27-52.

Multicultural Mathematics, Anti-racist Mathematics: What can thatbe?

George Gheverghese JosephUniversity of Manchester, UK. Email: [email protected]

At a Conservative party conference, the then British Prime Minister, Ms. MargaretThatcher said: “Children who need to know how to count and multiply are being taughtanti-racist mathematics, whatever that be.” The background to Prime Ministerialoutburst is quite interesting, and I would like to believe that I had a part in it. Aweek earlier, I addressed a conference of mathematics teachers from inner city schools.The inner cities are where you find some of the most deprived areas of Britain, andwhere teaching could be quite difficult. These are concentrations of ethnic minoritypopulations, particularly people of Asian and Afro-Carribbean origins. And for somereason they unusually decided to televise snippets of that talk, and particularly aquestion that I was asked as to what I thought of multicultural mathematics. To tellyou the truth, my interest or knowlege of multicultural mathematics at that time wasstill in its embryonic stage. I thought it was a good thing, and certainly if it was tied upwith history which had tended to neglect or devalue the contributions of large sectionsof the world populations to the subject. I tried to bring in history into my classroomteaching, both at the school level as well as at the university level. I remember oncebeing absolutely amazed by how students, reacted when I introduced ‘Non-Euclidean’geometry using history. Groups of students who previously found it totally irrelevant,probably half of them sleeping, suddenly woke up.

So we were trying at the conference to find out what would engage the schoolchildren of the inner city schools. It was around the time that Nelson Mandela wasin the news. If I remember correctly, a musical jamboree had been organised in hishonour. So somebody then asked how, using South Africa as an example, would oneteach mathematics. So I suggested that one way may be to split up the class into threegroups, ‘blacks,’ ‘whites’ and ‘coloureds’ according to the proportion in the three groupsin South Africa, divide the area of the classroom according to the share of the landavailable to the three groups and get each group to stand in the area allocated to them.The result was a huge concentration of students representing blacks in a relativelysmall area with hardly much space for them to stand and a lot of room for the studentsrepresenting the whites. The coloured (consisting mainly of Indians and mixed race)were mainly concentrated into towns since there were restrictions during the apartheidon their owning land elsewhere. One of them asked me would this be anti-racist? So Isaid we could call it anti-racist mathematics.

What I was trying to show there was that for mathematics to be relevant to mostpeople, it should engage with people’s preoccupations, with people’s concerns and in-terests. It does not really matter what is the subject that you take up but you have tomake it sufficiently interesting for the students. For example, a group of youngsters

190 Multicultural Mathematics, Anti-racist Mathematics

Western Europe

Sicily Hellenistic world

Jund-i-Shapur (Persia)

Cordoba (Spain)Toledo

(Spain)

Cairo (Egypt)

Baghdad (Iraq) India

China

Figure 1: An alternative trajectory for the ‘Dark Ages.’

may be interested in the shapes and designs of the hubs on the wheels of cars. Thiscould offer some good examples of symmetry. In a way for many, mathematics is seenas so remote, so irrelevant and so dull that they get turned off by the subject from theiryoung days, resulting in mathphobia.

At the same conference, a black teacher asked me whether there was any mathe-matics in Africa before the colonial period. The question was revealing for underlyingit was a view of mathematics which we had consciously and subconsciouly imbibed ofconsidering it unthinkable that Africans could produce mathematical knowledge. Theview had fostered the myth that mathematics was a civilizing gift that Europe hadbrought to the colonies, a Promothean spark that in time would enable the backwardnatives to penetrate the secrets of science and technology and enter the world.

I asked the teacher to tell me what he meant by mathematics. He was surprisedwhen a distinction was made between Mathematics (with a capital ‘M’) and mathemat-ics (with a small ‘m’). Mathematics with a capital ‘M’ is a seminal discipline that someof us make a living from and mathematics with the small ‘m’ is what most of peopleunderstand as mathematics and most people use as mathematics. There is a differencebetween them. Mathematics with a small ‘m’ is and has been a universal activity. Nosociety, however small or remote, has ever lacked the basic curiosity and ‘number sense’that is part of the global mathematical experience. The need to record information thatgave birth to written language also brought forth a variety of number systems, eachwith its own strengths and peculiarities. Why is this so difficult to accept and so oftenignored?

What I am going to argue is that (putting in as provocative a fashion as possible),the answer lies in the nature of Eurocentrism. European mathematics had playeda considerable role in the self-consciouness of Europe, its perception of itself as thegreatest of cultures. It appropriated the contributions of non-Western cultures whilesimultaneously making them invisible. The traditional view of the way mathematicsdeveloped takes the form of a unilinear trajectory. Mathematics begins in Greecearound 600 BC and end around 400 AD. One then has the ‘Dark Ages,’ followed by

Joseph 191

Egypt

Greece

Mesopotamia

Hellenistic world

Dark Ages, but Greek learning kept alive by the Arabs

Renaissance

Europe and her cultural dependencies

Figure 2: A modified Eurocentric trajectory.

the Renaissance which was partly a result of the discovery of Greek learning. Afterthat, devolopment of mathematics restarts and continues in Europe and her culturaldependencies.

This is what I have described elsewhere as ‘classical’ Eurocentric trajectory. Butthere were already problems with this unilinear trajectory as early as first few decadesof the century. The work of scholars such as Neugebauer showed us higher level ofmathematics in Mesopotamia and Egypt and the debt owed by the early Greeks tothese civilisations.

The trajectory is now a little more complex. There is some recognition of Egyptand Mesopotamia. And a growing recognition of the Arabs but mostly as custodians ofGreek’s learnings, that is those who kept Greek learning alive before it was discoveredby Europe. Even within this modified trajectory there is no recognition of other math-ematical traditions, for example, written traditions such as Chinese, Indian or Mayan(in Central America).

But it is the notion of a stagnant period called the ‘Dark Ages’ that poses seriousproblems. Even European historians would now have doubts about characterising aperiod by such a name. However, historians of mathematics continue to subscribe tothis outdated notions. In any case, the areas which were under darkness does notinclude any area outside the Euroasian peninsula which has come to be referred to asthe separate continent of Europe. In the rest of the Asiatic and part of the Africanworld as well as the American continents, there were considerable developments goingon. Scientific knowledge was being transmitted across cultures, the catalyst being theIslamic civilisation of the 9th to the 14th centuries (Figure 1).

I will refer to this mathematical tradition as Arab, since the texts and communi-cation of that period took place in Arabic. There were contributions coming throughfrom the Hellenistic world, India and later China. Centers of learning changed fromJund-i-Shapur (important even before the rise of Islam) to Baghdad, and then to Cairoand later Cordoba and Toldeo in Spain. Some recent evidence indicates that there wasa movement later to North and West Africa (Magrheb). I wish I knew at the time of theconference of mathematics teachers from inner city schools which I mentioned earlierwhat I know now. I could have provided a better answer to the teacher who asked meabout mathematics in Africa.


Indian Brahmi numerals, c. 300 BC

Indian Gwalior numerals, c. AD 500

Eastern Arabic, c. 800

Western Arabic, or Gobar, c. 950

European apices, c. 1000

European (Durer), c. 1500

Figure 3: The evolution of present-day numerals.

When one goes on to consider the nature and range of influences that went intothe making of Arab mathematics during the period of the so-called ‘Dark Ages,’ onehas a very rich picture of multiculturalism in mathematics (Figure 1). There arethe Egyptian and Babylonian influences going into the formation of classical Greekmathematics, the mathematics associated with names such as Thales and Pythagoras.We then have a growing divergence between the classical Greek and Hellenistic tradi-tions where the latter is associated with names such as Euclid, Apollonius, Archimedesand Diophantus where new influences from Egyptian and Babylonian traditions makethemselves felt in Alexandria on the African continent. There are links between Hel-lenistic and Persian traditions, where the transmissions are not necessarily throughbooks or written records but through trade and travel where the silk route must haveplayed an important role. And when we come to the influences on Arab mathematics,the transmission of ideas from India becomes more important from around 850 AD.This is clearly illustrated in the evolution of our number system (Figure 3).

The Figure shows the genesis of our number system, starting with the IndianBrahmi system or possibly some Chinese variant, the introduction of zero, the estab-lishment of a full positional system, the evolution of East and West Arab numerals, andthe transmission across Spain and Sicily westwards to Europe. A parallel movementeastwards from India to Indo-China and South East Asia (Java, Sumatra). The simi-larities between the Gwalior system of representing numbers to our own numerals aresufficient for us to call our system Indo-Arab numerals or even Indian numerals.

So far I have been concentrating on a manifestation of Eurocentrism that takesthe form of ‘omissions and appropriation’. There is also another manifestation ofEurocentrism which may be described as ‘exclusion by definition’. In this case, you areexcluding certain mathematical traditions by the way you define mathematics. Such anexclusion is justified on the grounds that the traditions have not either been influentialin the evolution of modern mathematics or because it appears strange or because somemathematicians (with a big M) consider that they do not satisfy the litmus test of whatis mathematics, notably the presence of ‘proof.’

By this form of deprivation, you are excluding some of the earliest representations

Joseph 193

Figure 4: One of the earliest representations of numbers in a cave.

of numbers and space. On our travels around Tasmania, we came across the followingdrawings in a cave situated on a remote beach. It has been dated to period around35,000 BC (Figure 4).

The intriguing question is: Did these drawing represent early numbers? Some oftheir shapes are strangely reminiscent of early Mesopotamian numerals. There is apattern and consistency in the representation. We do not know what they are butwould it be unreasonable to assume that they are numerical symbols?

Let me take another case which I have discussed in The Crest of the Peacock. TheIshango bone (Figure 5) and the latest dating of it in a new edition by Marshak putsit around 18,000 BC. This is something I wish I knew about when asked whetherthere was any mathematics in Africa. There have been all sorts of speculations aboutwhat it was used for and what the representation on it signify. It is interesting tonote that the numbers represented at the bottom are prime numbers from 10 to 20.Another row shows a form of duplication going on: 3, 6, 4, 8, 5, 10. The most plausibleexplanation given by Marshak is that the bone is in fact a lunar calendar. The numbersin each row adds up to 30. Was such a calendar important? Here, we should lookat the calendars in terms of the habitat and livelihood of the Ishango people. Thebone was found near Lake Edward on the borders of Zaire and Zambia. The Ishangowere probably some of the earliest people we know of who were both agriculturistsand food-gatherers/hunters. During the dry season they would come down the hillsto the lake to catch fish, hunt animals who came to drink water and gather sea food.Near the end of the dry season they would move to the hills where they would plantcrops and live on their produce. There is sufficient archaeological evidence to supportthis conjecture. The calendar would therefore be an important necessity to follow thislife style. Now I would describe this bone as a mathematical artefact since it was notmerely keeping tallies of kills etc which you find with some of the earlier bones, but it is


Figure 5: The Ishango bone.

a conceptual device useful for keeping account of the passage of time and synchronisingwith economic activities of the inhabitiants.

Now consider another form of device which some have questioned about its mathe-matical worth (Figure 6). The Figure is of an Inca Quipu (1400 AD). The Inca Empireoccupied an area which constitute the present-day Peru in South America. The drawingis taken from a a book written by a Spanish commentator around the time of theSpanish conquest. It is a fairly complex device for storing all sorts of information.Numerical information could be stored using a positional number system with the helpof various types of knots, mainly consisting of figure of 8 knots, single knots and longknots. In the illustration given, and on one of the strings, you will notice one small knotrepresents one thousand, then a space followed by 3 S’s represent 300, 5 S’s represent 50and 1 represents a unit. When taken together, the number represented in our notationis 351. Each main cord is the sum of the numbers represented in the subsidary cordsand the sum of all main cords would give you the number in the top cord. This is quite acomplex system of retaining the information. There is a whole population census kepton strings that looks like a cleaning mop. On that mop you have the information aboutpopulation by age, by sex and by two different ethnic groups with sub-totals and maintotals all still distinguishable. There are over 400 quipus in the Berlin museum itselfwith other collections in London, Paris and the United States. There are hardly any inPeru.

Consider another example from the same continent, the Mayan civilisation who onthe eve of the Spanish conquest of 1519-1520 occupied over 300,000 square kilometresand covered present-day Belize, central and southern Mexico, Guatemala, El Salvadorand Honduras. The Mayans had a highly developed numeration system (Figure 7).Incidentally, when people say that the Indians were the only group to discover zero,this is not correct because the Mayans also had a zero within a positional numbersystem. The Mayans used a vigesimal (or base 20) system and their symbol for zerolooked like an egg shell. Their positional system was irregular in that after units, 20′s,instead of 400, they had 360 (i.e., 18 x 20). This irregularity may have been a result oftheir using a number system for calendrical and astronomical purpose (Figure 8). Asa result, their system lacked the main strength of the Indian system of being able tomultiply or divide by 10 by adding or removing one of the zeroes from the right handside of the number.

They had other systems of number representation, including face numerals (Figure

Joseph 195

Figure 6: An Inca official holding the quipu. ‘Inca abacus’ can be seen at the bottomleft.9). Well worth showing children who are taken aback that boring numbers can berepresented by interesting and somewhat frightening facial representations. You couldhave face numerals side by side with the bar and dots.

A question often asked is who is the earliest known woman mathematician? Inmany histories of mathematics, the name of Hypatia crops up. But to provide somealternative names, I would suggest Gargi, an early Indian woman astronomer and anunknown mathematical scribe who is present in a Mayan representation (Figure 10).

Look at the person at the top right corner. How do you know that the person was amathematician? The Mayans had different way of representing mathematical scribes.A common mode was to represent a human form with a mathematical document identi-fied by dots and dashes (or Mayan numerals) under his/her armpit. It dates back to thebeginning of common era. It is interesting in that drawing that a deity is representedas giving out the knowledge, coaxed by some of his human attendants. In the middle ofthe illustration you see the knowledge being collected and being analyzed. The stone


3 9 18 20

= (1 x 7200) + (18 x 360) + (5 x 20) + 0 = 13780

Figure 7: Mayan numerals.

section shows you face numerals and basically tells the dates on a Mayan calendar. Itis a highly sophisticated system.

The question often asked is whether all these examples constitute mathematics. Iwould say that it is mathematics with a small m. These were people who were thinkingin mathematical terms and in some cases using it for specific purposes, for constructingcalendars, keeping numerical records or embellishing myths. When talking aboutmyths, we have probably one of the earliest evidences in a recorded book from Chinacalled Chou Pei (Figure 11). Students find this interesting. Ask them to count thecircles on the right and they soon discover it is a magic square of order 3.

Here is a more recent example of ‘ethnomathematics,’ probably still in use in somebazaars in Africa, Middle East and Persia (Figure 12). The background is that incertain shops, when purchasing a carpet which entails a heavy outlay, you may agree onterms whereby you pay the shop keeper in instalments. Assume that you have agreedon the total cost of the carpet (principal), the rate of interest charged per month (r)and the number of months over which payments have to be made (n). The shop keepercan tell you very quickly what this mothly installment is. A student of mine carriedout a comparative study of the method we would use in modern mathematics with thetraditional method used by the shop keeper. Also under what circumstances would thetwo methods be equal, i.e. when would M ∗ be ≈ M ? The rest of it is straight forwardmaths where you expand a particular power series retain the first three terms anddoing that you get equation(4). You then carry out the substitutions shown in the abovefigure. It is very clear if you did not have a calculator the traditional method would bequite simple compared to the modern method where you have to calculate (1 + r)n.Consider the example where n = 24 month, p = $3000 and the annual r = 12% youwould find that both methods produce answers very close to one another: traditionalmethod, M = $140 per month and by modern method M = $141.22 per month. So hereis the case where (some people call it ethnomathematics) the mathematics prevalentin the market place is worth studying seriously. This is a problem that could be setfor senior classes. It is a useful corrective to students who are slightly contemptousof old fashioned methods when they can fall back on their calculating machines. Myfinal example is taken from a group in the United States who you would not normallyassociate with mathematical aptitudes, i.e, the African slaves who were forced to workon cotton plantations in the South. Thomas Fuller was such a slave. He was broughtto Virginia at the age of 14 after being forcibly transported from his birth place inWest Africa and became well known as a calculating prodigy. At the age of 70 hewas tested to see how quickly he could do mental sums. He was asked the number

Joseph 197

Long-count introduction glyph (glyph of the deity who is patron of the month Cumku on the sacred calendar)

17 katuns 17 x 18(20)2 = 122400 days

0 uinals

13 Ahau (day on the sacred calendar reached by counting forward the total number of days on the long-count calendar from the starting point of the Mayan calendar)

0 kins

0 tuns

9 baktuns 9 x 18(20)3 =

1 296 000 days

Figure 8: A Mayan calendar.

of seconds in a year and a half and gave the correct answers in two minutes. He wasthen asked the number of seconds a man has lived since his birth. He gave the correctanswer: 70 years 17 days and 12 hours (which was presumably his age at the time).Asked a third problem, his answer took almost ten minutes, at least partly because theproblem was not stated correctly initially. Fuller was used by the anti-slavery groupsto counter the argument that the Africans were incapable of thinking. The main plankof the pro-slavery position was that Africans were hardly human at all. They could nothandle abstract subjects such as mathematics and science. Incidentally, that was quitea common view of black people. The political philosopher, David Hume (who is seeneven today as the epitome of rational thought), also had his own pseudo philosophyrelating to black people justifying them being treated differently. We would very rarelycome across Hume’s racist views in a political science book today just as Marxists nevertalk about Karl Marx’s views about blacks.

There are four dimensions to the interests in Fuller. These are calculation prowess(i.e. a comparison between different mental prodigies), psychological (i.e., an interest inabnormal mentalities) and liberatory (which I mentioned earlier as means of counter-ing the inferiority argument) relating to blacks. But very few people, as far as I know,until the study by Paulus Gerdes and John Fauvel, discussed the ‘cultural’ dimension.The question is: Where did Thomas Fuller learn to calculate? There were obviously no


1 2 3 4

5 6 7 8

1211109

13 14 15

191817

16

0

Figure 9: Mayan ‘head variant’ numerals.

schools for slaves. The methods he learnt must have been something which was partof his culture. We know that he originated from an area which had fairly sophisticatedmethods of computation involving considerable mental work. The Yoruba method ofmultiplication is an interesting and in some cases an efficient method. So the culturalargument could be quite important in this context.

The last strand of my talk relates to a point I alluded to earlier. There is a widely-held view that non-European mathematical traditions, however ingenious are theircomputations and algorithms, lack an essential litmus test of ‘good’ mathematics andthat is a concept of proof. To provide a clear focus to the discussion, let us concentrateon Indian mathematics.

When certain historians distinguish between mathematical traditions of India andWest, they normally characterise the Indian tradition being algebraic, empirical andhaving no rigorous proofs compared to Western (especially Greek) which is charac-terised as geometric, abstract or anti-empirical and having rigorous proofs. Let meillustrate this with a quotation from Morris Kline:

There is much good procedure and technical facility but no evidence that they considered proof

Joseph 199

Figure 10: Mayan representation of mathematicians.

at all. They had rules, but apparently no logical scruples. Moreover, no general methods ornew viewpoints were arrived at in any area of mathematics. It is fairly certain that the Hindus(i.e., the Indians) did not appreciate the significance of their own contributions. The few goodideas they had, such as separate symbols for the numbers, were introduced casually with norealisation that they were valuable innovations. They were not sensitive to mathematicalvalues. (Morris Kline, 1972, p. 190)

I have taken Morris Kline as an illustration. I could take examples from otherauthors as well, including G.E.R. Lloyd. But Kline is sufficient. Now I think Kline’sview is based on a complete misconception. How did this misconception arise? Partlybecause of the way that one sees the sources of Indian mathematics. When we lookat Aryabhata’s Aryabhatiya we have merely statements of results. Proofs are oftenfound in commentaries. If you study the Bhaskara-I’s commentary on Aryabhatiya, itprovides both flesh to Arybhata’s cryptic verses as well as demonstrations. Now theWestern tradition, probably following on Greek tradition, has in the same text both thestatement of results as well as the proofs. Commentaries do not serve the same functionas in Indian mathematics. Remember, this is a tendency that runs right throughIndian mathematics upto Srinivas Ramanujan. Ramanujan’s ‘lost’ notebooks contain anumber of results which has provided life’s work to a number of mathematicians. Thatdid not mean that there were no proofs at all.

Proofs have different purposes:

• Psychological: To convince the student. Success depends on notation, a way inwhich an arguement is formulated, organised and presented.

• Social and Cultural: Proofs are social and cultural artefacts. How a proof works,depends on how its intended audience come prepared to follow it. For instance,the claims made by proofs about mathematical objects are culturally determined.For example, consider the difference between Euclidean vs Navajo (or IndigenousAustralian) view of space. How space is viewed is an important element in proof.


Figure 11: Magic squares in China.

• Logical: A Greek preoccupation: In Greek tradition, proof quite often concen-trated just on logical elements.

Within the Indian tradition, demonstration or Upapatti (as it is known) primarilydepends on the audience you are aiming at. Clearly you use different ‘proofs’ fordifferent audience. The important thing is that you have to convince a student andalso have to look at the background of the student to find out what they are comingwith. This is the reason that ‘Euclidean’ geometry never received a receptive audiencein India at all before the coming of modern mathematics. There were various attemptsespecially in Moghul times to introduce ‘Euclidean’ geometry to Indian mathematicsbut the attempts failed.

Just to illustrate this let me take an example that has been discussed by M.D. Srini-vas.

Say what is the hypotenuse of a plane figure, in which the side and upright are equal to 15 and20? Show the upapatti underlying the usual mode of computation.The upapatti follows: It is two-fold, one ksetragata (‘geometric’) and the other avyaktya (‘al-gebraic’). The geometric demostration must be shown to those who do not understand thealgebraic one. (Bhaskaracharya’s Bijaganita)

Look at the Pythagorean theorem which is very familiar to everyone. This is takenfrom Bhaskracharya’s Bijaganita. The Figure asks that what is the hypotenuse ofa plane figure in which the side and the upright are equal to 15 and 20? Show theUpapatti underlying the usual mode of computation. Then he goes on to say that youhave 2 different ways of demonstration.

One is the geometric demonstration for the people who have a strong visual sense and theywould be convinced by seeing and that is called Ksetragata. The other is the algebraic one. Itis important you show the right proof to the right people depending which is the one that theyunderstand best. The geometric is not shown to the algebraic and vice versa.

Joseph 201

Let P = Prinicpal; N = Number of Months; r = montly interest rate M = Monthly Payment (using popular calculation) M = Monthly Payment (using modern calculation) and I = Interest

M = [P + I ]N1 where I = P [12r]1

2N12

So

And

(1) (POPULAR)

(2) (MODERN)

WHEN IS M M ?

M = P + PNr1N

12

M = r (1+r)N P

(1+r)N - 1

Rewrite (2) as(3)

(4)

(5)

(6)

Expand as a power series and retain first three terms

Substitute (4) in (3) and simplify:

where

For small q (0 < q < 0.5),

Substitute (6) in (5) to get:

for large N and small r

Example: N = 24 months, P = $3000, Annual r = 12% M = $140 per month M = $141.22 per month�

M = rP11 -

(1 + r)N

1(1 + r)N

12

1(1 + r)N

1 - Nr + (N + 1)Nr2

M PN (1 - q)

12

q = (N + 1)r

11 - q

1 + q

1 1N 2M MP + P(N + 1)r

Figure 12: Popular calculation.

To conclude, the general tenor of my argument may be summed up in the followingway. Why is Eurocentrism an aspect that should be taken into account by anybodywho wants to use history in the teaching of mathematics? And I put it in the followingterms. Eurocentrism has prepared us to consider it unthinkable that the non-Europeancould produce mathematical knowledge. It fostered the myth (referring to the timeof colonisation) that mathematics was a civilizing gift that Europe got through thecolonies. The Promothean spark that in time would enable backward native to pen-etrate the secrets of science and technology to enter the modern world. There wasa savage counterpart created to the western minds. There was an imperial ideologylegitimising the traditional mathematical development as a purely European product.Even after the demise of Europe, the prejudices concerning the origins of mathematicsand science have been especially difficult to come back as they are still very functionalto the legitimation of the economic and the political supremacy of the western powersin the contemporary world.

This is putting it in a very provocative fashion. I will end with a personal story.Around the time that South Africa became independent, I was invited by the AfricanNational Congress to advise on the restructuring of the mathematics curriculum par-


ticularly for the black universities but also for the schools. I found two very interestingfactors at work. First, I was amazed to find that in the black universities students couldcomplete a degree in mathematics without studying calculus. When one asked why thiswas so, the answer was that under Apartheid, calculus was seen as too abstract for theblacks. And this was a seriously-held view!

Second, in some of the white universities, black students could take courses understrictly controlled circumstances. I was surprised at the conference to come acrossa number of mathematics teachers who held diploma in biblical studies. What hadpresumably happened was that some of the white universities actually taught themmathematics but ended by giving them diploma in biblical studies. A number of peopleknew what a diploma in biblical studies meant and it is possible that some of thegovernment officials had connived in perpetrating this fraud. But as long as there wasno threat of students being taught such ‘subversive’ subjects as mathematics, nobodycomplained. So, when people tell me there is no politics or culture in mathematics, thissentiment has a hollow ring in the context of South Africa or even an inner city schoolin England.

References

Joseph, G.: 2000, The Crest of the Peacock: Non-European Roots of Mathematics, 2ndedn, Princeton University Press.

Nelson, D. Joseph G.G., W. J.: 1993, Multicultural Mathematics, Oxford UniversityPress, Oxford.

Infinite Series across Three Cultures: Background and Motivation

George Gheverghese JosephUniversity of Manchester, UK. Email: [email protected]

The subject of the essay is infinite series across cultures, I will concentrate mainly onthe non-mathematical aspects relating to it.

Two powerful tools contributed to the creation of modern mathematics in the seven-teenth century: the discovery of the general algorithms of calculus and the developmentand application of infinite series techniques. Many of you have been introduced to cal-culus, (i.e., the general algorithms of calculus consisting of differentiation, integrationand other techniques) and probably know that the names normally associated withthe development of that stream are Newton and Leibniz. The other stream was thediscovery and applications of infinite series and again the European names that areassociated with it are Mercator, Wallis, Gregory, Newton and Leibniz (Figure 1). Thesetwo streams of discovery reinforced each other in their simultaneous developmentbecause each served to extend the range of application of the other.

However, what is less known is that the origin of the analysis and derivations ofcertain infinite series, notably those relating to the arctangent, sine and cosine, was notin Europe, but an area in South India which now falls within the state of Kerala. Froma region covering less than a thousand square kilometres north of Cochin and duringthe period between the fourteenth and sixteenth century, there emerged discoveries ininfinite series that predate similar work of Gregory, Newton and Liebniz by at least200 years.

There are a number of questions worth asking about the activities of this group ofmathematicians/astronomers (from now on referred to as the Kerala School) apart fromtechnical ones relating to the mathematical content of their work. In this talk I willconsider specific questions relating to the social landscape in which the Kerala Schooldeveloped, the mathematical motivation underlying their interest in a particular se-ries, the arctan series (and its special case, the ‘pi series’). To provide a cross-culturalcontext, I will compare the Kerala work with those in China during the eighteenthcentury and only briefly mention the European work of the seventh century since ithas had adequate exposure in the literature.

Let us begin with a brief introduction to the chronology, the actors and subject mat-ter of Indian mathematics (Figure 2). Some of the earliest texts in Indian mathematicswere the Sulbasutras. These were essentially manuals for surveyors containing in-structions constructing sacrificial altars (vedi) and locating sacred fires (agni) that hadto conform to certain shapes and measurements if they were to be effective instrumentsof sacrifice. In trying to construct a circular altar equal to the area of a square altar, thesulbkaras (i.e., the authors of these manuals of which three were important, namelyBaudhyana, Apastamba and Katyayana) came across the problem of what we wouldnow describe as the incommensurability of ‘pi.’ And in constructing a square altar

204 Infinite Series

CREATION OF MODERN MATHEMATICS (17th C)

Discovery and Applications of Infinite Series

General Algorithms of Calculus

(Newton and Liebniz)

(Mercator, Wallis, Gregory, Newton and Liebniz)

Figure 1: Origin of calculus.

double the area of another square altar, they came across the problem of the incom-mensurability of

√2. Here we have the beginnings of an Indian preoccupation with

these two magnitudes which surfaces in a different form later in Kerala mathematics.However, a more direct inspiration for Kerala mathematics were the works of Aryab-

hata and his commentator, Bhaskara-I (Figure 3).In 499 AD (i.e., 1500 years ago) at the age of 23, Aryabhata, composed his seminal

text Aryabhatiya. An Arabic translation of the text entitled “Zij al-Arjabhar” was madearound 800 AD. The influence of the astronomical and mathematical ideas in the text,both inside and outside India cannot be overestimated. His influence prevailed at leastin Kerala for about a thousand years. When we talk about the Kerala work we havein mind the period from about the birth of Madhava (c. 1350 AD) to about 1600 afterwhich there are texts but they are not important (Figure 4).

What the Figures 2 and 3 indicate is that the history of Indian mathematics isa very long one and so is the history of numeracy among its inhabitants. Being aconference on science education, Figure 5 may be of special interest. It goes back toa period around 300 BC and is from a Jaina text called Sthananga Sutra. The topicsstarred were the ones taught to everyone and consisted of patiganita, kalasavrna, rajjuand possibly rasi as well. The other topics, namely yawat-tawat, varga, ghana, varga-varga, vikalpa constituted more advanced mathematics. What it shows is a societywhich valued numeracy and the skills of calculation were present among many of itspeople.

The story of the discovery of Kerala mathematics sheds some fascinating light onthe character of the historical scholarship of the period. In 1832, Charles Whish read apaper to a joint meeting of the Madras Literary Society and the Royal Asiatic Societyin which he referred to five works of the period, 1450-1850: Tantrasamgraha (A Digestof Scientific Knowledge) of Nilakantha (1444-1545), Yuktibhasa (An Exposition of theRationale) of Jyesthadeva (fl. 1500-1610), Kriyakramakari (Operational Techniques)of Sankara Variyar (c. 1500-1560) and Narayana (c. 1500-1575), Karanapaddati (AManual of Performances in the Right Sequence) of Putumana Somayajin (c. 1660-1740)

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1800

1700

1650

1550

1500

1450

1400

1350

1300

Sankara Varman (1800 - 1838)

Putamana Somayaji (1660 - 1740)

Achuta Pisharoti (1550 - 1621)

Jyesthadeva (1530 - 1610)

Narayana and Sankara Variar (b. c. 1500)Chitrabhanu (1474 - 1550)

Nilakantha (1444 - 1543)

Damodara (b. 1410)Paramesvara (1380 - 1460)

Madhava (1340 - 1425)

Sadratanamala

Karanpaddati

Yuktibhasa

Kriyakramakari

TantrasamgrahaAryabhatiyabhasya

Figure 2: Indian mathematics: Kerala school.

and Sadratnamala (A Garland of Bright Gems) of Sankara Varman (1800-38) (Figure6).

An important feature of the last four texts is their claim to have derived their mainideas from Madhava (c. 1340-1425) and Nilakantha who are referred to as acharyas (orteachers). It is possible that Madhava wrote a comprehensive treatise on astronomyand mathematics, including sections on infinite series. And it is probably to the con-tents of this text that others who came after him refer to in such glowing terms. Sucha work remains to be discovered.

These authors form part of a tradition of continuing scholarship in Kerala over aperiod four hundred years from the birth of Madhava in 1340 to the probable death ofPutumana Somayajin in 1740. In the present state of knowledge of source materialsit is difficult to assign many of the developments to any particular person. The resultsshould be seen as produced by members of a school as it were, spread over severalgenerations (Figure 7).

Now what did their work consist of? Let me give you a flavour by quoting fromJyesthadeva’s Yuktibhasa. This is a literal translation and relates to the arctan serieswith the contents in the brackets inserted for purposes of clarity. Note that capital Sine(Cosine) are sometimes called Indian sine (cosine) and is the product of radius and oursine (cosine).

The product of given Sine and the radius divided by the Cosine is the first result. From thefirst (and then the second, third, . . . etc.) results, obtain (successively) a sequence of resultsby taking the square of the Sine as the multiplier and the square of the Cosine as the divisor.Divide (the above results) in order by the odd numbers 1, 3, 5, . . . etc. to get the (full sequenceof) terms. From the sum of the odd terms, subtract the sum of the even terms. (The result)becomes the arc. In this connection, it is laid down that the (Sine) of the arc of (that of) itscomplement, whichever is smaller, should be taken here (as the ‘given Sine’); otherwise, the

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-1000

-500Year

0

500

1000

1500

Harappan Period Weights and Measures

Vedic PeriodBaudhayana

Apastamba

Satapatha BrahmanaSulbasutras

Jaina and Buddhist Period Sthananga Sutra

Bakhshali ManuscriptAryabhata AryabhatiyaBrahmagupta BrahmasphutasiddhantaBhaskara I AryabhatiyabhasyaMahavira GanitasarasamgrahaBhaskara II Lilavati

"Classical" Period

Kerala PeriodMadhavaNilakanthaJyesthedeva

Tantrasamgraha

Yuktibhasa

Figure 3: Chronology of Indian mathematics.

terms, obtained by the (above) repeated process will not tend to a vanishing magnitude.

There are a couple of interesting features about the Yuktibhasa. First, its most reli-able version is in Malayalam and not Sanskrit. This is an important point since prac-tically all major texts on Indian mathematics or astronomy were written in Sanskrit.Second, there is no translation in English of the text available yet. This is unfortunate,but the reason is simple. We require someone with an unusual combination of skillsto produce a good translation: someone conversant with old Malayalam (very differentfrom the present Malayalam), someone with knowledge of technical Sanskrit, some onewith a reasonable knowledge of mathematics and preferably astronomy and someonewho possesses what I would describe as mathematical imagination. I would like totake this opportunity to pay tribute to Professor K.V. Sarma, who has a good modicumof all these skills and who has over the last forty years with a single-minded devotionand hard work brought to us the treasures of Kerala mathematics and astronomy.Whenever I present seminars in different places and different continents on Keralamathematics, I am asked is there any Yuktibhasa available for them to read, and I saythey have to know Malayalam since there was a modern Malayalam translation fiftyyears ago!

If the quotation of Jyesthadeva is put in modern notation, it becomes quite straightforward. I will not go into the technical mathematics of this expression. But what wehave here is the well known arctan series, usually known as the Gregory series namedafter James Gregory, a Scottish mathematician, who studied the series in 1671. In mybook, The Crest of the Peacock, I have argued that it should be called the Madhava-Gregory series, since it has been attributed by a number of members of the KeralaSchool to their founder, which would then predate its first appearance with a detailedderivation three hundred years before Gregory.

There is another aspect to the Yuktibhasa which is interesting. As the very name

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Harappan Period

Vedic Period

Jaina and Buddhist Period

"Classical" Period

Kerala Period

Babylonian and Egyptian Mathematics

"Chou Pei" - Earliest Chinese Text

Rise of Greek Mathematics

Sulbasutras

Rise of Chinese MathematicsEuclid's Elements

Chinese "9 Chapters"Rise of Mayan Mathematics

Rise of Arab Mathematics

Al-Khwarizmi's "Algebra"

Inca Quipu

Rise of European Mathematics

MODERN MATHEMATICS

Figure 4: Time lines: India and the rest of the world.

Yuktibhasa implies, unlike any other Indian mathematical text known to me of thatand earlier periods, the text contains a detailed exposition of the rationale (or proofs)usually in a verbal form, consisting of a mixture of technical terms and katapayadinotation, a refinement of Aryabhata’s alphabet-numeral system of notation.

It is from this rationale that one puts together the derivation of the arctan seriesaccording to Kerala mathematicians. I will not consider the detailed derivation here.Instead, a few words about the approach. The approach involves what is known as thedirect rectification of an arc of a circle, i.e., the summation of very small arc segmentsand reducing the resulting sum to an integral. From the Madhava-Gregory series, theKerala School was able to derive the series for ‘pi,’ known in mathematical literature asthe Leibniz series. I would suggest that in all fairness, it should be renamed Madhava-Leibniz series.

Before I leave this subject, let me say something more about the method of directrectification that formed the basis of the Kerala approach to the derivation of a numberof infinite series. This may be of some interest to the mathematicians among you.This is a very interesting geometric technique different from the method of exhaustionused in the Arab and European mathematics. In the Kerala case we sub-divide an arcinto unequal parts and while in the other (Arab and European) case there is a sub-division of the arc into equal parts. The different technique used in Kerala was notbecause the method of exhaustion was unknown to the Indians. Indeed, it is likelythat Aryabhata used the method of exhaustion to arrive at his accurate estimate ofthe circumference for a given diameter. The ‘exhaustion’ method was probably avoidedbecause the calculation, involving working out the square roots of numbers at eachstage of the calculation, was a tedious and a time-consuming task. What we have here

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1. PATIGANITA (ETYMOLOGY : "SAND-CALCULATION")

(I) PARIKARMA : Number representation and the four fundamental operations of arithmetic

(II) VYAVAHARA : (Arithmetic problems, including the "Rule of three")

2. KALASAVRNA : Advanced treatment of fractions

3. RAJJU : Plane geometry calculations as carried out by means of a rope

4. RASI : Mensuration of plane figures and solids

5. YAWAT-TAWAT : Study of that which is unknown or algebra

6. VARGA : Problems involving square and square-root

7. GHANA : Problems involving cube and cube-root

8. VARGA-VARGA : Problems involving higher powers and higher roots

9. VIKALPA : Permutations and combinations ()

Figure 5: Maths curriculum according to Sthnanga Sutra.

may be an interesting foundational difference between what I would call the Indianapproach and the Greek-Arab-European approach. In the Indian case, numbers weremerely entities to be operated on, and the stress was on operations rather than thenumbers themselves. As a result Indian mathematics steared clear of any philosophicaldifficulties with incommensurability. For example, surds (karani) were accepted as“proper” numbers from the time of the Sulbasutras and rules for handling them weredeveloped. In place of “rational-irrational” classification, a notion of “exact-inexact”numbers may have prevailed.

What motivated the Kerala School to undertake the work that they did? The mo-tivation may be found in a verse from Aryabhatiya which happens to be one of themost famous verses in Indian mathematics. It tells you how for a given diameter youcalculate the circumference of that circle:

Add 4 to 100, multiply by 8, and add 62,000. The result is approximately (?) the circumferenceof a circle whose diameter is 20,000. (Aryabhata’s Aryabhatiya (Verse 10))

Certain historians of mathematics (such as Kay and Morris Kline) have argued thatthe Indians were not aware of the fact that π could never be exactly determined. I seethis confusion arising in the minds of these historians because of the mistranslation ofthe word Asana as “approximate” or “rough inaccurate value” as in the quotation. Theword is more subtle term than that. What it conveys is the notion of unattainability.“Unattainable” is something that one can never reach. Unless one understands thisone can not understand the interest of the Kerala School in this quotation.

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NILAKANTHA (b. 1444)Aryabhatiyabhasya : "Commentary on Aryabhatiya"

Tantrasamgraha : "A Digest of Science"

JYE�STHADEVA (Fl. 1550)

Yuktibhasa : "An Exposition of Rationale"

NARAYANA (fl. 1525)/SANKARA VARRIER (fl. 1550)

Kriyakramakari : "Performance in Correct Order"

PUTAMANA SOMAYAJI (c. 1660-1740)

Karanapaddati : "Operational Methods"

SANKARA VARMAN (1800 - 1838)

Sadratnamala : "A Garland of Pearls"

Figure 6: Major texts of the Kerala school.

Let me illustrate this point with a long passage from Nilakantha’s commentary,Aryabhatiyabhasya. It is worth reading carefully.

Why is only the approximate value (of circumference) given here? Let me explain. Becausethe real value cannot be obtained. If the diameter can be measured without a remainder, thecircumference measured by the same unit (of measurement) will leave a remainder. Similarly,the unit which measures the circumference without a remainder will leave a remainder whenused for measuring the diameter. Hence, the two measured by the same unit will neverbe without a remainder. Though we try very hard we can reduce the remainder to a smallquantity but never achieve the state of ‘remainderlessness.’ This is the problem. (Nilakantha’sAryabhatiyabhasya (1500 AD))

What it shows is that Nilakantha and others understood the ‘irrational’ nature of π.So the question is what did they do as a result? The following passage from Sankaraand Narayana’s Kriyakramakari suggests a strategy:.

Thus even by computing the results progressively, it is impossible theoretically to come to afinal value. So, one has to stop computation at that stage of accuracy that one wants and takethe final result arrived at by ignoring the previous results.

Indian mathematicians were not generally preoccupied with the philosophical im-plications of numbers as mathematical objects. Faced with irrationality, they tried toarrive at as accurate an estimate as possible. And this is what is being suggested inKriyakramakari.

However, in applying the infinite series approach to estimate the circumference,the Kerala mathematicians came across a serious difficulty. The problem is that theMadhava-Leibniz series converges very very slowly. For example, summing the first 19terms on the right hand side of: π/4 = 1−1/3+1/5− . . . would give a highly inaccurateestimate of π as 3.194.

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Madhava (ca. 1340 - 1425) Paramesvara (ca. 1380 - 1460) Damadara (b. 1410) Nilakantha (1444 - 1543) Chitrabhanu (1474 - 1550) Narayana (ca. 1525 - 1610) and Sankara Variyar (ca. 1500 - 1560)

Damodara (b. 1410) Jyesthadeva (ca. 1500 - 1575) Achuta Pisharoti (ca. 1550 - 1621)

Figure 7: Teacher-student lineage in the Kerala school. (The names underlined aregenerally recognised as the major figures of the Kerala School.)

The problem was tackled in two directions: (a) rational approximations by applyingcorrections to partial sums of the series; and (b) obtaining more rapidly convergingseries by transforming the original series. There was considerable work in both direc-tions as shown in detail in Yuktibhasa and Kriyakramakari. As an illustration of (a)from the Yuktibhasa, consider the incorporation of the following correction term to theMadhava-Leibniz series: Fc(n) = (n2 +1)/(4n3 +5n) where n is the number of terms onthe right hand side. Applying this correction where n = 11 , the implicit estimate of πis 3.1415926529 which is correct to 8 places. And this interest in increasing the accuracyof the estimate continued for a long time, so that as late as the nineteenth century theauthor of Sadratnamala estimated the circumference of a circle of diameter 1018 as:314, 159, 265, 358, 979, 324 correct to 17 places! What the work exhibits is a measure ofunderstanding of the concept of convergence, of the notion of rapidity of convergenceand an awareness that convergence can be speeded up by transformations. Similarwork was found in modern mathematics only as late as the end of the 18th century.

Incidentally, there was a whole range of other achievements of the Kerala School inmathematics and astronomy which I will not discuss here, except to mention that usingvery similar approaches they derived the Sine series, Cosine series and something thatI think is of interest to mathematicians in general, the Taylor series. So the ubiquitousTaylor series was already known in India about two hundred and fifty years before itentered modern mathematics.

To understand the context in which the mathematics developed, there is a need totake a broad look at the social landscape of medieval Kerala society and seek answersto the following questions:

• What was the nature of the social structure of medieval Kerala?

• What was the pivotal role of the Kerala temple?

• How was scientfic knowledge acquired and disseminated in medieval Kerala?

Each of these questions could well provide enough subject matter for another essay.Let me very briefly bring out a few points. When I initially started research on thissubject, I thought I found a fairly plausible explanation for the genesis of mathematicsand astronomy in this geographically remote part of India. In a way, why I found re-search in this area very interesting was because it upset a whole lot of preconceptions,including some of my earlier conjectures.

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METHOD OF DIRECT RECTIFICATION

Find the length of an arc by approximating it to a straight line

Involves summation of very small arc segments and reducing the resulting sum to an integral

INTERESTING GEOMETRIC TECHNIQUE: The tangent is divided up into equal segments while at the same time forcing a sub-division of the arc into unequal parts

Contrast with "method of exhaustion" in European and Arab mathematics where there was a sub-division of an arc into equal parts

Adoption of "infinite series" technique rather than the "method of exhaustion" for implicitly calculating p was not through ignorance of the latter in Kerala

A Foundational Difference In Approach

INDIAN : Numbers are entities whose value depends on their efficacy in mathematical operations

EUROPEAN (GREEK) : It was from measurability that countability and other operations stemmed

++

++

++

++

Figure 8: The approach.

As I mentioned before, the members of the Kerala School were predominantly Nam-buthri Brahmins with a few who came from sub-castes, such as the Variyars and thePisharotis, traditionally associated with specific duties in the temple. Within a mainlytwo-tier caste system, consisting of Brahmins and Nairs, two institutions operatedto strengthen and sustain the economic and social dominance of the Nambuthris toa degree not known elsewhere in India: the janmi system of land-holding and theNambuthri control of vast tracts of land owned by temples. There were other factorsthat helped to strengthen the economic and social powers of the Nambuthris. The Nairspractised the marumakkattayam (matrilineal) system of descent without the formalinstitution of marriage. Sexual alliances between Nair women and Nambuthiri menwere permitted, indeed sometimes encouraged, with children of such unions remainingthe sole responsibility of their mother’s family. At the same time, the Nambuthrisoperated a system of patrilineal descent (makkatayam), with a form of primogeniturethat allowed only the eldest son to inherit land and property and to marry Nambuthriwomen. The eldest son was also required to provide for the material needs of hissiblings consisting of younger brothers and unmarried sisters (of whom there werea number given the operation of the system).

Madhava and all those who knew and followed him lived and worked in large com-pounds called illams in villages with predominantly Nambuthri settlements. Set wellaway from roads to prevent contact with others, often surrounded by a high wall, eachillam had its own well for water, a tank for bathing and a number of outbuildings. Manyof these illams belonged to households that owned large landed properties and were

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very affluent. With their estates farmed by workers or tenants from lower castes andoften under the management of Nairs, the Nambuthris, and particularly the youngersons, enjoyed considerable leisure and were expected to pass their time in study andritual observances.

These illams provided a base for the education of the young in Sanskrit works, in-cluding mathematical and astronomical classics, notably the Aryabhatiya of Aryabhata(b. 476 AD) and its commentaries. Not only was traditional knowledge transmittedin these illams by rote, but they also provided a centre for research and scholarship.Sometimes, the scholars wrote commentaries on the classics and in those commen-taries they appended their own discoveries as additions and supplements. The shortdistances between the illams, the role of the temple and political stability combinedto provide for long and stable development, usually based on generations of teacher-student relationships. A study of their interaction with certain temple personnel (espe-cially, the ambalavasis such as Sankara Variyar and Achuta Pisharoti) may shed lightboth on how non-Brahmin Hindus were recruited into their circle as well the process bywhich a wider dissemination of the results of their work in mathematics and astronomytook place into the neigbouring areas, notably today’s Tamilnadu.

Now even a cursory examination of the social background of the members of theKerala School would indicate that many were Nambuthri Brahmins. But Madhavawas not one. He was an Empran Brahmin: a member of a group who were tryingvery hard to be identified as Nambuthris. Yet he was pursuing activities such asstudying mathematics and astronomy which per se did not constitute “high” statusactivities. The most notable member after Madhava, Neelakanthan, belonged to thehighest rank among the Nambuthris. He was a somayagi, one of the select sub-casteamong the Nambuthris, who could carry out the soma sacrifices. But there were alsoother members of the Kerala School who were not brahmins. There was, for instance,Sankara Variar, where the name Variar indicated that he belong to the Ambilavasis, acaste of temple servants. And similarly with Achuta Pischaroti. This would indicatethat the Kerala School were an interesting group following an interest in mathematicsand astronomy that did not have great social value or status, a group that to someextent cut across caste lines and a group who had considerable interactions with thetemple personnel. Rajan Gurukkal’s study of the medieval history of Kerala and theimportance of the temple culture is particularly illuminating. The temple may havefulfilled an important purpose: it served as an institution for acquiring and dissemi-nating knowledge. lt was an influential organisation since it combined religious powerwith secular power, being in many cases powerful landlords in their own right. Thetemple served as a medium through which the Nambuthris exerted their power andkept other groups in check. There are clearly parallels between the power of the Churchin medieval Europe and that of the Temple in medieval Kerala.

Another aspect, delving into the background of the members of the Kerala School,would indicate that a number of the Nambuthris may have been younger sons. Thisfact could lead to an interesting theory. As mentioned earlier, the Nambuthris followeda strict system of primogeniture, so that all landed property went to the eldest son.There was the additional twist. Only the eldest son could marry a Nambuthri woman.

Joseph 213

The younger sons never married but formed sexual partnerships with Nair women.So we had a situation of a number of Nambuthris freed of all economic and familyresponsibilities, a truly leisured class.

From these facts it would be a simple matter to posit the following scenario. Agroup of younger sons, who had very little to do and coming from extremely well-off circumstances, especially since in the Kerala context then, the Nambuthris werealso the biggest landlords exerting their control directly or through the temple, wereable to live a life of leisure. They had no family responsibilities and their religiousduties were confined to a few and not very demanding rituals. Some wrote eroticpoetry and a many others whiled away their time in other pursuits. But there werea few who pursued their interest in astronomy and mathematics over a period of aboutthree hundred years, sustained by the institution of ‘guru-chela’ prevalent among theNambuthris of that time. While this explanation is attractive, it would seem somewhatsimplistic. First, it does not account the presence and the important influence of non-Nambuthris as members of the Kerala School. Second, this explanation ignores thesymbiotic nature of the relationship between the traditional jyotish who came from thelowly Kaniyan caste and the Nambuthri jyotish. Third, the granthaveri (i.e., villagerecords) of Kerala of this period is full of information about the metrical precision ofa number of artisans and craftsmen (such as the carpenter, the trader, the builderand the architect). A number of them showed some awareness of the developmentstaking place in astronomy and mathematics during that period. The granthaverie andtemple records remain a good but relatively untapped source of information about the‘calculating people’ of the period.

Incidentally, a study of the social context of Kerala mathematics has an additionalbonus. There is a deeply entrenched notion in standard histories of mathematics thatall non-European mathematics is utilitarian. A number of Indian scholars have falleninto the same trap. They search for the motivation behind Kerala mathematics in as-tronomy, navigation and other practical pursuits. One should never ignore the practicalmotivation. After all many of the members of Kerala School were both mathematiciansand astronomers. The texts of that period cover both subjects. However, a lot of thework on infinite series do not have any direct applications to astronomy. So whatled them on in their pursuit of knowledge? I have this vision, of a group of ‘pure’mathematicians sitting around in Kerala between the 14th and 16th centuries, likeHardy and Littlewood in Cambridge, indulging in their passion and probably boastingof the fact that the mathematics that they did was of no use to anyone! Some ofthem probably delighted in long and tedious calculations, such as the one reportedlyundertaken by Madhava in calculating the Sine tables to 12 places of decimals! Abouta hundred years later the Arab mathematician, Jamshid al-Kashi, working in theSamarkand Observatory obtained an implicit estimate for π, correct to 16 places ofdecimals, by circumscribing a circle by a polygon having 805306368 sides! There seemedalso in this case to a veritable fascination with numbers and a boundless delight incalculation which was far removed from any utilitarian concern.

The mathematics produced by the Kerala School was not trivial nor elementary inany sense. And this would bring into question another stereotype regarding Indian

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mathematics. Standard histories of mathematics would want us to believe that mathe-matics in India which was elementary and involved mainly arithemetic, virtually cameto a stop with Bhaskara II in the 12th century. The existence and content of Keralamathematics would question this interpretation.

An important reason for taking a cross-cultural perspective in examining the devel-opment of a particular area in mathematics is that it provides a useful indication ofdifferences in methods and motivations between different mathematical traditions. InEurope, the details of the circumstances and ideas leading to the discovery of the arctanseries by Gregory and Leibniz are well-known. It was an important event because itwas a precursor to calculus. In an attempt to discover an infinite series representationof any given trigonometric function and the relationship between the function and itssuccessive derivatives, Gregory stumbled on the arctan series. He took, in terms ofmodern notation, dθ = d(tanθ)/(1 + tan2θ), and carried out term by term integrationto obtain his result. Leibniz’s discovery arose from his application of fresh thinking toan old problem, namely quadrature or the process of determining a square that hasan area equal to the area enclosed by a circle. In applying a transformation formula(similar to the present-day rule for integration by parts) to the quadrature of the circle,he discovered the series for arctan. It must be pointed out, however, that the ideas ofcalculus such as integration by parts, change of variables and higher derivatives werenot completely understood then. They were often dressed up in geometric languagewith, for example, Leibniz talking about “characteristic triangles” and “transmutation.”

The Chinese work is interesting for a different reason. Infinite series, as a math-ematical object, was introduced into China divorced from its European context, i.e.,calculus. The introduction of European mathematics into China began in the closingdecades of the sixteenth century, when the Chinese first came in contact with theJesuits. In their intention to spread their religion in China, the Jesuits arrived fromEurope bringing with them both new technological gadgets as well as scientific theorieswhich, though not updated with more recent discoveries in Europe, proved a sufficientnovelty and attraction for the educated classes. In 1601, the Italian Jesuit, MatteoRicci (1552-1601) began his translation of the first six books of Euclid’s Elements intoChinese in 1607. Later, in the last few decades of the Ming dynasty, many astronomicalbooks were translated into Chinese. But most of the scientific books translated werepre-Newtonian publications. In early Qing dynasty, after listening to a debate betweena Jesuit astronomer, Adam Schall, and a Chinese astronomer, Yang Guangxian, theKangxi Emperor, became interested in Western science. In answer to an invitationto send more mathematicians and astronomers, Louis XIV of France sent a group ledby J. de Fontaney, “the King’s mathematician,” and asked them to make astronomicalobservations, study the flora and fauna, and learn the technical arts of China. In1690, the French Jesuits began teaching mathematics to the Emperor and his courtiers.Pierre Jartoux, a French Jesuit, arrived in China in 1701 and taught at the court. Heintroduced three results new to Chinese mathematics: the power series for sine, versedsine and for π which was derived from arcsine function. The last result was attributedto Newton. For none of these results did Jartoux provide a proof. The calculus neededwas not known in China until the middle of the nineteenth century.

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Ming Antu (d. 1765) was an astronomer who worked with the Jesuits in cartographyand later on reforming the astronomical system. At the time of his death, he wasthe director of the Imperial Board of Astronomy. In his book, Ge Yuan Mi Lu Jie Fa(Quick Methods of Trigonometry and for Determining the Precise Ratio of the Circle)contains the statement and proof of nine formulae, including the “three formulae ofMaster Jartoux.” It is possible that Ming Antu was introduced to the three formulae byJartoux himself. His proofs are based on the generalisation of a method occurring bothin Chinese and European tradition: the method of the division of the circle. In China,it is found in Liu Hui’s commentary on the premier text, Chiu Chang Suan Shu, fromthe beginning of the Christian Era. The idea of the method is to approximate thecircle by inscribing polygons, the number of sides which is doubled at each step. Thismethod was extended by using continued proportions (lu) as an algebraic language, sothat it applies to the measurement of any arc. In 1720, Takebe Katahiro, a Japanesemathematician, expressed for the first time the square of the length of the arc of thecircle as an infinite power series of the sagitta (or the cosine of the half angle). Both theChinese and Japanese derivation were heavily based on their common mathematicaltradition.

I will end by some stray reflections on certain intriguing connections between Ker-ala mathematics and some subsequent developments. An interesting question is whyis it that Kerala school which came so close to the concept of the limit seem to shy awayfrom it? If they could have incorporated the limit into their work, calculus would havebeen first established in Kerala. We know that Bhaskara II had already resolved theidea of infinitesimal in his astronomical work. The missing element, in my view, wasthe concept of limit. I would suggest that the answer may lie to some extent in thenature of Indian mathematics.

To illustrate from a later period, consider the case of Master Ramachandra. In 1850,Yesudas Ramchandra wrote a book in which he tried to revive the spirit of algebra “soas to resuscitate the native disposition of (the Indians) that had been eroded over thecenturies.” The book was republished nine years later in England as a result of theefforts of Augustus De Morgan, an English logician and mathematician. De Morganpointed out in the preface, Ramchandra’s essential contribution was the applicationof the theory of equations as found in Bhaskara II’s Bijaganita to the solution of anelementary problem in calculus—the obtaining of the maxima and minima of a function. The function could be quadratic or of higher order. And he did this without the helpof differential calculus making the theory of equations as the starting point.

This attempt should be seen in the context of a widespread perception, even today,that may be traced back to Colebrooke’s book on Indian algebra, first published in 1817.This perception is well summed up by his remark that the Indians had “cultivatedalgebra much more, and with greater success than geometry; as is evident from thecomparatively low state of knowledge in the one and the high pitch of attainmentsin the other.” So that, according to De Morgan, one should see Ramchandra’s effortas bridging the discontinuity between an Indian mathematical tradition which wasperceived as algebraically strong but geometrically weak and modern calculus withBhaskara’s theory of equations serving as the bridge. Ramchandra certainly subscribed

216 Infinite Series

to this view while De Morgan believed that the strength of the book lay in drawingupon the native resources and not on the “imported science of his teachers.” Butneither Ramchandra nor De Morgan saw the book as being useful only to the Indians.Ramchandra wrote the book in the hope that his “labours will be of some use to thosemathematical students who are not advanced in their study of the differential calculus,and that the lovers of science, both in India and Europe, will give support to myundertaking” (Preface to Indian edition, p. v). And De Morgan, whose interest in thepedagogy of mathematics teaching was well known, recommended that

selections from Ramchandra’s work might advantageously be introduced into elementary in-struction in this country (England). The exercise in quadratic equation which it would afford,applied as it is to real problems, would advantageously supersede some of the conundrumswhich are manufactured under the name of problems producing equations. (Treatise, Prefaceto English Edition, p. xiv-xv)

Yet this brave attempt at building a pedagogic bridge between two mathematicaltraditions was a failure. The Treatise did not gain acceptance in any Indian school andwhile there is the intriguing suggestion by Mary Boole, the widow of the renownedalgebraist, George Boole, that English students were being taught to solve problemsin maxima and minima by “other simple devices similar in essence to Ramchandra’sand probably superior in efficiency,” the interest petered out there as well. The bookwas reviewed poorly in India when it was first published though it picked up well afterDe Morgan’s endorsement—a characteristic common to many other Indian endeavourswhich gain in value only after Western endorsement.

There is also another intriguing connection, which I will merely mention for youto ponder, and that is between Kerala mathematics and Ramanujan. Here the ideais that if one looks at some of the early works of Ramanujan (i.e., before he went toEngland), these are a few problems that involved the π series which he published inan Indian mathematics journal. Some of these remind us of the Kerala work. This isjust a conjecture but it is worth pursuing. Remember that Ramanujan came from theIyengar Brahmin caste. The Iyengars are found right across what we would call Kerala(although it was not part of Kerala but of the Madras Presidency at that time) andTamil Nadu. Ramanujan’s mother was, according to contemporary accounts, a well-known local jyotish. She practised her arts not only in individual homes but in localtemples as well. A jyotish is usually well versed in calculation techniques. So instead oftreating Ramanujan as a freak, consider his background, including the possibility thathe may have been doing ‘ethnomathematics’ which combined his natural ability withwhat he learnt from the two English texts to form the basis of his remarkable worklater. Now there are cases of Iyengars and Nambuthris particularly around the areasof northern Kerala, mixing together within the temple. The temple was, as I mentionedearlier, an important centre for dissemination of knowledge.

We can extend our speculation further: Kerala mathematics travelling West. Twoconnections I want to bring to you. One connection is through the Arabs and their linkswith Kerala. Now, we know that the works of al-Haytham, the great Arab scientist,particularly on geometric series, were known in some of the Madrassas in Kerala. So,was it possible, that through the medium of the Arabs that some of the mathematics

Joseph 217

and astronomy of the Kerala School went west? But, more important connection wasthe possible role of the Jesuits. There is evidence that Matteo Ricci on his way toChina spent some time in Cochin. In fact for a number of Jesuits who followed him,Cochin was a staging post on the way to the China. As I mentioned earlier, the Jesuitsof that time were not merely priests but also scholars, very knowledgeable in scienceand mathematics. In fact, if one wanted to be trained as a mathematician in Italyat that time, we couldn’t do better than go to a Jesuit school. A number of reportsthat the Jesuits sent from India and China to their headquarters in Rome containedappendices of a technical nature which were then passed on by Rome to those whounderstood them, including the notable Italian mathematicians of those days such asCavalieri and Cardona and others. We require to follow this link closely, for at themoment there is only circumstantial evidence. It is gratifying that research in thisarea is starting. Finally, what about Kerala mathematics and China, any possiblelinks? The more I look at the works of Ming Antu and his associates, the more I seesome distinct resonance between their work and Kerala work. Again, the question is:Did some of the information go to China through the medium of Jesuits? An intriguingquestion!

In conclusion, I would like to emphasize the need to rewrite the history of Indianmathematics as it is presented in many historical texts. The ‘new history’ should reflectsome of the more recent work done by the Indian scholars, people such as Gupta,Shukla, Kuppana Sastri, Sarma, and Bag to mention a few. The excessive dependenceon work done during the last century as sources of information should surely decrease.Otherwise, there is a danger of the same mistakes being repeated ad infinitum. And ofcourse, the medieval phase of Indian mathematics needs to be highlighted particularlysince it was crucial to the development of modern mathematics. Victor Katz’s book isone beacon of hope in that direction.

References

Edwards, C.: 1979, The Historical Development of the Calculus, Springer-Verlag, NewYork.

Gurukkal, R.: 1992, The Kerala Temple and Early Medieval Agrarian System, VallatholVidyapeetham, Sukapuram.

Hayashi, T. Kusuba, T. and Yano, M.: 1990, The Correction of the Madhava Series forthe Circumference of a Circle, Centaurus 33, 149–174.

Jami, C.: 1988, Western Influence and Chinese Tradition in an Eighteenth CenturyChinese Mathematical Work, Historia Mathematica 15, 311–331.

Joseph, G.: 2000, The Crest of the Peacock: Non-European Roots of Mathematics, 2ndedn, Princeton University Press.

Marar, K. and Rajagopal, C.: 1944, On the Hindu Quadrature of the Circle, Journal ofthe Bombay Branch of the Royal Asiatic Society 20, 65–82.

218 Infinite Series

Rajagopal, C. and Rangachari, M.: 1986, On Medieval Keralese Mathematics, Archivefor History of Exact Sciences 35, 91–99.

Rajagopal, C. and T.V.V., A.: 1951, On the Hindu Proof of Gregory’s Series, ScriptaMathematica 17, 65–74.

Rajagopal, C. and Venkataraman, A.: 1949, The Sine and Cosine Power Series in HinduMathematics, Journal of the Royal Asiatic Society of Bengal 15, 1–13.

R.V., T. and Aiyar, A. (eds): 1948, Yuktibhasa Part I, Mangalodayam Ltd., Trichur.

Sarma, K.: 1991, A History of Kerala School of Hindu Astronomy, VishveshavaranandInstitute, Hoshiarpur.

Sarma, K. and Hariharan, S.: 1991, Yuktibhasa of Jyesthadeva, Indian Journal ofHistory of Science 26, 186–207.

Whish, C.: 1835, On the Hindu Quadrature and the Infinite Series of the Proportion ofthe Circumference to the Diameter . . ., Transactions of the Royal Asiatic Society,Great Britain and Ireland 3(part III), 509–523.

Yan, L. and Shiran, D.: 1987, Chinese Mathematics: A Concise History, ClarendonPress, Oxford.

How should ‘Euclidean’ Geometry be Taught?

C. K. RajuCentre for Studies in Civilizations, New Delhi, India. Email: c k [email protected]

Introduction

I grew up on the classical presentation of the Elements, as found in books like thoseby Todhunter. It had one or two confusing points, but the work as a whole had acertain persuasive charm and seductive beauty to it that still lingers with me. Thefascinating drawings of Japanese temple geometry1 are, to my mind, the best exampleof something that today still evokes that sense of beauty. Some history is needed tounderstand how geometry has reached the present state of ugliness and confusion inthe NCERT (National Centre for Education, Research and Training) texts (especiallythe text for Class 9), and what should be done to correct it. Tracing the history alsohelps to arrive at a clearer understanding of the Elements, needed for any correctiveprocess.

The Arabic-Islamic Tradition of Geometry

First, ‘Euclidean’ geometry is also a strong Arabic-Islamic tradition. There are atleast three dozen known commentaries and translations of the Elements in Arabic,including those of al Kindı, Thabit Ibn Qurra, al Farabi, al Haitham, Ibn Sına, andNasiruddin at Tusı. Unlike 19th century European historians, Arabs did not feel anyneed to hide the fact that they got their initial knowledge of geometry from others: theHaji Khalfa records2 that Caliph al-Mansur (754-775) sent a mission to the Byzantineemperor, from whom he obtained a copy of the Elements among other Greek books.Caliph al-Mamun (813-833) similarly obtained a copy of the Elements from Byzantium.According to the Fihrist, a late Arabic index of books, al Hajjaj translated it twice in a‘Haruni’ (for Harun ar-Rashid 786-809) and a later ‘Mamuni’ version.

1Japanese Temple Geometry Problems, San Gaku, Selected and translated by J. Fukugawa and D. Pedoe,Winnipeg, Canada, 1989. I am indeed grateful to Prof. E. C. G. Sudarshan for presenting me with a copy ofthis book.

2T.L. Heath: 1956, The Thirteen Books of Euclid’s Elements, Dover Publications, New York, 1908, I, 75. Itshould be pointed out that Heath has a curiously ambivalent attitude: while he prominently quotes the HajiKhalfa at p. 75, to establish that Arabs had translated copies of the Elements, on p. 4 he asserts regardingthe “apparently circumstantial accounts of Euclid given by Arabian authors” that “the origin of their storiescan be explained as the result of (1) the Arabian tendency to romance, and (2) . . . misunderstanding.” Hegoes on to assert (p. 4) that these accounts were intended “to gratify a desire which the Arabians alwaysshowed to connect famous Greeks in some way or the other with the East” and cites (p. 4, note 6) the HajiKhalfa to conclude that “The same predilection made the Arabs describe Pythagoras as a pupil of the wiseSalomo, Hipparchus as an exponent of Chaldean philosophy or as the Chaldean, Archimedes as an Egyptianetc.” In short, Heath’s attitude is to accept as true, from Arabic sources, whatever suits him, and to rejecteverything else with some racist remarks.

220 ‘Euclidean’ Geometry

It is necessary here to point out that ‘translation’ usually meant ‘rewriting’ thebook. This was particularly the case with the Elements, because the book apparentlynever was entirely as elementary as it first seems. As recorded in the Fihrist, fromthe earliest times of Heron of Alexandria, all commentaries and translations of theElements endeavoured “to solve its difficulties,” and explain “the obscurities in Euclid”.3Not the least of these obscurities concerns the name ‘Euclid.’ The Arabs spoke of‘Uclides,’ which they derived from Ucli, a key, and des, measure or particularly measureof earth (= geo-metry), so that Uclides meant key to geometry.

Why was Uclides so important to Arabs? Why did so many key Arabic thinkersrewrite Uclides? Why was Uclides a standard part of the curriculum of later Islamicthinkers? The ‘standard’ histories of geometry, being concerned almost exclusively withthe West, do not ever seem to have bothered to raise this question. The importanceof the question, in understanding the Elements, will become clear later on, when weanswer it.

Euclid the Geometer: A Name or a Person?

While the Arabic-Islamic tradition of the Elements is quite clear, it is not so clear thatthere was any actual person called Euclid who wrote the Elements. The only Euclidknown to classical Greek tradition was Euclid of Megara, a contemporary of Plato.When medieval Europe first came to know about the Elements and Aristotle from theArabs, Europeans thought that Uclides was a reference to Euclid of Megara. Thisbaseless belief about this standard text was taught in Universities like Paris, Oxford,Cambridge for over five centuries: the first English translation of 1570, for instance,attributed the Elements to Euclid of Megara.4 The scholarship of the late nineteenthcentury has veered around to the view that it was impossible that Euclid of Megaracould have been the author. The reasons for this shift need to be made quite explicit.

If one discounts later Arab sources, as Heath does, our belief in the historicity ofEuclid rests wholly and solely on a single remark attributed to Proclus. In this remark,Proclus is not particularly definite about Euclid, for his language admittedly showsthat he is the first to speak of Euclid, and is proceeding on speculative inferences aboutevents some seven centuries before his time:

All those who have written histories [of geometry] bring to this point their account of thedevelopment of this science. Not long after these men [Hermotimus of Colophon and Philip-pus of Mende] came Euclid, who brought together the Elements, collecting many of Eudoxus’theorems, perfecting many of Theaetetus’, and also bringing to irrefragable demonstration thethings which were only somewhat loosely proved by his predecessors. He must have been bornin the time of the first Ptolemy, for Archimedes [who comes after the first Ptolemy] mentionsthe Elements; and further, they say that Ptolemy once asked him if there was in geometryany shorter way than that of the elements, and he answered that there was no royal roadto geometry. He is then younger than the pupils of Plato but older than Eratosthenes andArchimedes; for the latter were contemporary with one another, as Eratosthenes somewheresays.5

3Heath, 21.4Heath, 109.5Proclus: 1992, A Commentary on the First Book of Euclid’s Elements, (Tr) Glenn R. Morrow, Princeton

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If Proclus is right and Euclid was much younger than the pupils of Plato, then hecould not possibly have been Euclid of Megara,a contemporary of Plato. If, however,Proclus is wrong about the date of Euclid, we could well conclude that he was alsoconfused about the person, in this vague paragraph, so we would be left with no basisto believe in any person called Euclid. (The story about there being no royal road togeometry has been told also about Alexander and Menaechmus; the relation of politicalequality to the geometric equality in the Elements is considered later.)

Prior to Proclus, this Euclid, if at all there was such a person, did not have thestature that he acquired in later times through the combined influence of Islamic andChristian rational theology, and colonial history. No author prior to Proclus mentionsEuclid, though there are references to other historians of geometry like Eudemus,Eudoxus, and Apollonius, a carpenter of Alexandria, who, according to Arab sources, issaid to have written a book in 15 sections to make geometry accessible to all. ClaudiusPtolemy, for example, does need to use geometry in the Almagest, e.g. the theoremof Menelaus, but he makes no mention of Euclid, even though the Great Library ofAlexandria was still intact in Ptolemy’s time, and there is ample evidence that henot only consulted it but relied on it heavily for his astronomical ‘observations.’ Itis unconvincing to assert that Ptolemy had no need of the Elements since they were,in a sense, elementary. All known commentaries on the Elements, such as those ofHeron, Porphyry, and Pappus, directly or indirectly mentioned in the Arabic literature,postdate Claudius Ptolemy who comes over two centuries after Cleopatra, the last ofthe Ptolemies who ruled Egypt.

In his commentary on Ptolemy, Theon of Alexandria (c. 4th century CE), too, doesnot mention Euclid. In the same context, Theon, however, does refer to his book on theElements:

that sectors in equal circles are to one another as the angles on which they stand has beenproved by me in my edition of the Elements at the end of the sixth book.6

Proclus himself acknowledges, (in the beginning of the quotation) that he is the firstperson to mention Euclid, stating that Euclid is NOT mentioned by earlier historians ofgeometry. So, is this quote from Proclus adequate to establish the historicity of Euclidor the antiquity of the Elements? Imagine for a minute that we are dealing with Arabtradition rather than Greek tradition, and apply to Greek tradition, the standards ofcritical historiography that Heath applies to Arabs. What would be the conclusion?If one is not a rank racist, the least one can do is to explore alternatives to the tra-ditional belief in the historicity of Euclid and the antiquity of the Elements. PerhapsProclus simply misjudged the antiquity of the Elements, like later Arabs misjudged theantiquity of Proclus’ works.

It is also possible that Proclus attributes authorship to Euclid in the same way aslater Arabic texts attributed various works, including the works of Proclus, to Aristo-tle—after all attributions were not so terribly important either to the NeoplatonistsUniversity Press, 56. Heath p. 1, and footnotes 2 and 3. Heath omits the first sentence. His footnote 2 assertsthat the word γε′γoνε “must mean” “flourished” and not “was born,” on the grounds that “otherwise part ofProclus’ argument [for the existence of Euclid] would lose its cogency.”

6Heath, 46; emphasis Heath’s, de-emphasis mine.


or to the Islamic rational theologians, as they were to later-day European historiansof science, or as they are to current-day information capitalism, where ownership isdecided on attribution. Arabic treatises customarily began by taking the name ofAllah, and after that attributing everything to a famous early source. This customcan still be observed in relatively remote places like the Lakshadweep islands whereit has survived. The custom of attributing everything to an early source—the earlierthe better—was a form of homage, and added authority to the text; it was not meantto be taken literally. Among Greeks, Pythagoreans followed this custom of attributingeverything to Pythagoras, and the continuity of Pythagoreans with Neoplatonism iswell known.

Mathematics and Religion

The most plausible alternative, however, is the following. Given the politics of theRoman empire in his time—with violent priest-led Roman-Christian mobs attackingNeoplatonists, murdering the most brilliant among them like Hypatia, and invokingstate-support to smash or take over Neoplatonic places of worship,7 and burn down theGreat Library of Alexandria—it would have been quite natural for Proclus, or someoneelse between Claudius Ptolemy and Proclus, to have simply invented a Greek calledEuclid to give an appropriate pedigree to their own teaching. In this context one shouldrecognize that mathematics was then viewed not as a ‘universal’ or ‘secular’ science,but as a key aspect of the religious and political philosophy of Neoplatonism. The chiefaim of Proclus’ prologue to the Elements is to bring out this dimension of mathematicswhich he felt was neglected by some of his contemporaries.

Pythagoreans recognized that everything we call learning is remembering, . . . although evi-dence of such learning can come from many areas, it is especially from mathematics that theycome, as Plato also remarks. “If you take a person to a diagram,” he says [Phaedo 73b], “thenyou can show most clearly that learning is recollection.” That is why Socrates in the Meno usesthis kind of argument. This part of the soul has its essence in mathematical ideas, and it has aprior knowledge of them . . ..8

The famous Socratic argument was as follows.

The soul, then, as being immortal, and having been born again many times and having seenall the things that exist, whether in this world or in the world below, has knowledge of themall; and it is no wonder that she should be able to call to remembrance all that she ever knewabout virtue and about everything; for as all nature is akin, and the soul has all things, thereis no difficulty in her in eliciting or as men say learning out a single recollection all the rest, ifa man is strenuous and does not faint; for all enquiry and all learning is but recollection.9

7e.g. in 390 the temple of Seraphis and the adjacent library of Alexandria were burnt down by a violentChristian mob. The magnificent temple of Dea Caelestis at Carthage remained open until c. 400; but manylaws were passed against pagan temples, and, in 401, the synod of Carthage twice asked the State toimplement these laws. Eventually, in 407 the Catholics forcibly took possession of Dea Caelestis and BishopAuerilus, Augustine’s lifelong friend, triumphantly planted his cathedra at the exact spot occupied by thestatue of the pagan goddess. H. Jedin and J. Dolan (eds) History of the Church, Vol. II, The Imperial Churchfrom Constantine to the Early Middle Ages, Tr. Anselm Biggs, Burns and Oates, London, 1980, p. 205.

8Proclus, cited earlier, 45, p. 37.9Plato, Meno, 81-83.

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Socrates then gave a practical demonstration of this by questioning a slave boy andeliciting the right responses regarding geometry.)

For Proclus, then, mathematics was not a ‘secular’ activity, but the key means ofpropagating his fundamental religious beliefs. This is the concluding thought of part Iof his prologue:

This, then, is what learning (µα′θησιζ [mathesiz]) is, recollection of the eternal ideas in thesoul; and this is why the study that especially brings us the recollection of these ideas is calledthe science concerned with learning (µαθηµατικη′ [mathematike]). Its name thus makes clearwhat sort of function this science performs. It arouses our innate knowledge . . . takes awaythe forgetfulness and ignorance [of our former existence] that we have from birth, . . . fillseverything with divine reason, moves our souls towards Nous, . . . and through the discovery ofpure Nous leads us to the blessed life.10

These religious beliefs were earlier championed within the Christian church byOrigen (also of Alexandria, and from the same school as Proclus). However, by Proclus’time, these religious beliefs (‘doctrine of pre-existence,’ equity) were exactly what werebeing abusively opposed and cursed by the church and its key ideologues (Augustine,Jerome, subsequently Justinian). It is well known that fundamental aspects of present-day Christian religious dogma, such as resurrection (as opposed to ‘pre-existence’), eter-nal (as opposed to temporary) heaven and hell, doctrine of sin (as opposed to essentialequity), etc., came about from the rejection of Origen and the acceptance of Augustineduring this period, starting from Constantine and ending with Justinian.

Therefore, Proclus, in writing on mathematics from the philosophical viewpoint,was right in the eye of a religious storm, at its dead centre in Alexandria, and exposedto great personal risk. Since Jerome had only just translated the Bible from Greekinto Latin, and Greek was still held in high regard in the Roman empire, inventing thename Euclid, to give an early Greek legacy to his teachings would have been the mostnatural strategy for Proclus.

If ‘Euclid’ was indeed invented to escape from religious persecution, then it would,have been entirely in keeping with the character of the Egypto-Greek Mysteries, ifthe name ‘Euclid’ had some ‘mysterious’ significance, as the Arabs thought. Proclus’fears, incidentally, were quite genuine, for soon after him, the school at Alexandria waspermanently shut down, at about the time that Justinian cursed Origen of Alexandria.

Can Authorship be Attributed to a Single Individual?

There is another way of looking at the question of authorship. It is clear that, fromat least the time of Theon and Proclus, through the Arabic and European rationalists,right down to the time of Hilbert, Birkhoff, and the US School Mathematics StudyGroup, there has been a continuous attempt to remove the obscurities in the Elements,and to update it. To look for a unique author for the Elements is like trying to tracethe origin of all the water in a mighty river back to its visually apparent source in asmall pond: this transparently neglects the vast underground drainage system thatcontributes most of the water to the river on its way to the sea.

10Proclus, cited earlier, 47, p. 38.


As for the apparent source itself, Europe got its knowledge of the Elements from thedecaying Arab empire, the Arabs got their knowledge of the Elements from the decayingRoman empire, the Romans got their knowledge and culture from the decaying Greekempire, and the Greeks, as Herodotus records, got their knowledge of geometry fromthe Egyptians. As I have argued in detail, elsewhere,11 the typical pattern is thatthe direction in which information flows has been from the vanquished to the militaryvictor, though this fact has often enraged the descendants of the military victors. Thereis ample evidence that 18th-20th century CE European historians of science reinventedhistory in a racist12 way to make it appear that this entire chain of information trans-mission had a unique beginning in Greece. These historians did not represent theGreek texts as merely one in a chain of translations and improvements into English,from Latin, from Arabic, from Greek, and from Egyptian texts, but represented theGreek text as the absolute beginning of this chain—as the original creative fount ofpractically all human thought! Since the geographical origin of the Elements (and all itsearliest commentaries) in Alexandria, in the African continent, could hardly be denied,the name Euclid, suggesting a Greek legacy, was critical to the process of appropriationvia Hellenisation.13

Why was this appropriation first attempted? Why were the Elements so importantto the rational theologians of Christianity? This is a complex issue to which we willreturn when we address the importance of the Elements for Islamic rational theology.

The Most Recent Clarification of Obscurities in the Elements

Let us first examine the most recent example of clarifying obscurities in the Elements.In recent times, a major step to modify the teaching of ‘Euclidean’ geometry was takenin 1957 when the US School Mathematics Study Group issued its recommendations onthe teaching of geometry.14 That recommendation, followed the studies into the founda-tions of geometry by Hilbert,15 Russell,16 and Birkhoff,17 etc. These authors addressed

11C. K. Raju: (to appear), Interaction between India, China, and Central and West Asia in Mathematicsand Astronomy, in A. Rahman (ed), PHISPC, New Delhi, 1999.

12Martin Bernal: 1991, Black Athena: The Afroasiatic Roots of Classical Civilization, 1, The Fabrication ofAncient Greece 1785-1985, Vintage. The use of the term racist, as distinct from Spengler’s term ‘Eurocentric,’refers also to the technology gap and the industrial revolution. See, M. Adas, Machines as the Measure ofMen: Science, Technology and Ideologies of Western Dominance, Oxford, New Delhi, 1990. While Bernal doesnot say much about the history of science per se (and neither do his detractors in the more recent debatein Isis), it is clear that the resurrection of Euclid, after the belated discovery that he could not have beenEuclid of Megara, is very much in line with the belief in a nineteenth century pattern of fabricating a Greekorigin for everything under the sun. A closer look at the material basis (palimpsets etc.) of the conclusionsof classical scholars will make clear the enormous amount of tinted speculation that underlies this belief.

13The Hellenisation itself proceeded by reference to the military conquests of Alexander and Julius Caesar,and the in-between period of Ptolemaic rule. Consequently the importance of these conquests got amplifiedout of all proportion to their global or even local significance.

14School Mathematics Study Group: Geometry: 1961, Yale University Press.15D. Hilbert: 1902, The Foundations of Geometry, Open Court, La Salle.16B. Russell: 1897, 1908, The Foundations of Geometry, London.17G. D. Birkhoff: 1932, A Set of Postulates for Plane Geometry (based on scale and protractor), Ann. Math.,

33.

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a variety of obscurities in the Elements. The most obvious of these obscurities may beput into the following classes.

1. Unsound definitions: e.g., those of point, line, plane etc.

2. Missing definitions: but the corresponding notions are used: e.g. area.

3. Hidden assumptions: e.g. the correspondence of lines with real numbers. Inaddition to these, there are subtler problems, relative to the current formalisticnotion of mathematics, such as

4. Axioms taken as self-evident truths (about empirical reality): this is also trueof the constructions used in proofs.

5. Redundant assumptions: e.g. the parallel postulate becomes redundant if oneadmits reals and rigid motions, or the notion of distance.

In judging these obscurities in the light of current formalistic mathematics, onemust, of course, keep in mind that the present-day formalistic epistemology of mathe-matics (axiom-definition-theorem-proof) itself historically originated from the analysisand clarification of these obscurities in the Elements. Furthermore, one must also bearin mind that there is nothing universal or ‘natural’ about the formalistic approach, andthat it is steeped in a particular theological and cultural tradition.18

The Unreal and Meaningless as the Sole Concern of Mathematics

The obscurities of type (1) are clear enough. One can define something ostensively (e.g.one can define the word ‘dog’ by pointing to an instance of a dog) or one can define it inother words. In the case of a geometric point, an ostensive definition seems somewhatunsuitable: Platonic philosophy requires that geometry should deal with idealisationsthat have no real existence. Hence one cannot point to a point. One can point to a doton a piece of paper; but no real entity like a dot can ever correspond to the ideal notionof a geometric point which is required not to have any real existence.

The alternative is a verbal definition. Consider the definition in the Elements: “Apoint is that which has no part, or which has no magnitude.” (The ‘Heiberg’ version hasonly the first part of this definition.) A person familiar with atoms and magnitudes maynot question this definition: but it communicates nothing to anyone else. (Besides, isone talking of real atoms here—elementary particles of some sort? The particle whichis closest to a point is the electron. But the electron cannot be a Euclidean point, fora circuit around a Euclidean point brings us back to where we started, whereas twocircuits around the electron are needed to return to the starting point, because theelectron has the paradoxical property of half-integral spin). Clearly, a verbal definition

18C.K. Raju: 1999, Mathematics and Culture, in: Daya Krishna and K. Satchidananda Murty (eds)History, Time and Truth: Essays in Honour of D.P. Chattopadhyaya, Kalki Prakash, New Delhi, 179-193. Reprinted in Philosophy of Mathematics Education, 11, (1999). Available at http://www.ex.ac.uk/ ∼PErnest/pome/art18.htm


of a non-real notion cannot avoid an infinite regress, for at no point can it terminate inan ostensive definition.

Thus, Platonic philosophy, by its insistence that the ideal should be non-empirical,eliminates both possibilities of an ostensive or a verbal definition, and the only optionleft is that of current formalistic mathematics, which regards the notions of point, line,etc., as meaningless, undefined notions. In other words, the current way of removingthe obscurities in the Elements is to adopt Russell’s definition of mathematics: “Mathe-matics may be defined as a subject in which we never know what we are talking about. . .!”19

Real Numbers and Euclidean Proportions

Obscurities of type (2) are examined later. Obscurities of type (3) are manifest in thevery first proposition of the Elements. The first proposition constructs an equilateraltriangle on a given segment AB. This process involves drawing two circles, the firstwith centre at A and radius AB, the second with centre at B and radius BA. Oneobscurity is that the two circles may fail to intersect, in the sense that the point ofintersection need not mathematically exist. If points on the circles correspond to (pairsof) rational numbers, there may be ‘gaps’ between them, such as the gaps between thenumbers 1, 2, 3. Indeed one is led to expect such gaps since the ‘Euclidean’ approach toproportions suggests a reluctance to use irrational numbers like

√2. It was the attempt

to clarify this obscurity in the first proposition of the Elements that led Dedekind to theidea of the real line as something that could be ‘cut’ without leaving any gaps. Needlessto say, the real numbers, as conceptualized by Dedekind are something necessarilyunreal, for there is no real process by which one can specify or fully name a real numbersuch as π.

The SAS Theorem/Postulate

The other obscurity in the proof of Proposition I. 1 is this: why is the radius measuredout twice? Can’t the first measurement of AB be re-used for BA? This is related tothe key obscurity concerning Proposition I. 4. This difficulty must have been noticedby every schoolchild who did geometry using the older ‘Theonine’ texts, like those ofTodhunter, current in India up to the end of the 1960’s. In the ‘Heiberg’ version,Proposition 4 of the Elements states that:

If two triangles have the two sides equal to two sides respectively, and have the angles con-tained by the equal straight lines equal, they will also have the base equal to the base, thetriangle will be equal to the triangle, and the remaining angles will be equal to the remainingangles respectively, namely those which the equal sides subtend.20

In brief: if two sides and the included angle of one triangle are equal to those ofanother triangle, then the two triangles are equal. We will refer to this as the Side-Angle-Side proposition, or SAS for short.

19The best that one can do is to interpret these meaningless notions using other meaningless notions likesets: e.g., a point is an element of a set, a line is a subset etc.

20Heath, p. 247.

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The key obscurity is this. In the Elements the proof of this proposition involvessuperposition: it involves picking up one triangle, moving it through space, rotating itas necessary, and applying it to the other triangle. The later theorems on the equalityof triangles (with the exception of I. 8) do not, however, use this procedure: they relyinstead on SAS.

There is no doubt at all that physical motion in space is implied, and there is aspecific Common Notion or Axiom to enable this proof to go through. Common Notion4 of the ‘Heiberg’ version asserts “Things which coincide with one another are equalto one another.”21 For those accustomed to reinterpreting this in terms of congruence,it should be pointed out that this clearly applies to distinct geometrical objects thatare brought into contact, and superposed, through motion. Likewise, Axiom 8 of the‘Theonine’ version asserts: “Magnitudes which coincide with one another, that is, whichfill the same space, are equal to one another.” If this is not a tautology, it must refer todistinct objects which are made to coincide with each other, by moving them about.

Physical Movement and Motion without Deformation

The doubt that must have entered the mind of every schoolchild is the following. Thismethod of picking and carrying greatly simplifies the proofs of all other theorems andriders: if it can be used in one place, why can’t it be systematically used in other placesas well? My teacher had no satisfactory answer why it was all right to do this in oneplace, but wrong to do it elsewhere. He simply said it is better not to do it, but couldnot explain why. But one may attempt an answer as follows.

Picking and carrying line-segments is a common enough thing: one must do thisevery time one ordinarily makes a measurement. But, by the late 19th century mathe-maticians were sceptical about the very possibility of making a measurement: movingan object might deform it. What sense did it make to say that a figure remainedidentical to itself as it was moved about in space? A shadow moving on uneven groundis continuously deformed; perhaps space itself is similarly ‘uneven,’ so that any motionmay involve deformation, and measurement may require more complicated notions likea metric tensor. The avoidance of picking and carrying in the proofs of the subsequenttheorems was interpreted, by the 20th century, as an implicit expression of this doubtabout the very possibility of measurement. It was argued against Helmholtz that mea-surement required (a) the notion of motion; furthermore this motion must be withoutdeformation, so that it required (b) the notion of a rigid body, and neither of these wasthe proper concern of the geometer, who ought to be concerned only with motionlessspace. (The notion of rigid body depends on physical theory; e.g. the Newtonian notionof rigid body has no place in relativity theory, for a rigid body would allow signals totravel at infinite speed.)

Historically, this doubt about measurement was expressed as a doubt about (a) therole of motion in the foundations of mathematics, and (b) the possibility and meaningof motion without deformation. In favour of (a) the authority of Aristotle was invokedto argue that motion concerned astronomy, and that mathematics was “in thought

21Heath, p. 224 et seq.


separable from motion.” The authority of Kant was implicitly invoked to argue thatmotion was not a priori, but involved the empirical, and hence could not be part ofmathematics. All these worries are captured in Schopenhauer’s criticism of the ‘Theo-nine’ Axiom 8 (corresponding to the ‘Heiberg’ Common Notion 4) which supports SAS:

. . . coincidence is either mere tautology, or something entirely empirical, which belongs notto pure intuition, but to external sensuous experience. It presupposes in fact the mobility offigures; but that which is movable in space is matter and nothing else. Thus, this appeal tocoincidence means leaving pure space, the sole element of geometry, in order to pass over to thematerial and empirical.22

In short, motion, with or without deformation, brought in empirical questions of physics,and Plato, Aristotle, and Kant, all concurred that mathematics ought not to be basedon physics, but ought to be a priori, and that geometry ought to be concerned only withimmovable space.

The Synthetic and the Metric Axiom Sets

The Hilbertian reading of the Elements, hence denies the possibility of measurement,so that the proof of Proposition 4 (SAS) fails. To preserve the structure of the Elementsit is then necessary to assume Proposition 4 as a postulate (the SAS postulate) thatcannot be proved from any more basic principles. This approach is called the syn-thetic approach.23 One way to describe this approach is by distinguishing syntheticinstruments from those found in the common instrument box of school geometry. Thesynthetic instruments are the straight edge (unmarked ruler) and ‘collapsible compass.’The last term is De Morgan’s graphic description of the impossibility of measurementwith the synthetic approach: distances cannot be reliably picked and carried becausethe synthetic compasses are loose and ‘collapse’ as soon as they are lifted from the pa-per. (‘Collapsible compasses’ may well be an accurate description of the then-prevailingstate of technology!) Hence, also the ruler is left unmarked. In this synthetic approach,the term equal used in the ‘original’ Elements is changed to the term congruence:motion is replaced by a mapping, so that it is not necessary to transfer figures fromone place to another, one only needs to shift one’s attention from one figure to the other.

The other way of clarifying the obscurity in the original Elements is to accept thepossibility of measurement, and to accept that the proof of Proposition 4 (SAS) is valid.This is called the metric approach, and has been championed by Birkhoff. The mainproblem with a full metric approach is that it completely devalues the Elements. EvenProclus does not claim any originality for his Euclid; the value of the Elements derivedfrom the nice arrangement of the theorems, so that the proof of any theorem usedonly the preceding theorems. With a full metric approach, even the arrangementof theorems in the Elements loses its significance: it is quite possible to prove the‘Pythagorean Theorem’ (I. 47), by cutting, picking and carrying, without recourse tothe preceding theorems.

22Schopenhauer: 1844, Die Welt als Wille, 2nd ed, 130, cited in Heath, p. 227.23For a detailed and easily accessible account, see E. Moise: 1963, Elementary Geometry from an Advanced

Standpoint, Addison Wesley, Reading, Mass.; B.I. Publications, Bombay, 1966.

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The synthetic and metric approaches being so different, the problem is to chooseone of them.

It is in deference to the synthetic formulation of the Elements, that the proposition4 of the ‘original’ Elements is now taught as the Side-Angle-Side (SAS) postulate. Thispermits one to continue teaching the Elements as a valid example of the deductivemethod of proof used in modern mathematics.

This is unacceptable for several reasons.

1. A metric approach makes ‘Euclidean’ geometry very simple: a straightforwardmetric approach could prove the ‘Pythagorean’ ‘Theorem’ (Proposition I.47) inone step, as in the YuktiBhasa proof.24 The synthetic approach was originallymotivated by the desire to justify the apparently needless complexity of the proofsin the ‘original’ ‘Euclid.’ The justification was needed because of the importanceattached to this text by Christian rational theology. The justification was soughtby denying the possibility of picking and carrying segments without deformation;hence, also, the possibility of measurement was denied. Thus, the syntheticapproach makes proofs more difficult, and is counter-intuitive—for it denies theeveryday ability to pick and carry, and compare and measure. (The ultimatejustification for denying the manifest flows from the Platonic-Kantian idea thatmathematics is a priori, and so ought not to be contaminated by the empirical.The other way of looking at this idea is that it demands that mathematics oughtnot to correspond to anything real, and hence ought to remain perfectly meaning-less.)

2. The synthetic interpretation of the Elements substitutes the key term ‘equal’ inthe ‘original’ by the new term ‘congruent.’ This key substitution clearly does notwork beyond Proposition I. 34. Thus, Proposition I. 35 states that “Parallelogramson the same base and in the same parallels are equal to one another.” Thisproposition asserts the equality of areas that are quite clearly non-congruent(when not identical). It follows that one must either abandon all propositions afterproposition I. 35 (including the ‘Pythagorean’ ‘Theorem’ I. 47), or else one mustabandon the synthetic interpretation of the Elements. It does not help to try todefine a general area through triangulation, as Proclus’ contemporary, Aryabhatadid25 since the notion of area is not defined anywhere in the Elements, and theusual formula for the area of a triangle is itself derived from I. 35. Some attemptshave been made to supplement the synthetic approach by axiomatically definingarea in a way analogous to the Lebesgue measure (overlooking the connection ofthe Lebesgue measure to the notion of distance). Area, however, is an intrinsicallymetric notion; indeed, it would be a rather silly enterprise to define area withoutfirst defining length.

24K.V. Sarma (Ed and Tr.): (to be published), The GanitaYuktiBhasa of Jyeshtadeva. For a description ofthe proof, see , C.K. Raju, ‘Mathematics and Culture’, cited earlier.

25Ganita 6-9. Aryabhatiya of Aryabhata (Eds and Trs) K. S. Shukla and K. V. Sarma, INSA, New Delhi,1976, pp. 38-45.


The schizophrenic method of denying metricity until proposition I. 35, and admit-ting it thereafter is only confusing to young minds. The whole project is born of thecompulsions of theology and racist history.26

The Current Text

We have substituted this with our own schizophrenic project. The schizophrenia de-rives from multiple inheritance. The formal structure of our educational system: schools,colleges, universities is patterned on the system prevalent in Europe, rather than theindigenous tradition of pathshala-s or Nalanda and Takshashila. The educationalsystem in Europe was for several centuries quite explicitly oriented towards theologicalconcerns. With the rise of industrial capitalism, in the last hundred years or so,there was a partial shift in the West towards more practical and utilitarian concerns.‘Euclidean’ geometry, for example, is no longer taught in British schools.

Independent India accepted industrial capitalism, and the elite in this country stillcontinue to regard education as a means of forging links to the metropolitan centre,so that even 50 years after independence most of the country remains illiterate, andeducation remains the preserve of the elite for one excuse (shortage of governmentfunds) or another (need to commercialise). Education, furthermore, has been ‘de-moralised,’ and the theological concerns of the West have been substituted by elitistchauvinism.

In line with the British legacy of bureaucracy, and the clerk’s dharma of evading re-sponsibility, our school texts are produced in clerkdom (which still controls education),by a duly constituted committee. The committee has sought to balance the require-ments of industrial capitalism (which needs the products of education), with thoseof chauvinistic history (which seeks to correct racist history without understandingtradition).

These contradictory requirements are reflected in the current NCERT text for Class9.27 On the one hand, this is how the NCERT text justifies the teaching of geometry“For instance, those of you who will become engineers, technicians and scientists willnot only find all this information useful but will also realise that you cannot do withoutit.” (Needless to say, there is no other concrete instance in the ‘explanation’ whichoccupies one paragraph in this vein of redundancy improving communication!) Butif practical usefulness were the sole justification for teaching geometry, then metricgeometry ought to be taught. Engineers, technicians and scientists, all, have no usefor geometry without measurement. (Not even relativists care much for spacetimegeometry based on the connection rather than the metric.)

On the other hand, a similar conclusion follows from the historical assertions withwhich the NCERT exposition of geometry begins [pp. 123-124].

The Baudhayana Sulbasutras . . . contains [sic] a clear statement of the so-called Pythagoras

26Martin Bernal, Black Athena, cited earlier.27A.M. Vaidya et al.: 1989, Mathematics: A Textbook for Secondary Schools, Class IX, NCERT, Ninth

Reprint Edition (sic) 1998, 124.

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theorem. The proof of this theorem is also implicit in the constructional methods of the Sulba-sutras.

The subtle way in which Western historians have exploited the notion of ‘proof ’seems to have quite escaped the authors of the text. Western historians have read-ily conceded that Babylonians, Egyptians, Chinese, Indians all knew earlier that thePythagorean theorem was true. They have maintained, however, that none of themhad a proof, hence none of them knew why it was true: they knew of the theoremonly as an empirical fact which they did not quite comprehend, much as an ass mightknow the theorem without comprehending it. Comprehension, therefore, still dawnedwith the Greeks. To refer to constructional methods as implicit proofs is to miss thecentral issue clarified above: the motivation for synthetic geometry is that empiricalknowledge is not only distinct from mathematics but that it cannot logically precedemathematics. Hence, if the second sentence in the above quote is true, then the verynotion of mathematical proof would need to be changed to accept empirical inputs.Needless to say, the committee does not intend any such revolutionary challenge tomathematical authority which is entirely beyond its terms of reference!

Therefore, on the third hand (surely committees have at least three hands!), the textlapses back into the synthetic geometry recommended by the US School MathematicsStudy Group. Like a proper committee report, the resulting text has included a littlesomething to suit every taste. So the text introduces the SAS postulate [p. 162] asthe “SAS (Side-Angle-Side) Congruence Axiom,” where ‘axiom’ is to be understood asfollows [p. 125]: “basic facts which are taken for granted (without proofs) are calledaxioms. Axioms are sometimes intuitively evident.” That is, an axiom, like a fact,belongs to the domain of empirical and physical, rather than the intuitively a priori—exactly the thing that was denied to motivate the SAS postulate and the notion ofcongruence in the first place! One wonders why, unlike most other committee reports,this report was not left to gather dust!

The natural casualty is the student who has to digest the whole thing, and so may beput off geometry for the rest of his life, especially if he is clear-headed. If congruence isexplained through superposition (‘Heiberg’ Common Notion 4, or ‘Theonine’ Axiom 8),as the text does (pp. 159-161), one has clearly a metric approach. Within a metricapproach, it is trivial to prove the synthetic congruence results proved in the text—infact there is then no need for a SAS congruence axiom, one has a SAS theorem, the wayit was proved in the ‘original’ Elements. To now prove these results, in the manner ofsynthetic geometry, on the ground that one is teaching the axiomatic method, is to teachthe axiomatic method as a completely mindless and elaborate ritual that one mustcomplete on the strength of the state authority that NCERT enjoys. What childrenare being taught is not the sceptical attitude which underlies the need for a proof, butmindless obedience to rituals which cannot be justified.

The hotchpotch geometry in the NCERT text for Class 9 is indigestible because ithas mixed up the Elements by mixing up elements that ought not to be taken together—like diazepam and alcohol—unless the object is to induce a comatose state. To makethe text digestible, one needs to sort out which geometry one wants to teach: metric,synthetic, or traditional. Even if one wants to teach all three they should be kept in


separate compartments: it is NOT a good idea to make the synthetic notion of congru-ence more intuitive by defining it metrically as the NCERT text does! The authors needto appreciate the incompatibility of the metric and synthetic approaches, and the waythese differ from the traditional approach, which incorporates an altogether differentnotion of mathematical proof.28

Traditional Geometry Distinguished from the Metric and the Synthetic

Enough has been said above about the incompatibility of the metric and syntheticapproaches; and I will briefly recapitulate the way in which both these approachesdiffer from the traditional approach. First, the authoritative traditional literatureis the sutra literature; the sutra style is well-known for its extreme brevity—like atelegraphic message, further distilled by digital compression. The sutra-s are notintended to serve primarily a pedagogical function, and they are not intended to beaccessible to all. Consequently, they have no place for proofs. Texts dealing withrationale, on the other hand, being less authoritative, have not been translated. Thekey text on rationale, available in English translation,29 is the YuktiBhasa, which, asstated earlier, proves the ‘Pythagorean theorem’ in one step, by drawing the figure ona palm leaf, cutting it, and rearranging the cut parts. An examination of rationale intraditional geometry shows the following.

What distinguishes traditional geometry from both metric and synthetic geometryis the traditional notion of proof (pramana). Though there have been many debates intradition on what constitutes pramana, the one ingredient that went unchallenged wasthe physically manifest (pratyaksa) as a means of proof. The traditional notion is notembarrassed by the empirical, and does not regard it as intrinsically inferior to meta-physics. Both the Baudhayana and the Katyayana sulbasutra-s begin by explainingthe use of the rope for measuring areas. Aryabhata defined ‘horizontal’ using a waterlevel, and a ‘perpendicular’ using a plumb line. The proofs in the YuktiBhasa clearlyaccept the physically manifest as a good argument. All this would horrify a modern-day mathematician, who believes that mathematics is a priori, and certainly logicallyprior to the physically manifest.

Asserting the sulbasutra tradition would clash with the entire tradition of educationin medieval and renaissance Europe, which was geared to theological purposes, andhence reinforced the philosophy of the authorities like Plato, and later Kant which jus-tified the deprecatory attitude towards the physical world. For Proclus, the key objectof teaching mathematics was not its military or political utility, which he regarded assubsidiary, but its ability to make the student forget the practical concerns of everydaylife and thereby discover his real self.

the soul has its essence in mathematical ideas, and it has a prior knowledge of them . . . andbrings of them to light when it is set free of the hindrances that arise from sensation. For oursense-perceptions engage the mind with divisible things . . . and . . . every divisible thing is an

28For the traditional notion of pramana in relation to mathematics, see C. K. Raju, ‘Mathematics andCulture’, cited earlier.

29Another text dealing with rationale, the Karanapaddhati is now available in a Japanese translation,being retranslated into English.

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obstacle to our returning upon ourselves. . . .Consequently when we remove these hindrances. . . we become knowers in actuality . . ..30

Rejecting this attitude is not a trivial matter for all of current-day mathematics de-pends upon the belief that mathematics is a priori and divorced from the empirical.

Nevertheless, the fact is that the Nayyayika notion of proof proceeds from a realisticphilosophical standpoint directly opposed to Platonic idealism. Classical Indian tradi-tion saw no need to regard mathematics as something necessarily metaphysical, andconsequently, there was no need for two separate procedures of validation: (1) a notionof mathematical proof, and (2) criteria (such as logical and empirical falsifiability) todecide the validity of a physical theory. Therefore, though metric, traditional Indiangeometry does not need to proceed from Birkhoff ’s axioms. Against this background,various other considerations are summarised in Table 1.

The second key point about the notion of proof concerns inference (anumana), aboutwhich different schools of thought had mutually different ideas which differed also fromthe idea of logical deduction underlying the current metamathematical definition of amathematical proof (which defines a proof as a sequence of statements each of which iseither an axiom or is derived from some preceding axioms by the use of modus ponensor similar rules of reasoning). The Lokayata explicitly rejected inference, at least inthe metaphysical domain (which includes modern mathematics), allowing its use onlyfor practical purposes. The Buddhist and Jaina traditions pose an even more funda-mental question: what should be the logic underlying proof? If one insists on regardingmathematics as metaphysical, as in the current formalistic approach, then what is thejustification for the use of a 2-valued truth-functional logic underlying mathematicalproof? Clearly, the formalistic approach cannot possibly answer this question—therebyshowing that allegedly ‘universal mathematical truths’ ultimately rest on a narrowbase of authority, localised in the West. Despite the authority, the belief is purelya matter of cultural prejudice, for the seven-fold classification (saptabhanginaya) ofthe Jaina syadvada of Bhadrabahu cannot be accommodated within 2-valued logic,while the ‘four-fold negation’ used by the Buddha, Nagarjuna, and Dinnaga cannot beaccommodated within a truth-functional framework. The logic of the empirical world,by the way, may be similarly quasi truth-functional, for quantum mechanics permitsSchrodinger’s cat31 to be simultaneously both alive and dead, without permitting anyarbitrary statement to be deduced from this ‘contradiction.’

The objectives of education, and the philosophical substance of the E lements

We now have before us, three distinct models of ‘Euclidean’ geometry: synthetic, metricand traditional . Which model one ought to teach depends upon the objectives ofeducation. The objectives of education in India prior to independence are well known,especially Macauley’s objectives of creating a cheap clerical workforce to help rule theempire. In independent India, as things stand, educational objectives have largely been

30Proclus, cited earlier, 45.31For details of the relation of quasi truth-functional logic to von Neumann’s postulates for quantum

mechanics, see C.K. Raju: 1994, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht.


Type of geometry I II III IVMetric Synthetic ‘Euclidean’ Traditional

Fundamentalsetup

(S, L, P, d, m) (S, L, P, B,≡) Semi-idealized(not real, notideal)

Real space

Distance d Not mentioned Lenghts Measured with arope

Measure of an-gles

m Not mentioned Only equalityand inequalitywith right angles

Measured physi-cally (e.g., with aplumb line)

Congruence forsegments

From d Given ≡ (for seg-ments)

Not mentioned(only equality,presumed pre-defined)

Not mentioned(equalitythrough ‘pickand carry’)

Congruence forangles

From m Given ≡ (for an-gles)

Not mentioned(only equality,presumed pre-defined)

Not mentioned(only measuredequality)

SAS Theorem Postulate Theorem (differ-ently proved)

Similarity andrule of three(equality aspecial case)

Area Additionaldefinition needed

Not defined (elselength would bedefined)

Not defined(only equality,presumed pre-defined )

Explicitlydefined throughtriangula-tion/rectangulation

Addition Real Numbers Congruenceclasses

Geometricconstruction

Floating pointnumbers

InequalityProportion Real numbers Congruence

classes + complexassertions (using‘betweenness,’inequality, andinteger addition)

Complexassertions usinginequality andinteger addition.Not in Book 1

Rule of 3

Instruments Scale, protractor,and compass (‘ge-ometry box’)

Unmarkedstraightedgeand ‘collapsible’compasses

Not explicitlystated

Rope

Note: S = set of points, L = set of lines (subsets of points), P = set of planes (subsets of points), d =distance, m = measure of angles, B = ‘Betweenness’ relation, ≡ = congrence for segments/angles.

Table 1: A comparison of metric, synthetic, ‘Euclidean’ and traditional geometry.

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decided in clerkdom by appealing to precedents established in the West. So, beforedeciding what the objectives of education ought to be, it would help to answer the twoquestions that were postponed earlier. Why were the Elements so important to Islamicand to Christian rational theology? Why were they such a necessary part of the theo-logical curriculum? (This is the sort of thing that modern-day mathematicians do notusually understand, since their education, geared to the needs of industrial capitalism,encourages a narrow view of the world, together with an unquestioning acceptance ofthe postulates and rules of inference laid down by mathematical authority.)

Very briefly, to understand this, one must situate Christian rational theology inthe context of the two traditions which it inherited. The first is that of Arabic-Islamicrational theology, which reached medieval Europe through Averroes and the debatethat preceded him in Islam, and deeply influenced the beginnings of Christian rationaltheology.

For the Arab rationalists (Mutazilah and falasifa) Uclides was important as a demon-stration of Neoplatonic principles, which they accepted as a key aspect of their theology,attributing it to Aristotle. The Arab rationalists aimed to deduce everything from thetwo key principles of equity and justice. The Elements provided a model of how even thephysically manifest could be deduced, starting from the principle of equity. The notionof equality in the Elements has obvious political and philosophical overtones of equity,that are quite lost upon those now accustomed to thinking in terms of congruence: theabsence of a royal road to geometry was an assertion about the political content ofthe Elements. Equity is contrary to Platonic ideas of the republic, and Proclus’ statedaim in writing his commentary on the Elements was to inform people about its deepphilosophical content—the doctrine of the oneness of humankind.

Secondly, Christian rational theology also inherited the legacy of the early Romanchurch and its confrontation with Neoplatonism over the issue of equity. Though thevery early church doctrines clearly favoured equity, and Origen’s theology is barelydistinguishable from Neoplatonism, the state-church after Constantine, found thisdoctrine of equity a gross political inconvenience. We have already noted the church’sconfrontation with Neoplatonism, ending with the closure of the Alexandrian schooland when Origen was formally condemned by the Fifth Ecumenical Council.32

Impelled by these contradictory inheritances, Thomist philosophy rejected equityas irrelevant, and retained only the process of rational deduction. The philosophicalimportance of the Elements was now confined to the process of rational deductionwhich could be used to persuade the non-believer, since both Islamic rationalists andal Ghazalı accepted that God was bound by Aristotelian logic.

How should Geometry be Taught?

Against this background, we can finally turn to the question raised in the title of thispaper. Which geometry should be taught depends upon the objectives of education. Ina democracy these objectives should be decided by consensus, or majority, or, at least,

32or, which amounts to the same thing, thought to have been so condemned for 1400 years. (Hair splittingover the 5th Ecumenical council is irrelevant here.)


informed public debate. In India, bad governance by the elite has made this impossible.We still follow a tightly hierarchical model: all knowledge is believed to reside at thetop management layer, even though it may be manifestly scientifically illiterate, or outof date! Committees are nominated only to make a pretence of oligarchy; but those ofus with the slightest experience in committee formation know that the whole structureaims to reflect the will at the very narrow top. This will is that the majority of people inthe country should be kept illiterate (so that they do not constitute a threat) and thatthe cream of educated people should be exported to the West (since that financiallybenefits the elite from which this creamy layer comes).

Under these circumstances, I cannot prescribe the objectives of education. But oncethese objectives are laid down, the following should help to arrive at an answer to thequestion raised in the title of this paper.

1. If the state policy is that education is justified by its linkages to industrial or infor-mation capitalism (“it is needed by future engineers, technicians and scientists”)it is not so clear that it is imperative to teach the classical method of proof. Wemust then consider what is increasingly likely to happen in the future: a computersimulation for which there is no numerical analysis, and no convergence proof.According to Hilbert’s ideas this would not count as mathematics. Nevertheless,such computer simulations may be increasingly used as the basis of everyday deci-sions: such as decisions about large financial investments. Briefly, if mathematicsis to be justified by its utility, then one should be teaching practical mathematicsrather than formal mathematics. In the case of geometry, this means that thesynthetic approach should be rejected in favour of the metric approach, and thateven with the metric approach, one could omit teaching proofs. It is true that thismight compromise understanding; but if education is justified by its utility, onemight as well explicitly accept that understanding is of lesser importance, for thetime thus saved could be used to teach some more useful things.

2. If the objective of education is to establish linkages to tradition, this tradition can-not be arbitrarily selected. The Neoplatonic origin of the Elements seems to meundeniable. On the other hand, Neoplatonism links naturally to Indian traditionnot only through Islam and the sufi-s, but also through direct contact, and strongconceptual similarities to Advaita Vedanta. The links were physical, with some250 ships sailing annually to carry out a huge trade with the Roman empire.They were also philosophical: Augustine, born some 50 years after Porphyry’sdeath, records that Porphyry (the very same student of Plotinus, who recordedthe Enneads and commented on the Elements) searched for a universal way forthe liberation of the soul in “the mores and disciplina of the Indi.”33 Therefore,it needs to be spelt out what state policy enables us to say that a certain sortof tradition at a certain point of time should be regarded as more valuable thananother tradition at a different point of time. For example, should one reject the

33John J. O’Meara,: 1982, ‘Indian Wisdom and Porphyry’s Search for a Universal Way’ in: R. Baine Harris(ed), Neoplatonism and Indian Thought, Sri Satguru publications, Delhi, 6.

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Buddhist or Jaina tradition, both of which rejected as wrong many more ancienttraditional things? Again, there is no reason why the medieval tradition in whichclearly ‘Uclides’ was part of the talım, of, say, Abul Fazl, should not be deemedto be as Indian a tradition as the sulbasutra-s. One cannot really say that themore ancient thing is necessarily a more authentic part of one’s tradition, for onemay quite recently have consciously rejected some ancient ideas like untoucha-bility. Depending upon which tradition is officially approved as worth teaching,one could then decide whether to teach one or more of traditional geometry, ormetric geometry (which trivialises the Elements), or synthetic geometry and themethod of proof (after resolving the issue over the method of proof to be adoptedin mathematics).There is also the following question. Though the geometry of the sulbasutra-s hasbeen called ‘ritual geometry’ because of the association of the sulbasutra-s withthe construction of vedis and citis, the fact of the matter is that this geometryhad purely practical significance, and lacked the theological orientation of the El-ements, from the time of Proclus. Practical significance is something that changesfrom time to time; to teach traditional geometry, devoid of its practical concernswould be to do violence to the tradition by reducing practical considerations toritualistic one’s.

3. If the objective is to teach a certain method of inference, or a certain method of‘proof,’ it is not clear that ‘Euclidean’ geometry is the best vehicle for it. One couldtake syllogistic examples from elsewhere.

Conclusions

1. Our current school texts in geometry must be corrected to distinguish clearlybetween metric and synthetic geometry.

2. One must decide which geometry to teach—metric, synthetic, or traditional—andstick to teaching that geometry. It is NOT a good idea to motivate synthetic con-cepts like congruence by appealing to the intuitive physical idea of superpositionwhich underlies metric notions.

3. If traditional geometry is also to be taught, the texts must further separate itfrom formal metric and synthetic geometry: it is NOT a good idea merely toclaim priority, as the present text does, for traditional geometry is fundamentallydifferent, since the traditional notion of proof differs fundamentally from thecurrent metamathematical notion of proof. One should first decide which methodof proof one wants to teach, and then develop a mathematics based on that methodof proof.

4. If the aim in teaching the Elements is to teach formal axiomatics, the authors oftexts should distinguish between meaningless formal axioms and empirical facts.If this is too hard a thing for educators to do, then it is too hard for schoolchildrento understand, and formal axiomatics ought NOT to be taught to schoolchildren.


5. The Elements have long been part of the theological curriculum because of theirphilosophical significance, first for Neoplatonists (to arouse recollection of one’strue Self), then for Islamic rationalists (rational deduction from equity), andfinally for Christian rationalists (rational deduction). Our objective in teachingthe Elements must be formulated in awareness of this significance, as also anawareness of Neoplatonic linkages to Indian traditions directly and via the sufi-s.

6. Our objectives must also recognize that no individual tradition can claim to bethe unique Indian tradition either as regards the matter of proof (pramana), or asregards the tradition of geometry: the sulbasutra-s, the YuktiBhasa, and Uclidesare all part of Indian tradition. Tradition should not be reduced to ritual byseparating it from its original context of practical usefulness.

7. If we choose to teach geometry purely for its practical utility, then this practicalusefulness needs to be clearly thought out in the context of future needs, to protecteducation from rapid obsolescence.

The Axiomatic Method: Its Origin and Purpose∗

S.D. AgasheIndian Institute of Technology, Bombay, India. Email: [email protected]

Introduction

This is an informal introduction to a formal paper that was published about 12 yearsago and has been reprinted here. It is also a brief description of what Prof. AmitabhaGupta and myself have been trying to do in our elective courses, “History and Philoso-phy of Science” and “Logic and Foundations of Mathematics” at the Indian Institute ofTechnology, Bombay, over the last 25 years or so.

After I encountered some problems in my ‘understanding’ of physics and mathe-matics, I was led to a study of history and philosophy of science and mathematics. Iwas forced to do a critical examination of a lot of what I had learnt. As a student,of course, I was not expected to critically examine what I was being taught. This,unfortunately, may be true of students anywhere! In our courses, however, we madestudents critically examine what they were taught as science and mathematics, ratherthan dogmatize about scientific knowledge.

I was then led to critically examine ‘axiomatization’. In such matters, we think itis best to “go back to the Masters.” So before reading Aristotle, Kant or Mill, I startedreading Euclid’s ‘Elements’. I would urge you to have a first-hand look at Euclid’s‘Elements’ before reading the paper. I have also appended the contents of Books I andII as given in Mueller, 1981.

The starting point for an understanding of axiomatization, it seems to me, is Propo-sition 14 of Book II: “to construct a square equal to a given rectilineal figure.” Whybother to do this? What is square and rectilineal figure? What does ‘equal’ mean?The way geometry was taught to me, ‘equal’ meant ‘equal in area.’ Had I been boldenough at that time, I would have asked my teacher: “What do you mean by ‘equal inarea’?” What is “area” of a figure? Why should I accept the “formula” that the area of arectangle is the product of its length and breadth? Further, what are length, breadth,and product? And most importantly, why should we do all this?

Looking at Books I and II, starting with II. 14 in a backward direction, one cansee perhaps an intuitive notion of ‘equality’ of figures as coincidence, and a notion of‘inequality’ as a part-whole relationship. One can then see that a problem can arisehere with some pairs of figures: neither they coincide nor does one of them fit insidethe other. One problem “leads” to another, one notion “leads” to another and we are alsoforced to make (or to grant) some assumptions. Having done this exercise, one sees in

∗This paper is reprinted from Journal of Indian Council of Philosophical Research, Volume VI, Number3, May-August 1989, with permission from the author. The introductory section and the appendix are addedin this version.

240 Axiomatic Method

it a vision of an ‘axiomatic approach’. Please try to go through this exercise yourself,and draw the figures.

As with Geometry, so with Arithmetic, Algebra, Mechanics, Electricity and Mag-netism, etc. Over the years, we have been spending a lot of time with the Masters!

Euclidean Geometry and the Axiomatic Method

Euclid’s Elements constitutes the earliest extant substantial presentation of a body ofmaterial in the axiomatico-deductive form.1 Through it the subject of geometry gotpermanently associated with axiomatico-deductive formulation which was then viewedas a method, so much so that the expression ‘more geometrico’ (the geometric way)became synonymous with axiomatico-deductive formulation. Thus arose the generalbelief, especially in methodological quarters, that Euclid’s Elements and, in particular,Euclid’s geometry were merely instances of the application of a previously thoughtout/discovered/known method, and, thus, that the axiomatico-deductive method existedprior to the axiomatico-deductive formulation of geometry.2

Using Euclid’s Elements as my principal evidence,3 I want to suggest that the truestate of affairs is the other way round. The axiomatico-deductive formulation of geome-try emerged out of a successful attempt—most probably by some of Euclid’s predecessors—to solve some geometrical problems. Once this was done, it was seen by these geometersand also, of course, by Euclid as an instrument of open-ended discovery. Only, then,could the germs of a method be seen in it.

1Although the name ‘Euclid’ is almost synonymous with the word ‘geometry,’ it should be noted that Eu-clid’s Elements deals not only with geometry but also with (the natural) numbers, certain incommensurablegeometrical magnitudes (and thus indirectly with a special class of irrational numbers), and a theory ofgeneral magnitudes. The Elements is divided into thirteen Books. Books I to IV, VI, and X to XIII dealwith geometrical topics. Books VII to IX are concerned with natural numbers. Book V—a very interestingone but, unfortunately, rather overlooked by physicists and philosophers of science—contains a theory ofgeneral magnitudes, which is in many respects similar to algebra and lays the foundation of a theory ofmeasurement. Each Book contains a number of propositions, which are either assertions (or theorems,in modern terminology), or problems. The theorems (for example, in Book I, Proposition 5: ‘In isoscelestriangles the angles at the base are equal to one another, and, if the equal straight lines be produced furtherthe angles under the base will be equal to one another’) are followed by a demonstration of the correctnessof the assertion (proof), ending in the proverbial ‘Q.E.D.’ (in the Latin version). The problems (for example,in Book I, Proposition 1: “On a given finite straight line to construct an equilateral triangle”) are followedby a construction and a demonstration that the construction, indeed, solves the problem, ending with theless familiar ‘Q.E.F.’. Some Books (I to VII, X and XI) have some definitions stated at the beginning. OnlyBook I has some postulates and common notions following the definitions. (In today’s terminology, these canbe called ‘specific axioms’ and ‘general axioms’ respectively).

2Although both Euclid’s name and the subject of geometry have become synonymous with the axiomaticmethod, unfortunately we do not find any elaboration of this method which says something about the genesis,evolution or purpose of the method, either in Euclid’s Elements or in any extant work by his predecessors(such as Plato and Aristotle, among others). There is, for example, no preface to the Elements. Plato,of course, alludes frequently to the ‘method of the geometers,’ and Aristotle has written in detail on the‘demonstrative sciences.’

3My main source is the second revised edition of The Thirteen Books of Euclid’s Elements (3 vols.)translated from the text of Heiberg with introduction and commentary by Sir Thomas L. Heath and publishedby Cambridge University Press in 1925. The book was reprinted by Dover Publications, Inc., in 1956. Thecontents of the Elements have been put together in the appendix in Ian Mueller’s Philosophy of Mathematicsand Deductive Structure in Euclid’s Elements published by M.I.T. Press in 1981.

Agashe 241

My view of the genesis of the axiomatic method emboldens me to suggest furtherthat in general a method, which is something consciously conceived, arises as theresult of reflection on an activity that is already being pursued ‘intuitively.’ Again,once the method is consciously conceived, it can engender new activity being pursuedconsciously in accordance with the method, i.e. methodically.

The Geometrical Problems and their Solutions

If the axiomatic method arose as a result of reflection on some geometrical activitybeing pursued ‘intuitively,’ what could this activity have been? I suggest that thisactivity was initiated by a problem which, although it is not explicitly posed in theElements, can be solved on the basis of another problem which is explicitly posed andsolved in Book II, Proposition 14, of the Elements: “To construct a square equal to agiven rectilinear figure.” This problem could well be called the problem of “squaringa rectilineal figure” by analogy with the name of a well-known problem of Greek ge-ometry: “squaring the circle.” (Euclid was not able to solve this latter problem, andtherefore, perhaps, does not mention it at all in the Elements). Let us note that Book IIends with Proposition 14; I might say that our teaching and learning of geometry—andof the axiomatic method-ought to begin with this proposition which actually enunciatesa problem.

But why is this problem of “squaring a rectilineal figure” important? The compari-son of two straight-line segments to find out whether they are equally long or not, and,if not, to find out which one of the two segments is shorter and which the longer is,practically speaking, a simple matter, if one is allowed to use a string or a rope.4 Euclidsolved this problem theoretically, allowing himself the use only of a straight-edge (todraw a straight line joining two given points) and of a pair of compasses (to draw acircle with a given centre and a given segment, of which that centre is an extremity,as a radius of that circle, i.e. without using a pair of compasses as a pair of dividers).In fact, this is reflected in his Postulates 1 and 3 of Book I. Euclid’s solution of thisproblem of the comparison of two straight-line segments is given as Proposition 3 ofBook I: “Given two unequal straight lines, to cut off from the greater a straight lineequal to the less.”

The corresponding problem for plane rectilineal figures is far from easy, even prac-tically speaking. We may, where possible, move one of the two given rectilineal figuresand try to place it on the other to see whether the two fit together perfectly, or whetherone of them can be fitted entirely within the other. (Common Notions 8 and 9 of Book Ireflect this approach. Common Notion 8: “And things which coincide with one anotherare equal to one another.” Common Notion 9: “And the whole is greater than thepart”). But very often neither of these two things will happen, even if the figures

4The comparison of two line segments to find out which one is the longer and which the shorter is perhapsthe earliest example of the idea of the comparison of two objects with respect to a given quality to detect whichone of the two has ‘more’ and which one ‘less’ of the quality. I have argued in another paper presented atthe workshop on ‘The Genesis and Purpose of Quantification and Measurement’ that this idea of comparisonwith respect to a quality is more primitive than the precursor of the notion of quantity. The Greeks, and inparticular Plato talked repeatedly of the notion of ‘the more’ and ‘the less,’ or ‘the greater’ and ‘the lesser’


have some definite and simple shape such as that of a rectangle. However, shouldboth the figures be squares, superposition will always yield a solution; in fact, we neednot even superpose the squares: we need only compare their sides. Note that thishappy situation is based on the observation that any two right angles fit, and thisrequirement is what perhaps led the geometers to define a right angle the way Eucliddoes (Definition 10, Book I: “When a straight line set up on a straight line makes theadjacent angles equal to one another, each of the equal angles is right”), and led Euclidto put down his Postulate 4, Book I: “And that all right angles are equal to one another.”

Another important observation would have to be made before one could proceedfurther with the problem. A given figure can be cut up or decomposed into parts andthese parts put together differently to obtain a different-looking figure. (This can beeasily seen by cutting up a square into two equal parts and putting these together toobtain a rectangle). Now, two such figures are not equal (in the sense of Common Notion8), but there is something special about them, namely, that their ‘corresponding’ partsare equal in the sense of congruence. At this point, the ancient geometers must haverealized that no further progress on the problem of comparison of figures was possibleunless one was willing to regard two figures, which were equal in parts, to be ‘equal‘.This is, of course, a weakening or widening of the notion of equality of figures, andappears as Common Notion 2 in Book I: “And if equals are added to equals the wholesare equals.” (The original Greek wording of this Common Notion does not suggestthe notion of addition in a numerical sense; rather, it suggests ‘putting together’—prostethe). This broadening of the original notion of equality as congruence allows oneliterally to transform a given figure, i.e., change its form or shape, while retaining its‘size,’ i.e., while keeping the new figure equal to the original figure. The problem ofcomparison of two figures could now be ‘reduced’ to the problem of transformation ofone figure into another through the techniques of ‘dividing’ and ‘putting together.’ Butthe fact that squares can be compared with ease would have suggested the followingalternative. Suppose, instead of trying to convert one of the given figures into the other,one tries to convert both the figures into squares; and, suppose, it turns out that theconverted squares are equal. Could we, then, assert that the two original figures wereequal? The astute Greek geometers saw that this was not justified unless the notionof equality was weakened further; thus, we have Common Notion 1 of Book I: “Thingsequal to the same thing are also equal to one another.”5

5Thus far, I have ‘accounted’ for three of the five Euclidean Postulates and four of the five EuclideanCommon Notions in Book I. (Mueller lists one more Postulate and four more Common Notions, but these arenot regarded as genuinely Euclidean and so are enclosed within square brackets). This leaves only one moreCommon Notion (Common Notion 3): ‘And if equals are subtracted from equals the remainders are equal’and two more Postulates; Book I, Postulate 2 is: “To produce a finite straight line continuously in a straightline” and Book I, Postulate 5 is the so-called ‘Parallel Postulate’: ‘If a straight line falling on two straightlines make the interior angles on the same side less than two right angles, the two straight lines, if producedindefinitely, meet on that side on which are the angles less than the two right angles.’ Postulate 2 is obviouslyrequired in most constructions where a point is to be obtained by the intersection of two straight lines orof a straight line and a circle. As regards Postulate 5, Euclid ‘postpones’ the use of this postulate as far aspossible; it, is involved for the first time in proving Proposition 29: “A straight line falling on parallel straightlines makes the alternate angles equal to one another, the exterior angle equal to the interior and oppositeangle, and the interior angles on the same side equal to two right angles.” In fact, this Proposition could

Agashe 243

Having agreed to the broadening of the notion of equality (of figures) through theCommon Notions 1 and 2, the problem of comparison of two figures is ‘reduced’ tothe problem of squaring of a figure. Naturally, Euclid takes up the simpler case of arectilineal figure, and, thus, arrives at the statement of his basic problem in Books Iand II, Proposition II. 14: “To construct a square equal to a given rectilineal figure.”

How does Euclid solve the problem? Or, rather, how did Euclid, or some predecessor,arrive at the solution we find given in the Elements? Certainly not by starting off withthe definitions, postulates and common notions, and brilliantly deducing one theoremafter another (there are forty-eight propositions in Book I and fourteen in Book II). Theproblem was solved by reducing it, in turn, to one or more problems. This approach toproblem solving was discussed much later by Pappus under the name of ‘the Method ofAnalysis and Synthesis,’ but we find allusions to it already in Plato. The ‘analysis’ partinvolves the formulation of auxiliary or subsidiary problems in what later appears asa ‘back tracking’ when the solution is finally described in the ‘synthesis’ part.

Although a triangle would be the simplest rectilineal figure, for obvious reasons Eu-clid prefers to tackle the rectangle first. So the problem of squaring a rectilineal figureis broken down into two sub-problems: (a) the problem of squaring a rectangle (thisconstruction is given in II.14) and (b) the problem of ‘rectangulating’ any rectilinealfigure (this construction is given in I. 45).

Euclid solves (a) essentially by transforming a rectangle into a gnomon (which is anL-shaped figure left when a smaller square is taken out of a bigger square; see shadedarea in the figure).

Figure 1: A gnomon.

A gnomon is clearly a difference of two squares, and wethus have the new problem of constructing a square equalto the difference of two squares. This problem can be solvedperhaps if we succeed in solving the problem of constructinga square equal to the ‘sum’ of two squares; this is preciselywhat the famous Pythagorean proposition amounts to, and itis Proposition I. 47, the last but one proposition in Book I, thelast (48th) proposition being the converse of the Pythagoreanproposition. Of course, Pythagoras’ Theorem in the specialcase of the isosceles right-angled triangle was known tomany civilizations before Euclid, and perhaps even beforePythagoras, and its ‘truth’ could be visually ascertained. Itmust have been natural to conjecture that the theorem was

true for any arbitrary right-angled triangle, but this already presupposes a broadenednotion of equality of figures. Indeed, Euclid makes use of this broadened notion inhis proof of Pythagoras’ Theorem by dividing the square on the hypotenuse into two

well have been taken as a postulate in place of Postulate 5. (The converse of this Proposition is containedin Propositions 27 and 28 which are proved without invoking Postulate 5, and this is incidentally the firstoccasion for Euclid to talk about parallel lines). I have put the verb ‘postpones’ in quotation marks, because,according to the view that I am putting forward here, this was not a deliberate postponement by Euclid onaccount of some inherent abhorrence of the parallel Postulate, as alleged by many critics, but rather it wasthe last step along one line of progress in Euclid’s ‘backtracking’ journey from Book II, Proposition 14 to theDefinitions, Postulates and Common Notions.


rectangles and showing the ‘equality’ of these rectangles with the squares on thecorresponding sides. Now, getting convinced about the ‘correctness’ of the Pythagoreanconstruction for the sum of two squares required further backtracking and ultimatelymust have led to the inverted or backward construction of Book I, or something similarto it, perhaps by some predecessors of Euclid. This involves, in particular, gettingconvinced that the diagonal of a parallelogram splits it into two equal triangles, andthat under certain conditions two triangles are equal. (Incidentally, Common Notion3 is ‘demanded’ or postulated in claiming that the gnomon is ‘equal’ to an appropriatesquare.)

In his solution of problem (b), i.e., converting a rectilineal figure into a rectangle (infact, Euclid gives a stronger construction I. 45: “to construct in a given rectilineal anglea parallelogram equal to a given rectilineal figure,” and to effect that the constructionI. 44: “to a given straight line to apply, in a given rectilineal angle, a parallelogramequal to a given triangle”), Euclid uses the obvious fact that a rectilineal figure can beeasily decomposed into triangles, so that one is led next to the problem solved in I. 44.

To summarize, I wish to suggest that investigations into the problem of comparisonof two rectilineal figures led the Greeks before Euclid to the realization that some‘concessions’ had to be made with regard to the notion of equality, which led to theformulation and investigation of some subsidiary problems, leading finally to a numberof postulates, common notions and definitions. Having done this, they then reversedthe whole process of thinking, making it appear to posterity that, almost by a miracle,from the small ‘acorns’ of a few innocent-looking definitions and postulates mighty‘oaks’ such as Pythagoras’ Theorem and II.14 could be grown. I have indicated thiswith reference to Books I and II, but the same could be said about the other geometricalbooks.

It should be noted, however, that the other non-geometrical books of Euclid’s Ele-ments, namely, those on natural numbers and general magnitudes do not invoke anypostulates explicitly but are based only on definitions. So they could well have beenthe result of an application in the forward direction of the axiomatic method discoveredby investigations in the reverse direction into some geometrical problems. Of course,geometers after Euclid—and even Euclid himself—did carry out further geometricalinvestigations in the forward direction, proving many interesting new theorems. Even-tually, Lobachevskii, and Bolyai followed, non-Euclidean lines of exploration. This laststep, after some initial resistance, later turned into reluctance, and a considerabledelay of about fifty years led to our modern conception of the axiomatic method asthe method of mathematics, involving notions of ‘definition,’ ‘axiom’ and ‘proof.’

The Purposes of the Axiomatic Method

Having discussed the possible genesis of the axiomatic method in rather great detail,I would like to turn to the several purposes or uses, to which it has been put subse-quently.

Agashe 245

The Mathematical Use

As mentioned just above, the axiomatic method was put to use in mathematics nosooner than it was discovered, and thus it was recognized to be a powerful instrument ofopen-ended discovery or derivation. This had several consequences. Firstly, the processof ‘derivation’ or ‘deduction’ came under close scrutiny giving rise to the subject of logic,and I would venture the guess that Aristotle’s investigations into logic were stimulatedmore by mathematics, particularly geometry, than by rhetoric or sophistic discourse.Eventually, this led to the feeling that, logic was an engine of deduction which requiredonly the turning of a handle to churn out new propositions from old. Now, deductiondone by mathematicians—at least the human ones—are not so mechanical as that, butit is possible to automate the process of deduction, and this is, indeed, what has beendone recently by ‘theorem-proving programs.’

The second, and rather unfortunate, consequence was that the postulates and com-mon notions, with the exception of Euclid’s ‘parallel postulate,’ were regarded as being‘true’ in some sense and so irreplaceable. Logic was then seen as an engine to derivenew, ‘less obvious’ truths from old, ‘more obvious,’ ‘self-evident’ truths. I doubt if theGreek geometers themselves regarded their postulates and common notions as ‘self-evident’ or ‘true.’ Three of the five postulates are not about propositions, that is, aboutany state of affairs in this world or in some other world. Rather, they are assumptionsabout what can be done in an ideal world. Of the other two postulates, equality of allright angles could have had some empiricism about it, but was finally assumed in orderfor some constructions to work. Finally, the ‘parallel postulate’ was necessitated bythe somewhat empirical fact that parallel straight lines cut by a transversal producedequal angles, but this, too, was necessitated by the conception of a square, say, ashaving all angles equal and right (Definition 22). (Euclid’s I.46 shows how to constructa square: “On a given straight line to describe a square”). The common notions were allrequired in order to surmount the problem of equality and comparability of (rectilineal)figures.

Of course, there was a happy side to the view that the postulates and commonnotions were self-evident. Thanks to the non-self-evident nature of the ‘parallel pos-tulate’, it eventually emboldened geometers to abandon it, to replace it by somethingequally non-self-evident and then, working the engine of deduction, squeeze out somestartling and ‘almost false’ consequences. But this development, in its turn, had theeffect that henceforth axioms (to use a single word for postulates and common notions)were deemed to be completely arbitrary and unprovable assertions, and, in an extremeview, even meaningless and having no relation with truth or reality whatsoever. Thiswas accompanied by the view that definitions also were completely arbitrary, and onemerely defined some terms (the ‘defined’ terms) ‘in terms of ’ some other terms (the‘undefined’ or undefinable? terms). Now clearly, for Euclid, definitions were far fromarbitrary, though he stretched himself too far, trying to define almost every geometricalterm. But it must be noted that nowhere did he or any of his predecessors, say thatterms like ‘part,’ ‘breadthless length,’ ‘extremity,’ etc., were undefined in the modernmathematical sense of being devoid of any connotations. They were undefinable in


a relative sense; they were simply left undefined in Euclid’s formulation. There wasnothing either undefined (meaningless) or undefinable about them.

However, towards the end of the nineteenth century there did arise a widespreadview of mathematics that it consists of setting out some ‘undefined terms’ and some‘unproved propositions’ at the ‘beginning’; and then, after giving some definitions ofdefined terms as and when one fancies, of proving or deriving some other assertionson the basis of or from the unproved assertions using sheer logic or rules of inference.The American mathematician Benjamin Peirce said, “Mathematics is the science whichdraws necessary conclusions”; and Russell, 1901, confessed (with tongue-in-cheek hu-mour): “Thus mathematics may be defined as the subject in which we never know whatwe are talking about, nor whether what we are saying is true.” (One realizes, of course,that mathematics is a creative or imaginative activity, and not a routine, mechanicalactivity, because necessary conclusions do not ‘follow’ easily or automatically from theunproved assertions; rather, they have to be conjectured and then ‘drawn out’ by hardwork.) This open-ended view of the axiomatic method in mathematics leads one tobelieve that one is free to start with arbitrary undefined terms and arbitrary unprovedassertions, and then to make arbitrary definitions in order to draw the conclusions, too,somewhat arbitrarily, i.e., as and when they occur to the mathematician, so that thewhole thing is a stupendous exercise in arbitrariness! Of course, Russell, 1919, himselfrealized that this was not so, for he said (about twenty years after his earlier quip):

Mathematics is a study which, when we start from its most familiar portions, may be pursuedin either of two opposite directions. The more familiar direction is constructive, towards grad-ually increasing complexity: from integers to fractions, real numbers, complex numbers, fromaddition and multiplication to differentiation and integration, and on to higher mathematics.The other direction, which is less familiar, proceeds, by analysing, to greater and greaterabstractness and logical simplicity; instead of asking what can be defined and deduced fromwhat is assumed to begin with, we ask instead what more general ideas and principles can befound, in terms of which what was our starting-point can be defined or deduced. It is the factof pursuing this opposite direction that characterises mathematical philosophy as opposed toordinary mathematics. But it should be understood that the distinction is one, not in the subjectmatter, but in the state of mind of the investigator. . . . The distinction between mathematicsand mathematical philosophy is one which depends upon the interest inspiring the research,and upon the stage which the research has reached; not upon the propositions with which theresearch is concerned.

I might add that many great mathematicians of the last hundred years or so havecontributed a lot to ‘mathematical philosophy’ in Russell’s sense, because they havecontributed to the process of axiomatization of mathematics in the original Euclideansense. Further, it must be added that usually one stipulates one or more of the followingrequirements for an ‘arbitrary’ set of axioms, namely, that they must be ‘consistent,’‘independent,’ ‘complete,’ ‘categorical.’

The Cartesian Purpose

The use to which Descartes sought to put the axiomatic method was the establishmentof indubitable truths. A proposition about whose truth we are ‘doubtful’ (such as ‘Iexist’) is sought to be established on the basis of some intuitively clear or indubitable

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propositions (such as ‘I think’). Thus, the axiomatic method is an instrument fordispelling doubt and for creating certainty. Of course, the process of finding out whethera seemingly doubtful proposition can, indeed, be indubitably established is one ofback-tracking, quite similar to the back-tracking in mathematics, where a conjecturedtheorem is sought to be proved. But the difference is that, in mathematics we do notbother about the ‘truth’ of the axioms, whereas in the Cartesian approach the ‘firstprinciples’ have to be indubitable and thus true.

Organization of Knowledge

Another use that has been found for the axiomatic method is that of ‘organizing a bodyof knowledge’ or ‘systematizing a discipline.’ Here, it is supposed that we already havea set of truths somehow obtained, but these truths are perhaps too many or seeminglyunrelated to each other. We then try to create some system or order by trying to discoverwhether a small subset of them can serve as a set of axioms from which all the rest canbe derived. One may, of course, question the utility of such an enterprise. The wholeexercise of organization is to start with the knowledge base that is already there. Thisbase would include terms whose meanings we already know and assertions whose truthwe are already confident of. But, if this is so, why bother to define the already knownterms in terms of ‘undefined’ terms, and to derive the already trustworthy assertions interms of some selected assertions? Perhaps one is trying to apply Ockham’s razor here,i.e., one is trying to obtain simplicity. But simplicity in the form of a small numberof axioms is won at the cost of complexity of derivations of the other truths from theaxioms.

Discovering Unknown Causes or Hypotheses

In this application of the axiomatic method, one starts with a known body of truthswith terms whose meanings are known. One then tries to discover a set of undefinedand unknown terms, a set of definitions of the known terms in terms of the undefinedand unknown terms; and, finally, a set of assertions whose truth is unknown in sucha way that the known truths, when reformulated using the definitions in terms of theundefined terms, can all be derived from the axioms. This is, of course, the game of(scientific) theory construction6. What is the point of such a game? Well, after theaxiomatization, using the axiomatic method in the forward direction as an instrumentof discovery, one may stumble across new consequences of the axioms, which, whenreformulated using the known terms, give us propositions whose truth can then beascertained. Their truth is not guaranteed, because the axioms are not necessarily(known to be) true. But the task of ascertaining the truth of new propositions canproduce new truths which, otherwise, we may not have bothered to look for. The axiomscould be called causes, hypotheses or principles of the body of knowledge or the sciencethat one is dealing with. Success in this approach at the initial stages depends uponthe size of the body of knowledge one starts with; usually, it does not pay to be too

6One would immediately think of the Kinetic Theory of Gases as an example.


ambitious, but one may gradually enlarge the body of knowledge and simultaneouslymodify the undefined terms, definitions and axioms, that is, the theory.

I may, finally add that perhaps one should not be too much preoccupied with ‘truths.’Taking the cue from the initial axiomatization of geometry, one should perhaps beequally concerned with problems, and should try to discover an axiomatization in thecourse of the attempt to find acceptable solutions.

Appendix

The Contents of the Elements (from Ian Mueller: Philosophy of Mathematics and De-ductive Structure in Euclid’s Elements, 1981).

“I give here in an English translation, which varies in many minor ways fromHeath’s, all of the first principles and propositions of the Elements as they are given inthe first hand in the body of the manuscript P. . . . Material which is added for clarity isput in parentheses; material excluded by Heiberg is put in brackets.

Definitions (Horoi)

1. A point is that which has no part (hou meros outhen).

2. A line is breadthless length.

3. The extremities (perata) of a line are points.

4. A straight line is one which lies evenly (ex isou) with the points on itself.

5. A surface is that which has length and breadth only.

6. The extremities of a surface are lines.

7. A plane surface is one which lies evenly with the straight lines on itself.

8. A plane angle is the inclination (klisis) to one another of two lines in a plane whichmeet one another and do not lie in a straight line.

9. And when the lines containing the aforesaid angle are straight, the angle is calledrectilineal.

10. When a straight line set up on a straight line makes the adjacent (ephexes) anglesequal to one another, each of the equal angles is right, and the straight linestanding on the other is called a perpendicular to that on which it stands.

11. An obtuse angle is an angle greater than a right angle.

12. An acute angle is an angle less than a right angle.

13. A boundary (horos) is that which is an extremity (peras) of something.

14. A figure is that which is contained by some boundary or some boundaries.

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15. A circle is a plane figure contained by one line [which is called its circumference(periphereia)] such that all the straight lines falling upon it [upon the circumfer-ence of the circle] from one point of those lying inside the figure are equal to oneanother.

16. The point is called the center of the circle.

17. A diameter of the circle is any straight line drawn through the center and termi-nated in both directions (ephhekatera ta mere) by the circumference of the circle,and such a straight line also bisects the circle.

18. A semicircle is the figure contained by the diameter and the circumference cut offby it.[A segment (tmema) of a circle is the figure, either greater or less than a semicir-cle, contained by a straight line and a circumference of a circle.]

19. Rectilineal figures are those which are contained by straight lines; trilateral bythree, quadrilateral by four, and multilateral those contained by more than fourstraight lines.

20. Of trilateral figures, an equilateral traingle is that which has its three sides equal,an isosceles triangle that which has only two of its sides equal, a scalene trainglethat which has its three sides unequal.

21. Further, of trilateral figures, a right-angled traingle is that which has a rightangle, an obtuse-angled that which has an obtuse angle, an acute-angled thatwhich has three acute angles.

22. Of quadrilateral figures, a square is that which is equilateral and right-angled,an oblong (heteromekes) that which is right-angled but not equilateral, a rhombusthat which is equilateral but not right-angled, a rhomboid that which has itsopposite sides and angles equal to one another but which is neither equilateralnor right-angled.

23. Parallel straight lines are those which, being in the same plane and being pro-duced ad infinitum in both directions, do not meet each other in either direction.

Postulates (Aitemata)

1. Let it be postulated (aitestho) to draw a straight line from any (pas) point to any(pas) point,

2. and to produce a limited straight line in a straight line,

3. and to describe a circle with any center and distance,

4. and that all right angles are equal to one another,


5. and that, if one straight line falling on two straight lines makes the interior anglesin the same direction less than two right angles, the two straight lines, if producedad infinitum, meet one another in that direction in which the angles less than tworight angles are,

6. and that two straight lines do not enclose a space.

Common Notions (Koinai Ennoiai)

1. Things equal to the same thing are also equal to one another.

2. And if equals are added to equals the wholes are equal.

3. And if equals are subtracted from equals the remainders are equal.

4. And if equals are added to unequals the wholes are unequal.

5. And if equals are subtracted from unequals the remainders are unequal.

6. And doubles of the same thing are equal to one another.

7. And halves of the same thing are equal to one another.

8. And things which coincide with one another (ta epharmodzonta ep allela) areequal to one another.

9. And the whole is greater than the part.

(Propositions)

1. On a given straight line to construct an equilateral triangle.

2. To place at (pros) a given point a straight line equal to a given straight line.

3. Given two unequal straight lines, to cut off from the greater a straight line equalto the less.

4. If two triangles have the two sides equal to two sides respectively and have theangle contained by the equal straight lines equal to the angle, they will also havethe base equal to the base, the triangle will be equal to the remaining anglesrespectively, (namely) those which the equal sides subtend (hupoteinein)

5. The angles at the base of isosceles triangles are equal to one another, and if theequal straight lines are produced further the angles under the base will be equalto one another.

6. If two angles of a triangle are equal to one another, the sides which subtend theequal angles will also be equal to one another.

Agashe 251

7. On the same straight line there cannot be constructed (ou sustathesontai) twoother straight lines equal to the same two straight lines (and) at (pros) a differentpoint, in the same direction, (and) having the same extremities as the originalstraight lines.

8. If two triangles have the two sides equal to two sides respectively and also havethe base equal to the base, they will also have the angle contained by the equalstraight lines equal to the angle.

9. To bisect a given rectilineal angle.

10. To bisect a given limited straight line.

11. To draw a straight line at right anlges to a given straight line from a given pointon it.

12. To draw a straight line perpendicular to a given infinite straight line from a givenpoint which is not on it.

13. When a straight line set up on a straight line makes angles, it will make eithertwo right angles or angles equal to two right angles.

14. If relative to (pros) some straight line and a point on it, two straight lines notlying in the same direction make the adjacent angles equal to two right angles,the straight lines will be in a straight line with one another.

15. If two straight lines cut one another, they will make the vertical angles (hai katakoruphen goniai) equal to one another.

16. If one of the sides of any triangle is produced, the exterior angle is greater thaneach of the interior and opposite angles.

17. Two angles of any triangle taken in any way are less than two right angles.

18. The greater side of any triangle subtends the greater angle.

19. The greater angle of any triangle is subtended by the greater side.

20. Two sides of any triangle taken in any way are greater than the remaining side.

21. If two straight lines are constructed inside (and) on one of the sides of a trianglefrom its extremities, the constructed straight lines will be less than the remainingtwo sides of the triangle but will contain a greater angle.

22. To construct a triangle out of three straight lines which are equal to three givenstraight lines; thus it is necessary that two taken in any way be greater than theremaining one [because also the two sides of any triangle taken in any way aregreater than the remaining side].


23. To construct relative to a given straight line and a point on it a rectilineal angleequal to a given rectilineal angle.

24. If two triangles have the two sides equal to two sides respectively but the anglecontained by the equal straight lines greater than the angle, they will also havethe base greater than the base.

25. If two triangles have the two sides equal to two angles respectively, but have thebase greater than the base, they will also have the angle contained by the twoequal straight lines greater than the angle.

26. If two triangles have the two angles equal to two angles respectively and oneside equal to one side, either the one adjoining (pros) the equal angles or the onesubtending one of the equal angles, they will also have the remaining sides equalto the remaining sides respectively and the remaining angle to the remainingangle.

27. If a straight line falling on two straight lines makes the alternate (enallax) anglesequal to one another, the straight lines will be parallel to one another.

28. If a straight line falling on two straight lines makes the exterior angle equal tothe interior and opposite angle in the same direction or the interior angles in thesame direction equal to two right angles, the straight lines will be parallel to oneanother.

29. The straight line falling on parallel straight lines makes the alternate anglesequal to one another and the exterior angle equal to the opposite and interiorangle and the interior angles in the same direction equal to two right angles.

30. Straight lines parallel to the same straight line are also parallel to another.

31. To draw a straight line parallel to a given straight line through a given point.

32. If one of the sides of any triangle is produced, the exterior angle is equal to theinterior and opposite angle, and the three interior angles of the triangle are equalto two right anlges.

33. Straight lines joining equal and parallel straight lines in the same direction arethemselves also equal and parallel.

34. The opposite sides and angles of parallelogrammic areas (parallelogramma cho-ria) are equal to one another, and the diameter bisects them.

35. Parallelograms which are on the same base and in the same parallels are equalto one another.

36. Parallelograms which are on equal bases and in the same parallels are equal toone another.

Agashe 253

37. Triangles which are on the same base and in the same parallels are equal to oneanother.

38. Triangles which are on equal bases and in the same parallels are equal to oneanother.

39. Equal triangles which are on the same base and in the same direction are also inthe same parallels.

40. Equal triangles which are on equal bases and in the same direction are also inthe same parallels.

41. If a parallelogram has the same base as a triangle and is in the same parallels,the parallelogram is double of the triangle.

42. To construct in a given rectilineal angle a parallelogram equal to a given triangle.

43. The complements (parapleromata) of the parallelograms around the diameter ofany parallelogram are equal.

44. To apply to (parabalein para) a given straight line in a given rectilineal angle aparallelogram equal to a given triangle.

45. To construct in a given rectilineal angle a parallelogram equal to a given rectilin-eal (figure or area).

46. To describe a square on (apa) a given straight line.

47. In right-angled triangles the squares on the side subtending the right angle isequal to the squares on the sides containing the right angle.

48. If the square on one of the sides of a triangle is equal to the squares on theremaining two sides of the triangle, the angle contained by the remaining twosides of the triangle is right.


(Definitions)

1. Any right-angled parallelogram is said to be contained by the straight lines con-taining the right angle.

2. Let any one of the parallelograms around the diameter of any parallelogrammicarea (together) with the two complements be called a gnomon.

(Propositions)

1. If there are two straight lines and one of them is cut into any number of segments,the rectangle (orthogonion) contained by the two straight lines is equal to therectangles contained by the uncut straight line and each of the segments.

2. If a straight line is cut at random (hos etuchen), the rectangle contained by thewhole and both of the segments is equal to the square on the whole.

3. If a straight line is cut at random, the rectangle contained by the whole and one ofthe segments is equal to the rectangle contained by the segments and the squareon the aforesaid segment.

4. If a straight line is cut at random, the square on the whole is equal to the squareson the segments and twice the rectangle contained by the segments.

5. If a straight line is cut into equal and unequal segments, the rectangle containedby the unequal segments of the whole with the square on the segment betweenthe sections is equal to the square on the half.

6. If a straight line is bisected and some straight line is added to it in a straight line,the rectangle contained by the whole with the added straight line and the addedstraight line is equal to the square on the straight line composed of the half andthe added straight line.

7. If a straight line is cut at random, the two squares together that on the whole andthat on one of the segments, are equal to twice and the rectangle contained by thewhole and the said segment and the square on the remaining segment.

8. If a straight line is cut at random, four times the rectangle contained by the wholeand one of the segments with the square on the remaining segment is equal to thesquare described on the whole and the aforesaid segment as on one straight line.

9. If a straight line is cut into equal and unequal segments, the squares on theunequal segments of the whole are double of the square on the half and the squareon the segment between the sections.

10. If a straight line is bisected and some straight line is added to it in a straight line,the two squares together, that on the whole with the added straight line and thaton the added straight line, are double of the square on the half and the squaredescribed on the straight line composed of the half and the added straight line ason one straight line.

Agashe 255

11. To cut a given straight line so that the rectangle contained by the whole and oneof the segments is equal to the square on the remaining segment.

12. In an obtuse-angled triangles the square on the side subtending the obtuse angleis greater than the squares on the sides containing the obtuse angle by twice therectangle contained by one of the sides around the obtuse angle, the one on whichthe perpendicular falls and the straight line cut off outside (the triangle) by theperpendicular towards (pros) the obtuse angle.

13. In acute-angled triangles the square on the side subtending the acute angle isless than the squares on the sides containing the acute angle by twice the rect-angle contained by one of the sides containing the acute angle, the one of whichthe prependicular falls, and the straight line cut off inside by the perpendiculartowards the acute angle.

14. To construct a square equal to a given rectilineal (figure or area).”

References

Heath, T.L. (trans.): 1925, The Thirteen Books of Euclid’s Elements, 3 Vols., CambridgeUniversity Press.

Mueller, I.: 1981, Philosophy of Mathematics and Deductive Struture in Euclid’sElements, M.I.T. Press.

Russell, B. A. W.: 1901, Recent work on principles of mathematics, InternationalMonthly, Vol. 4, pp. 83–101. Reprinted as ‘Mathematics and the Metaphysiciansin Mysticism and Logic and Other Essays, London, Longmans Green, 1918. Issuedas a paperback by Penguin Books Ltd. p. 75.

Russell, B. A. W.: 1919, Introduction to Mathematical Philosophy, George Allen andUnwin Ltd. Reprinted by Simon and Schuster.

Approaches to the Periodic Table

Rudolf KrausUniversity of Toronto, Canada. Email: [email protected]

Despite its value to students of chemistry in predicting the structure of an element’selectron orbitals, the periodic table was not developed on the basis of electronic struc-ture. This is often overlooked by modern educators. A possible reason is that manymodern science textbooks are written by scientists, who have spent a great deal of timeand effort mastering their fields, but at the cost of historical training. Some sift thoughthe history of their discipline for only those ideas that support currently acceptedpositions. Another common error shows all scientific research leading inevitably to ourpresent position. Famous discoveries and famous scientists risk complete reinterpreta-tion in accordance with modern theory. This is poor history, and it is at best erroneous.At its worst, it presents a distorted view of scientific thinking and scientific processes,and engenders a misplaced faith in the authority of science.

I intend to show that a historical approach to the teaching of science benefits stu-dents in several ways. By presenting chemical topics from a historical point of view,students develop an appreciation for the development of science, and learn to seetheories as dynamic entities that change as new information is discovered. Historicexperiments, in general, rely upon common materials and use techniques and instru-ments that can be easily duplicated. For example, Lavoisier’s discovery of oxygen canbe duplicated with nothing more complicated than a spirit lamp, a magnifying glass,and a supply of lead.

As a case-study, I have examined high-school chemistry textbooks with regard totheir presentation of the periodic table, including the CHEM Study program introducedin the United States in the 1960’s and a current text, Merrill’s Chemistry, one of thecurrent texts used by the Ontario Board of Education. These will be compared toMendeleev’s own approach in his Principles of Chemistry, the 1891 edition.

The Chemical Education Material study, or CHEM Study, arose from a combinationof changes within the field of chemistry, and a general enthusiasm for curriculumreform in the United States. The National Science Foundation awarded monies toa group of university chemists who wished to reform secondary chemistry education.These professors brought together a number of high-school teachers and universitychemists, and designed a new curriculum. As might be expected from such a group,which contained only one specialist in education out of hundreds of members, therewas a strong influence from professional science.

The professional group introduced the periodic table after a discussion of atoms andbonding. The structure of the periodic table was then revealed as a reflection of thenature of electronic orbitals, and the order in which they fill. Instead of a systematicdescription of the properties of elements, quantum mechanics was introduced. Thisfocused on the structure of the atom, and the filling of electron orbitals. Then, the

258 Periodic Table

authors showed that elements with similar electron structures have similar properties.This kind of descriptive chemistry puts the cart before the horse, and was com-

pletely anachronistic. Historically, the similar properties of elements led chemists tobelieve that their electronic structures were similar. Logically, deductive reasoningbuilt from facts to generalizations. The academics that wrote CHEM Study presentedtheir material in the opposite order. Why might this have been the case?

When considering their new curriculum, the CHEM Study, these authors did notassess what the average student needed to know (as an employee and as a citizen).Instead, they focused on the four percent of the class who were to become universitystudents of chemistry, and decided what knowledge would be useful for them. As anexample, here is a list of questions that were asked during the creation of the CHEMStudy. The underlying message behind these questions was that knowledge of chemicalprocesses is important, and CHEM Study only needed to adjust the proportions of thevarious sub-disciplines of chemistry in their curriculum to be successful.

1. Should atomic structure and the nature of chemical bonding be discussed early orlate in the course?

2. Should the descriptive chemistry include a detailed discussion of some of therecently discovered “exotic” compounds, or should it adhere rather closely to thecompounds that have relatively high stability under atmospheric conditions?

3. To what extent should algebra, as used in the gas laws and in equilibrium calcu-lations, be included in the course?

4. To what extent should the gas laws themselves be treated, as contrasted with anapproach based more directly on kinetic theory and molecular motions?

5. To what extent should the text be based on laboratory experimentation alreadyperformed by the student?

6. What is the most effective way of acquainting students with stoichiometry andgetting them to the point where they can work with it readily?

7. How useful is the mole concept, and is it reasonable to define the mole as anumber rather than continue to give its historical definition?

8. To what extent should various interpretations of experimental observations bepresented? For example, how many acid-base theories should be used in inter-preting chemical reactions?

9. To what extent should the treatment of the elements attempt to cover the wholeperiodic table in contrast to concentrating on a few selected elements?

10. How much treatment of radioactivity should be included?

11. What level of vocabulary should be used as compared with vocabulary usuallyfound in books at the high school level?

Kraus 259

12. How much emphasis should be placed on industrial practice and practical appli-cations of chemistry?1

The need to teach atomic structure and chemical bonding was unquestioned despitethe fact that many great chemists and important chemical industries had prosperedwithout them. Instead, the CHEM Study questioned the extent of this need.

This academic bent was responsible for the assertion of theoretical considerationslike the atomic theory of structure, Avogadro’s hypothesis, and the kinetic moleculartheory of gases within the first three chapters in a cursory, authoritative manner. Thesetheories were to be proved in later chapters of the text; unfortunately many of theseso-called proofs relied on data that the student could not determine in the laboratory,and lacked the background to understand. The worst offender was chapter fourteen,entitled “Why we believe in atoms,” which cited the electrical nature of atoms, thedetermination of charge/mass ratios in CRT tubes, evidence from X-ray diffraction,and microwave and infrared spectroscopy as proof of the existence of atoms. Exceptfor the first, these experiments required equipment beyond the abilities and budgetof an average high-school. Even if they had been available, they relied on a hostof assumptions in optics, mechanics, the nature of light, and mathematics in orderto produce meaningful data, and these assumptions contradicted the spirit of inquirypromoted in the introduction.2

Other evidence of academic motivation was seen in the vocabulary. Rather than usethe full names of chemical compounds (sodium chloride), or the common substancesthat are equivalent (table salt), chemical abbreviations were used almost exclusively(NaCl). Quantitative results were also emphasized, as can be seen in this sampleproblem.

Exercise 11-4Suppose that 0.099 mole of solid NaOH is added to 0.100 litre of 1.00 M HCl.

1. How many more moles of HCl are present in solution than moles of NaOH?

2. From the excess number of moles and the volume, calculate the concentration ofexcess H+(aq)

3. Calculate the excess concentration of H+(aq) from the difference between theinitial concentrations of HCl and NaOH.3

The middle chapters of the book, from thirteen to eighteen, all dealt with subjectsthat in my opinion are useless to the non-chemist. Practice in stoichiometry (mea-surement of quantities consumed and produced in reactions), proof of the existenceof the atom, quantum mechanics, the nature of chemical bonding, electron orbitalhybridization, and cis-trans isomerism were perhaps not chosen with the interest of

1Merill, R.J., and Ridgway, D.W.: 1969, The CHEM Study Story, W.H. Freeman and company, SanFrancisco, p. 7.

2CHEM Study: 1962, Chemistry—An Experimental Science, W.H. Freeman and company, San Francisco.3CHEM Study, Chemistry

260 Periodic Table

the public in mind. In addition to the difficulty of applying these theories, the ideas ofphysicists Max Planck and Niels Bohr on the quantization of energy and structure ofthe atom were adopted uncritically, as was the electron exclusion principle of WolfgangPauli. Relatively simple practical applications of chemistry, such as developing film orchemical batteries, were at best mentioned briefly in the laboratory manual. Practicalapplications of chemistry are not only more concrete to the students, and thus moreeasily taught, but accurately reflect the average student’s involvement with chemistry.

CHEM Study did address this problem in chapters nineteen to twenty-three. Therewas a resurgence in the importance of laboratory work and descriptive chemistry. Stu-dents investigated properties of carbon chemistry, halogens, the third-row elements,alkaline earths, fourth and fifth-row transition metals, and some sixth and seventh-row rare earths. Emphasis was placed on carbon rings in chapter nineteen, and theradioactive properties of the rare-earths in chapter twenty-three. The last two chap-ters, twenty four and twenty five dealt with biochemistry, and the chemistry of the solarsystem, especially the chemical makeup of the third planet. Absent was a chapter onchemistry in the workplace, or chemistry in the environment.4 While this descriptivechemistry is well done, it comes late in the text, and attempts to survey most of modernpractice at the time, instead of treating fewer topics in depth.

While claiming to be a general course for all students, the CHEM Study coursepresupposed a good grounding in algebra, and routinely used graphs and charts topresent data, as well as reporting quantities in terms of significant figures with ex-ponential notation. Additionally, the emphasis on uncertainty calculations introducedsome statistics to the laboratory. The general student of chemistry must have beenwell-versed in mathematics to have succeeded in this course.

All of these difficulties were particularly ironic because the writers of CHEM Studypromoted chemistry as an experimental science, or at least they claimed to. The fulltitle of their book was Chemistry—An Experimental Science.5 Within it, they claimedthat laboratory work was essential to understanding chemistry. This could be seenclearly in the units of CHEM Study concerned with descriptive chemistry. They wereconcerned with a systematic approach to the elements of the periodic table, studyingand learning their properties. Unfortunately, they were less concerned with commonchemicals familiar to students. This, coupled with their emphasis on vocabulary, re-sulted in a sharp distinction between the laboratory and the real world for manystudents.

In addition to discrepancies in the content of CHEM Study, there were problemswith method as well. The “after the fact” laboratory experiments, which were suppos-edly meant to confirm the theories expounded in the text, actually promoted a dogmatickind of experimentation. The correct answers were already known to the students, andof course the students found a way to reach them. This kind of thinking is not at allsimilar to the processes of actual scientists, and can mistakenly teach the students thatthere is “one right answer” which they would obtain if they were skillful experimenters.Of course, this may be exactly what was meant by the writers of CHEM Study, but this

4ibid5ibid.

Kraus 261

emphasizes the importance of scientists, not that of science.CHEM Study had lost sight of the history of its own discipline; everything that

they taught reflected modern academic chemistry. This was a level of abstractionthat students neither wanted, nor needed. Even the biographies of famous scientistsincluded within the chapters reflected modern practice; many of the featured chemistswere practicing at the time of the study, and some were on the committee that producedthe textbook. Also implied is that there is no diversity of cultures, races or gendersamong chemists. The students found this class difficult, and of limited value.

Many of the concepts taught in this course will never have application outside achemistry laboratory. Despite its claims at universality, CHEM Study seemed onlyan attempt to bring high-school chemistry up to-date, reflecting both contemporaryprogress in the field, and the expectations of undergraduate chemistry programs.

A second example of modern secondary chemistry comes from the Ontario Ministryof Education. A close examination of one of their approved textbooks for secondarychemistry, Chemistry, by Merrill, shows us a different approach.6 The Merrill book hasa better grasp of the history of science, and is careful in avoiding the school of ‘GreatMan’ History. Mendeleev is presented in context as the best of several systematizersof chemistry, whose periodic table was more complete than the efforts of Doberinerand Newlands, and whose chemical periods were more developed than earlier ideas oftriads or octaves. This kind of history gives the student a better grasp of the nature ofscience, and shows that scientific theories are selected on the basis of utility, not on thebasis of truth.

The Merrill writers discuss atomic structure in chapter four, and after coveringelectron clouds and probability, move to the periodic table. According to them, “theperiodic table is constructed in the following manner. Use the arrow diagram onpage 128 to determine the order of filling the sublevels. Each s sublevel can contain twoelectrons . . . ”7 Clearly, they have reinterpreted Mendeleev’s efforts in terms of modernelectron orbital theory. Only four chapters later do the authors discuss periodic trends,following this overview with a look at some typical elements.

This look is mostly superficial, with most of the classroom time devoted to the textand the demonstrations of the teacher. Laboratory practice is limited to a cookbookstyle similar to that of CHEM Study. For most of the laboratory questions, the correctanswers are given in the teachers manual, which undoubtedly creates the impressionthat there is one right answer to get. This approach also assumes that the observationsof the students is unrelated to their conceptual systems. To their credit, the Merrillwriters have significantly reduced the amount of mathematics in their course, relativeto CHEM Study. Students no longer need to be mathematicians in order to be chemists.

While Merrill’s Chemistry has lesser theoretical approach than CHEM Study, it stillpresents the periodic table ahead of the empirical evidence on which it was based. Ifscience is empirical and imaginative, then why not let the students find this evidence

6Merill: 1995, Chemistry, Glencoe/McGraw-Hill, New York. This text is approved for the grade 13 OACprogram, which is a course for advanced students who have already had two years of general secondaryscience.

7ibid., p. 141.

262 Periodic Table

for themselves? Filling an unjustified framework with data contradicts this empiricalapproach. Additionally, valence electrons, or any other kind of electrons, were unknownto Mendeleev. His belief that indivisible atoms precluded any such ideas.

So how exactly did Mendeleev come upon the idea of the periodic table? The answerto this question is of educational as well as historical value because it is unlikelythe student has understanding of the electronic configuration of atoms. Other meansshould be used to convince the student of the structure and utility of the periodic table.

Dmitri Mendeleev’s own chemistry textbook, Principles of Chemistry, the first toever present the periodic table as part of the curriculum, discusses different factors thatled to the periodic table. Electronic orbitals did not make the list. Thompson’s discoveryof the electron was not foreseen by Mendeleev, who would have denied the possibleexistence of sub-atomic particles. The factors that Mendeleev did cite for studying theelements in a systematic way included isomorphism, (by which he means the analogy ofcrystalline forms and analogous compounds), relations of volumes of these analogouscompounds, composition of their saline compounds, oxides and hydrides, crystallinestructures, and their atomic weights.

All of these properties can be investigated in the laboratory, and Mendeleev’s ownstudents did so. Unlike the Ontario program and CHEM Study, Mendeleev did not havea separate laboratory book, or lists of experiments for students to try. Instead, all of hisassertions could be demonstrated for, or performed by, the students. It was assumedthroughout the body of the work that the students would be confirming everything byexperiment. In the second appendix to his book, Mendeleev stated:

Under the all-penetrating control of experiment, a new theory, even if crude, is quickly strength-ened, provided it be founded on a sufficient basis; the asperities are removed, it is amendedby degrees, and soon loses the phantom light of a shadowy form or of one founded on mereprejudice; it is able to lead to logical conclusions, and to submit to experimental proof. Willinglyor not, in science we all must submit not to what seems to us attractive from one point of view oranother, but to what represents an agreement between theory and experiment; in other words,to demonstrated generalization and the approved experiment.8

Role of experiment was not meant to be a demonstration of theory; it was a deter-mination of theory. The importance of students gathering experimental data was clearfrom the organization of Mendeleev’s text. The periodic law was first fully explainedin the beginning of the second volume. All of the first volume was concerned withdescriptive chemistry, and we can safely assume that Mendeleev proceeded according tothe organization that he created for his textbook. Dalton’s law of multiple proportionswas verified through numerous tests, and when it had been confirmed, the studentsused it to investigate the oxide types of various elements. The arrangement of the ele-ments with respect to increasing atomic weight, oxide and hydride type, were the mainsupporting evidence for the structure of the table. Mendeleev himself was careful tosupport the Law of Periodicity with several tests that the students (or other chemists)could easily repeat.

8Dmitri Mendeleev: 1891, Principles of Chemisty, trans. George Kamensky. Longmans, Green, and Co.,London, Vol. 2, p. 435.

Kraus 263

So, unlike the creators of CHEM Study, Mendeleev had a deep interest in theexperimental verification of scientific theory. He included a short paper in his textbookon the application of one of Newton’s queries to the field of Chemistry. Clearly, nothingcould be admitted as fact until it was supported by evidence. The evidence for hisperiodic law was carefully and thoroughly presented with this idea in mind, making itboth good science and good pedagogy.

His careful examination of crystalline structure is a good example of Mendeleev’scommitment to experimental support. He reported that the angles of the prisms ofaragonite, strontianite, and witherite all belong to the rhombic system, and have thefollowing angles:9

CaCO3 116 10′

SrCO3 117 19′

BaCO3 118 30′

Likewise, the crystalline forms of calc spar, magneseite, and calamine belong to therhombohedral system, with the following angles:

CaCO3 105 08′

MgCO3 107 10′

ZnCO3 107 40′

As a result of this similarity, Mendeleev deduces that Zinc is more similar to Mag-nesium than Zinc is to Calcium.

Other relations are gathered from the crystallization of certain salts with water,and noting the amount of water of hydration. Since ferrous sulfate can hydrate itselfwith seven molecules of water, we will immerse it in copper sulfate to determine thehydration state of copper. Because the copper deposits in the same form as the iron,both iron and copper must be analogs, both forming salts with seven molecules of water.

This idea is generalized to compounds of the form RX , where X is a univalentelement, and R is an element combined with it. Observing that only eight types ofcompounds are observed in nature; RX , RX2, . . . RX8, Mendeleev deduces that theremust be only eight groups of elements. To determine the group that an element belongto, its compounds with univalent hydrogen and bivalent oxygen are examined.

Mendeleev’s approach to classification was largely empirical, and still fits well intoa modern laboratory setting. Students can be given a variety of common elements totest for density, melting point, and crystal structure. For corroboration, oxides canbe prepared, and relative proportions can be determined. Once a sufficient number ofsamples have been analyzed by the students, they should be in a position to group them

9Ibid., v. 2, p. 2.

264 Periodic Table

in classes. After some discussion, the students can be given the data for other elementswhich are not practical to measure in the lab, and assemble their own periodic table.

Once this has been completed, students will be able to appreciate periodic trends,and see relations between neighboring elements. This provides a much better basisfor understanding electron orbitals and atomic structure than abstract mathematicsdoes. This also reflects the pedagogical arguments of Derek Hodson.10 He argues thatscience teaching is much more teacher-directed in practice than the curriculum wouldhave us believe. In order to compensate for this, and return to the stated goals of thecurriculum, we should encourage teachers to learn something about the philosophy ofscience, and create new curriculum to reflect that philosophy. This includes portrayingscience as having a range and variety of methods which are applied when they are use-ful, not in terms of an all-encompassing scientific method. The variety of collaboratingevidence which Mendeleev brings to support his Periodic Law is an example of thisrange and variety.

Mendeleev’s experimental approach is also supported by child psychologist JeanPiaget, whose work describes stages of learning.11 Many students need examples fromwhich to generalize abstract rules. By conducting experiments without knowledge ofthe correct results, these students will think for themselves. This will make furthergeneralization and abstraction easier. Mendeleev’s inclusion of subjects like astronomy,biology, geology, and meteorology allowed for better interrelations between sciences.This in turn, benefits the students who are already familiar with these topics. ThePrinciples also incorporated chemical problems relevant to the economic developmentof Russia. This kind of practical application provides even more concrete examples tostudents, and educates future citizens about their country.

A lesson in the authority of science is the final benefit available with an approachinspired by the Principles. Students will likely have confidence in their collectiveefforts, and even more in Mendeleev’s published results. Introducing an unknownelement, such as Argon, should cause quite a difficulty for the students. A noble gaswill be unreactive to their tests, and will not have a clear place in the table that theyhave constructed. They will have to revise their table in order to include the noblegases before these tensions are resolved. This can show the students that no theory isperfect, and that the utility of a theory is not a measure of its validity.

While I have not examined this issue directly, the ideas of classification and tax-onomy are not unique to Mendeleev. Other nineteenth century chemists were tryingto organize the list of elements into a structure.12 Taxonomy was an important partof botany and zoology at the time, and can be considered an entire style of thinking,because it was such a prevalent concern in the nineteenth century.13 The connections

10Derek Hodson, Towards a More Philosophically-Oriented Science Curriculum, Science Education, v. 72.11Piaget, J.: 1970, Psychology and Epistemology, The Viking Press, New York, pp. 63-88.12The discovery of radioactivity would make this a much more difficult enterprise. For this reason, the

window in which a classification system was possible was limited. See Bensaude-Vincent’s “Mendeleev’speriodic system of chemical elements,” British Journal for the History of Science, v. 19, pp. 3-17.

13For more information on styles of thinking, see Hacking, “Style of Scientific Thinking or Reasoning:A New Analytic Tool for Historians and Philosophers of the Sciences,” ed. by Kostas Gavroglu, KluwerAcademic Publishers, Boston, 1994, pp. 31-48.

Kraus 265

between society’s concerns with classification and Mendeleev’s own thinking are leftto the sociologist of science, but I am sure that this influence exists, and did influenceMendeleev in some way.

An approach to chemistry that is closer to Mendeleev’s is long overdue. Instead ofconducting experiments in which the goal is already known, the instructor should allowthe students to investigate chemical properties with less guidance than customary. Aslaboratory tests proceed, students will see the relations between elements. At thispoint, they are ready to appreciate Mendeleev’s work, and not before. This approachwill challenge students to think for themselves, investigate unknown quantities, inshort, to practice the empirical method that is often advocated and seldom achieved.

Not only does this approach emphasize Mendeleev’s chemical ideas, but it uses theexact educational approach that he advocated. While famed as a chemist, Mendeleevis also important as an instructor. He understood the need to support theories withexperiments, and advanced no theories to his students which he could not first prove.Modern students would also benefit from this method of teaching. In addition to thegain in chemical knowledge, a conceptual understanding of the periodic table aidsstudents in appreciating the difficulties of research, allows them to combine laboratoryresults with experimental theory, and demonstrates the strengths and weaknesses ofscientific authority.

266 Periodic Table

Alternative Frameworks in Electricity and Conceptual Change

A.B.SaxenaRegional Institute of Education, Ajmer, India.

1 Introduction

During the last couple of decades large number of studies have been conducted toexplore the nature of alternative frameworks (Driver and Easley 1978). These studieshave been conducted in different areas of physics such as force, motion, acceleration,heat, light and electricity. (For a review of such studies, see for example, Driver et.al. 1985, Novak 1987 Osborne and Freyberg 1985, Watts and Gilbert 1983). In view ofprevailing misconceptions in different areas, attempts have been made for conceptualchange (e.g. Eylon and Linn 1988: Saxena 1992, 1994, Smith et al. 1993, Shipstone1988 Thorley and Woods 1997). Some models have also been proposed for this purpose(e.g. Clement 1987, Driver and Oldham 1986, Gilbert and Watts 1983, Hashweh1986, Smith et al. 1993) and the necessary conditions for conceptual change has beendiscussed (Posner et al. 1982).

In this article, we shall confine ourselves to conceptions and alternative frameworksrelated to current and its flow through resistors in a simple circuit. In the sectionthat follows, a review of students’ concept of current, and related difficulties shall bepresented. It is followed by discussion on the stability of these concepts and conditionsthat are responsible for it. The effect of classroom instructions and its little impact onthe students’ previous ideas is significant in this respect.

Several strategies based on models for conceptual change have been used to achieveit. These are discussed in the next section. Finally the implications of research findingsparticularly in terms of curriculum construction and teacher education are discussed.

2 The Electric Current and Related Alternative Frameworks

Many studies have been conducted to map the students’ conception of (direct) current insimple circuits at various levels of education, for example at primary level (Summers,Kruger and Mant 1998), at secondary level (Saxena 1994, Shipstone 1984, 1988), andat undergraduate level (McDermott and Shaffer 1992, Saxena 1990, 1996, Shipstone1984). Cross-cultural studies have also been conducted (e.g. ASPEN 1991) to comparetheir nature across the globe.

For example, at the lowest level, in some studies students have been, found topredict lighting of the bulb with the help of one wire (Osborne 1981). As far as currentis concerned Shipstone (1984) observed four models of current. These are:Model I: This is known as clashing current model. In this model current leaves boththe electrodes and is consumed as it passes through the various circuit elements suchas resistors bulbs etc.

268 Electricity and Conceptual Change

Model II: Contrary to clashing current model, in this model, current is assumed to flowin one direction only. The current gets weakened as it passes through various circuitelements. The element that is farthest from the anode receives the least current.Model III: This model assumes that the current is shared between various componentsin the circuit. The components having equal resistance get equal current. In this modelalso, current is not conserved.Model IV: This is the scientific model of current. It differs from Model II in the sensethat constant current flows in a series circuit and it does not get consumed.

Apart from these models, in some cases students use a model of current whichdoes not fit into any of these models. For example, in some cases the use of constantcurrent flowing out of the source has been reported (Cohen, Eylon and Ganniel 1982,McDermott and Shaffer 1992). In this model, magnitude of current in the circuitdoes not depend upon the circuit elements. Use of constant current model has beenreported in other studies as well (Saxena 1994). Another model known ‘sequence model’(Shipstone 1984) has also been reported in the literature (e.g. Saxena, 1994). In thismodel the current is affected ‘down the stream’ only. It could be explained using (figure1).

r1 r2

+ V

Figure 1: A resistor.

In this approach constant current is assumed toflow out of the source of current, say, cell. If theresistor r2 is varied, its effect is only on the currentpassing through the resistor r2 and not on currentpassing through the resistor r1.

Non-conservation of current in a series circuiti.e. different amount of current passing throughresistors r1 and r2 is also obtained using erroneoususe of Ohm’s law (Saxena, 1992). In this the current

passing through individual resistor is calculated as, current through resistor r1 = V/r1;current through resistor r2 = V/r2. Obviously, the current is not conserved. Non-conservation of current is also reflected when students are asked to predict which bulbwould glow (figure 2), when bulb B2 is fused. Many students opine that bulb B1 wouldglow and B3 would not (Saxena 1994, 1998).

B1B2 B3

+

Figure 2: A bulb.

This kind of model of current is also observedwhen children attempt to light the bulb with one wireonly (McDermott and Shaffer 1992, Shipstone 1998).

The concept of resistors connected in series andparallel is introduced at secondary level (Balasub-ramanian et. al. 1985). However, even at under-graduate level, some students fail to recognise thetype of connection (McDermott and Shaffer 1991,Saxena 1992). They tend to categorise the connection

according to geometrical shape in the diagram rather than the actual connections. Theyare also not able to predict the effect of connecting another resistor in parallel, on thecurrent and total effective resistance in the circuit.

McDermott and Shaffer (1991) provide in detail the difficulties faced by students

Saxena 269

while explaining the behaviour of electric current in a simple circuit. These are re-lated to concept of current, potential difference, resistance and qualitative reasoningof behaviour of electric current. Many students fail to recognize that a circuit diagramrepresents only electric elements and connections and not actual physical or spatialrelationship of various elements. This poses considerable difficulty when studentswere required to make connections according to a given circuit diagram. Studentswhile studying the transition from electrostatics to electrokinetics historically andamong students, Benseghir and Closset (1996) compared their thought processes. Theyfound that scientists use the electrostatics in early efforts to conceptualise the conceptof current. Similarly, part of the students’ reasoning in electrokinetics comes fromconceptual basis which includes a more or less intuitive knowledge of electrostatics.

3 Stability and Origin of Alternative Frameworks

The simple evidence of stability of alternative frameworks comes from the fact thatthey persist despite formal education in school and college over a number of years.Some of the studies cited earlier were conducted on undergraduate students (McDer-mott and Shaffer 1991, Saxena 1992, 1996) and sixth-form college (Shipstone 1984).In another study conducted on undergraduate students (Saxena 1998) for a period ofthree years, students concept of current was evaluated annually using a questionnaire.The results of the study indicated that the students exhibited many misconceptionsthroughout the course of study. In many students alternative frameworks persisteddespite teaching for three years. These students had physics as one of the major subjectof study. In this context Aron (1995) states:

The pre- and mis-conceptions found to be widely prevalent among students in introductoryphysics courses extend to students in upper division courses, to secondary school teachers, tograduate students, and even to some university faculty members, the proportion of individualsexhibiting such difficulties decreases significantly but does not drop to zero discontinuouslybeyond introductory level.

Another study, conducted on students enrolled for electrical engineering programmeshowed that spontaneous conceptions survive formal training and they had difficultyin applying Ohm’s law. This predicament which persists after five semesters of formaleducation in electronics, is apparently rooted in inadequate conception of voltage andcurrent (Metioui et. al. 1996). Further, it is found that lack of coherent links betweenelectrostatics and circuits in typical electricity instruction is responsbile for the highdegree of difficulty of that subject. Moreover, theorectical view also accounts for differ-ences in success of students’ learning in the context of a standard high school physicscourse (Gutwill et. al. 1996).

Many reasons have been given that could be responsible for the origin and persis-tence of the alternative frameworks. Eylon and Linn (1998) argue that uniformity ofintuititve conception developed suggests that there must be well defined mechanismbehind the origin of alternative frameworks. However, there is no agreement on themechanism itself. It is suggested that the kinaesthetic or sense experiences make theireffect on the human beings much before they are able to formalise them. The common


misconception that it requires a force for a body to move with constant velocity comesin this category of alternative frameworks.

Another source of origin of alternative framework is ascribed to metaphorical use oflanguage in everyday life. ‘Much electric current is consumed when electric heater isused’ falls in this category. Solomon (1983) is of the view that exposure to non-scientificexplanation through mass-media and other means could be one source of generation ofalternative frameworks. The inability of the learners to distinguish between scientificworld of the laboratory and the classroom and the life world of outside environment,and to switch over from one world to another is the reason of many learners’ problems(Solomon 1983). Mohapatra and Bhattacharya (1989) have suggested that induced in-correct generalisation during teaching and outside could possibly be operating to gener-ate alternative frameworks. Further, Mohapatra (1991) has suggested that the episodicconceptualisation could also be the source of some alternative conceptions. Saxena(1994) has suggested linguistic interference and world association of possible mecha-nisms responsible for the development of alternative frameworks. With their continualuse over time for explanation of events and observations, these frameworks becomereadily available at subconcious level and are integrated with procedural knowledge.Hashweh (1986) points out that procedural knowledge is difficult to change. Further,it could be due to linguistic interference as is observed in persistence of sentencestructure in the speaker’s native language to construct sentence in a new language.Another explanation is cited in the form of Einstelling effect in which a previous con-ception is strongly tied to certain features of the problem or situation through previousexperience. The situation is similar to stimulus-response conditioning in behaviourism.

4 Attempting Conceptual Change

As long as the existing conception continues to help ‘understand’ some of the observa-tions it does not get changed. Unless specific conditions are not created that questionthe validity of existing conception, the conceptual change does not take place. Solong as the existing conception continues to serve, though in limited domain, it isretained. Posner, Strike, Hewson and Gertzog (1982) suggest four necessary conditionsfor conceptual change. These are:

1. Dissatisfaction with existing conception: Conceptual change occurs only whenone feels that minor change will not work. Dissatisfaction with the existingconception is necessary for conceptual change.

2. The new conception should be intelligible: It is necessary for the learner to un-derstand the new conception minimally. He should be able to represent it and seehow the experience can be structured on its basis.

3. The new conception must appear plausible initially: At the outset, the newconception must appear to be able to solve problems and help understand situ-ations, that cannot be dealt with the existing conception. It should also appearconsistent with coneptions already accepted by the learner.

Saxena 271

4. The new conception should be fruitful to the learner: Apart from the proper-ties of being intelligible and plausible, the new conception should help achievesomething of value to the learner. It should have potential to explain new areasof experiences, observations and domain.

For these reasons, exposure to a new idea through structured curriculum usingguided experiment for a short period may not be successful to make conceptual changein many students. Such a situation was observed in an attempt to make conceptualchange (Saxena, 1992) wherein it was observed that, “in one third of cases studentsfailed to solve similar problems. This could be due to variety of reasons. The time forexperimentation was nearly two hours. Students worked in small groups rather thanindependently. Perhaps, working for a longer period individually and having morelearning experiences would have given better results.”

One possible strategy to achieve conceptual change could be to make use of demon-strations during teaching. However, all demostrations may not be meaningful to thelearner. Roth et. al. (1997) analysed in detail the characteristics of demonstrationsthat help learning. On the basis of results obtained, it is suggested that in all activitiesincluding conducting experiment, discussion about design of the experiment, explain-ing the observations, representing the observations and their analysis are consideredas social practices in which students participate. The effective demonstration activityshould (Roth et. al. 1997):

• engage students in talking about and representing phenomena;

• engage students in discussion about scientific inquiry and construction of vari-ables such as to produce a consistent theoretical framework and construction ofvariables that allow them to keep account of systems despite change;

• engage students in discusion about the mutually constituitive function of lan-guage game and phenomenon, situated language, and knowledge which assist inthe seperation of signal from noise;

• have students generate evidence and theory, set up a forum in which these arehammered out, and decide on future evidence to be needed and constructed.

Another strategy for conceptual change has been to use examples and analogies(Brown 1992, Clement 1987). To identify anchoring examples separate diagnostic testis used. Conceptual change is obtained with the help of Socratic dialogue, bridginganalogies and anchoring examples. To be successful the examples must be under-standable and believable to the students, the analogy must be clear to the students.Otherwise, the analogy must be clarified by the teacher in order to be explicit. Finallyqualitative visualisable models may be developed to give mechanistic explanation ofthe phenomena. Unless students are able to ‘see’ in the same way as the teacher theyfail to evoke the desired phenonomena. To explain, the role of battery in a circuit witha bulb, Shipstone (1985) suggested the analogy of boiler and radiator. Similarly, therole of emf source is compared with water pump which can cause water to move from


Conception C1 Conception C2

Domain R1 Domain R3Domain R2

conflict 2

conflict 1 explainsexplains

explains

Figure 3: A model for conceptual change based on Hashweh (1986). Conflict 1 and 2are to be resolved for conceptual change.

a place of lower gravitational potential to a place of higher potential (Halliday andResnick 1987). At primary level Summers et. al. (1998) use bicycle chain analogy forcurrent. However, the use of analogies is not without suspicion. Duit (1991) warnsthat the use of analogy create some dificulties for the learner because many scientificphenomena can be explained using abstract concepts and sophisticated mathematicaltechniques. Treagust, Harrison and Venville (1996) are not sure about the nature ofchange obtained as a result of using an analogy because it is not conclusive whetherthe analogy contributed to conceptual change or whether the analogy merely providedstudents with a means to express themselves with the language which was otherwiseunavailable to them.

The instructional material provided to the students in support of the activitiesconducted in the class plays an important role in making conceptual change. Smith,Blakeslee and Anderson (1993) concluded that it requires the support of appropri-ately designed instructional materials in order to use conceptual change strategiessuccessfully. Moreover, the conceptual change approach should probably be thoughtof as a coherent approach to teaching rather than as a collection of individually usefulstrategies.

4.1 The Process of Conceptual Change:

Several models for conceptual change have been suggested. The process of conceptualchange could be divided into four subprocesses (Hashweh 1986):

1. discarding of old conception,

2. acceptance of the new conception for consideration as an alternative,

3. conflict between the existing conception and the new conception, and

4. acceptance of the new conception and its availability for future use.

Diagramaticatly it could be represented as shown in figure 3. It shows that theprevious concept C1 is able to explain the observation in a limited domain R1. Exposureto domain R2 generates conflict (1) as the existing concept C1 is not able to explain the

Saxena 273

View P

View S2

Time

(Instruction)

(View Equality)

(View Hierarchy)

View S3

View S2

View S1

View P

View S1 View S3

Figure 4: Two routes for conceptual change (Thornton 1995).

observations in this domain. It is assumed that conflict (1) is resovled by adoptingconcept C2 which better explains in domain R2. However adopting conception C2 doesnot resolve conflict (1). Moreover, another conflict (2) occurs between conception C1and C2. Both types of conflicts are to be removed for successful conceptual change.

Thornton (1995) suggests two possible routes of conceptual change: View equalityand View hierarchy. These are shown in figure 4. View equality shows equality amongthree possible conceptions and, therefore, one could go from any of these views to thedesired view P . In view hierarchy, the three views S1, S2 and S3 are hierarchical inthe sense that someone holding the view S1 has to move through S2 and S3 inorder toreach view P . Hence, he is less likely to reach to view P than those holding the viewS2 or S3. Sometimes combination of view equality and view hierachy could also occur.

Driver and Oldham (1986) has suggested five stage teaching model to obtain con-ceptual change. The stages in this model are: orientation, elicitation of ideas, restruc-turing of ideas, application of ideas and review. Restructuring of ideas is the mostcrucial stage which includes clarification and exchange of ideas, exposure to conflictingsituations, construction of new ideas and their evaluation.

5 Implications

Teacher education is an important component to improve efficacy of teaching. There aretwo important components that are to be paid attention to: (i) teaching strategy and(ii) teachers’ attitude towards science (physics). The first part includes developmentof teachers’ awareness towards students’ ideas about electricity, their conception ofcurrent, potential difference etc., and procedural knowledge to employ Ohm’s law etc.Further, it would encompass strategies that could be adopted to remove alternativeframeworks. Finally it includes the approaches that could be used in introducing thescientific concepts related to electricity. Aron (1990) points out that two approachescould be adopted to introduce electricity. One approach first introduces the concept ofcharge and arrives at the concept of current at the later stage. The other approach first


introduces the concept of current and the concept of charge is brought in later. Eitherof the two approaches could be adopted without encountering any difficulty.

Further, it implies that while planning and transacting the curriculum, the teacher

• identifies the common alternative frameworks among the students, related to thetopic;

• develops a list of activities that help to remove the identified alternative frame-works; and

• tests the efficacy of his/her approach.

This needs to be investigated and explored in the context of various topics. It is notnecessary that the same approach is adopted while teaching various topics. A techniquesuch as the drawing of concept maps requires its use over long duration before its gainscould be readily obtained. This is because students need practice before they obtainmastery in drawing of concept maps. Moreover one could also reasearch on variousmodes of using concept maps during teaching.

The second component of teacher education is concerned with teachers’ attitude.Some suggestions are given below:

• Science to be described as social activity rather than individualistic. The role ofcooperative work and social interaction to be given due importance.

• Science is not to be taken as a value free pursuit, rather it be discussed in thesocial, moral and ethical context.

• Science to be considered as the result of creative, sometimes restructuring en-deavour, rather than linear and accumulative.

• Extreme inductivism, ‘free’ observations and experimentation are to be discour-aged. The role of hypothesis making and construction of coherent body of knowl-edge is to be encouraged.

Finally, more and more research evidence is being obtained that shows students’competence is heterogeneous, not unitary. It depends upon interaction between in-dividual and the context. Therefore, one single task would not do justice with theevaluation of students’ competence because it hides the heterogeneity of performance(McGinn and Roth 1988).

6 Conclusion

‘Electricity’ was taken in this paper as one example to illustrate the problems andapproaches related to teaching of physics. It shows that the classical approach ofteaching adopting transmission model is to be replaced by variety of strategies thattreat the learner as active agent, having his/her own ideas. Sensitivity of the teacherin this regard can take him a long way to make the learning more meaningful.

Saxena 275

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Common Man’s Science and Its Role in Making General ScienceEducation Meaningful

Rakesh PopliBirla Institute of Technology, Ranchi, India.

1 Introduction

It is no exaggeration that general science education in India has been a disaster. Ourexperience in villages of South Bihar1 and the city of Ranchi shows that science edu-cation in primary, middle and high schools is not fulfilling its stated objectives2 in anymeasure. It is neither enabling students “to understand science concepts, principlesand theories” nor “to use the process of science in daily-life situations in solving prob-lems, making decisions and extending one’s own understanding.” As far as inculcationof a scientific outlook is concerned, the picture is even bleaker. Instead, science isa burden on poor students who have to remember all the tongue-twisting keywords,concepts, principles, derivations, explanations, etc. Other workers in various parts ofIndia have come across similar experiences.

This phenomenon is not confined to village children or first-generation learners.Even urban children attending well-endowed schools often find science awesome andburdensome. Many of these students may be able to score ‘good’ marks in examinationsby dumping a lot of unconnected information into their short-term memories, but it isneither intellectually enlightening nor practically useful.

For almost two decades, science education has been made compulsory for all stu-dents in India upto class X. While the basic idea of enlightening all with the light ofscience is unexceptionable, in practice the only thing it has given to a vast majorityof students is a formidable stumbling block on the path to matriculation. In the areaof science popularization too, efforts by prominent scientific organizations have hardlystirred the general public. All this brings into sharp focus the question whether themeaning and content of science for common people (and common children) has to bethe same as for professors Newton and Maxwell and their modern successors.

There is, therefore, need to review the scheme of science education as a part ofgeneral education. This necessarily involves a reconsideration of the nature of scienceitself—-in particular, a consideration of how science interfaces with the day-to-day livesof all people and how they can interact with and benefit from it.

1Rakesh Popli: 1987, Popularization of Science Among Tribal Youth, Report of project supported by DST,Govt. of India, Vikas Bharati Bishunpur. A part of this report deals with the interaction of high schoolstudents with science curricula and concludes that these curricula are hopeless. See also, Rakesh Popli:unpublished 1992, An Evaluation of Science and Mathematics Proficiency Levels of Rural School Studentsin Ranchi District. This Report encompasses a survey of Class IV and Class VIII students of about 25 schoolseach. The results are almost uniformly dismal, regardless of the quality of management of the schools.

2National Council of Educational Research and Training: 1986, Science Education for the First Ten Yearsof Schooling.

280 Common Man’s Science

In this paper we review some aspects of the nature of science and point out why it isfound so difficult and alien by general public and students. We then propose the conceptof Common Man’s Science (CMS) which can help make general science education livelyand meaningful. CMS is a community- and context-specific assortment of items fromthe totality of science. It is related directly to natural phenomena in the lives of allpeople of a community.

CMS is seen to be derived from two sources: (a) empirical facts, generalizationsand observations accumulated over generations, and (b) relevant parts of conventionalsciences dealing with subjects of interest to all people at appropriate phenomenologicallevels. The nature of CMS is examined in some detail and it is distinguished from‘traditional’ and ‘folk’ sciences. Possible objections based on notions of ‘oneness ofscience’ and ‘pre-scientific knowledge-systems’ are dealt with.

In the next part, a concrete but illustrative outline of the proposed curricula ofCMS at the primary (Class I-V) and secondary (Class VI-X) levels of school educationis given which would be conducive to the best intellectual appreciation of science aswell as practical benefit of all students in India. The role of CMS in senior secondaryand higher education and science popularization among communities at large is brieflydiscussed.

2 Science in relation to the common man

2.1 The Nature of Science

The formulation of a scheme of science education as a part of general education requiresa consideration of the nature of science to some extent and of the purpose(s) of scienceeducation in the overall scheme of general education. Therefore, we shall first lookinto some aspects of the nature of science before defining Common Man’s Science. Theterm ‘science’ used in this paper refers to the body of scientific knowledge of naturalphenomena, i.e. it does not cover social phenomena.

In the history of mankind, observation of natural phenomena, search for general-izations and inter-relations, and utilization of such knowledge for practical benefit, hasbeen an important aspect of life. Some of these generalizations are rather limited inscope; others have wide ranges of applicability. Some are directly and readily verifi-able; others have been discovered and validated over many generations, for example,that progeny born of marriages between close blood-relatives are more prone to somediseases than other people.

What is conventionally called ‘science’ is a narrower scheme whose scope is ex-tremely wide in principle. It aims particularly at making vast generalizations andbringing all phenomena within the ambit of a few laws. This includes not only phenom-ena of day-to-day life but also those very far removed from ambient conditions. It coversman-made phenomena, and even those that have never taken place. Similarly, theobjects of scientific investigations are not only those readily accessible to the generalpublic but all conceivable objects. Thus, for example, Newtonian mechanics is equallyapplicable to the motions of a motorcar, a ball thrown up at any angle, a bird flying inthe sky, and the Moon.

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The general principles and theories of science can embrace such a vast array of ob-jects and phenomena only at a certain cost: these deal more with increasingly abstractconcepts and operations than with actual objects and phenomena of daily life. Forexample, Newtonian mechanics deals with point-objects (particles), forces, momenta,etc., which are all considerably abstract. Quantum mechanics, which covers evenwider ground, involves much more abstract entities like wave-functions. In Biology,classification of forms of life becomes an exercise in abstraction if it is to cover all forms,not only those of direct interest to a given community at a given time. The difficulty ofstudents and common people in interacting with science is to be viewed in this light.

Conventional science has been sub-divided into disciplines and sub-disciplines, ofwhich Physics, Chemistry and Biology are usually taught in general education. It isinteresting to note that these sciences differ from one another not only in content andterminology but also in methods employed. For example, in Atmospheric Science andCosmology, hardly any experiment can be done. Biology does not follow the hypothetico-deductive method followed in much of Physics. It may also be noted that there is nounique basis for the division of science into branches: it is quite dependent on need.

An important aspect of science—important from the point of view of general education—is phenomenology. It may be noted that a given body of phenomena may be understoodand discussed at various levels of abstraction or, we may say, various levels of phe-nomenology. At the lowest level is that description which may be obtained by a directand simple observation with the bare senses. Above that, successively higher levelsof phenomenology and phenomenological theory can be conceived of. For example, therising and setting of the sun, the moon and the stars may be observed directly. Themonthly or annual variations in their timings may be tabulated systematically. Thesame may be done with the phases of the moon. All these phenomena (plus eclipses) arereadily explained by a geocentric phenomenological theory in which the sun, the moonand the stars revolve around the earth with various periods. The heliocentric (sun-centred) theory represents a higher level of phenomenology which explains even morephenomena like the planetary motions and the stellar aberration. Still higher levelsof phenomenology can encompass terrestrial motions too, albeit in a more abstract andmathematical way. It would be naıve and short-sighted to claim that one particularlevel of phenomenology (say, heliocentric) was ‘the truth’ or ‘science’ and another level(say, geocentric) was a ‘false notion’ or ‘not science.’

2.2 Common Man’s Science

By the term ‘common man’ we do not mean a particular class of people, but refer tothe common denominator of lives of all people in a community. Thus, even a scientistis a common man when not working as a specialist. Common Man’s Science (CMS) isthat part of science which is relevant to life and problems of the common man. Justas science curricula can have different contents and levels of treatment for variouspurposes, say ‘science for physicians’ or ‘science for painters,’ CMS is to be consideredas that part of the totality of science which is (i) of use to the common man, and(ii) accessible to him, i.e. the level of phenomenology is such that the common manmay understand and work with it. The science of food, water, human body, motions


of objects including vehicles, housing, weather, life of common plants and animals,celestial objects and calendars, various consumer goods, etc.– such are the topics whichmake up the subject matter of CMS. But subject headings alone do not make CMS. Inorder to distinguish CMS from the ‘science’ of the above subjects taught conventionallyin schools, three important points may be noted.

First, CMS treats these subjects at an appropriate level of phenomenology. Aswe have already discussed, taking up any aspect of nature at the level of generalprinciples or theories or high levels of abstraction means going far away from the actualphenomena of concern to the common man. For example, in discussing food, a chemistmay be interested in different chemical constituents of food items and their variousreactions in the human body mediated by various enzymes. The common man is notinterested in details of these reactions. He is interested in the various practical char-acteristics of whole food items, e.g. their digestibility, their mutual complementarityor incompatibility, the energy and other benefits given by each, etc. He is interestedbroadly in the general process of digestion and particularly in how this process ishelped or hindered by various spices, the state of the body and the state of the mind.He is also interested in correlations like that of eating carrots with prevention and cureof night-blindness.

Second, CMS does include the understanding of nature acquired by communitiesover the ages, e.g. compatibility of specific spices with particular foods. Whether suchunderstanding is considered a part of science or ‘pre-scientific’ is a matter of definition.Either way, it can hardly be denied that much of this understanding of nature andknowledge of its phenomena is useful and readily accessible to the common man. Partsof it have been subjected to scientific investigation and validated, e.g. breast-feedingbeing the best for babies and useful for mothers. Other parts may be at various stagesof investigation; yet others may not have been investigated yet. Certain pieces of suchtraditional understanding have been further generalized by scientific researches andmade more abstract, without affecting the validity of the earlier understanding in itslimited domain. The geocentric understanding of the commonly observed motions ofcelestial bodies is an example. Such understanding is a part of CMS unless provedwrong by systematic investigation.

Third, the practice of CMS is integrated and practical rather than disciplinary. Theemphasis is on dealing with common phenomena of life in more and more systematic,analytical and creative ways, not on delving into one particular narrow aspect of a phe-nomenon to the exclusion of all others. Organization of the subject matter of CMS will,therefore, be done largely in terms of departments of life, not in terms of conventionalscientific disciplines. Of course, this is not to rule out the inclusion of topics, theoriesand principles of conventional disciplines needed for a practical understanding of lifephenomena.

2.3 Some Clarifications

Let us point out that CMS is to be distinguished from ‘traditional sciences’ and ‘folksciences’. It is, of course, true that CMS bears a close relationship with these, iscommunity-specific in content and emphasizes continuity with earlier knowledge. How-

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ever, the term ‘traditional sciences’ usually refers to closed systems belonging to pastages, whereas CMS is very much contemporary and open. Also, CMS is not boundby any ‘theoretical’ basis these sciences may have in ancient philosophies but utilizestheir phenomenology. Thus, for example, empirical facts of Ayurveda like properties ofvarious plant-products, in terms of their effects on the human body, are useful parts ofCMS, but not necessarily the underlying notions like the five elements (mahabhutas).The overlap of CMS with folk sciences is obvious, but the former does not share thesuperstitions and witch-craft which go with the latter. Besides, CMS freely draws fromthe modern sciences where appropriate and useful. For example, knowledge about andcorrect use of a modern drug like paracetamol can be a part of CMS. Results of the latestinvestigations into sleep can be a part of CMS. Also, CMS seeks to utilize elements ofthe method of science (e.g. experiment) within the common man’s environment.

It may also be noted here that CMS is not just a collection of facts. It can enable oneto understand nature, to make simple calculations where the parameters are quantifi-able, to experiment, to discover and to invent.

Some popularizers of science refuse, in the name of ‘oneness’ or ‘unity’ of science,to recognize the distinct identity of CMS.3 One must ask what meaning they attachto ‘unity.’ If they simply mean that science encompasses all cognitively meaningfulstatements about nature and its phenomena, then surely this unity does not precludepartitioning of the one science into various sciences for purposes of convenience. Norcan it prevent the common man from parameterising a given situation differentlyfrom the conventional scientist. If ‘unity’ means reducibility of all objects of natureto elementary particles and all phenomena to a few fundamental laws, this reducibilitycan be admitted, if at all, in principle only. Even when such reducibility is fully realizedin highly abstract terms, phenomenology will retain its importance in practice. Afterall, don’t biologists treat life in terms of cells and even whole organisms, and notnecessarily in terms of atoms of which these are made? Similarly, the common mancan understand nature at a level of phenomenology suited to his purposes.

Another objection may be raised by those who consider science to have a beginning(a few centuries ago) and do not recognize the existence of any science outside theparticular system that was born then. They may object to the inclusion of any othersystem like folk sciences into CMS. We would like to point out that whatever point oftime may be considered as the beginning of science, it must be admitted that someknowledge and understanding of nature existed among various communities prior tothat. Not only that, a method of exploring nature existed. That understanding and thatmethod may be useful to the common man even today, depending upon circumstances.A substantial part of folk knowledge may not have been scientifically validated yet,but where a certain item has been strongly believed over many generations, and hasnot been scientifically invalidated, it makes sense to consider it provisionally a part ofscience. In conclusion, we may say that such knowledge may either be considered a

3For example, Prof. B.M. Udgaonkar declared emphatically at the Fourth People’s Science Congress heldat Mumbai in 1990 that, science being one, there could be no such thing as “People’s Science,” and theadjective “People’s” qualified only the word “Movement” in “People’s Science Movement.” He thereby impliedthat there was no need to re-orient science education to make it relevant to the common public.


part of science or, if it is considered ‘pre-scientific,’ it should be integrated into scienceeducation. It would be irrational to let this philosophical issue stand in the way of thecommon man benefiting from past experience.

3 CMS curricula in general education

3.1 The General Scheme

Before going into the curricula, it is pertinent to consider briefly the purpose of thescience part of general education. The main purpose, in our view, is (a) to develop ascientific outlook and scientific appreciation of nature among all citizens, (b) to enablethem to solve their own day-to-day problems in a scientific manner, and (c) to begenerally aware of the emerging science and technology scenario, whether beneficialor detrimental, and to be able to make personal and social decisions where necessary.

It may be noted here that a learning of the general principles and theories wellknown to scientists, key concepts of physicists, etc. is not necessarily needed to ac-complish (a), (b) or (c). And certainly it is not sufficient. Therefore, we do not agreewith decision-makers who insist on making the learning of key concepts, principlesand theories a major objective of general science education; this objective should applyonly to specialized education in conventional sciences.

Instead, the above purposes can be eminently served by making CMS an integralpart of general education at all stages. We have seen in the last section that phe-nomenology relating to any topic (e.g. food) can be obtained at many different levels.It follows that CMS relating to any topic of interest to the common man can be treatedat many different levels of sophistication. Hence, it is possible to design CMS coursesfrom the lowest to the highest stages of education.

In particular, the science part of primary and secondary education should be com-pletely re-organized along the lines of CMS. This will mean allowing all children toobserve, understand and manipulate nature at a level of phenomenology naturallysuited to them and will ensure full scope for a flowering of their scientific creativity. Insecondary classes, attention may be focussed on phenomenology of practical subjectslike health, environment, mensuration and technology. Some rudiments of physical,chemical and biological sciences, e.g., velocity, acceleration due to gravity, atoms andmolecules, micro-organisms, etc., will be needed in CMS, but in a phenomenologicalway. Hypothetico-deductive systems like Newtonian mechanics and conventional elec-trostatics, which can neither be directly verified by simple experiments, nor are ofpractical use to the common man, may be left out.

At the senior secondary and tertiary levels, a separate stream may specialize inconventional sciences as at present, but it would be desirable to continue CMS at asuitably higher level for all students. It is suggested that CMS be taught at theselevels in two ways: (a) as general science which will enable all people to solve their ownproblems related to health, environment, etc., and to understand community, nationaland international issues, e.g., big dams and missile proliferation, besides familiarizingthem with the latest developments, e.g., laser-based communication systems, and (b) asprofessional CMS courses which would prepare science teachers, science popularizers

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and researchers tackling community-level science-related problems. In recent years,some eminent scientists have called for school and college students devoting theirattention to certain problems at the phenomenological level, e.g., surveying the floraand fauna in every corner of the country. In our view, such an activity would fit CMScurricula in a natural way.

We now spell out detailed outlines for CMS curricula at the primary and secondarystages of education. This exercise is only illustrative and is intended to give concreteshape to the concept of general science education indicated above. No attempt has beenmade here to prepare class-wise syllabi, nor to chalk out in detail the breadth and depthat which the given topics are to be treated, partly because such details are location- andcommunity-specific. Such syllabi can be prepared, once the idea is accepted in principle.It may be noted that the CMS curricula outlined below are meant for all students. It isnot our contention that some students should learn CMS and some others should learnconventional sciences.

3.2 CMS curricula for the primary level (Age 6-11, Class I-V)

At the primary level, apart from the general considerations relating to CMS, we mustkeep in mind the age-related needs of children. The general science curricula at thisstage should consist mostly of (a) inculcation of healthy habits, and (b) developmentof elementary scientific skills of observation, experimentation, reasoning, classificationand manipulation. Observation starts in the earliest classes and slowly progresses toinvolve other skills. Illustrative lists of topics are given below.

Inculcation of healthy habits : This is not something to cram but to do regularly.Some discussion may be necessary.

• Maintaining personal cleanliness—washing the face and eyes, cleaning theteeth, taking bath, wearing clean clothes, combing the hair, washing thehands with soap and water after defecation and before meals.

• Keeping surroundings clean; disposing of garbage properly.• Eating, sleeping and waking at the proper times. Playing.• Eating healthy foods and avoiding unhealthy ones (even if attractively packed

and aggressively advertised). Caution against junk foods and drinks.• Eating in the proper way: eating enough but not too much, washing up and

settling down (possibly with a small prayer) before eating, proper chewing,washing up afterwards, etc.

• Not suppressing bodily urges as for urination, defecation, sneezing, etc.• Keeping the correct posture, keeping eyes at sufficient distance from book,

notebook or TV.• Not handling electricity (A.C.), moving machines or medicines.

Development of scientific skills : This development takes place informally and inan elementary way. For example, experiments for younger children (upto age 8)


are merely activities and demonstrations. In later classes, children start control-ling particular parameters consciously. In any case, there is more of doing andobserving than of describing in ‘scientific’ terms. Here is an illustrative list ofitems.(i) Observing the environment keenly and carefully, e.g.,

• Trees, bushes, herbs, creepers in the environment; parts of a plant;• leaves of various trees (observing and copying the shapes);• animals, birds and insects; their various organs;• parts of the human body (those which can be seen and felt);• demands of the body (hunger, thirst, activity, rest and waste expulsion);• water bodies/water supply: where water comes from;• common machines/accessories and their functions, means of transport;• clothes and their materials, relation with season;• common cereals, pulses, vegetables, fruits, edible leaves and their respective

plants;• rising and setting of the sun, phases of the moon; recognizing a few stars,

planets and constellations; clouds.

(ii) Manipulation and experimentation, e.g.,

• making various objects and geometrical shapes with clay;• making designs and toys with paper, plant parts and waste materials;• planting and growing useful plants; observing growth;• use of simple tools, e.g. spade, screw-driver;• experimenting with air, water, sunlight and shadows, magnet, lenses, mir-

rors, electric cells and lamp, etc.;• experimenting with sense-perception, e.g., binocular vision, visual illusions,

directionality of hearing.

(iii) Reasoning and classification, e.g.,

• classification of things into living and non-living; animals and plants; ani-mals, birds and insects; domestic and wild, etc.;

• classification of water bodies into stagnant and flowing;• classification of foods according to solid/liquid state and according to taste;• understanding the reasons behind rules of hygiene;• classification of vehicles driven by muscle-power and by various fuels and

electricity; hence various forms of energy.

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(iv) Concept formation: this should proceed informally and in relation withphenomena observed, e.g.,

• temperature (related to weather and fevers);• energy (related to various kinds of vehicles and equipment);• density (related to floats and sinks, rate of fall);• micro-organisms (related to curds-formation and infectious diseases);• oxygen, carbon dioxide, nitrogen (related to air and plant and animal life);• cause and effect (related to fuel and motion, fall and injury, etc.).

It may be noticed that many of the topics given in the above list are common withthe existing curricula. However, the emphasis in the CMS scheme proposed here isdifferent. For example, in classifying objects into living and non-living, our emphasis isnot on memorization of the points of contrast but on observation, preferably carried outduring outings into a rich environment, e.g. forest or garden, and on identifying classesof objects, their behaviours and sequences of events. There should be no hurry tojump to pre-determined conclusions or to dip into abstract analyses. Demonstrations ofvarious spectacular behaviours of air, water, etc. should be aimed at arousing children’scuriosity rather than at proving some principles.

There is no room for formal definitions of work, energy, etc. and their relations withforce at this stage. It is abstract and useless. Nor are details of internal anatomy andphysiology included in the CMS curricula.

3.3 Curricula for the Secondary Level (Age 11-15, Class VI-X)

The CMS curricula at the beginning of the secondary stage have a significant overlapwith those at the late primary stage in terms of topics but there is a difference in thelevel of treatment. Thus, while general observation is to be continued, the emphasisis to shift gradually to a systematic study of phenomena. Observation is not the solesource of information at this stage; knowledge is provided from textbooks too, but it isstill related to daily life for the most part.

The CMS curricula at this stage consist of matters of direct concern to the commonman, viz. (a) health, (b) environment, (c) mensuration and analytical aspects, and (d)agricultural or industrial technology. In middle classes (VI-VIII) these subjects maybe treated mostly in terms of traditional parameters. However, as further details aretaken up, it will become necessary to bring in technical terms. Elements of physicaland biological sciences will, therefore, have to be taught, though in a phenomenologicalway.

3.3.1 Health Science

In CMS, health science begins with understanding the importance of health and relat-ing it to parameters under the direct control of the common man, e.g. food, sleep, work,


exercise, cleanliness, state of mind, etc. Children need not be burdened with unnec-essary details of human anatomy and physiology or of cell structure or of pathologicaltests. They should be made familiar with the phenomenology of health and disease,and enabled to take elementary care of their health themselves.

It should also be noticed that, in health education under CMS, the inner observationof the state of the body also plays an important role. For example, the natural rhythmsof the body are to be observed in this way. This inner observation, though alien toconventional sciences, is an elementary skill for the common child. Given below is anillustrative list of topics.

• Holistic definition and supreme importance of health.

• Pillars of health: balanced food and water, fresh air, balanced activity and rest,right expulsion of wastes, right state of mind, cleanliness, being free from addic-tions, vaccination.

• Symptoms of health: appetite for good food, thirst, deep sleep, proper expulsionof wastes, cheerful mind, desire for right activity and right relationships withothers.

• Physical and mental hygiene.

• Human body and its systems (broad idea).

• Natural rhythms and balance of the body.

• Natural capacity of the body to correct internal imbalances and deal with externalinvasions (injuries, infections, etc.)

• Signals and warnings given by the body and their significance, e.g. heaviness ofthe stomach means a meal or snack should be skipped. Various possible causes ofheadache, fever, etc. Preventing diseases by heeding warnings and taking timelycorrective measures.

• Disease: breakdown of the first line of defence.

• Exercises, play-activity, yoga and their importance.

• How to eat.

• Balanced food in terms of cereals, pulses, vegetables, etc.

• Constituents of foodstuffs: proteins, energy-giving matters, vitamins and miner-als. Implications for diet.

• Processed, refined and preserved foods: need to avoid highly refined foods andthose containing added chemicals, junk foods and drinks.

• Effects of different foodstuffs and spices on our bodies.

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• Broad idea of the process of digestion of food: various stages, time taken, involve-ment of various chemicals (names of individual enzymes not necessary) and thebrain.

• Importance of drinking water; how to keep water clean.

• Importance of adequate and deep sleep. The sleep cycle. How to sleep.

• Managing constipation and diarrhea. Self-examination of the stool.

• Care of the eyes, ears, teeth, hair and skin.

• For girls: menstrual cycle, its significance and related hygiene.

• Common diseases, their causes, prevention and home remedies.

• First aid; care of the sick, the young and the old.

• Measuring body temperature and pulse rate: normal values.

• Science and technology: helping and hindering man’s health.

• Different systems of medicine and the systems to be preferred in various condi-tions.

• Selecting and reporting to a doctor. Pathological tests.

• Story of eradication of smallpox; attempts at eradicating/controlling malaria andpolio.

3.3.2 Environmental Science

At the secondary stage, a broad awareness of the abiotic and biotic factors of theenvironment and their relationship with the common man’s life is necessary. Thisnaturally brings in some chemistry and biology. It is recommended that the treatmentof environment in terms of technical parameters be taken up only after class VII orVIII. An illustrative list of topics is given below.

• Five basic constituents of non-living nature: air, water, soil, sunlight, and space.Their importance for all life, their pollution and protection.

• Air: importance, constituents, role of green plants in purification, pollution byvehicles, industrial wastes, etc.

• Water: importance, sources and cycle, pollution, purification and conservation,drainage and soak-pit. Water-management.

• Soil: formation, various types, pollution, erosion and protection.

• Sun’s radiation: its energy being stored in plants and ultimately providing food toevery living being and most energy sources. Various colours and photon energies.


• Space: pollution due to crowding, noise and radiation.

• Forest: importance, how to reap resources, conservation and planting.

• Foodstuffs: how to recognize pure/fresh/ripe/juicy fruits and vegetables. Commonadulterants and surface contaminants. Need to wash fruits, vegetables.

• Clothing: various natural and artificial fibres; relation with season, health andconvenience.

• Housing: materials and designs; elementary map- making.

• Earthquakes, cyclones, floods and droughts. Their causes.

• Various kinds of energy and sources, renewable and non-renewable. Need forconservation. Tapping Sun’s energy.

• Biosphere: variety of flora and fauna; friends and foes of man. Caution againstsnakes, scorpions, flies, mosquitoes, etc.

• Micro-organisms: friends and foes. Sterilization.

• Simple experiments with air, water, soil, sun-light, plants and photo-synthesis.

• Exploratory and constructive projects as per local conditions. (Examples: explo-ration of tunnels and living places of rats, colonies of ants, etc.; making soak-pits,tree-planting, preventing soil erosion.)

• Natural resources: need for conservation. Man’s survival needs versus secondaryones.

• Sanitation: importance and practical arrangements.

3.3.3 Mensuration and Analytical Sciences

The mensuration part of the proposed curricula will be found to have a considerableoverlap with conventional curricula. In the CMS scheme, however, the interface withthe common man’s life is to be kept up. For example, in weights and measures, thelocal units must also be taught and related to the standard units. Secondly, there is tobe a lot of emphasis on doing (making measurements, estimating by ‘feeling’ and thenverifying by actual measurement).

The essential elements of the Gregorian, the Vikrami and other locally prevalentcalendars must form a part of studies. Their dependence on the motions of celestialobjects (as seen from the earth) should be explained and these matters demystified.Watching of the night-sky and identifying its salient features should be an importantpart of education at this stage. This should set the stage for critically examining manysuperstitions and beliefs prevalent in the society.

A discussion of elementary Chemistry, Physics and Biology is inescapable in con-temporary CMS. However, the criteria of accessibility to and usefulness for the common

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man must be kept in mind. Thus, for example, there is no need of going over the entireperiodic table; mention of 20-30 elements should be enough. An illustrative list oftopics is given below.

• Units of length, mass (weight), time, area and volume: quasi-quantitative, localas well as standard.

• Practice of making correct measurement. Rough-and-ready assessment.

• Idea of extremely small objects (upto nuclei) and very large ones (galaxies).

• The sun’s revolution as seen from the earth. The solar (Gregorian and Saka)calendars.

• The phases of the moon. The moon’s revolution around the earth. The lunar Hijriand the luni-solar Vikrami calendars.

• The shape and rotation of the earth. Day and night. The seasons.

• Solar and lunar eclipses: description and explanation. Rahu and Ketu. Watchingan eclipse safely.

• Sky-watching: recognizing the planets, some prominent stars and constellations.

• The nature of stars, planets and comets.

• Pressure: atmospheric and hydrostatic.

• Mixtures, compounds and elements. Chemical reactions. Organic and inorganiccompounds. Common examples from environment and human physiology.

• Metals and non-metals. Conductors, insulators and semi-conductors.

• Horizontal motions of objects. Speed and velocity. Friction: sliding and rolling.Acceleration. Vertical motion and acceleration due to gravity. Motion of projec-tiles. Periodic motion.

• Sound: wave-motion. Loudness and pitch. Decibel. Echo and reverberation.

• Heat, heat transfer and relation with temperature. Thermal expansion and con-ductivity.

• Elements of electricity. Charge and current. Attraction and repulsion betweencharges and between currents. The electric circuit. A.C. and D.C. voltages. Ohm’sLaw. Power and its calculation.

• Attraction and repulsion between magnetic poles. Electro-magnets.

• Behaviours of mirrors and lenses (broad idea).


• The atomic nature of matter. Atoms and molecules. Parts of the atom: theelectron, the nucleus. Protons and neutrons.

• X-rays and other radioactive radiations. Their effects on body tissues and genes.

• Units of energy and power: Joule, calorie, Watt. Examples in mechanical, ther-mal, electric areas. Calorific values of a few common foodstuffs and fuels.

• Cell: smallest living part of the body. Different kinds.

• Elements of genetics: how information about characteristics is written into eachcell and how these are transferred to offspring. Genes and DNA (elementaryideas).

• Things which can be quantified and those which cannot (at present).

• Prevalent superstitions and their analyses. Reasons behind social customs.

3.3.4 Technology: Agricultural and Industrial

Under CMS, technology too is to be discussed at a phenomenological level. Thus,computer chips as well as fertilizers can be discussed fruitfully without necessarilygoing into details of electronics and chemical reactions. Here is an illustrative list oftopics.

(i) Agriculture:

• Various crops and respective requirements of conditions (soil type, water, sun-light, etc.). Crop rotation.

• Seeds: indigenous, exotic and hybrid. Different requirements and yields.

• Manures and composting; role of legumes in enriching the soil.

• Fertilizers: different kinds and compositions. How to prepare solutions. Whenand how to administer.

• Management of pests and diseases. Use of neem and other domestic means.Pesticides, their correct use and hazards.

• Indigenous and foreign species of cattle and birds. Special requirements of foreignbreeds.

• Biogas: concept, construction of plant, use.

• Solar cooker, improved chulha, improved implements.

(ii) Industrial Technology:

• Use of simple hand-tools. Study of a bicycle. Simple repairs.

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• Major parts of an automobile engine and their functions.

• Household use of electricity and precautions. Power levels of various implements.

• How electricity is generated and distributed (simple ideas).

• Common domestic equipment (electric and non-electric), their parts and func-tions, e.g. pressure cooker, kerosene stove, radio, TV, computer, etc. Maintenanceand simple repair.

• Refined and processed foodstuffs: added chemicals including synthetic coloursand flavours. Unhealthy nature of all these, particularly ice creams, bottleddrinks, etc.

• Soaps and detergents: their proper use and possible effects on skin. Caution.

• Reading the list of ingredients and other information on a label.

• Computer: concept, language and uses.

3.4 Science Popularization

If school science education needs a CMS orientation, science popularization needs iteven more. The subject matter of science popularization efforts is broadly along thelines indicated under 3.2 and 3.3 above. Among educated communities, the terminologyof conventional science, e.g. proteins, X-rays, atmospheric pressure, etc. may be freelyused whereas, for the uneducated communities, the traditional parameters may beused for the most part and new ones introduced slowly.

A word must be put in here about science popularization among housewives inparticular. Contrary to any impression that the phrase ‘Common Man’s Science’ mightgive about CMS being male-oriented, the fact is that it concerns housewives morethan any other class of people. Indeed, it would not be too much of an exaggerationto say that CMS essentially comprises the experience and wisdom of generations ofhousewives, systematized and enhanced by modern scientific discoveries. Vigourousprogrammes of CMS education should be launched for housewives living under variousconditions, e.g., rural, urban, etc.

There should be emphasis on understanding and defending the vital resources ofthe common man, having confidence in the indigenous culture on the basis of scientificunderstanding, attacking problems in a systematic way, and investigating matterswhich appear mysterious (e.g. ghosts). Above all, innovation must be looked for, rec-ognized and nurtured. Village and district level organizations (science centres) shouldbe started on a massive scale and entrusted with these responsibilities. Such centresmust be manned by CMS personnel including housewives rather than by conventionalscientists.


4 Conclusions

With education and research in conventional sciences getting more and more limitedto exotic phenomena, abstract theories, general principles and industrial processes faraway from the ambient conditions, scientific enlightenment of the common man andsolution of his ordinary problems is being neglected. In particular, general scienceeducation is losing its direction and purpose. In the foregoing, we have pointed out thedoubly disastrous effect of the present science curricula at the school level: the studentsare needlessly burdened with formalism which most of them cannot learn and cannotuse, while they do not get the opportunity to learn practical skills and attitudes thatthey could well learn and use.

We have reviewed some aspects of the nature of science and formulated the conceptof common man’s science, which readily makes an interface with the day-to-day lives ofall citizens and can play a crucial role in making general science education meaningfuland purposeful. Common man’s science is that part of science which is at once usefulfor and accessible to everybody in a community. CMS draws upon both traditionalunderstanding and modern science at a suitable level of phenomenology. We haveshown above how CMS is a distinct part of science, and how it relates to traditionaland folk sciences as well as conventional sciences.

We have pointed out that in as much as the purpose of general education is not tomake one an expert in any one discipline but to enable one to solve the problems of life,and to have an intelligent appreciation of all that happens around one, the science partof general education has to mean CMS. We, therefore, advocate CMS as an integralpart of general education at all stages.

At the primary school level, what is desirable is inculcation of healthy habits anddevelopment of scientific skills of keen observation, experimentation, classification,reasoning and manipulation with the hands and simple tools. At the secondary stage(Class VI to X), some topics of particular interest to the common man can be taken upfor detailed and systematic study. These topics are (a) health, (b) environment, (c) men-suration and analytical aspects, and (d) agricultural or industrial technology. FromClass VII onwards, elements of Chemistry, Physics and Biology, which are essential foran understanding of all the above subjects, can be introduced explicitly under part (c).All the above topics are to be taken up at an appropriate phenomenological level so as tobe directly accessible to and useful for the common man. The more abstract concepts,general principles and theories (particularly the hypothetico-deductive systems likeNewtonian Mechanics) are to be left out of general education curricula, being of interestto specialists alone. It has been further suggested that CMS be made an essentialsubject at the senior secondary and higher stages of education too, enabling studentsto relate science to matters of interest to the community, the country and the worldat large. Besides, professional CMS courses should be offered for would-be schoolteachers, science popularizers and researchers.

The re-orientation of general science curricula along the lines of CMS should be seenin the overall context of injecting sense into the otherwise mad, mad world of education.The widely publicized slogans—of making education child-friendly, reducing the weight

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of the school-bag (which, according to the Yash Pal Committee, consists not so much ofreducing the amount of learning required as of making it ‘learnable’), and reversingthe increasingly anti-nature and anti-people trend in education—will remain emptyslogans without curricular changes along the lines indicated in this paper.

Such changes in the education system are bound to have an enormous impact onfuture generations. Children, liberated from the tyranny of senseless cramming andgiven an opportunity to learn science in a natural and useful way, will be able to learnmore thoroughly and creatively. They will be able to raise questions about prevalentcustoms and ways and, indeed, about the world of science and technology itself. Notonly will all students understand the nature around them better, but also those who goon to specialize in sciences will make better and more creative scientists, having had athorough familiarity with phenomenology. Even those terminating their studies at thematriculation level will be able to follow science and technology developments throughvarious media throughout their lives. Further, children of educationally backwardsections of the society will be able to compete on a more even ground, the naturalphenomenology being their home territory. We have actually seen both in tribal highschools and in primary-level non-formal education centres that children take to CMSas naturally as fish to water. This seems to be the only logical way of bringing aboutsocial justice in education—a way which is advantageous to all and disabling to none.

It may be mentioned that even in so-called developed countries like U.S.A., thereis widespread concern about students not imbibing the concepts and principles of sci-ence. They plan to pump even greater amounts of resources than before to make theirpopulation ‘scientifically literate’.4 The situation in countries like India is different.We do not have the same priorities as U.S.A. Every citizen here does not have to learnthe principles of science just because these are a part of the human heritage. Nor dowe have to struggle against the dogmas of medieval Europe. On the other hand, wehave a wealth of traditional wisdom that can be integrated with modern science. Also,we have urgent problems of hunger, disease, superstition, stagnation in production,and general ignorance. India can show the world how to utilize general education insolving these problems, without giving up on advancement in conventional sciences, byadopting the above approach.

Acknowledgement

Helpful discussions with Professor Dharmendra Kumar are gratefully acknowledged.

4American Association for the Advancement of Science (AAAS): 1989, Science for All Americans (Project2061), AAAS.

Attitude Towards Science: An Analysis.

Daya PantNCERT, New Delhi, India.

1 Introduction

Importance of bringing about improvement in the outcomes of learning of science can begauged from the time devoted to the teaching of science at school stage, right from thejunior school as environmental science through middle and secondary stage to seniorsecondary school. Although, all the learners will not be studying science at a laterstage but as effective citizens they need to possess the skills and competencies forunderstanding and use of science and technology in their daily life. It is useful formaking personal and public decisions on various issues, such as, polluting industriesand its locations, testing of drugs, use of banned drugs, and governmental decisionsregarding projects having a bearing on our environment (Miller, 1996). Understandingof science means understanding the nature of science which involves developing notonly the appropriate skills and competencies but also the relevant attitudes and values(Lederman, 1992) which are conducive to the learning of science in ways commensuratewith the socio-cultural mileu (Roth and Roychaudhry, 1994).

However, research relating to bringing about improvement in the learning outcomesof the science students has not changed the situation much (Linn, 1992). Scienceinstruction mostly, involves reading out textbooks to students (Holiday, 1984). In acountry like India where curriculum varies from state to state, and other facilities, likelaboratories etc. which promote learning by doing are lacking, the textbooks assume acentral place in the teaching-learning of science and they almost dictate the curriculumfollowed by the teachers and students (Gottfried and Kyle, 1992; Chiappetta et al.,1993).

The text books not only provide instructional strategies to teach certain facts butthere is a hidden curriculum that is woven into these facts and their presentation(Richardson, 1985; Watt, 1993; Kumar, 1989). This hidden curriculum influences thevalues and attitudes students develop towards science and its use.

It is not only the content of science text, but the exercises, diagrams and the activi-ties in the text also have importance for their potential influence on the understandingof science (Holliday and Whittacker, 1978; Holliday, 1981). The messages that arecontained in them regarding nature of science, its methodology, and the attitudes andvalues reflected in them influence their relevance in daily life (Jegede and Okebukola,1991).

Therefore, the content along with these other aspects of the textbook’s such as,questions, figures, tables, diagrams, activities etc. may be analysed so as to assesshow do they present the nature of science, its methodology and social dimension.

298 Attitude Towards Science

2 Present study

This study analysed the content, including questions, figures, tables, diagrams etc.,of the secondary school science textbooks published by NCERT (National Council ofEducational Research and Training). The analysis was carried out to ascertain ifthe books adequately present an account of the nature of science, its methods andprocesses, its linkages with society, and its use in daily life.

3 Procedure

The procedure involved using the criteria developed by science educationists (Chi-appetta et al., 1987, 1993) partially modified (see Appendix A) to suit the specificobjectives of the present study and the results are set out in tables 2 to 11. Interraterreliabiliability between the two raters was 90%.

Apart from the analysis using the criteria identified to assess the nature of scienceand its representation, the book was also reviewed with reference to the psychologicalview point of the learners and the criteria employed for analysis of the textual material,generally, in respect of organization, presentation and lay out.

The results are discussed along with the overall organization of the textbook withrespect to the perspective the textbook presents to the reader on the nature and phi-losophy of science.

4 Result and discussion

The analysis revealed that the four themes characterizing the nature of science, in-cluding its methodology, thinking skills, and social linkages were not represented in abalance manner in the IX and X class science text books. The themes and subthemesused in the analysis are given in the Appendix A.

Total items I II III IV Total items of Percentageanalysed agreement agreement106 74 10 3 9 96

Table-1: Table showing the agreement between two raters on the four themes ofnature of science.

These trends are also apparent in the analysis of the text books published in India(Kapalli, 1998) and abroad (Chiappatta, et al., 1993) and they have important implica-tions for the learning of science. Details are presented below:

4.1 Analysis of IX class text book

In this book the representation of the four themes was not quite proportionate as can beseen from the table 2. (Figures in parenthesis inside all the tables indicate percentagesrounded off to nearest whole number.)

Theme I: Basic Knowledge of Science had fifty percent share followed by the themeII, Investigative Nature of Science. The theme III, Processes of Science and the theme

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Themes underlying nature of ScienceUnit analysed I II III IV TotalParagraphs 153 91 28 46 318

(48%) (29%) (9%) (15%) –Questions 102 171 4 12 289

(35%) (60%) (1%) (4%) –Figures 120 17 9 10 156

(77%) (11%) (6%) (6%) –Tables 17 2 – – 19

(89%) (11%) – – –Highlights 12 6 5 4 27

(44%) (22%) (19%) (15%)Total 404 287 46 72 809

(50%) (36%) (6%) (9%) –

Table-2: The proportion of the four themes underlying the nature of science in IX classtextbook of NCERT.

IV Interaction of Science, Technology and Society, each getting less than ten percentshare of the total units analysed. The contribution of the paragraphs to the themeIII and IV is not quiet as unbalanced, as questions and figures. The theme III shouldhave been better represented through the intext questions, as good questions shouldbe aimed at encouragement of thinking and application among students. (Shepardsonand Pizzini, 1991).

The highlighted text infact, is relatively the most balanced component as far as thepresentation of different aspects of nature of science is concerned. The text has all theingredients of the material which if presented in the right proportion could make it abetter book. The sub theme categories introduced for the present analysis were foundrepresented in the text, although their proportion was not balanced (tables 3, 4, 5, 6, 8,9, 10, and 11).

The nature of science as the knowledge of science was presented most frequently asfacts, principals and models as can be seen from table 3.

There is a need to portray it more as a product of joint efforts of scientists overa period of time and also portrayal of the continuing efforts to improve upon them.Even presentation of the hypothesis, resulting from the existing knowledge or thenew hypothesis which need to be worked upon in areas of ongoing activity were notpresent in the text. The linkages of the present material with the information alreadyknown/taught to them or material asking them to recall information was almost absent.

The nature of science as an investigative endeavour has been well represented inthis book, claiming one third of the total units as can be seen from table 4.

Although, all the aspects of investigative method are present, there is a concen-tration of the material which “requires them to make a calculation” or “requires themto reason out an answer” as compared to the material which “requires them to learnwith the help of a graph” or engages them in a thought experiment or activity. A newcategory was added to this theme of the nature of science which involved highlighting


Subthemes within theme-IUnit analysed a b c d TotalParagraphs 143 7 3 – 153

94 5 2Questions 3 – 99 – 102

(3%) (97%)Figures 118 2 – – 120

(98%) (2%) – – –Tables 17 – – – 17Highlights 12 – – – 12Total 293 9 102 – 404

(73%) (2%) (25%)

Table-3: The proportion of the subthemes within the theme I, Knowledge of Science inIX class textbook of NCERT.

the lack of experience or bias in the student’s mind resulting in faulty reasoning ordifferent outcome of the experiment. Paragraphs and questions were presented in abalanced manner presenting the different aspects of investigative nature of science.But figures and tables did not present such balanced view of nature of science asinvestigative. Tables especially could be an effective way of presenting the influenceof bias and lack of experience, on the outcomes of experiments and reasoning of stu-dents. Apart from these lacunae, other aspects of investigative nature of science wereadequately highlighted in the text.

Science as a thinking process was not represented so well in this book as can beseen from table 5.

Only six percent of the total units analysed depicted this theme, as a result therewas no material whatsoever available on empirical nature of science and objectivity ofscience; within whatever limited material was presented in this theme, there was con-centration on “How a scientist experimented?” and “inductive and deductive reasoningin science.”

It is significant to note that there were only four questions which highlighted thistheme. Since, questions can focus the attention of the learners on the thinking pro-cesses of science, therefore it is of utmost importance that there be enough questionswhich highlight this theme. Tables could also have been used to depict at least twoimportant aspects of science as a thinking process “historical development of an idea”and “the way culture influences scientific thinking”. Highlighted box items in the textcould be the model to introduce more of the units on thinking processes of science. Onesubtheme introduced for this analysis regarding the role of culture on the scientificthinking was found represented in the highlighted text.

However, more subject matter needs to be introduced to take care of the “use ofassumptions” in scientific thinking which is a very important aspect of the processesof science and was not found in the text. Use of assumptions could be very easilyintroduced through not only paragraphs but questions which make the learners thinkat different outcomes with different assumptions. Even the highlighted text could have

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Subthemes within theme-IIUnit analysed a b c d e TotalParagraphs 25 2 26 11 27 91

(27%) (2%) (29%) (12%) (30%)Questions 2 10 86 66 7 171

(1%) (6%) (50%) (38%) (4%)Figures 6 1 – 1 9 17

(35%) (6%) (6%) (53%)Tables – – – 2 – 2Highlights 2 – 1 – 3 6

(33%) (17%) (50%)Total 35 13 113 80 46 287

(12%) (5%) (39%) (28%) (16%)

Table-4: Proportion of the subthemes within the theme-II Investigative Nature ofScience in IX class Textbook of NCERT.

been useful to put across this sub theme by quoting incidences where the assumptionsof scientist created difficulty in arriving at solutions.

The linkages between science, technology and society was represented by 9 percentof the total units analysed. However, almost about half of the subject matter represent-ing this theme presented the usefulness of science and technology for society as can beseen from table 6.

One third of the total units were found devoted to the discussion of social issues.Negative effects of science were not represented in the text book at all. A new categoryintroduced under this theme, limitations of science was found represented through fewunits. The other aspects of interaction between science, technology and society suchas acceptance of divergent ideas across authority, groups, individuals, and careers inscience were not found discussed in the text.

Paragraphs represented only three aspects of interaction between science and so-ciety, usefulness, and limitations of science for society, and social issues, while ques-tions, figures and highlighted text represented only two aspects, usefulness of science,and social issues. Tables completely omitted presentation of this theme. Figuresand questions could have very efficiently communicated the interaction of science andtechnology with society especially negative effects of, and careers in science. Tablesshowing the increase in number of industries in catchment area and resulting pollutionlevel of the rivers, figures depicting how industrial waste causes the water to getpolluted, ozone layer thinning down, green house effect etc. could be the phenomenonwhich need to be highlighted in the text in a simplified manner. Besides, the utensilswhich have possible health hazards due to aluminium coating etc. are the instances oflimitations of science and technology which ought to be communicated. The selectionof the particular information which communicates limitations of science or its negativeeffect could be the subject decided by the writer keeping in view the developmentallevel and previous knowledge of the learners.


Subthemes within theme-IIIUnit analysed a b c d e f g h i TotalParagraphs 9 4 – – 9 3 2 1 – 28

(32%) (14%) (32%) (11%) (7%) (4%)Questions – 1 – – 1 – – 2 – 4

(25%) (25%) 50%Figures 5 – – – – 1 1 2 – 9

(56%) (11%) (11%) (22%)Tables – – – – – – – –Highlights 1 1 – – – 2 – 1 5

(20%) (20%) (40%) (20%)Total 15 6 – – 10 4 5 5 1 46

Table-5: Proportion of the subthemes within the theme-III, Thinking Processes in IXclass textbook of NCERT.

4.2 Analysis of Xth Class Text book

Analysis of this book revealed that the nature of science is presented in a lop sidedmanner just as in the IX class science text book as can be seen from table 7.

However, the relative proportion of the themes in this book was slightly different.Science as knowledge and facts was represented by about half of the units analysed (47percent) as can be seen from table 8.

In comparison with the paragraphs and the highlighted text, questions, figure’s andtables presented knowledge of science in greater proportion; within this theme all thedifferent sub themes were found represented. However, there was concentration offacts, concepts and theories, as well as recall of information in the content.

Investigative nature of science was presented by 11 percent of the units analysedas can be seen from table 9.

Maximum contribution to this theme was made by questions, highlighted text andfigures, although overall representation of this theme was poor. There was concen-tration of the reasoning aspect contributed by questions. The figures included moreinstances of the subtheme which involved students in answering questions using ma-terial such as, maps, tables etc. The paragraphs contributing to this aspects of natureof science were very few but each one of the subtheme was covered through them eventhough there was one paragraph of each kind. Except the new category added for theanalysis in the scheme which intended to look for material dealing with bringing outof the students’ own bias and lack of experience influencing their reasoning, was notfound represented by any unit of analysis. Tables did not contribute to this theme,although use of tables could have been made to ask learners to make a calculation,and “reason out answer” etc. with the help of data which learners have to use toanswer questions, or examine to detect trends or make a critical assessment based onobservations presented. Highlighted text contributed, primarily, through a few unitsto the thought experiment or the thought activity. Overall there is poor representationof this theme in the text book.

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Subthemes within theme-IUnit analysed a b c d e f g TotalParagraphs 28 – 5 13 – – – 46

(61%) – (11%) (28%)Questions 6 – – 6 – – – 12

(50%) (50%)Figures 9 – – 1 – – – 10

(90%) (10%)Tables – – – – – –Highlights 2 – – 2 – – 4

(50%) (50%)Total 45 – 5 22 – – – 72

(63%) (7%) (31%)

Table-6: Proportion of the Subthemes within the theme-IV, Interaction of Science,Technology and Society in X class textbook of NCERT.

The nature of science as thinking process was very poorly represented in X class textas can be seen from table 10. Only six percent of the total units analysed representedthis theme. Except for the highlighted box items, all other units which presented thistheme were very few in number. Infact figures, questions and tables were, one each,presenting this theme. The paragraphs presenting this theme of nature of scienceconstituted ten percent of total paragraphs, while highlighted text contributed maxi-mally to this theme. Almost thirty percent of these units presented science as thinkingprocess inspite of the fact that there were few instances of each sub theme such ashow scientists experiment, how ideas develop over time, empiricity and objectivity ofscience, and the use of assumptions.

However, within this theme almost all sub themes were found represented, exceptthose relating to the discussion of “evidence and proof.” More use of tables could havebeen and questions could have been made apart from more paragraphs to highlight thistheme. Tabular material could highlight this theme effectively, for instance, listingout the changes in the scientific research and concommitent changes in the societyand policy or sharp changes in science at different epochs will highlight the influenceof culture on the scientific thinking. Tabulating data supporting one hypothesis andrefuting the other and elaborating on the contextual facts causing variations could betabulated along side highlighting the discussions relating to evidence and proof.

Questions and figures could also highlight the thinking processes of science. Ques-tions which promote thinking among students could be framed instead of those whichmake students recall information provided in the text. For instance the text discussesthe natural resources and question is framed, “Can you name one technology thatuses these resources?” instead a question could be framed, “Can you think of waysin which the depletion of natural resources through technology could be restricted?” or“Write how the technology which facilitates mankind can become counter productive?,”or “Which characteristics of the birds are suitable for their survival?” Figures which


Themes underlying nature of scienceUnit analysed I II III IV TotalParagraphs 109 10 28 156 303

(37%) (3%) (9%) (50%)Questions 128 55 1 30 214

(61%) (26%) (0.47%) (13%)Figures 56 7 1 18 82

(76%) (8%) (1%) (15%)Tables 24 – 1 11 36

(67%) (3%) (31%)Highlights 9 3 10 10 32

(31%) (9%) (31%) (28%)Total 316 75 41 235 667

(47%) (11%) (6%) (36%)

Table-7: The proportion of the four themes underlying the nature of science in X classtextbook of NCERT.

present evidence leading to different conclusions could be presented and students maybe asked to critically examine these as proof of different hypotheses.

The paragraphs presented all the sub-themes except two, namely, discussion ofevidence and proof, and influence of culture on scientific thinking. Both these aspectsof scientific thinking need to be emphasized through paragrapahs, tables, figures andquestions.

Interaction of science and technology with society was presented fairly adequatelyclaiming one third of the total units analysed as can be seen from table 11.

However, the various aspects of this interaction were not represented in a balancedmanner. Usefulness of science and technology was presented by 40% units, and socialissues by 48%, but negative effects of science and technology and limitations werepresented through 6 and 4% units respectively. Acceptance of divergent views acrossindividuals, authority levels and cultures was presented by two paragraphs but caraerin science and technology were not presented at all. This absence of any mentionof careers in science and technology has a repercussion for the image of scientists.Knowing that science is studied not only for becoming a scientist but also for pursuinga career.

Over all inspite of adequate number of units, this theme presented the interactionof science with society in terms of its usefulness and social issues. But the otherimportant aspects like negative effects of science, its limitations, the careers in scienceand technology and existence of divergence and its acceptance across authority levels,individuals and groups was not presented adequately.Overall organization of the book: The two books were also reviewed from the pointof view of:

1. the presentation of the content and its implications for inculcation of the appro-priate attitudes and values towards science,

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Subthemes within theme IUnit analysed a b c TotalParagraphs 103 4 2 109

(95%) (4%) (2%)Questions 9 – 119 128

(7%) (93%)Figures 51 5 – 56

(91%) (9%)Tables 11 2 1 14

(79%) (14%) (7%)Highlights 9 – – 9

(100%) 9Total 183 11 122 316

(58%) (4%) (38%)

Table-8: The proportion of the sub themes within the theme-I, Knowledge of Sciencein X class textbook of NCERT.

2. the layout of the books in terms of figures, tables, and other features and

3. the students’ reactions to the overall organization of the book.

Presentation of the Content: The organization of the content of the textbook in-fluences the levels of comprehension (Vidal-Abraca and Sanzose, 1998). The com-prehension of the text in turn will have influence on the inculcation of appropriateattitudes and values towards science and its relevance in life. Shallow comprehensionwill not result in application of the knowledge to real life situations. On the other handdeep levels of comprehension are likely to result in understanding the relevance of theknowledge in real life and, hence the positive attitudes towards it.

The science curriculum framework sets apart the middle level science competen-cies from secondary level science competencies. Therefore, the two books could havebeen presented as a continuity with IX class textbook carrying a brief mention ofthe expected competencies, attitudes and values related to science, supposedly de-veloped among the students at middle stage; and those that are to be developed atthe secondary stage. Such an explicit statement of the objectives to be attained andcompetencies to be developed at different stages, termed linking of the textual content,enhances the comprehension of the text (Vidal-Abraca and Sansoss, IWB). Besideslinking the textual contents to the readers previous knowledge, the text could alsomake a direct reference to the diferent aspects of the nature of science, such as, itshould essentially project science as not only the product but also as a process ofenquiry (Kapalli, 1998). However, the reference to the nature of science may be madeusing the vocabulary and language suitable to the developmental level of the IX and Vclass students.

The general planning of the book, and its contents may be guided by the perspectiveexplicitly stated in the first section. The logical linking up of the different chapters tothe perspective and their sequencing results in coherence of the ideas presented in the


Subthemes within theme-IIUnit analysed a b c d e TotalParagraphs 2 1 2 1 4 10

(20%) (10%) (20%) (10%) (40%)Questions – – 7 48 – 55

(13%) (87%)Figures 6 – 1 – – 7

(86%) (14%)Tables – – – – – –Highlights 1 – – – 2 3

(33%) – – – (67%)Total 9 1 10 49 6 75

(12%) (1%) (13%) (65%) (8%)

Table-9: Proportion of the sub themes within the theme-II, Investigative nature ofscience in X class textbook of NCERT.

text (Vidal Abarca and San Joze, 1998). It would also help facilitate teachers task byincreasing comprehension of the students as it draws atttention to those aspects of thetext, which need to be highlighted while teaching and also while framing questions,to adequately communicate the nature of science and its processes. Not only in thebeginning of the book but each chapter also needs to be put into focus. The chapters or afew chapters together should carry a introductory block which provides the connectionbetween previous chapters and the forthcoming ones. Although in the present bookeach chapter does begin with an introductory paragraph but it does not cover compre-hensively the expanse of the information in the chapter, thereby leaving it to the readerto sort out their own agenda in terms of the highlights and issues. In a science textbook, this gap may make the readers focus on the issues and content quite irrelevantto nature of science and miss the objectives of learning of science widely not by a smallmargin, as the readers tend to assimilate new information in the already conceivedcognitive structures. In the case of learning of science the previously conceived ideasmay be quite irrelevant and divorced from the reality, prompted sometimes by fantasiesor folklore.Layout of the book: A review of the layout of the books revealed that they arevery dull and unattractive. The figures and tables are set out in very small print,sometimes the figures are presented without any caption. When the figures appearwithout caption its potential value for the students comprehension is much less, thana figure independently appearing. As the figures make more visual impact on thestudents and stay in their memory, they have to be presented complete with expla-nation and labelling. Movement wherever necessary and possible should be depictedto communicate conceptual understanding of the process, for instance in electric motoror the dynamo the direction of movement of current or the magnetic coil etc.

The figures which are very small do not invite the attention of the reader, especiallythe students at this stage. The figures are not appropriately drawn. Where there isa need for real figures line drawings were shown and where line drawing would have

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Subthemes within theme-IIIUnit analysed a b c d e f g h i TotalParagraphs 2 4 3 3 11 1 – 4 – 28

(7%) (14%) (11%) (11%) (39%) (4%) – (14%) – –Questions – – 1 – 1Figures 1 – – 1Tables 1 – – 1Highlights 3 2 – – 1 – 2 2 – 10

(30%) (20%) (10%) (20%) (20%)Total 7 6 4 3 12 1 2 6 – 41

Table-10: Proportion of the sub themes within the theme-III, Thinking Processes in Xclass textbook of NCERT.

served the purpose real figure, a bad one was shown. The transfer of the learning toreal life situation is hindered when the figures are not appropriately drawn or drawnwithout the natural perspective. It becomes extremely difficult to identify them in reallife, for instance the figure of a moss or a touch-me-not plant when seen drawn outof proportion, not knowing its real life dimensions, will hinder the recognition of theplant in its real habitat. Sometimes the figures/gadgets are oversimplified and showndiagrammatically which comes in the way of comprehension of the real life gadgets andfigures. The specific comments and instances which could be improved are given below:IX class Text book: The figures in the chapters 1, 2 and 3 are very large whereas inchapters 6, 7, 8 and 10, the figures are small. In chapter 14, on electricity, the figuresillustrating various kinds of electric circuits, connections, voltmeter and resistances inseries etc., are all hypothetical. In order to identify and set up an electric circuit in reallife the real life ammeter would have served the purpose better. It has been seen thattransfer of learning to handle these objects in real life is poor among students becausethey do not comprehend the circuit from the incomplete diagramatic representation.

In chapter 16 even the figures of birds are drawings and not photographs. Basedon these figures the identification of plants and animals in real life situations becomesextremely difficult. Even if the dimensional characteristics are given, the identificationis still quite difficult in real life situations. Only when these living creatures are shownin appropriate real life perspective, their identification becomes easier.X Class Text book: In the X class science textbook the figures (see Appendix B) areoften presented without the labelling of different parts (figures 1.2, 1.3, 1.4, 3.4, 12.6).The figure 1.2 and 1.3 illustrate the working of combustion engines but in the absenceof labelled parts in the figure, the interest and comprehension remains much below thedesired level.

Figure 2.4 shows distillation of petrol, the figure is entitled distillation tower but itlooks like a cylinder. A real photograph of the tower along with the diagrams wouldcommunicate the process better. Figures 7.2 (c) on water contamination looks like apuzzle as to how the water is being contaminated.Other features: Glosarry of terms, concepts and explanations would have made adifference by introducing certain specific references to the words, terms and concepts


that deal with the nature of science and these could be included in the glossary.

Subthemes within theme-IVUnit analysed a b c d e f TotalParagraphs 63 6 9 76 2 – 156

(40%) (4%) (6%) (48%) (1%)Questions 9 1 2 18 – – 30

(30%) (3%) (6%) (60%)Figures 11 – 7 – – 18

(61%) (39%)Tables 8 – 3 – – 11

(86%) (14%)Highlights 5 – 5 – – 10

(50%) (50%)Total 96 7 11 109 2 – 225

(43%) (6%) (5%) (46%) (1%)

Table-11: Proportion of the sub themes within the theme IV, Interaction of Science,Technology and Society in X class textbook of NCERT.

Students’ reactions to the organization of the book: There were 20 studentswhose reactions were recorded. These twenty students were drawn from all sorts ofschools. There were 10 from public schools, 20 from government schools, and 10 fromcentral schools. There were fewer students from public schools because public schoolsrarely prescribe textbooks of NCERT. They all were asked the same question: “Howare your science books?” Out of the total, twenty reported that the books were dull andboring while others said they were o.k. These twenty reporting that the books were dulland boring were asked an additional question: “What about other books?” In responseto this, there were twelve who said the same thing about the other books also, rest feltthat the other text books were alright.

In order to assess the understanding of the tables and graphs another question wasasked: “What do you understand by this graph or figure?” In case student did notvolunteer much information, supplementary questions were asked. The supplemen-tary questions were: “What do you understand by this table?,” or “Why this graph isdrawn?,” or “What can be found out from this table or graph?” The students’ responsesrevealed that they did not understand graphs or tables or the purpose they served.

5 Conclusion

Overall, in the IX class textbook there is a heavy focus on the knowledge aspect andinvestigative aspect of the nature of science. In the former category more materialcould be on history of science. In the latter category there was emphasis on deduc-tions and reasoning out an answer and even content relating to answering a questionusing material was present. However, there was no content devoted to inclusion of

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investigative methods relating to the use of charts, tables, graphs or involving them inexperimentation or helping them become more aware of the personal biases that enterinto investigative processes. There is low concentration of material portraying, scienceas thinking process and, the linkages of science with society.

In the former category more content could be added. However, the material needsmore emphasis on empirical nature of science and quantitative assessment as well asthe use of assumptions in thinking needs to be emphasied thereby strengthening theneed for learning the methods of science relating to qualitative assessment, and alsothe values relating to the rationality and openness to evidence.

In the latter category whatever little content was present, protrayed the usefulnessof science for society and negative effects of science and technology, the emphasis oncareers, limitations of science and the portrayal of the democratic traditions, as againstthe dogmatic and authoritarian, was absent.

Thus in the X class textbook the content was dominated by two themes underlyingthe Nature of Science, Basic Knowledge of Science and Interaction of Science withSociety. The two other aspects of Nature of Science relating to Investigative methodand Thinking processing had very little presence, the latter having weightages almosthalf of the former. Thus, the book lacks the emphasis on methods and processes ofscience. The knowledge aspect presented science as facts and also as the history ofdevelopment of science.

Interaction between science and society presented the usefulness of science issuesbut the negative aspects of science and its limitations were represented by negligi-ble content while careers and the values of science that call for openness and anti-dogmatism and authoritarianism were not mentioned at all. Out of the few units thatreferred to the investigative nature of science most were aimed at calculation aspectonly. Similarly, the units that represented different processes of science and relatedvalues were hardly one or two of each kind.

Thus while IX class textbook is tilted more in favour of presenting science as BasicKnowledge and Investigative endeavor, X class books presents it as Basic Knowledgeand Social Interaction. Both the books lack emphasis on processes of science which areresponsible for inculcating the thinking skills and valuing process. Even the presen-tation of science as social affair, its negative effects, and limitations of science aughtto be emphasied more so as that learners do not develop unjustifiable single mindedeuphoria about omnipotency of science for all problems and ills of society.

Apart fram the content, the organization of the book needs to be more focussed andcontextualised with reference to the science related previous learning skills, compe-tencies of the learners, and the objectives to be attained by present text content. Notonly overall content, each chapter has to be put in perspective dovetailing each figure,graph, questions, tables etc. The vocabularly has to be brought to the level of thereader. Textbooks, thus improved are likely to result in capturing the interest of thestudents and, balanced development of science related comptencies in them.

6 Appendix A

Categories for analysing science textbooks:


The categories and subcategories (Chiappetta et. al, 1991a) have been describedand examples provided to enable comprehension of the rules of categorisation. Readthe categories carefully, before attempting to analyse the units in text.

1. Science as a body of knowledge: Science is characterised as a body of informationabout various natural phenomena. Scientific knowledge has been arrived at bythe application of methods of science. Knowledge in science includes facts, con-cepts and principles which are supported by evidence and are largely replicable.The type of text included under this category is one from which the studentreceives information. Textbook material in this category:

(a) Presents facts, concepts, laws and principles.i. Facts: Can be observed or demonstrated by accurate observaion. For

example, humans have a vertebral column.ii. Concepts: As facts accumulate, they begin to show certain relationships.

This pattern is referred to as a concept. For example, all animals pos-sessing a vertebral column belong to a group called vertebrates.

iii. Law: A statement of a relation or sequence of phenomena invariableunder the same conditions. For example, Boyle’s law.

iv. Principle: Constituent of a substance giving distinctive quality or effect.For example organic solvents dissolve organic compounds.

(b) Presents hypotheses, theories and models. Hypotheses and theories arescientific speculations regarding relationships between facts.

i. Hypotheses: Invented to explain a set of facts, a speculation that remainsuntested. For example, a hypothesis proposed by Sutton that genes arepresent in a linear fashion on a chromosome.

ii. Theory: An invention by scientists which has empirical support and fitsknown facts. It is arrived at inductively to explain a set of facts. Ahypothesis for which evidence is present, becomes a theory. For example,Darwin’s theory of organic evolution.

iii. Model: This is arrived at deductively from observations. The DNA modelproposed by Watson and Crick was based on X-ray crystallographic pat-terns. For example, the model of the solar system based on observationsand calculating distances.

(c) Asks students to recall information or knowledge which has been providedpreviously in the textbook.

2. Science as a way of investigation: This category includes; those parts of the textwhich stimulate thinking and doing by asking the student to “find out.” Thiscategory involves the student in the processes of science such as observing, mea-suring, classifying, inferring, recording data, making calculations, experimenting.Paper and pencil, and hands-on activities are included. Textbook material in thiscategory:

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(a) Requires the student to answer a question through the use of materials. Forexample, fix a rubber band at one end and hold the other end with yourfinger. Now pluck the rubber band and listen to the sound produced. Hearthe sound produced as the rubber band is stretched. Does the sound changeas you change the length of the band?

(b) Requires the student to answer a question or learn by the use of tables,charts, i1lustrations and sources of information other than the textbook.For example, look at the two figures. The bow in the X figure has potentialenergy. It can exert force on the arrow and make it move.

(c) Requires the student to make a calculation. For example, a bus travels 200mts in 40 seconds. In 1 second it will travel- metres.

(d) Requires the student to reason out an answer. For example, Would sea waterhave a lower or higher boiling point than distilled water?

(e) Engages the student in a thought experiment or activity. For example, antsare attracted to certain food items more than others. Devise an experimentto find out what types of food attract ants.

(f) Presents the material and incidence which bring out how the students ownbias and lack of experience influence his observation. For example error inreading the level of mercury and level of water could be due to inexperience.

3. Science as a way of thinking: This category would include the text material wherethe student is told how the scientific enterprise operates. It includes the scientificmethods and problem solving.This category is different from Catetory 2 in that the student does not have toanswer questions. Instead the student is told about how science in general ora scientist in particular discovered, invented ideas, or experimented. Textbooksmaterial in this category;

(a) Describe how a scientist experimented. For example, Edward Jenner ob-served that milkmaids showed very few incidents of small pox. He hypoth-esised that they develop immunity because they came into contact with cowpox. He experimented by taking serum from cows suffering from cow poxand infecting healthy people. He observed that the inoculated people did notsuccumb to small pox. He deduced that there is something in the serum ofcows that prevents small pox.

(b) Shows historical development of an idea. For example, in 1776, AlessandroVolta discovered that when two strips of different metals are dipped in anacid solution, an electric current begins to flow through the wire connectingthe two strips. This simple source of current or a cell is called a Voltaic cell.The principle discovered by Volta was used to construct another cell withan improved design by J.F. Daniel in 1836. This gave steadier current butwas cumbersome since liquid electrolytes were used. This disadvantage wasovercome by the invention by Lechlanche of the drycell in 1866.


(c) Emphasises the empirical nature of science. For example, the ionisation ofair produced by X-ray discharges electrified bodies. The rate of dischargedepended on the intensity of an X-ray beam. As a result, careful quantitativemeasurements of the properties and effects of X-rays could be made.

(d) Illustrates the use of assumptions. For example, to assume how moleculescan rearrange and change, we assume they must be built of smaller frag-ments called atoms. With this assumption, we can again explain diferencesbetween two molecules because they contain different atoms.

(e) Demonstrates how science proceeds by inductive and deductive reasoning.For example, In Mendel’s experiments with pea plants, it was noticed re-peatedly that when a pure tall plant was crossed with a pure dwarf plant,the progeny was all tall. Subsequent experiments with pairs of this progenyproduced tall and dwarf plants with a 3:1 ratio. The results led him to thinkthat “tallness” was dominant over “dwarfness.”

(f) Shows cause and effect relationship. For example, Take an ice cube on a plateand leave it on the table. After a while you notice that the ice has melted toform water. Ths warm temperature of the room caused the ice to becomewater.

(g) Shows evidence and proof. For example, “Hypothesis”: Number of chromo-somes generally remains constant from cell division to division, thus eachsuccessive generation would have twice the number of chromosomes theirparents had. However it is found that successive generations of the samespecies have identical number of chromosomes. Thus the hypothesis is incor-rect.

(h) Presents the scientific method or problem solving steps. For example, ascientist first gathers information to identify the probability. He then collectsmore information through observations, measurements, etc. He thinks overthe observations and possibilities. He tests each possibility by experimentsor repeated observations to collect data. He then calculates, compares anddraws conclusions.

(i) Presents material which brings out the influence of culture on scientific think-ing. For example, not looking at the eclipsed sun or moon or offering prayerduring eclipse and holding in esteem plants.

4. Interactions of science, technology and society: Check this category if the intentof the text is to illustrate the effect or impact of science on society. This aspect ofscientific literacy describes how science and technology helps or hinders mankind.It involves social issues and careers. Nevertheless, in the presentation of this kindof material the student receives knowledge and does not have to find out. Text inthis category:

(a) Describe the usefulness of science and technology. For example, we havelearnt to extract energy from animal wastes such as cowdung or plant wastes

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like sugarcane bagasse. One successful method is to ferment animal wastesin closed vessels and produce a gas called biogas. The waste from the biogasplant can be used as manure in fields and plantations.

(b) Discusses the limitations of science and technology for society. When the textpresents material relating to the areas where science and technology has notbeen able to solve problems due to the unresolved issues or new innovationsare required to help resolve issues, e.g. Polymer substances whin make upgarbage, their disposal is a severe problem and this puts a limitation on theuse of this technology.

(c) Describes the negative effects of science and technology. For e.g. sometimesscience is used in harmful ways. Once people learnt that certain substancesexplode easily, they made bullets, bombs and crackers. These were devisedfor our safety and security. Some people misused bullets to kill wild animalsand people.

(d) Discuss societal issues related to science and technology, e.g. Some peoplefeel that rain forests should be cut down. They argue that the cleared areascan be used for farming, which is necessary to feed the growing population.Other people believe rain forests should not be cut down. They point out thatgood yields from crops are possible only for a few years. That is because thetropical sun and large amounts of rain that these areas receive soon destroythe soil by moving water. The good soil is carried away by erosion. Thus theland becomes useless for farming.

(e) Brings out the acceptance of divergent ideas across individuals, and author-ity levels or groups when the text reports material which makes explicit theinstances whom the thinking of a particular individual or cultural group orperson of rather lower authority level was acceptad by others for examinationor use, such as, use of technology developed in one part of the world beingused by others or a junior scientists’ paper or innovation being recognized bysenior irrespective of his experience or level of authority.

(f) Information about careers in science and technology. e.g. To prepare for amechanical enginering career, you should opt for subjects like mathematics,physics and chemistry in high school.


7 Appendix B

Fig. 1.2Fig. 1.3

Fig. 1.4

Fig. 3.4

Fig. 7.2 (c)

Figure 1:

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Fig. 12.6Fig. 2.4

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Science Textbooks in Tamil—Encounter of Modern Science withTraditional Knowledge Forms.

T.V. VenkateswaranCentre for Development of Imaging Technology, Thiruvananathapuram, India. Email: [email protected]

1 Introduction

Modern Educational systems instituted in India during the colonial period usuallyevokes two responses among the scholars. One treats the educational edifice as avaluable legacy, left by former rulers, albeit, unwittingly. The others, consider it asdiametrically opposite—as yet another instance of the metropolitan powers deliberateattempt to keep down the hapless colonies for their exclusive benefit.

With the prefix ‘modern’ to the word education, the first response focuses on thesocial mobility that colonial education provided to hitherto suppressed and depressedclasses of people.1 The spread of ideas like democracy, scientific rationality, rationalityand nationalism is traced as a worthy benefaction, with the colonial educational systemregarded as having ushered in ‘modernization.’2 On the other hand, the alternativefocuses on how education was a ‘mask of conquest’3—a sort of tool to obtain the consentof the oppressed; and how it colonized the minds. Gauri Viswanathan argues thatthe introduction of literary studies in place of religion by the British operated a veiledmechanism of social control to keep the Indian society governable without the excessiveuse of violence.

Scholarship thus is intertwined in inescapable dualism, with weak explanatory po-tential. The first response would be unable to explain how a well-articulated Macaulayancolonial educational project could turn out to be a patronizing agent of change, ul-timately leading to the demise of colonialism itself. On the other hand if moderneducation was only a ‘mask’ and a ‘colonizing mind’ project, how could it generate aclass of people who vociferously opposed colonialism? Both these dualist responsestreat the recipient society as passive and fail to consider the possibility of ‘natives’ ac-tively engaging with the colonial project and re-appropriating elements in the colonialeducational system.

The way out is possibly to seek a solution in the mode of transmission and exchange1See Hardgrave, Robert: 1969, Nadars of Tamilnad, University of California Press, Los Angeles, for the

impact of education on caste structure. Specifically, the book takes the case study of how Nadars, a backwardcommunity, acquired wealth and education and moved upwards in the caste hierarchy.

2Ghosh, Suresh Chandra: 1995, The History of education in Modern India, Orient Longman, is arepresentative of this view.

3See Vishwanathan, Gauri: Masks of Conquest—Literary Study and British Rule in India, ColumbiaUniversity Press, New York. She argues that the introduction of literary studies in place of religion bythe British operated a veiled mechanism of social control to keep the Indian society governable without theexcessive use of violence.

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of knowledge between the metropolitan and colonial cultures. Extending the pointmade by the sociology of science, this paper seeks to examine the ‘native’ attemptto divest western science of its European cultural codes and to assimilate modernscience into the native cultural cosmos. As Aparna Basu points out: “education wasa central concern in the nationalist quest for self-identification for it was in educationthat the cultural agenda of colonialism had been most succinctly expressed,”4 and thusan investigation into the content and character of textbooks on science during thenineteenth century would be rewarding.

In the cultural ecology of colonialism, European missions, emergence of scientificnaturalism and social changes ushered in at the turn of the century, this paper at-tempts to document the toils of native intellectuals in skillfully balancing the tra-ditional and modern. Textbooks being one of the main conduits for the spread of‘modern’ scientific knowledge, this paper specifically underscores the ‘native’ effortin ‘neutralizing’5 and ‘domesticating’6 the publication and dissemination of sciencetextbooks during the nineteenth century by Tamil intellectuals (vernacular literati).7

2 Educational Policies and its Impact

During the nineteenth century there were mainly two types of educational systems inTamil Nadu: a.) an educational rooted in indigenous practices called Payal schools andb.) Modern schools established by European missionaries and East India Company.

As every other society, Indian society too had its own traditional system of schoolsfor training the young and transmitting knowledge from generation to generation.There were indigenous village schools,8 called ‘Payal’ or ‘patasalas’—in various parts ofTamil Nadu to impart basic literacy, numeracy and to train children in various usefularts. Dharam Pal claims that there was a Macaulayan programme of erasure of villageschools—akin to that of de-industrialization. De-education under the colonial BritishRaj may be argued; however, it remains that the education provided in these indigenousschools were discriminatory, and was disproportionately in favour of the upper caste.During 1835, while the Brahmin population constituted only one twentieth of thatin the Madras Province, out of every five students in patasalas, one was from the

4Basu, Aparna: 1998, ‘National Education in Bengal 1905-1912,’ in Sabyasachi Bhattacharya (Ed), TheContested Terrain, Orient Longman, New Delhi, 54-67.

5Raina, Dhruv & Irfan Habib: 1996, ‘The Moral Legitimization of, Modern Science: Bhadralog reflectionson theories of evolution,’ Social Studies of Science, 26, 9-42.

6Raina Dhruv: 1997, ‘The Young P C Ray and the Inauguration of the Social History of Science in India,’Science Technology & Society, 2, 1, 1-39.

7I am aware of the fact that this expression of ‘intellectuals’ smacks of ‘elitism.’ The emergence ofmodern (English) educated strata has diversely been characterized as ‘middle class,’ ‘elite’ and so on. I amfollowing K N Panickar, who, applying the Gramscian notion, uses ‘intellectuals’ to characterize this strate.‘Autodidact,’ as conceptualized by the Dhruv Raina and Irfan S Habib is more appropriate, nevertheless aswe are not focusing on specific individuals but wish to underscore a social class, we use the term Tamilintellectuals. I am also aware that these ‘Tamil intellectuals’ were not a homogenous group but wereinternally differentiated. However, the contradictions within the Tamil intellectuals were more pronouncedconsequent to the cultural politics since 1920s.

8Pal, Dharam: 1983, The Beautiful Tree, Biblia Impex Pvt Ltd, New Delhi: A uncritical exalteddocumentation of the indigenous schools surviving from earlier period to that of early Raj.

Venkateswaran 321

Brahmin community. Also, the education offered to various castes was not uniform;it was skewed to fit to the students caste-designated role. Thus a Brahmin could learnastronomy, logic, arithmetic and law, but a trader would be provided with education inbazaar mathematics and so on. Higher education obviously was restricted to Brahminsand a few other upper caste sections. It goes without saying that female education wasdismal and the education of Sudhra caste almost absent.

Radhakrishnan remarks thatthe nature of indigenous instruction from the perspective of its stages and methods, characterand quality and prevalence and characteristics of domestic instruction showed its imperfectionand inadequacies. But viewed . . . from the perspective of Pre-British Indian Society, what weperceive as its limitation was perhaps only some of the manifestations of an educational systemwhich was designed and developed to reproduce the society in all its discriminating dimension.9

It is well documented that the Payal schools used classics and texts composed incadjan leaves, on the other hand, syllabus, schedule and prescribed textbooks wereabsent. While the payal schools were discriminatory, in general the modern schoolsestablished by the missionaries during the nineteenth century admitted students fromall classes of people.

As Keay notes, the payal schools were not replaced or erased but were graduallyincorporated into the mainstream modern school system.10 In fact, in South India, suchtypes of Payal schools did not completely fade away, but were progressively broughtunder the control of the State.

To start with, it was the missionaries who instituted modern educational institu-tions in Tamil province. Portuguese established a Tamil school as early as in 1567and eight students began their course in language at Punnakayal, a coastal town insouthern Tamil Nadu.11 There is a reference to school master (by implication to school)in an East India Company record of Fort St George dated 1678.12 However, it is notknown whether the school serviced only the whites or was open to the natives too.Nonetheless, such efforts were far and few, and with the absence of printing presses,hardly any textbooks were published. The age-old practice of committing to memory,and the use of Cadjan leaves, were resorted too.

By the late eighteenth century, the Society for Promotion of Christian Knowledgeand the Danish Missions instituted schools and Rev Schwartz established a numberof schools at Tanjore, Ramnad and Sivaganga. Essentially the efforts were on thepart of various European missions who in addition to evangelical work also took uponprovision of school education.13 ‘Evangelical belief in the transformation of human

9Radhakrishnan, P.: 1986, Caste Discrimination in indigenous Indian education I: Nature and extentof education in early, 19th century British India, Working paper No. 63, Madras Institute of DevelopmentStudies, Madras.

10Keay F. E.: 1989, Ancient Indian Education; An inquiry into its origin, development and ideas, OxfordUniversity Press, London.

11Jayaseela, Stephen: 1998, Portuguese in Tamil Coast: Historical Explorations in Commerce and Culture1507-1749, Navajothi, Pondicherry.

12Gover, Charles: 1982, Report on the Results of Educational Census of Madras 1871, Government Press,Madras, 45.

13See for details, Satthianandan, S.: 1894, History of education in the Madras Presidency, ChristianLiterature Society, Madras.


character through education and the conviction that conversion to Christianity re-quired some amount of learning, promoted the cause of modern education in India.’14

Lalitha Jayaraman notes that15 “in the period prior to 1833, the missionaries mainlyconcentrated on establishing elementary school teaching through the medium of mod-ern Indian languages . . .”

While the East India Company as such was not keen on the spread of educationamong its colonial subjects,16 during the 1820s, Sir Thomas Munro, Governor of MadrasPresidency, took interest in the spread of education to the masses. Munro commis-sioned district officials to gather information regarding the spread, reach, content andstructure of education then prevailing in various districts of Madras Presidency. Re-flecting on the dismal state of affairs in education, he favoured the spread of educationin the Presidency at the Companys expenses. He promoted the establishment of oneschool for Hindus and one for Muslims in each major town and at least one school ineach Talook (Tehsil). By 1830 there were 70 Talook schools and by 1835 it was only81 all over the Madras Presidency, implying that the establishment of modern schoolwere essentially enclavist. While the provincial schools were conducted in the mediumof English and the Zilla through both English and Vernacular, the Talook schools wereessentially vernacular schools.

The policy of promoting education in the vernaculars received a set-back with theflirtation of the British with the ‘filtration’ theory of education, cogently advocatedby Macaulay in his famous 1835 minutes. Concurring with Maculay, Lord Bentinckordered that “His Lordship in council is of the opinion that the great object of theBritish Government ought to be the promotion of European literature and scienceamong the natives of India and that all the funds appropriated for the purpose ofeducation would be best employed in English education alone.”17 The Macaulayanminutes assiduously advocated ‘English education’ in addition to ‘class education,’ andthus there was a fundamental change in the colonial educational policy. It argued:18

to place within the reach of higher class of natives the highest instruction in the Englishlanguages and in European literature and science so as not only to improve the intellectualand moral condition of the people, but also to train a body of natives qualified by their habitsand acquirements to take a large share and occupy higher situations in the civil administrationof the country.

The filtration theory argued that it is better to provide quality English educationto a small class of native people, who would be ‘brown in colour’ but ‘white in habits

14Niranjana, Tejaswini: 1992, Siting Translation, Orient Longman, New Delhi.15Lalitha, Jayaraman: 1986, History of Education in the Madras Presidency 1800-1857, MPhil Thesis,

Madras University (unpublished), 62.16In the charter act of 1813, a provision was incorporated that made lawful but not obligatory on the part of

the East India Company to set aside funds for the revival and improvement of literature and encouragementof the learned natives of India and for the promotion of knowledge of the sciences among the inhabitants ofthe British territories in India. See Sharp, C.H.(Ed): 1920, Selections form the Educational Records 1781-1839; Part I Calcutta, 22. But the efforts were taken earnestly only after a decade, in 1823.

17Resolution of the 7th March 1835 in Sharp, C. H.(Ed): 1920, Selections form the Educational Records1781-1839; Part I, Calcutta.

18Cited in Satthianandan, S.: 1894 History of Education in the Madras Presidency, Christian LiteratureSociety, Madras.

Venkateswaran 323

and mentality.’ Thus the earlier policy of the East India Company to support ‘oriental’education—education in Sanskrit, traditional knowledge and vernacular literature—were reversed.

The new Macaulayan policy had indeed definitely impeded the spread of vernaculareducation in British Indian territories; nevertheless, in Madras Presidency it was notcompletely arrested.19 Missionaries were also very active in Madras Presidency in pro-viding elementary education; furthermore most of the missionary elementary schoolswere consistently vernacular in the medium of instruction. However, the unrealisticpolicy of exclusive English education did not last long, and the Governor General LordAuckland in his minutes of 1839 departed from the stringent policy of Bentinck andnoted that spread of mass education through English is not a feasible one. Furtherhe also pointed out that the vernacular education may be economical, “than throughEnglish, which require the employment of an English master on a salary at least twoor three times as high as would be adequate for a native master who had received anEnglish education and at the same time perfectly conversant in his own tongue.”20

Further the minute desired that the “leading facts and principles of our literatureand science be transferred by translation into vernacular tongues”21 and argued “thejustness and importance of the advice of the Honorable Court that such a series of classbooks should be prepared under one general scheme of control and superintendence.”In conclusion the Government of India in its order22 stated that “class book consistingof selections from English work, or, of compilation drawn up and adapted for nativepupils should be prepared at the charge of education funds of all the presidency.” Asystem consonant with Lord Aucklands prescription was soon drawn-up by the MadrasGovernment and a scheme for bestowing annual prizes to vernacular compositions withthe object of procuring expositions of standard English works of the character23 waspracticed.

The Educational Despatch of Sir Charles Wood in 1854, described as the ‘MagnaCarta of Indian Education’ suggested a major deviation from the ‘filtration’ theory ofeducation and advocated the spread of mass education at an elementary level. Thoughthis despatch also endorsed the desirability of ‘English education’ at secondary andhigher levels of education, it accepted the use of vernacular at primary levels. Thedespatch recommended to24

recur to the past scheme of education viz., the classical language of the East as the mediafor imparting European knowledge. This object of extending European knowledge must be

19Ghosh, Suresh Chandra: 1995, The History of Education in Modern India, Orient Longman, New Delhi.20C. H. Sharp (Ed), Selections form the Educational Records 1781-1839; Part I Calcutta, 1920, (p. 162).21ibid, 156-157.22Minute of the Governor General in Council, dated 21st Nov, 1839 in Sharp, C.H.(Ed): 1920, Selections

form the Educational Records 1781-1839; Part I, Calcutta, 147-170.23In 1841, Robertson’s ‘History of America’ was translated into Tamil and was given the annual price. The

textbook was latter prescribed a text book in the Madras University.24Educational Despatch 1854 (No. 49 Dated 19th July 1854) (Popularly referred to as Woods Despatch)

1854, (copy appended in the Arubthnot, J.(Ed), Selections from the Records of the Madras GovernmentNo. II, Papers relating to Public Instructions, comprising of the proceedings of the Madras Department ofPublic Instructions, Fort St George Press, Madras, 1855).


effected by means of the English language in the higher branches of institutions and by meansof vernacular language of India to the great mass of people.

and furthermore, that25

. . . we must emphatically declare that the education which we desire to see extended in Indiais that which has for its object the diffusion of the improved arts, science, philosophy andliterature of Europe, in-short of European knowledge.

With the acceptance of the major recommendations of the dispatch, a Directorate ofPublic Instruction (DPI) was instituted in each province to ‘control and inspect over thewhole educational system.’26 The despatch also advocated a system of grant-in-aid to‘various agencies for the spread of education among the natives of India.’27 Thus manya payal schools as well as elementary schools established by the missionaries couldreceive support from the state in the form of grant-in-aid. This resulted, progressively,in brining much of the elementary educational institutions in the Madras Presidencyunder the supervision of the state.

No. of Schools No. of ScholarsSchools under directGovernment management 73 2148Under Governmentinspection 112 4020Missionary Schoolsrecieving Grant-in-aid 303 8973Total 488 15141

Source: Report of the Director of Public Instruction for the year 1856-57

Table 1: Vernacular Schools in the Madras Presidency during 1856-57

The grant-in-aid system not only triggered the spread of the mass education, butalso ensured spread in terms of the caste groups who received modern education. Thus,by 1872-73, the general average male literacy rate in the Madras Presidency was 5%and in Madras district it was 18%. In the Presidency, Hindus had a literacy rate of4.8%, Muslims 4.9%, Native Christians 7.4%, European and East Indians 63.3%, Jains12.9% and others 18.4%.28 One of the significant consequences of modern educationwas that—at least a few from the oppressed classes could receive education as much asthe Brahmins or caste Hindus. As the missionaries were arguing that education couldbetter one’s social standing, those caste sections in the lower hierarchy could lay claimfor social mobility.

25ibid, (p. 2).26ibid 34-41.27See Manickam, S.: 1988, ‘Grant in aid and Christian mission in Madras,’ in Studies in Missionary

History, Christian Literature Society, Madras, 82.28Data compiled from The Report of the Administration of the Madras Presidency, 1872-73, Part II, Madras,

1873, 37.

Venkateswaran 325

Till about 1870, all schools other than under direct government management hadautonomy to choose the text book and also prepare their own scheme of studies. How-ever, with the introduction of government exams, adoption of inspection, schools receiv-ing grant in aid, inclusive of many a missionary schools, had to recourse to use of textbooks approved by the government. The Textbook Review Committee in its report alsodirected each province to set-up a text book committee to ‘approve suitable textbooks’for use in school receiving government aid. In practice, in many a case it meant that,it was only the textbooks produced by the government or prescribed by it were used.

The Education Code of 1881, while reducing the grants to the high schools andcolleges, increased the grants to the primary schools. The Hunter commission of 1882also recommended the spread of elementary education and stated that29

while every branch of education can surely claim the fostering care of the state, it is desirablein the present circumstance of the country to declare the elementary education of the masses,its provision, extension and improvement to be that part of the educational system to which thestrenuous effort of the state should now be directed in a still larger measure than heretofore.

The Hunter commission also favoured progressive retraction of the Governmentfrom the educational sector. It suggested a mode of grant-in-aid scheme to agencies andalso recommended vesting elementary schools with Municipal and Local boards. By1922, in Madras Presidency, merely 4% of the students were attending the governmentschools. The result was an expansion of elementary schools under private management.Previously, though class books were prepared and published, the accent given were forpromotion of ‘sound vernacular literature’ and most of such publications were usedas supplementary texts to instruction in the school. Meanwhile, Hunter commissionadvocated that only books approved and prescribed by the government be used in theschools receiving state aid. This resulted in production of books with specific characterand style of ‘textbooks,’ even on topics such as sciences.

The net result of these policy changes was relatively widespread primary educationamong the vernacular literati, mostly in vernacular medium, predominantly underprivate management with modest autonomy in choice over textbooks.

3 Science for Natives—Early Nineteenth Century

It was the missionaries who took lead in propagating modern science in India. Eventhe efforts by the colonial government in early period in the Madras Presidency wereessentially a missionary affair, with most of the compliers and authors of textbooksbeing European missionaries.

Though the proclaimed aim of the public instruction was ‘improved European lit-erature and sciences,’ even during 1850s while, mathematics and geography were in-troduced into the scheme of studies, natural sciences (natural philosophy & naturalhistory) were, mostly, absent from the scheme of studies for vernacular schools. InTalook schools, which were essentially vernacular schools, the natural science wasnot a separate subject of study, nonetheless, book titled Joyces Dialogue on Scienceswas a prescribed text for Tamil prose for 3rd and 4th classes. This book was a Tamil

29Report of the Indian Education Commission 1882, Calcutta, 1883, 586.


translation of a English elementary work on physical sciences prepared by the Cal-cutta School Book Society and published in Tamil and Telugu by the Madras SchoolBook Society around 1827. Halls Outline of Astronomy, Ed by Rev T.S. Pratt, was aprescribed text for Tamil prose for 5th class. Later, a book titled Brief and familiarsketch of Europe published by the Madras School Book Society was also used as a textfor Tamil prose. This book though, essentially on the history of Europe, information oninventions, institutions and natural phenomena of Europe, thus providing additionalinformation on certain aspects of natural sciences.

Woods dispatch advocated provision of education in natural science and thoughthe subject did not find a place in the revised scheme of studies, it was suggestedthat “the pupils should be made to write from dictation, striking passages of historyor important facts of Natural Philosophy or Natural History being selection for thatobject, so that their very copy book may be made to serve the purpose of commonplace books.” Moreover, lessons on natural science and inventions were included inthe vernacular language readers.

Thus we find the following in the Tamil readers published by the Director of Pub-lic Instructions in the Madras Presidency: In the first reader, while there were nosubstantial chapters on science, natural philosophic topics such as ‘soul, heaven andhell’ were included. But, the second book of lessons in reading, contained elementarylessons on physiology, natural history, and astronomy. Lessons on head, eye, noseand ear were part of physiology and animals such as cow, crow, ass sheep, cat andso on where on natural history and seasons, and natural phenomena such as ice, iceskating etc formed part of natural philosophy while lessons on stars, moon and sunwere taught as part of the astronomy. In the third book of lessons in reading, naturalhistory included lessons on minerals, vegetables and animals kingdoms. A chapteron ‘creation’ attempted to provide basics of natural philosophy, chapters on naturalphenomena such as atmosphere, dew, rain, lightning and thunder. The minerals suchas gold, silver, lead and tin, iron, copper and brass were part of mineralogy. Lessonson vegetables included coconut, palmyra, cotton, grains, coffee, tea, tobacco and areca.Swan, cock, hen, reptiles, bat etc. were on animal kingdom. Lessons on astronomyprovided basics on the sun, moon and the stars and few astronomical events such aseclipse. The Brief sketch of Europe, though was primarily intended to teach history ofEurope was also a prose reader and it contents included manner, customs, institutions,events, objects and scenery. Nonetheless, the natural phenomena observed in Europeare described in terms of Natural History.

Rev Percival, a missionary and a professor of vernacular literature at the PresidencyCollege, prepared these series of Tamil readers, assisted by natives. While the serieswere pruned of every Christian element, allusion to European outlook remained. Thus,for example, chapter on ‘creation’ was retained and the tone and tenor of the works werenatural philosophic in perspective.

Even the titles of books published before the 1870s provides evidence that thepublications by the missionaries on scientific subjects were in the paradigm of ‘naturalphilosophy.’ In the catalogue compiled by John Murdoch the following are classified

Venkateswaran 327

under ‘Natural Science’:30

1. On General Knowledge, Rev C Rhenius.

2. Tattuvanul Surukkam, [On astronomy, natural history in the form of questionand answer], anonymous, however a publication by missionaries.

3. On the Sub-division of Knowledge, Published by the Madras School Book SocietyDepot, a translation of Dr. Ballantyne’s work.

4. Siruvar Kalvi Thunai, [Catechism of general knowledge], anonymous.

5. Thattuva Sastram, (Natural Philosophy), Rev E Sargent.

6. Catechism of Natural Philosophy, Rev E Sargent.

7. Joyce’s Scientific Dialogue, Madras School Book Society.

8. Lectures on Natural Philosophy, anonymous.

9. Oriental Astronomer, Rev HR Hoisington, [a complete system of Hindu Astron-omy].

10. Hall’s Outline of Astronomy, Ed by Rev TS Pratt.

11. Astronomy, Christian Vernacular Education Society.

12. Wild Animals, anonymous.

13. Domestic Animals, anonymous.

14. A Reader on Natural History, published by the Madras Government.

15. Anatomy, Physiology and Hygiene, Dr Green.

16. Atma Vasa Vivaranam, [The house I live in—a popular account of the humanbody].

17. Chingalpat Civil Dispensary, anonymous (Government publication).

18. Health and How to Preserve It?, Dr Lowe.

19. Midwifery Adapted to India, Dr Green.

20. Bazaar Medicines, Dr Waring.

21. Asuva Sastram, [on horse], anonymous.

22. Maddu Vakadam, anonymous.30Murdoch, John: 1865, ‘Classified Catalogue of Tamil Printed Books with Introductory Notices’, (repub-

lished by the Tamil Development and Research Council).


23. Gun Powder Manufacture, anonymous.

24. Indigo Cultivation, anonymous.

(Note: the first 14 publications are on ‘natural sciences’ and the rest on medicine,technology etc.,) In addition to the above, four books on mathematics and 35 books ontraditional medicine were also ‘noticed’ in the said catalogue of Tamil printed works.

While the Government schools and most of the other private schools not under themissionary management essentially used the government textbooks, the missionariesprepared their own textbooks and readers. In 1854, South Indian Christian TextbookSociety was formed to prepare textbooks with Christian elements. Latter in 1858 thissociety was merged with the Madras Branch of the Christian Vernacular EducationSociety (CVES). Many of the vernacular books issued by this society were chiefly forthe purpose of school education.

The book Thattuva Sastram (Natural Philosophy) by Rev E Sargent,31 a mission-ary, appears to have been popular, as reprints of this book appeared as late as 1898.The book was written drawing upon heavily from the works of Dr Arnott. The bookThathuva Sasthram, firstly describes the32 “atomic concept, physical forces of nature(attraction, repulsion and inertia), mechanics, explanations of natural phenomena,hydrostatics, pneumatics, hydraulics, acoustics, heat or caloric, light or optics, elec-tricity (galvanism), magnetism (electric telegraphy), weightless matter” and so on.In the introduction the author, Rev Sergent, asserts that “unlike humans, inferioranimals have no natural capacity to learn.” The ‘nature’ here implies the inclinationof God. However humans have innate capacity to learn from their parents and gatherknowledge through life experience and by exerting oneself.”33 The author states:

During earlier days, prior to the proper pursuit of Natural Philosophy, deception was ga-lore. People were misled and deceived by blending astronomy with astrology, chemistry withalchemy. When various principles of natural philosophy became known in (the western) coun-tries, superstition was eradicated.34

Natural philosophy was defined by the author as “knowledge that describes prop-erties of matter in the universe, laws of motion of the bodies and how the knowledgeis practically useful to man.”35 The book also approvingly cites Francis Bacon, andgoes on to illustrate the contributions of Galileo, Boyle, Newton, Franklin, Herschel,Laplace, and Davy.

The author, to illustrate the magnificence of the creation by the ‘True God’ advancesthe argument of ‘prime mover.’ While some of the indian tradition also held the view of‘God as the designer,’ christianity the way explained by the missionaries attemptedto show that the ‘first cause’ was True God and the motion in the universe is thegrand ‘effect’ and that the modern science provides ample evidence to this. the author

31Rev E Sargent: 1874, Thathuva Sasthram, Church Mission Press, Palayamcotta, (in Tamil).32ibid, 16-17.33ibid, 1.34ibid, 3.35ibid, 6.

Venkateswaran 329

reasons that the study of natural philosophy is “not only for material progress butalso for spiritual progress—one who acutely studies natural philosophy will realize thegreatness, intellect and kindness of the creator (God).”36

Rev Fish Green, an American missionary who established a medical mission atJaffna in the early nineteenth century observes that “omen, black-magic and such non-existent ‘sasthras’ had their sway over people unchecked and they caused havoc. Wepublish this book with the desire and intent to establish, Chemistry, the techniqueof classifying elemental matter instead of Rasayana, Astronomy instead of Jothista(astrology), True knowledge instead of ‘false education,’ and eradicate ‘superstition’in individuals as well as ‘in society’.”37 He refuses to even consider ‘Rasayana’ asan equivalent and admissible term in Tamil for ‘chemistry’ instead coins a new word‘Chemistham.’38

The Bhoomi Sasthram, by Rev Rhenius, considered to be the first science pub-lication in Tamil, states “to enlighten (native) Tamil” as its object of publication.39

The condescending tone is hard to miss. The missionaries saw the task of teachingnatural philosophy as a way to civilize the natives. The missionary Murdoch was bluntbut forthright, when he wrote to his family at distant Glasgow, “You ask about thetelescope that you sent me. It answers the purpose tolerably. I may mention that ithad considerable effect on the minds of youth in causing him to disbelieve Buddhism,as it showed the mountains of the moon and the satellites of Jupiter. This may, perhaps,surprise you. I have however only room to mention that the religion of the people isquite opposed to European geography and astronomy, and, consequently, if the latterare true, the former is false.”40

It can be evidently seen that, in the Tamil publications of the missionaries, thenatural philosophy was so construed as to challenge the traditional knowledge of thenatives or to elucidate the alleged corroboration of the newly revealed religion and thegospel by the truths of natural philosophy. Missionary Tamil publications on scienceduring the early nineteenth century highlighted the ‘superstitions’ of the natives pur-ported to wean away the heathen brethren from the path of ignorance and to lead themto the true knowledge. At the same time it was also an effort to establish a “connectionmade by reason, between Christian truths and empirical knowledge.”41

K N Panickar notes:42

Incorporation of colonial cultural elements was marked in the textbooks in the Indian lan-guages produced by the government, Christian missionaries, voluntary organizations and pri-vate individuals. These books both through diction and content guided the impressionable

36ibid, 11.37Green, F.: 1875, Chemistham, Nagercoil London Mission Press, Jaffna; in the preface to his book

‘Chemistham.’38In the periodical ‘Udyatharagai,’ Vol. I, Issue 1, the equivalent term for ‘chemistry’ is left blank by Fish

Green. He articulates this view explicitly in his work ‘Chemistham.’39Fr Rhenius: 1832, Bhoomi Sasthram, Church Mission Press, Chennai.40Letter of 8th June 1847, reproduced in Henry Morris, The life of John Murdoch, Christian Literature

Society, Madras, 1906, 20.41Studdert-Kennedy, Gerald: 1998, Providence & Raj; Imperial mission and missionary imperialism, Sage,

New Delhi, 64.42Panickar, K. N.: 1995, Culture, Ideology, Hegemony, Thulika, New Delhi, 129.


minds of young children to a cultural universe alien to their life experience. . . . This was notalways achieved through a dismissal or denigration of indigenous culture, but by locating thecultural ideals in the achievements of western society.

The dissemination of modern science by the missionaries had a close relationshipwith their spiritual mission of spreading the word of Gospel and was closely linked tothe mundane colonial project of ‘civilizing the natives.’ John Murdoch remarks that“. . . the aims of education are (1) to promote the temporal well-being of the people ofIndia (2) to elevate them intellectually (3) to raise their moral character.”43 Treating‘literature, philosophy and science as aspects of the one morally informed source ofauthentic knowledge’44 was a strategy of missionaries ‘to ground morality and socialbehavior in an analytical appreciation of institution, obligation and law.’45 TejaswiniNiranjana observes that “missionaries . . . functioned as colonial agents in the forma-tion of practice of subjectification, not only in their role of priests and teachers, butalso in the capacity of linguists, grammarians and translators.”46 Furthermore sheargues that the discourse on education, theology, historiography and literature by themissionaries was by setting up a series of opposition between tradition and modern,developed and underdeveloped, and this discourse informed the ideological structureof the hegemonic apparatus of colonial rule.

The colonial project is candidly unveiled in the report submitted by the DPI in 1868.The report, while attempting to explain the not-so-impressive record in productionand dissemination of literature in the vernacular, notes that “the substitution of newliterary books for those now possessed by the Hindus which have their roots in thepast history of the people, could only be effected very slowly”47 which clearly indicatesthe cherished hope that the European knowledge and western culture will replace theindigenous.

As the consequence of these colonial cultural intrusion, more strongly felt during thelatter half of the nineteenth century, natives organized cultural defences by creatingalternative cultural practices or by revitalizing the traditional institutions. The intel-lectual leaders were enchanted by modern science, especially its promise for materialprogress.48 Thus, in their endeavor to decolonize the educational system the nativesnever failed to “negotiate a space for the reception of science and technology from thewest.”49 At the same time, native intellectuals were also disenchanted with modernscience, especially natural philosophy, as this knowledge form not only had its origin inthe west, but was being used as a resource to deprecate native society. Eventually, asSabyasachai observes that “. . . however critical, the reception [of modern science] was,

43Murdoch, John: 1881, Education in India: A Letter to Rippon, Christian Knowledge Society Press,Madras, 42.

44Studdert-Kennedy, Gerald: 1998, Providence & Raj; Imperial mission and missionary imperialism, Sage,New Delhi, 64-65.

45ibid, 64.46Niranjana, Tejaswini: 1992, Sitting Translation, Orient Longman, 34.47Report of the Director of Public Instruction, July, 1868-69, Madras 1869, 59-60.48Raina, Dhruv & Habib, Irfan: 1996, The Moral Legitimization of Modern Science: Bhadralog reflections

on theories of evolution, Social Studies of Science, 26, 9-42.49Bhattacharya, Sabyasachi (Ed): 1998, The Contested Terrain, Orient Longman, New Delhi, 4.

Venkateswaran 331

inevitably on the agenda” of the intellectual class.50

4 Science by Natives During Late Nineteenth Century

Thought the (in)famous Maculays minutes, Woods dispatch and numerous other gov-ernmental reports advocated instruction in ‘European literature and sciences,’ the in-struction in natural sciences in vernacular schools were slow to materialize. Lack ofstandard textbooks, incapacity to teach science in other than English medium, lack oftrained teacher with adequate knowledge in science while at the same time ease withvernacular languages were presented from time to time as hurdles for instruction ofscience in the vernacular schools.

By 1870s there was a renewed craving for introduction of science in vernacularschool education. Native associations such as British Indian Association, missionary-educationist such as Murdoch as well as official government reports favoured introduc-tion of instruction in science at vernacular schools. The British Indian Association in itsmemorial to the Governer General lamented that “at present an acquaintance with thehigher branches of knowledge can be obtained only by a study of the English language,and it is this which presents the greatest obstacles to the general and rapid prorogationof useful knowledge in the country” and pleaded for education in vernacular languagesand also instruction in modern science.51 Murdoch in his ‘Letter to Lord Ripon, Viceroy’remarked that ‘instruction in natural science is a vexed question.’52 Director of PublicInstruction in Madras Presidency, Powell concurred that “it is unquestionable thateverywhere, the old curriculum of studies will have to make room for some new subjectscalculated to give a wider and a clearer view of nature and her laws, and to drawforth the powers of observation implanted in man, but hitherto left undeveloped inmost countries, and especially in India . . .”53 and that “ordinary education will haveto embrace such subjects as a general knowledge of man’s frame and constitution, theelements of physics.”54 But he cautioned hasty introduction of such subjects of studyin the lower schools and argued that observational and experimental science shouldnot just be an optional paper but a compulsory one in the university examinations likeFA and BA. Slowly, but inevitably, instruction in natural science was introduced andgaining ground in the scheme of studies prescribed for vernacular schools.

In no less measure efforts in promotion of science education as a part of generalpublic instruction was impelled by educational developments back home. The RoyalCommission on Scientific Instruction favoured that “instruction in the elements ofnatural science can be, and eventually ought to be, made an essential part of course of

50ibid51Memorial from the British Indian Association to the Victory and Governor General of India in Council,

Naik JP, Selections from Educational Records, Vol II, Development of University Education (1860-87),National Archives of India, New Delhi, 1963, 6-28.

52John, Murdoch: 1881, Education in India: A letter to his excellency the most Hon’ble The Marquies ofRipon, Viceroy and Governor General on India, CKS press, Vepery, Madras, 42.

53Cited in Satthianandan, S.: 1894, History of Education in the Madras Presidency, Christian LiteratureSociety, Madras, 93-94.

54ibid


instruction in every elementary school.”55 The committee on revision of textbook in itsreport recommended ‘encouragement of the study of Sanskrit and physical sciences.’56

The Secretary to the Government of Madras Presidency conceded to the recommenda-tion and requisitioned ‘the Director of Public Instruction to submit his proposal forintroducing elementary textbooks on the subject into the ordinary school course.’57

Educational Code of 1881 as well as Hunter commission of 1882 echoed similar viewsand elementary science education was incorporated into the school curriculum. Theseculminated in a new code for grant-in-aid, that required the lower primary class havetwo optional subjects and upper primary school four optional subjects among suchsubjects of instruction like object lessons, sanitation, agriculture and few other sci-entific discipline. To meet the new educational demand, text books in these areas wereproduced from 1880s.

The marginalization of missionaries from the vernacular textbook publication wasfurther accentuated by certain developments in the metropolis. With the ascendancyof scientific naturalism in England during the 1850s, the cultural competence of theclergy to comment upon scientific discipline was called into question and clergy werebeing relegated to the domain of the spiritual. Scientific disciplines such as magnetism,galvanism (Electricity), geology and thermodynamics constructed in Europe were fastdisplacing the traditional disciplinary boundaries such as natural history and naturalphilosophy. In the new dispensation the scientific authorities were not Butler or Paleybut Huxley and Spencer.58 Huxley’s series of science primers formed the basis forpreparation of textbooks in the vernacular in the Madras Presidency.59 Meanwhile, theparadigm of natural sciences were also undergoing sea change. Scientific naturalismwas replacing natural philosophy as the paradigm and subsequently, the object of thescience education itself got changed. Though the Huxley’s report still used the languageof ‘mental and moral’ improvement, as the object of scientific instruction, in deferenceto the then prevailing Victorian attitudes in England, goals such as, economical pros-perity and social improvement were also gaining accentuation.60

With the rapidly changing social order under colonialism, new professions wereopen for the modern educated natives and they constituted and articulated themselvesas the ’new middle class.’ Having received education in English language and culture,they commanded a new authority in the colonial ’political society’ these educated na-

55Cited in John, Murdoch: 1881, Education in India: A letter to his excellency the most Hon’ble TheMarquise of Ripon, Viceroy and Governor General of India, CKS press, Vepery, Madras, 46.

56Report of the Committee for the revision of English, Telugu and Tamil School Books in the MadrasPresidency, Government Gazette Press, Madras, 1874, 72.

57GO (Edl) Government of Madras, 338, No. 5-9, 3rd Oct 1874.58Paley William: 1802, Natural Theology: Or Evidences of the Existence and Attributes of the Deity,

Collected from the Appearance of Nature, the Woods Despatch of 1854 suggested it as a textbook.Furthermore Huxley is cited with acceptance in the educational reports emanating during 1880s, especiallyfor the preparation of syllabus for science.

59Committee of Madras School Book and Vernacular Literature Society invited person to prepare editedtranslation of primers edited by Huxley. Report on the public Instruction in the Madras Presidency 1873-74,Government Press, 1874, 94.

60For contemporary reponse to Huxley’s report and its implication for Indian Education see, John,Murdoch: 1881, Education in India: A Letter to Lord Ripon, CKS Press, Madras.

Venkateswaran 333

tives self styled as the ‘new middle class,’ sought made claims to the privileges and ashare of governance under the British political tradition. This emerging vernacularliterati, quite independently of their class and caste origins, were politically aware andactive as theorists, strategists, organizers and spokespersons on behalf of the emergingautonomous social group of incipient national bourgeois.

The Tamil Brahmin, traditional custodian of knowledge, seamlessly took advantageof modern education and the acquired benefits accruing out of it. Being the traditionallawgiver, he could exercise his pre-existing hegemony in the civil society through hiscaste status while his modern education gave him a new found authority in the ’colonialpolitical society.’61 As Aparna Basu notes, along with the Bengali Bhadralok and theChitapavan of Maharastra, it was the Tamil Brahmin who assumed political hegemonyin the respective provinces.62 While the Tamil Brahmin retained his devotion to San-skrit, on the other hand he was also a promoter of Tamil so as to hegemonize othervernacular languages of the Madras province. Hence, among the vernacular languagesof the Madras province, Tamil was the forerunner. In addition another social groupthat forged a self identity of ‘Saiva Vellalars’ (which included caste groups such asVellalars, Mudaliars and Chettiyars) were also acquiring new status and power withinthe colonial set-up.63 As Sabyasachi Bhattacharya notes ‘contest between nationalismin education with the colonial state (was) inseparably intertwined historically withthe contest for hegemony within the colonial society’ and during the late nineteenthcentury most of the educated vernacular literati organized themselves into variouslocal socio-political organizations associated with educational service.64

The emergent forums were usually styled as ’scientific and literary societies.’ Read-ing rooms, societies for debates and organizations championing for educational ad-vancement as well as social reform were instituted in many provincial towns. As arepresentative of these movements, the Villupuram Literary Society in 1882 and theVillupuram Educational Society in 1885 were initiated with the objective to “discussliterature and science subjects and for educational and social reform.”65 At the turn ofthe century there were more than 100 such societies and reading rooms in variousprovincial towns of the Madras Presidency. In these societies ‘irrespective of theirreligious persuasion, Indian intellectuals found in science a neutral pursuit that was tobecome a common meeting ground and serve as a means of articulating counter colonialpolitical stance,’66 and as K.N. Panickar observes being conduits for the dissemination

61MSS Pandian: 1996, Towards National Popular, ntoes on self-respecter’s Tamil, Economic and PoliticalWeekly, Dec 21, 3323-3329. See also Arooran, K Nambi: 1980, Tamil Renaissance and the Dravidiannationalism 1905-1940, Kudal Publishers, Madurai.

62Basu, Aparna: 1974, The growth of education and political development in India 1898-1920, OxfordUniversity Press, 232.

63See Irschik, Eugene F.: 1969, Politics and Social Conflict in South India—the Non-Brahman movementand Tamil Separatism 1916-1929, University of California Press; also Washbrook, D. A.: 1976, TheEmergence of Provincial Polity—The Madras Presidency 1870-1920, Cambridge University Press

64Bhattacharya, Sabyasachi: 1998, The Contested Terrain, Orient Longman, New Delhi, 6.65Tirumizi, S.A.I.: 1989, Scientific Associations in British India, NISTADS, New Delhi.66Habib, Irfan & Raina, Dhruv: 1989, Introduction of Scientific Rationality into India, a Study of Master

Ramachandra-Urdu Journalist, Mathematician and Educationist, Annals of Science, 46, 597-610.


of colonial ideology, these institutions provided a useful platform for intellectual ex-change.67

Even as early as 1850s, educated literati of the Madras Presidency formed their ownsociety for the production and publication of vernacular textbooks. Madras UpayuktaGranda Karna Sabha (society for production of useful books) was established in 1847,by the former native students of the Madras University, for the specific purpose ofproduction of vernacular textbooks. This society was active for few years, and manyof their textbooks were also used by the government and government aided schools.Following the implementation of the new scheme of studies, that made compulsory forall schools receiving grant-in-aid from the government, to use only government ap-proved textbooks, even many a vernacular missionary school resorted to use of govern-ment textbooks, rather than those published by the CVES.68 Meanwhile, in 1870s theMadras School Book Society found in 1820 was refurbished as Madras School Book andVernacular Literature Society and was activated for the production of textbooks andvernacular literature. This society, though received the patronage of the government,had its own management committee, in which over a period of time natives came todominate.69 Having got the institutional space and the required cultural competencythrough higher education, natives could by late nineteenth century lay claim to beacceptable professional expert to dispense and purvey scientific knowledge.70 The edu-cated native expert could now legitimately unseat the missionary ‘expert’ in productionof textbooks in vernacular for school education.

With the persistent demands made by natives as well as missionaries, though withdiverse purposes, by the1880s, science was introduced into the elementary education asa subject of study. This necessitated textbooks in Tamil. Initially, textbooks, were morea handbooks for teachers in elementary schools than textbooks for direct use by thestudents. The textbooks were styled as ‘nature readers’ consisting of ‘object lessons,’and were in the paradigm of ‘Scientific Naturalism.’ Drawing upon the ideas of Huxleyand Tyndall, these works eschew anthropomorphism, anthropocentrism, and teleologi-cal views of nature. These books emphasized empiricism and scientific rationality. Thefollowing are representative titles published71 at the turn of the century that exemplify

67Panickar, K.N.:1995, Culture, Ideology, Hegemony, Thulika, New Delhi, 88-89.68Murdoch laments that the sale of CVES books have fallen off considerably and investigating the reason

for it, it was found that in schools receiving grant-in-aid, teachers prefer to use the government textbooks,and this trend was noticed even in the boarding schools of the missionaries. John, Murdoch: 1982, Educationas a Missionary agency in India—A letter to the Church Missionary Society, Caleb Foster, Vepery, Madras.

69The members of the managing committee of the society in 1895 were: Mr Abdur Razak Sahib,Mr Bilderbeek, Mrs Brander, Mr Krishnamachariyar, Mr Bangyya Chettiyar, Revt Sell, Mr SeshagiriSastriyar, Mr Staart, Mr Tamotharam Pillai, Mr Velupillai, Mr P Vijayaranga Mudaliyar.

70Note that most of the native authors were college professors, school headmasters, educational officials orother professionals.

71See the following catalogues for a full list of textbooks produced and used during the late nineteenthcentury: ‘Madras State Bibliography of books 1867-1900’ Tamil Development and Research Council, Volumespublished in 1961, 62, 63 and 64; ‘Madras State Bibliography of books’ for the years 1911-15 and 1916-20published respectively in the years 1974/77, and 1978; ‘Classified catalogue of the Public Reference Library’1867-89, 1890-1900, 1901-10, 1911-15, 1916-20, 1921-25 published respectively in the years 1894, 1961,1964, 1965, 1971.

Venkateswaran 335

the process of replacement of ‘natural philosophy’ by ‘scientific naturalism.’

• A. Periyanayagam, Bhouthiga Pustagam, 1903.

• Diwan Bahadur Krishnamachariyar, Nature reader, 1904.

• V. Koli Pillai, Elementary Pada Rathinangal—Prakurithi, Mulathava RasayanaSasthrangal 1910.

• V.K. Narayanasamy Iyer, Iyarkai Porutpadam, Vol I and Vol II, 1910—for elemen-tary school teachers.

• A. Sivaprakasa Iyer, Tavara Sastra Vina Vidai, 1910.

• B. Narayanasami Iyer, Practical lessons in science and geography [Vol I & II]1914/15.

• J. Viswanathiya, Tavara Nur Churukam for kindergarten and primary classes—1912.

The Nature Readers72 by V Krishnamachariar, an active member of the SPCA (So-cieties for Prevention of Cruality to Animals), and also once the secretary of MSB &VLS, had the following lessons related to natural sciences: Morning light, the moonand stars, sunshine and shadows, homely talk about animals and deeds of kindness[our cow, the sheep, the stag, the horse and so on . . .], air around us, plants and flowers,frog and duck, debate between the wind and the sun, seaside scenery, coconut tree, cartand cycle, the Palmyra tree, the Banyan tree, a sparrows nest and birds house.

Samuel V Koil Pillai in preface to his book titled “Civics, Nature Study and Elemen-tary Science” states that “nature study—i.e., physics and chemistry—should be thoughtin such a way so as to use drawings and easily available equipment to demonstrate andby encouraging analytical approach by observation . . .”73 The first part of the book wason Civics. The second part was on ‘Nature study and elementary science.’ The secondpart had the following chapters: Botany [consisting of 14 lessons] Zoology [Consistingof 24 lessons] Geology, Meteorology and Minerals [consisting of 34 lessons] the thirdpart of the book was devoted to ‘health and temperance.’

In his book titled ‘Nature Study,’ V.K. Narayanasami Aiyar observes “this subjecthas been only recently introduced into the curriculum of studies . . . and it is not likelythat most elementary school teachers will be able at present to deal with the subjecteffectively and intelligently . . . It is mainly with a view to give a sort of guide tothe elementary school teachers [that this book is published]”74 This book “suppliesmaterials for giving a course of lessons on (1) plants and animal life (2) the surfaceof the earth (3) the simplest physical and chemical phenomena . . . for giving them an

72Krishnamachariar, V.: 1905, Nature Readers, Madras, Preface iii-v.73Pillai, Samuel V Koil: 1912, Civics, nature study and elementary science, Kalaratnakaram press, Madras,

v-vi.74Aiyar V. K. Narayanasami: 1910, Nature Study, I and II, Ananda Steam Press, Preface i-viii and 1-5.


idea of climate, products etc., of their places and for enabling them to understand theimportant rule of health and sanitation.”

Subsequently, by 1920s the textbooks were cast in the modern disciplinary frame-work of Natural sciences, and are so arranged to contain sections on physics, chemistryand biology. A representative list of textbooks of this genre is:

• K. Dooraisamy Iyengar, Iyarkai Sasthram, 1920. This book contained lessons onphysics, astronomy geology and so on.

• B. Narayanasamy Aiyer, Practical textbook for science and geography. This bookhas eight sections with 44 lessons. The sections are: Earth, Wind, Atmosphere,Sky, health and sanitation and so on.

• R.C. Kasthuri Rangaiyar, Iyarkai Arputhangal, 1911.

• V. Krishnamachariyar, Iyarkai Porut Padam, 1920.

Discipline specific textbooks, such as on botany [for illustration see R. Gopala IyersJeeva-Vargam]75 and on zoology commence to appear by 1920s. Also from the prefaceand other notes in these text books one can gather that these books were no longer‘guides’ and ‘aids’ for teachers but were ‘proper school textbooks’ (in the modern sense)to be used by students for self study and instruction.

A detailed examination of the science textbooks in the nineteenth century divulgescertain trends. Modern science, as the colonial government and the missionaries in-troduced it, located the achievements of sciences in European cultural ideals. In thecolonial and missionary literature science was frequently and habitually referred to as‘European science’ or ‘European knowledge.’76 The natives too used the same idiom,77

but from the late nineteenth century subtle chances could be noticed, and more often,science was prefixed with (naveenam) ’modern’ rather than ’European.’78 These andother cultural codes inscribed in the modern science transmitted from the metropolishad to be removed or at least blunted. To receive modern science into his cosmos, theTamil intellectual had to first universalize science.79

It is with this intent that Sivachidampara Iyer argued:80

75Iyer, R. Gopala: 1924, Jeeva-Vargam, Part I, Mc Millan & Co., Madras.76One needs only to just glance to the education reports-often the reference is to European science or

knowledge. See the writings of Murdoch for the illustration of missionaryio usage.77See for example the mast of the periodical Arivu Vilakam published since 1901, that the magazine will

publish articles on ‘Indian Philosophy, English (Western) philosophy, English natural sciences, religioustruths . . .’

78As Panickar notes there was no articulated debate on the suitability of the use of the expression ‘Westernscience,’ however one can hardly fail to notice the use of neutral expressions such as ‘Natural science’ or‘modern (naveena) science’ in the popular Tamil publications from about the 1900’s.

79Universality of science was taken for granted by the Indian intellecutals. They did not face the questionwhether science was ‘western’ or ‘new’ as in the case of China. About 1640 there was a discussion in Pekingas to whether the new science were primarily or primarily new. The Chinese objected to the word ‘western’used by the Jesuits in the titles of the scientific books which they wrote and translated. They insisted thatit should be dropped in favour of ‘new.’ Panickar, K. N.: 1995, Culture, Ideology, Hegemony, Thulika, NewDelhi, 10,ff.

80Iyer, Sivachidambara: 1906-07, Arivu [Knowledge], Sentamil, 5,, 330.

Venkateswaran 337

Few psychologists maintain that every one is not endowed with rational capacity and thatthe rational capacity of a person depends upon his race. While this claim cannot be totallyrejected the assertion can not be accepted. telegraphy, steam engines and such other wondermechanisms evident the intellect of the inventor and not manifest their race or social status.

Another intellectual, Ramaiyar81 argued that the discoveries are validated not bylooking at the race or colour of the discoverer but by proof (presented by him) andfurther asserted that the “[usage of] expressions such as ‘Eastern science’ and ‘Westernscience’ are to be rejected.”82 Tamilar Nesan, a monthly science magazine launchedby native intellectuals, argued, knowledge about means of earning a living may varyamong people and depend upon their profession. All the rest of knowledge is commonheritage of all—from sweeper to a lord; [this knowledge] is essential for every one; andby striving every one can acquire this knowledge.83 Similar sentiments to universalizeand legitimize modern science can be noticed in the writings of natives.

Sashtra Vichitram or Wonders of Science was a popular book by M. Natesan.84 Asthe title—Vichitram—indicates, modern science is visualized as ‘strange’ and ‘queer’sasthram (science). A glance at the various articles in the Vidhya Varthamani, a Tamilperiodical devoted to education published since 1897 reveals the allusion to ‘wonder,’‘strangeness’ and ‘oddity’ of the modern science. The allusion to the ‘strangeness andoddity’ of modern science during this period is palpably obvious from the title of theTamil periodical ‘Vinodha Vichitra Patrikai,’ published since the 1900s to popularizescience.

Thus it can be argued that the natives reasoned the notion of ‘modern’ as ’novelty’—something new. Naveenam, the expression used in Tamil to denote ‘modern’ also im-plies that which is ‘novel,’ ‘new.’ The telegraph, steam engines and such other modernartifacts, and the emerging knowledge about Nature such as electricity, magnetism,and so on, fascinated the imagination of the natives as being novel and new.85 Inthe writings of the natives during the late nineteenth century, one can hardly failto notice the use of words such as Vinodham and Vichitram (wonder, strange, queer,oddity) while referring to modern science. Through the metaphor of ‘novelty’ the alienknowledge was legitimized in the native cosmos.

‘That which belongs to the present’ is also suggested at by the expression ‘naveenam.’The usage such as Naveena Ulagu (Modern world) implies an understanding of ‘hereand now.’ This case is well illustrated by the writings of Ms M. Lakshmiyammal,a regular columnist in Tamilar Nesan. While translating the article ‘The future ofEconomic and Scientific Thought’ a speech by Prof. Soddy, the article in Tamil was titledas Eni Pzhaikum Vazhi (The way to prevail henceforth)—that is, the modern science

81Ramaiyar: 1923-24, Civilization and Progress, Tamilar Nesan, VIII, 250-60.82ibid83Editorial: 1917-18, Namadhu Sangam, Tamilar Nesan (in Tamil), I, 1-9.84Natesan, M.: 1888, Sastra Vichitram or wonders of Science, VN Jubilee Press. The book contains science

activities and simple elementary scientific principles, which were published as a serial in the periodical,‘Viveka Chinthamani.’ The book was reprinted in 1902 and again in 1913. The popularity of this book couldbe gauged from this.

85Fascinated by the novel devices being invented, Vaidyanatha Iyer composed books on Submarine (2ndEd 1914, 3rd Ed 1915), Airship, Airplane (1915), Telegraphy and so on.


is construed and presented as ‘knowledge required for the present age.’ In this articleshe argues (in addition to stating the views of Prof. Soddy) that material progress andmoral progress are not necessarily antithetical. Recourse to ‘modern knowledge’ isthus justified by the logic that ‘modern science is the knowledge of today and hence onecannot flee from it.’

This temporal logic—that the ‘modern’ ensue after the ‘ancient’ is also effectivelyused to legitimize modern science without always necessarily needing to be contriteabout traditional knowledge forms. For now the natives could argue that the ‘past’ issuperseded, besides the present is different from the past and hence each can haveits own rational; but only that these rationales are different. The rhetoric of temporallogic also assisted the natives to overcome the colonial rhetorical demarcation betweentradition and modern. The traditional knowledge can thus be safely located in thepast—as ancient science, and the modern could be legitimately assimilated into thenative cosmos.

In this discursive strategy, the idea of ‘progress’ and ‘evolution’ came in handy forthe native intellectuals to insulate traditional knowledge forms as well as legitimatelyassimilate modern science. Knowledge was now seen as an ever growing, evolvingentity. Tamilar Nesan averred that “knowledge is not unchanging . . . but evolves . . .”and further it contended that “. . . if we do not revitalize our traditional knowledge andat the same time assimilate modern knowledge, which at present is lacking among us,we would not be able to progress . . .”86

V.K. Narayanaswamy Iyer elucidated that “(our) ancestors held five elements [Pan-cha Bhoothams]—Prithvi (Earth), Appu (Water) Theyu (Fire) Vaayu (Air), Agasam(Sky) to be the basic elements and that all the created materials are composed ofvarious combinations of these five basic elements. However, chemists maintain thatfire and sky have no mass (weight) and also that fire is an energy dependent on matter.Therefore we shall look at the chemistry of the other three Pancha Bhoothams—Air,Water and Earth.”87 This work is a typical exemplar of the genre that placed andpresented the modern science in the frame work of the traditional categories. Thechapters of this textbooks are classified as Air, Water, Earth, Fire (heat) and sky(about natural phenomena, weather and so on). Ekambaranathaiyar, in his articleon poisonous snakes makes a remark on the traditional treatise ‘Chitraduram,’ beforeembarking to detail the modern antidotes and remedies for snakebites. He adducesthe Chitraduram as an ‘ancient adage.’ Lakshmiyammal in the article on bacteriologyrenders the word (concept) immunity as ‘Vaishnava Shakthi’ in Tamil. In his work‘Bhoogola Vasaga Pusthagam’88 (Geography reader), S.K. Divasigamani, observed that‘knowledge comes by open-eyes and working hand’ and that . . . in the lessons on thesun, the moon and the stars, the facts are so explained as to enable the children tounderstand something of Hindu ‘Panchangam,’ thus to bring them in close relationto the life they have to lead . . .. The textbook ‘Vaana Sashtram (astronomy)89 by

86Nesan, Tamilar: 1917-18, Namathu Sangam, I, 1-9.87Narayanaswamy Iyer, V.K.: General Elementary Science (in Tamil), 4th ed., 157.88Divasigamani, S.K.: 1925, Bhoogola Vasaga Pusthagam, Macmillan & Co., Madras.89Iyer, Balakrishna: 1913, Vaana Sasthram, Hindu Educational Trading & Co., Kumbakonam. Note the

Venkateswaran 339

Balakrishna Iyer elucidates the rational behind the ‘Panchangam’ besides providing anintroduction to modern astronomy. These are in striking contrast to the representationof the tradition in the hands of the colonialist, who paints it habitually as ‘superstitious’or at the least superfluous beliefs indicative of the mental and moral depravation anddecadence of the indigenous culture. In contrast, in the narratives of the natives,traditional knowledge form is neither deprecated nor eulogized, but is presented asknowledge of the past. The repertoire of colonial binaries,90 tradition/modernity; civi-lization/barbarism, is thus subdued by the natives in the narratives contained in thetextbooks authored by them.

The translation theory anticipates cultural ‘refraction’ in the act of translation, andthe way certain concepts of Duncan’s geography primer were re-rendered into Tamil isilluminating. While George Duncan in his original English version states that

Hindus hold the water of the Ganges sacred from Gangothri (Ganga Avatari) . . . however,particular portions (are) held more sacred than the rest, to which pilgrims resort from all partsof India to perform their oblations and to carry of the water to be used in future ceremonies . . .

However, J.M. Velupillai a native intellectual translating the same book into Tamilfor use in the schools states that91

the following six rivers dry up in summer, nevertheless, (rivers) originating in Himalayas muchflow will be there during the summer than in the other three seasons . . . among this there is noother river as useful as Ganges . . . (Ganges) flows through thickly populated regions . . . Maybe it is due to the immense benefit accruing to the people, that Hindus hold (Ganges) as sacredwater.

Thus it can be clearly seen that even translation was not just mechanically render-ing what is in the source language into the target language, but an act of re-rendering,and a kind of cultural translation. The process of drift, invention, mediation, and attimes even fabrication of links that did not exist before, form some of the repertoire ofnarratives adopted by the natives to render modern science as legitimate within thecultural cosmos.

5 Summary

Shapin92 suggests that diffusion of scientific knowledge across boundaries—betweencountries, between town and country, between social classes—should be seen as politi-cal and a logistical problem. Transmission of knowledge between the colonial metropo-lis and the colonized province, especially in the context of colonialism in the nineteenthcentury Tamil Nadu provides an interesting location for study.

If the instruction in modern science through vernaculars was not shown same en-thusiasm as that of spread of European literature by the colonialists, the prevailing

name of the publishers.90Sing, Jyotsna: 1996, Colonial Narratives; ‘Discoveries’ of India in the Languages of Colonialism,

Routledge, 8.91Velupillai, J.M.: 1813, Bala Bhotha Boogola Sasthram, (Original by Duncan), CKS press, Madras, 10.92Shapin, Steven: 1982, Nibbling at the teats of Science; Edinburgh and the diffusion of science in the

1830s, in Ian Inkstar and Jack Morrell (Ed.), Metropolis and Province, science and British culture 1780-1850, Hutchinson, 151-178.


Victorian ideology may have had a role, but the view that modern science is difficult toconvey through the vernaculars was entrenched among the colonialist and the educatedelite that even while addressing a memorial to the Viceroy for instruction on modernscience through the medium of vernaculars, the British Indian association admittedthat instruction of higher standard is not feasible in vernacular.

Thus, during the first half of the nineteenth century even while the instruction inEuropean literature and science was proclaimed time and again instruction in sciencewas scanty, that the Madras Mail, a daily English news paper lamented that: “Aman may become a Master of Arts in Madras, without knowing why apple falls tothe ground, where rain comes from, what is the meaning of a burning stick, why hehas to breath constantly, or what sun means by occasionally disappearing at incon-venient times.”93 Nonetheless the topics on natural philosophy and natural historythat was found in the textbooks were embodied with natural theology. Before the1880s most of the titles of science textbooks published were in the idiom of ‘NaturalPhilosophy’ and were primarily about basic principles of natural philosophy, astronomy,natural history and geography/geology and further as noted earlier, authored mostlyby missionaries. The books on astronomy were contrasted with astrology and invari-ably contained arguments about the popular belief about the eclipses.94 The bookson geology/geography argued the alleged evidences of the Christian Truths and wereafflicted with the Paleys Evidences.95 In the paradigm of ‘natural philosophy’ duringthe early nineteenth century, the ideology of Europe as the ideal was being promoted,while traditional knowledge forms were being threatened and marginalised. As JulianMartin96 notes “natural philosophy was never a socially disengaged, purely intellectualactivity and natural philosophical pronouncements were believed to entail assertionsabout the political order.”

The colonial educational programme was seeking to hegemonise and dominate incultural terms, the native society. The Macaulayan flourish of ‘Indian in blood butEuropean in taste’ was not an accidental slip, but the general urge. Thus the ‘colo-nial subject’ was the ideal of education. The native intellectuals were not passive tothese colonial maneuvers, but were actively engaged with the modern science beingintroduced into colonial Tamil society as part of the colonial subjectification, duringthe nineteenth century. There were a host of historical factors that contributed to thenatives acquiring determining role as purveyors of knowledge in the Tamil society evenunder colonialism. In this process of reproduction of knowledge the native intellectualswere also ‘producing’ knowledge forms suited to their cultural and political require-

93A plea for physical sciences in our school and universities, Madras Mail, 4th March, 1874.94Christian Vernacular Education Society, Graganangal Yerpadum Kararnangal, 1880; challenges the

traditional Hindu popular mythological belief on Rahu and Kethu being the cause of Eclipse and provides‘scientific’ explanation to the eclipse. Christian Vernacular Education Society, ‘Pagola Sasthramum JothistaSasthramum,’ 1891 aims to show ‘belief in Jothista Sasthram leads to calamity.’

95Christian Vernacular Education Society, Yerimalaigalum Bhoomi Atherchiyum Sristipin Athisiyan-galum, 1894; clearly alludes to the ‘biblical creation’ and justification of Genesis based upon ‘theory ofgeology’ as understood at that period.

96Martin, Julian: 1991, Natural Philosophy and its public concerns, in Stephen Pumfrey etal., (Ed), inScience, Culture and Popular belief in Renaissance Europe, Manchester University Press, 116.

Venkateswaran 341

ments.Due to the policy changes prompted by the Woods Despatch and the recommenda-

tions of the Hunter Commission, elementary education was spread in its reach in theMadras Presidency and was progressively placed under private management. Whilethe native intellectuals were not able to completely recast the colonial policies in theeducation sector, they could exercise a significant influence. With native intellectualsacquiring education in English and modern science, the monopoly of missionaries inprinting and publication was disputed. By occupying a preeminent position in theMadras School Book and Vernacular Literature Society, the natives sought an insti-tutional base for challenging the missionary monopoly of production of vernaculartextbooks. When textbook publication was liberalized (but with government retainingits power to scrutinize and approve), the natives published textbooks from their nativeprinting houses as well. Thus, by the turn of the century, the native intellectuals almostdisplaced the missionaries from the textbook production scene. Gradually the nativeintellectuals entered into publication and printing.

Native intellectuals, besides being educated in modern science were also the tra-ditional elite of the society, and had to come to terms with the modern knowledge;but the modern knowledge was being transmitted by the colonial system with westerncultural codes. Having got a determining role in the production of textbooks, the nativeintellectuals, through the process of translation and composition of vernacular text-books, divested modern science of its western cultural meaning. In the process, modernscience was not only neutralized but also ‘domesticated’—that is, native intellectualsredeemed whatever was salvageable from the traditional knowledge systems. Eventu-ally the natives endeavored rendering modern science into the vernacular languagesand, in the process, reconfigured and domesticated modern science.

The dislodging of the European missionaries was further hastened by the shiftin knowledge form taking place in Europe. Scientific naturalism was fast replacingnatural philosophy, and clergy were being restricted to ecclesiastical domains and theircompetency in ‘scientific’ domain being questioned. At the turn of the century, thenative intellectuals who had by then acquired the ‘right’ professional higher educa-tion could claim to be more competent to compose science textbooks, rather than themissionaries or colonial officials.

Through the process of translation, by establishing a series of transit points, thenative intellectual was attempting a trans-cultural conceptual bridge building. Therhetorical repertoire of naveenam as ‘novelty, here-and-now, of-the-present’ was de-ployed to mollify the colonial binary of the traditional and modern. In the age ofnationalism when science came to be the measure of progress achieved by the nation, byconjuring up a civilization and by salvaging parts of the past, the native intellectualswaged a symbolic war. This study also confirms the conception put forth by DhruvRaina that the role of the history of science, in purveying of science, was one of es-sentially ‘lamenting the loss of golden past’ and a ‘battle-cry for a resurgent India.’97

97Raina, Dhruv: 2000, Lamenting the Past, Anticipating the future: A chronology of popular sciencewriting in India (1850-1914), in Narender K Shegal etal., (Ed), Uncharted Terrain—Essays on SciencePopularisation in Pre-independence India, Vigyan Prasar, New Delhi.


Thus, through the process of science textbooks, the native Tamil intellectuals wereinventing a space for articulating a counter colonial perspective during the nineteenthcentury. The reception of the modern science by the natives was not passive andonce they obtained space for inscribing their ideology in the textbook, they utilizedthe opportunity. However, this study clearly shows that the reaction of the native toreject modern science as unsuited to our culture or take a revivalist position were rareduring the nineteenth century.

In conclusion, following, Roger Cooter and Stephen Pumfery “scientists, sciencecommunicators and audiences define their relationship to something called science and. . . that (the) relationship is embedded in the particularities of their different cultureand ideologies,”98 it is contented that, as textbooks have a crucial role in shapingthe dogmas of the period, aside from seeing the efforts of the native intellectuals asreproduction of ‘modern science,’ it should also be viewed as ‘production of ideology.’99

98Cooter, Roger & Pumfrey, Stephen: 1994, Separate spheres and public places; reflections on the Historyof science popularization and science in popular culture, History of Science, XXXII, 237-67.

99Ideology in the sense of ‘the imaginary relationship of individuals to their real conditions of existence.’

Index

a priori, 118A.F. Chalmers, 58A.J. Ayer, 76A.K. Biswas, 40A.P. Shukla, 41, 42A. France, 48A. J. Harrison, 204AAAS, 112, 317abiotic, 311abstract

concepts, 316concepts and operations, 303cosmological picture, 178concepts, 294theories, 316

abstraction, 283Abul Fazl, 259academic chemist, 204academic historians, 199acceleration, 289acid-base theories, 280acidic, 198acidic principle, 198Adam Schall, 236Adas, 54Advaita Vedanta, 258African-American Baseline Essays, 53Afrocentrism, 116ahistorically, 198AI, 98al Farabi, 241al Ghazalı, 257al Haitham, 241al Hajjaj, 241al Kindı, 241al-Hayatham, 238Ala Samarapungavan, 167Alan Sokal, 85, 116Alessandro Volta, 333Alexander, 243Alexandrian school, 180Algebra, 262algebra, 280alkaline earths, 282Almagest, 243alphabet-numeral system of notation, 229Alternative

frameworks in electricity, 289alternative

conceptions, 292

frameworks, 289, 291, 296alternative framework

origin, 292American Indian Science and Engineering Soci-

ety, 53American Universities, 39Amitabh Ghosh, 40Analytical

Sciences, 312analytical

arguments, 207Ananda K. Coomaraswamy, 42anatomy, 309ancient philosophies, 305Anderson, 4Andrew Ross, 116antagonism, 115antagonists, 199Antanio Favaro, 175anthropology, 167anti-Aristotelian way, 178anti-dogmatism, 331anti-evolutionism, 115anti-foundationalist, 104anti-intellectualism, 21, 86anti-racist, 211anti-racist mathematics, 211anti-realism, 71anti-realist, 58anti-reductionism, 62anti-science, 21, 116antiscientific views, 5Antoine Lavoisier, 198Apastamba, 225Apollonius, 214, 243Arab and European mathematics, 229Arab mathematics, 214Archimedes, 175, 179, 214, 242areas of physics, 204Aristotelian, 163, 181

causality, 48conceptual scheme, 175dynamics, 29logic, 257Scholasticism, 46view, 175world-view, 176, 177

Aristotelian science, 185Aristotelianism, 46

Aristotle, 175, 178, 192, 242, 243, 249, 250, 257,261, 267

thesis, 183Arithmetic, 262arithmetic, 209Arnauld, 76Aron, 291, 295Arthur Kornberg, 113artificial intelligence, 98Aryabhata, 221, 226, 251Aryabhatiya, 221, 226, 230Aryabhatiyabhasya, 231Ashmore, 106Asian and Afro-Carribbean origins, 211ASPEN 1991, 289astrology, 105Astronomical, 47Astronomy, 46astronomy, 46, 169, 228, 286Atmospheric Science, 303atomic

nature of matter, 314structure, 280theory of structure, 281

atomic physics, 43atomic structure, 281Atomism, 46Atomists, 179atoms, 199, 206, 279, 284, 334Augustine, 245, 258Augustus De Morgan, 237authoritarian, 135, 331authoritarianism, 331autonomy view, 97Avogadro’s hypothesis, 281axiom, 255, 266axiomatic

approach, 262method, 253, 262, 263, 266, 268, 269

axiomatico-deductive, 262axiomatization, 261, 268Axioms, 253axioms, 255, 259Ayurveda, 305

BAAS, 209Babylonians, 253Bacon, 48Baconian empiricism, 47Baghdad, 213balance of forces, 103Barber, 54Barnes, 77, 95Basalla, 54Baudhayana Sulbasutras, 252

Baudhyana, 225Baudrillard, 104Beardsley, 4beginning of science, 305behaviour

atoms, 202ions, 202molecules, 202

Behaviourism, 97behaviourism, 97, 98

psychology, 97behaviourists, 97Behrens, 54beliefs, 312Benjamin Peirce, 268Benoit Mendelbrot, 126Benseghir and Closset, 291Berkeley, 71, 76Berkeleyan idealism, 72Berlin, 54

museum, 216Bernal, 246Bertrand Russell, 5, 23Bhaskara-I, 221, 226Bijaganita, 222biochemistry, 282Biogas, 314biological

condition, 202science, 309

Biology, 303, 312biology, 204, 286, 311Biosphere, 312biotic factors, 311Birkhoff, 245, 250Birkhoff ’s axioms, 255Bishop, 112, 115Bishop Auerilus, 244Black-Body radiation, 31Blacks in Science: Ancient and Modern, 53Bloor, 77, 89, 91, 94–98, 103Bloor & Barnes, 55Bolyai, 266bonding, 279Boorse, 95Boster & Johnson, 54botany, 286Bown, 4Boyle, 206Boyle’s law, 135, 332breast-feeding, 304Brethren of sincerity, 48Brown, 293Browne, 116Bruno Latour, 116

Bucky ball, 208Bucky balls, 196Buddhist, 259

and Jaina traditions, 255Burtt, 61, 119Byzantium, 241

C.P. Snow’s, 196Cairo, 213calculus, 225

algorithms, 225differential,, 238

calendars, 312, 313Caliph al-Mamun, 241Caliph al-Mansur, 241caloric

thermodynamics, 29carbon

chemistry, 282rings, 282

Cardinal Bellarmine, 94Cardona, 239careers

science, 323science and technology, 326

Carr, 42Cartesian, 76

purpose, 268approach, 269dualism, 72epistemology, 72model, 72split, 47

Case Study, 163categorical

thinking, 184view, 178

cattle and birds, 314causal view, 96causality, 61, 96

Aristotelian, 48order, 61

causation, 61Cavalieri, 239celebration of science, 111, 117celestial bodies, 304cell structure, 310central science, 204centrality of science, 125change, 165characteristics, 304charge/mass ratios, 281Charles Darwin, 54Charles Eliot Norton, 41Charles Whish, 226

CHEMStudy, 280–285study, 203Study program, 279Study Story, 281

CHEM Study, 279, 281, 282Chemical

Education, 200synthesis, 207, 208

chemicalanalysis, 209bonding, 280, 281composites, 206compounds, 281concept, 205, 207constituent, 198contexts, 201curriculum, 209education, 196, 200, 201, 203, 205, 207element, 206elements, 206equilibrium, 206facts, 204industry, 202knowledge, 202, 287phenomena, 205philosophers, 206philosophy, 206processes, 280reactions, 280species, 205substance, 198synthesis, 208

chemical educationaim, 200

Chemical Education Material study, 279chemical knowledge

applications, 202Chemistry, 285, 303, 312chemistry, 44, 46, 200, 202–204, 206, 207, 279,

280, 282, 287, 311, 335aims, 204citizens, 201courses, 203, 205educators, 201environment, 282instruction, 203laboratory, 283learners, 203physics, 206solar system, 282textbook, 284

chemists, 201, 203, 206, 207chemists and scholars, 204Chiappetta, 332

Chiappetta et al., 319child psychologist, 286children’s theories, 167China, 213Chinese, 253Chinese encyclopaedia, 42Chinese science, 61Chiu Chang Suan Shu, 237Chomsky, 97, 104, 106Chou Pei, 218Christian rationalists, 260Christian science, 62circuit diagram, 291cis-trans isomerism, 281citizen, 209clashing current model, 289, 290classical approach of teaching, 296classical Greek, 214classical Greek mathematics, 214classical Greek tradition, 242classical view of realism, 117classification, 308, 316classification and manipulation, 307classification and taxonomy, 286classification of forms of life, 303classification system, 286classroom

teaching, 211Claudius Ptolemy, 243, 244Clement, 289, 293Cleopatra, 243clinical interview, 167Clothing, 312CMS, 302–307, 309, 312, 314–317

curricula, 306education, 315

CMS curricula, 307, 309Cobern, 60, 61Cobern & Aikenhead, 118Cobern, Gibson & Underwood, 124Cognitive

Science, 133, 163science, 137, 165

cognitiveconflicts, 175developmental research, 165entity, 159psychologists, 178revolution, 98science, 98structures, 76, 328turn, 154

Cognitive-historical, 164cognitive-historical, 137cognitively, 57

Cohen, Eylon and Ganniel, 290Colebrooke, 237Collingwood, 61Collins, 21, 86, 98, 99colloquial positivism, 117colonial

science, 209common

laboratory procedures, 202common domestic equipment, 315Common Man’s Science, 302, 303, 315, 316common notions, 264community of science, 62community- and context-specific, 302community-level, 307compound, 198, 206, 208compound nature, 198compound nature of water, 198compounds, 204, 206comprehension, 327computer science, 41concept

of resistors, 290charge, 295common man’s science, 316convergence, 232current, 291, 296formation, 309fundamental, 206limit, 237map, 125proof, 220

conception of constructivism, 72conception of current, 295conceptions

alternative, 292conceptions of knowledge, 72concepts, 198, 201, 206, 207, 301, 317, 324, 332

abstract, 316and principles of science, 317chemistry, 195science, 165, 196

conceptuallearning, 208structures, 166

Conceptual change, 166conceptual change, 165–167, 173, 175, 289, 293–

295approach, 165conditions for, 292

conceptual development, 173conceptual scheme

Aristotelian, 175modern, 175

conceptual space, 159

conceptual systems, 283conceptual understanding of the periodic table,

287conceptualizations of science, 126conceptually networked, 204confidence and skill, 202conformation, 205congruence, 259Congruence Axiom, 253conjectures and refutations, 24connectionist model, 159conservation of energy, 122constant current, 290Constituents of foodstuffs, 310constraints, 172construction

hypotheses, 202constructive empiricism, 71, 94constructivism, 71, 77, 80

Kantian,, 72social, 21, 85–87, 91, 94, 95, 97–99, 106, 117varieties, 71

constructivist, 21, 85, 104–106programme, 96teaching methods, 13

constructivists, 100content of science text, 319context

discovery, 193contextualised, 331contextualist, 104continuum hypothesis, 91conventional curricula, 312Conventional science, 303conventional sciences, 302, 306, 310, 316, 317conventionally, 302convergence proof, 258convergent thinking, 24Coomaraswamy, 42Copernican Revolution, 47Copernican revolution, 140Copernicus, 100copper, 192Cordoba, 213corporeal nature of the media, 185Corsiglia & Snively, 56Cosmology, 303Costa, 113counter-inductive, 176counter-intuitive, 176, 196, 251course

chemistry, 201, 203courses

chemistry for citizens, 204cramming, 317

Crease, 112creation science, 52creative imagination, 202critical

assessment, 324pedagogy, 116unbiased observation, 201

critical-logical-analytical thinking, 10crops, 314cross-cultural

research, 167studies, 289

CRT tubes, 281crtical thingking

skills, 13crystallization, 285cultural

capital, 114chauvinism, 63enterprise, 196hegemony science, 63imperialism, 52

cultureexpansionist, 54

curricula, 302, 309CMS, 306reforms, 203science, technology and society, 13science-technology-society, 123

curriculum, 40, 242, 280, 286construction, 289educational implications, 106hidden, 319

Czeslaw Milosz, 41

D.C. Phillips, 86D. Mazlish, 48Dark Ages, 212Darwin, 47, 60

theory of organic evolution, 332theory, 98theory of evolution, 138

David Hume, 28, 219David W. Ridgway, 281day and night cycle, 167day/night cycle, 167, 171De Caelo, 185De Motu, 175, 176De Revolutionibus, 71Dea Caelestis, 244deconstruction

science, 121deconstructionist, 103

affectation, 103Dedekind, 248

deduction, 267reasoning, 330

deductivemethod of proof, 251reasoning, 176, 322, 334

definition, 266science, 62

DeLoria, 53demonstrations, 293denser media, 192Densmore, 21Derek Hodson, 286derivation, 267derivations, 301Derrida, 102Derridadaism, 103Descartes, 48Descartes’, 72descriptive chemistry, 280, 282design of experiments, 202Desmond & Moore, 60development

European thought, 48mathematics, 213science, 61, 279, 331science concepts, 165scientific skills, 307

developmental level, 323, 327dialectic, 138differential

calculus, 238Diophantus, 214disc earth, 168discourse

science, 63discovery, 175, 176

electron, 284epistemic, 176Greek learning, 213

Disease, 310disease, 317disequilibrium, 179diSessa, 165divergent thinking, 24Dmitri Mendeleev, 284DNA, 114

extraction, 114model, 332synthesis enzyme, 113

Doberiner, 283dogma, 48dogmas, 317dogmatic, 331domain, 58

empirical, 253

physical, 253thought, 62

domainsknowledge, 63

domains of knowledge, 117dominant discourse of science, 63Drabkin, 175Driver, 58–60, 289Driver and Easley, 165, 289Driver and Oldham, 289, 295Drori, 115Drosophila, 113drugs, 204drycell, 333dual earth, 168dualism

Cartesian,, 72Duit, 294Durant, 112Durkheim, 88, 89Durkheimian view, 96Duschl, 59, 118dynamics, 180

Aristotelian, 29Dyson, 112

E.H. Carr, 195eclipse, 313eclipses, 313ecological systems, 122Edgar Jenkins, 111Edinburgh Strong Programme, 87education, 165, 255, 260

and research, 316CMS, 315health, 310higher stages, 316liberal, 10technical, 10

educational implications for the curriculum, 106educationally backward, 317Edward Jenner, 333Egyptians, 253Einstein, 176Einstelling effect, 292Eleaticiam, 46electric current, 289, 291electrical

engineering programme, 291nature of atoms, 281

electricity, 262, 289, 295, 296, 308alternative frameworks, 289

electrokinetics, 291electromagnetic

theory, 44

electronexclusion principle, 282orbital hybridization, 281orbitals, 279, 286structures, 280

electronicconfiguration, 284orbitals, 284structure, 279structures, 280

electrostatics, 291, 306circuits, 291

element, 204, 206and a compound, 206

element, mixture and compound, 206elementary particles, 305Elements, 241–244, 257–262

Arabic-Islamic tradition, 242elements, 280empirical

consistency, 59explanation, 96facts, 259inputs, 193issue, 195knowledge, 253naturalistic science, 93nature of science, 322, 331, 334observations, 193, 207question, 200tests, 201

empirical-experimentalinquiry, 122

empiricism, 72empiricist, 28

framework, 165, 170views, 25

empiricity, 325energy, 308, 312energy and power, 314enlightening, 301Enneads, 258environment, 306, 308, 309, 311, 316

laboratory, 208environmental science, 13, 311episodic conceptualisation, 292epistemic nature, 176

discovery, 176epistemic strength

discovery, 176epistemological, 43, 52, 65

egalitarianism, 106hegemony, 52perspectives, 55pinnacle, 63

pluralism, 65, 66position, 117presuppositions, 170pyramid, 64, 118, 122reconstruction, 175relativists, 51

epistemology, 11, 55, 75, 77, 111, 118, 156Cartesian, 72naturalization, 156science, 156

Eratosthenes, 242Eric Hoffer, 118Ernst von Glasersfeld, 71Escherichia coli, 113essentialism, 178estimating, 312ethical, 41ethnic minority populations, 211ethnomathematics, 218, 238ethnomethodology of science, 100ethnoscience, 54, 106Euclid, 175, 214, 242–246, 261, 262, 265

historicity, 243the geometer, 242

Euclidean geometry, 222, 241, 246, 251, 252, 255,259, 262

Eudemus, 243Eudoxus, 242, 243Eurocentric trajectory, 213Eurocentrism, 214European

chemical philosophers, 206mathematics, 212

Evolutiontheory of, 53

evolution, 118East and West Arab numerals, 214number system, 214

evolutionary biologists, 118examples and analogies, 293exclusion by definition, 214exclusivity of science, 62existence of atom, 281experimental science, 282experimentalist, 147experimentation, 307, 308, 316, 331experiments, 312explanations

of the seasons, 167of the weather, 167

extracted DNA, 113extremist social constructivism, 117Eylon and Linn, 289, 291

face numerals, 216, 217

facts, 324, 332factual, 167factual question, 167falasifa, 257fallibilism, 77fallibility of science, 14falsifiability

Popperian,, 72Falsificationism, 46Faraday, 126Farrington, 24feminist science, 13fetal tissue research, 126figure of 8 knots, 216Fihrist, 241, 242Finneran, 117First Nations science, 62five elements, 305flattened sphere, 168folk

knowledge, 305science, 302, 304, 316

food items, 304Foodstuffs, 312force, 181, 289, 303

balance, 103formal

axiomatics, 259definitions, 309logic, 154mathematics, 258metric geometry, 259synthetic geometry, 259

formalism, 316formalistic approach, 255foundations

geometry, 246mathematics, 261modern thought, 104

four elements, 177Four Western Imperatives, 118fourth and fifth-row transition metals, 282fractal geometry, 126framework theory, 166, 170Francis Crick, 119Frederick Grinnell, 58Fredric Jameson, 116Freeman Dyson, 116Freud, 47Freyberg, 289Fuller, 52function

maxima, 237minima, 237

fundamental

concepts in chemistry, 206principles, 202

G.E.R. Lloyd, 221Galilean

Platonism, 47world-view, 177

Galileo, 48, 175, 199experiments with pendulum, 199

Gardner, 98Gargi, 217Garrard & Wegierski, 118Garrard and Wegierski, 64gas laws, 280gases, 198Gaskell, 111Gauss, 43Ge Yuan Mi Lu Jie Fa, 237gedanken, 185Geertz, 61general

education, 301, 306, 316, 317principles, 306, 316principles of science, 303public, 301science, 306science curricula, 316science education, 200, 301, 306, 307, 316theories of science, 303

general aim of chemistry, 200general education, 200generalization, 302generalization and abstraction, 286generative justification, 164generative question, 167genetic arrangements and chromosomal structures,

113geocentric, 173, 303, 304geocentric phenomenological theory, 303geography, 122, 209geology, 286geometric equality, 243Geometry, 262geometry, 207, 241, 243, 250, 257–259, 267

foundations, 246teach, 260traditional, 254, 259

geometry of the sulbasutra-s, 259Georg Cantor, 91George Bernard Shaw, 39George Boole, 238George Wald, 43Gernet, 61Gibson, 51Gieryn, 58

Gilbert and Watts, 289Gillespie, 203, 204Gillispie, 204Gilmer, 117Giroux & McLaren, 116gnomon, 265goals of courses in chemistry, 203gold, 192good pedagogy, 285good science, 199, 285Goodstein, 115Gottfried and Kyle, 319Grant, Sleeter, & Anderson, 116gravity concept, 168Greek

atomists, 177thought, 46

Greeks, 253Gregorian, 312Gregorian and Saka, 313Gregory, 225Gregory series, 228Gross, 116, 119Gross & Levitt, 5, 112Gross and Levitt, 99Grove, 5growth

science, 200, 201growth of science, 201Guba & Lincoln, 59Gunther Stent, 113Guthrie, 24Gutwill, 291Gwalior system

representing numbers, 214

Haji Khalfa records, 241Haldane, 126Halliday and Resnick, 294halogens, 282Hamlet, 42Hans Jonas, 39Harding, 118Hardison, 122Harun ar-Rashid, 241Haruni, 241Hashweh, 289, 292, 294Hawking & Penrose, 61, 117health, 306, 309, 316

education, 310science, 309

healthyfoods, 307habits, 307, 316

heat, 289

Heath, 243Hegel, 88, 98hegemony, 51, 118Heidegger, 64, 104, 106, 118Heilbron, 4Heisenberg, 42, 43heliocentric, 173, 303

theory, 42, 303hellenistic

astronomy, 48Persian traditions, 214science, 46traditions, 214world, 213

Helm, Hugh and Novak, 165Helmholtz, 249Hendrick Hart, 119Henry, 77Henry Giroux, 116hermeneutic

circle, 121interpretation, 119

hermeneutical problem, 29hermeneutics, 120Hermotimus, 242Heron, 242, 243Hertz, 39Hesse, 58hidden

curriculum, 319higher

mathematics, 268stages, 316

Hijri, 313Hilbert, 245, 246, 258Hindu

science, 106society, 42

historian, 85geometry, 243mathematics, 213science, 41, 200

historical, 41, 43, 58evolution of institutions of science, 47aspects of science, 41continuity, 201development of an idea, 333episodes, 197relativism, 99

historicityEuclid, 243

historiesgeometry, 242mathematics, 217

historiography, 53, 58

history, 42, 44, 122, 195, 211, 241and epistemology of science, 13and philosophy of mathematics, 261and philosophy of science, 4, 6, 15, 21, 32,

40, 43, 44, 72, 176, 195, 197, 199, 200,261

of chemical education, 205of chemical synthesis, 209of chemistry, 200, 204–207of development of science, 331of Indian mathematics, 239of mankind, 302of science, 9, 23, 39–41, 43, 46, 96, 175, 195,

199, 200, 204, 207, 246, 283, 330of science in India, 40of scientific ideas, 40, 41, 46, 47of synthesis of chemical compounds, 208what, 42, 195

Hodson, 55Holiday, 319Holliday, 319Holliday and Whittacker, 319hollow sphere, 168Holton, 5, 112, 115, 117homeostasis, 122Horton, 61Horwood, 60hotchpotch geometry, 253Housing, 312HPS, 21

and science education, 6, 11in teacher education, 15

humananatomy, 310genome project, 126

humanisticissues, 135studies, 135

Hume’s racist views, 219hunger, 317Hunter Havelin Adams, 53hydrostatics, 193Hypatia, 217, 244hypotheses, 332

construction, 202hypothesis, 209hypothetico-deductive

method, 117, 303mode of reasoning, 209systems, 306, 316

Ian Hacking, 207Ibid, 192Ibn Sına, 241ideal chemical experiment, 199

idealism, 77, 93and relativism, 92Berkeleyan,, 72

Idealists, 61Idealists view, 61idealize, 199idealized systems, 193ideas of chemical synthesis, 208ideology for science education, 201ignorant of history, 42IIT Kanpur, 39–41IIT, Bombay, 261imagination, 176Immanuel Kant, 28imperative

economic, 118naturalism, 118scientistic, 118technocratic, 118

Imperial Board of Astronomy, 237implications

curriculum, 106for science education, 85of research findings, 289of social constructivism, 103

Inarticulate Science, 111Inca Quipu, 216incommensurability, 72

Kuhnian, 72Incompleteness theorem, 90incorporeal, 183India, 213

history of science, 40industrial and social progress, 39

Indianastronomy, 228Brahmi system, 214geometry, 255mathematics, 220–222, 226, 228, 230, 239numerals, 214science, 47, 55

indigenousculture, 315knowledge, 63

individual phenomena, 202individualistic, 296Indo-American programme, 39Indo-Arab numerals, 214induction, 176inductive

generalizations, 178method, 25reasoning, 176, 322, 334

inductively, 176inductivism, 46, 296

inductivist, 28, 178industrial, 314

and social progress in India, 39chemist, 204

inertia, 134, 181infinite

cardinal numbers, 91infinite series, 225, 231inner observation, 310innocent of philosophy, 42innovation, 315inquiry learning, 13inscriptionalist, 104instruction, 165, 170instructional strategies, 319instrumental

causation, 61knowledge, 61

instrumentalism, 71, 72, 94interaction of science with society, 331interaction of science, technology and society, 321,

325, 330interdisciplinary

nature of chemistry, 203science curricula, 123

interestscience, 122, 123, 202science and chemistry, 203

interest in chemistry, 202International History, Philosophy and Science Teach-

ing Group, 6introduction

zero, 214intuitive

framework theory, 168knowledge of electrostatics, 291notion of equality, 261physical idea, 259physics, 166scientific views, 168theories, 170

investigativenature of science, 320, 322–324, 328, 331processes, 331

Ionian Nature-philosophy, 46irrational

numbers, 248theories, 95

irrationality, 96, 115Ishale at-Kindi, 48Ishango bone, 215Islamic

rationalists, 257, 260science, 46, 62, 106thinkers, 242

isomorphism, 284issue of synthesis, 204Issues in Science and Technology, 116Ivan Sertima, 116Ivan Van Sertima, 53

J.B. Cohen, 41J.D. Novak, 165J.F. Daniel, 333J. de Fontaney, 236Jacob Bronowski, 22Jaina, 259James Conant, 9James Gregory, 228James Rutherford, 9Jamshid al-Kashi, 235Japanese temple geometry, 241Jean Piaget, 286Jegede and Okebukola, 319Jenkins, 112Jerome, 245John Cairns, 113John Fauvel, 219John McDowell, 77John Polkinghorne, 127Johnson, 59Jon D. Miller, 5Joseph Novak, 13Joseph Priestley, 198Judson, 114Jund-i-Shapur, 213Justinian, 245Jyesthadeva, 226–228

K.S. Gandhi, 41K.V. Sarma, 228K. Tobin, 78Kant, 41, 71, 250, 254, 261Kantian, 93Kantian constructivism, 72Kapalli, 327Karanapaddati, 226Karl Mannheim, 89Karl Marx, 219Karl Popper, 113katapayadi, 229Katyayana, 225Kawagley, 52, 53, 55, 56, 60, 63Kay, 230Kepler’s Harmony of the World, 126Kerala

mathematics, 226, 228, 235, 238school, 225, 228, 230

Kevin Finneran, 116Kevles, 115

key concepts, 306khichdi geometry, 253kinematics, 164, 180kinetic molecular theory of gases, 281kinetic theory, 204, 280knots, 216knowledge

construction, 60indigenous, 51–53instrumental, 61nature, 89procedural, 292representation, 159science, 171, 320–322, 327, 331scientific, 154social interaction, 331society, 89validity, 106

Kosambi, 42Kosslyn, 97Kriyakramakari, 226, 231Kronberg Castle, 42Kuhn, 24, 41Kuhnian incommensurability, 72

laboratory, 207common procedures, 202experimentation, 280

Ladriere, 54Lakatos, 96Lake Edward, 215language, 166Laplacian certainty, 117Larry Laudan, 86lateral thinking, 24Latour, 99–102Latour and Woolgar, 99, 102–104Laudan, 21, 58, 96Laudan and Stove, 99Lavoisier, 198, 199, 279Lavoisier’s four experiments, 198law

free fall, 175inertia, 176nature, 208periodicity, 284

Layton, 112, 115Leach, 58lead, 192learning

chemistry, 205science, 165, 166, 171, 320, 328skills, 331teaching chemistry, 203through science, 203

Lebesgue measure, 251Lechlanche, 333Lederman, 319Lehman, 103Leibnitzian Mathesis Universalis, 47Leibniz, 225levels

abstraction, 303phenomenology, 303

Levitt, 116, 119Lewenstein, 111Library

Alexandria, 243Library of Alexandria, 244light, 289

particle/wave, 53liking for science, 201limitations of science, 203limited, 302Linden, 55linguistic

interference, 292turn, 154

linking of the textual content, 327links with physics and biology, 204Linn, 319Linus Pauling, 113Liu Hui, 237Lobachevskii, 266local units, 312Locke, 76, 77logic, 99, 267

and reason, 48and science education, 10Aristotelian, 257formal, 154mathematics, 261

logicaldeduction, 255inconsistency, 173modality, 193positivistic, 154

logical positivism, 117lunar, 313

calendar, 215luni-solar, 313Lynda Birke, 115Lynn White, 115Lyotard, 55

M.D. Srinivas, 222M.I.T., 39M. Chastrette and C. N. R. Rao, 203M. J. Frazer, 200Macauley, 255

Macquare, 206Madhava, 226, 227Madhava-Gregory series, 228Madhava-Leibniz, 231Madhava-Leibniz series, 229Madras Literary Society, 226magic square, 218Magnetism, 262mahabhutas, 305Malebranche, 76, 77Mamuni, 241manipulation, 308, 316Mannheim, 95Maori science, 62map the students’ conception, 289Marshak, 215Martin Eger, 112Martin Heidegger, 117Martin Kline, 200Marx, 47, 88Marxist, 42Mary Boole, 238materialism, 135mathematical

artefact, 215knowledge, 212philosophy, 268proof, 253, 255reasoning, 193

mathematics, 46, 212, 245, 247, 253, 255, 258,261, 266–268, 281, 283, 335

Africa, 212, 213, 215Arab, 214curriculum, 223development, 213devlopment, 47education, 71European and Arab, 229higher, 268Indian, 222, 226, 239Kerala, 226, 228, 235, 238logic, 261modern, 251pedagogy, 238teachers, 211

mathemticsArab, 214

Matteo Ricci, 236, 239matter

atomic nature, 314Matthews, 52, 60Mauss, 89Max Delbrock, 113Max Planck, 31, 282Maxwell, 301

Mayan civilisation, 216Mayer, 3Mazlish, 43McDermott and Shaffer, 289–291McKinley, 55measurements, 312mechanical

composites, 206particles, 206philosophy, 206

Mechanics, 46mechanics, 169, 262, 281mechanistic world picture, 135media, 192medicine, 46medium

quicksilver, 192zero density, 192

Mendel, 334Mendeleev, 283–287

chemical ideas, 287experimental approach, 286

mensuration, 306, 309, 312, 316mental

models, 166, 168, 171models of the earth, 168prodigies, 219representation, 168training, 209

Mercator, 225Merton, 95, 105Mertonian

norms, 105social attributes, 205

meta-scientific, 21metaconceptual awareness, 167metamathematical definition, 255metamathematical notion of proof, 259metaphysical, 61, 82, 93, 134, 255

domain, 255realism, 75, 92

metaphysicians, 177metaphysics, 11, 32, 64, 72, 75, 111, 117, 118,

127, 254meteorology, 286method

chemical analysis, 209proof, 259science, 197, 203, 305

methodological, 43methodology and epistemology of science, 9Metioui, 291metric, 255metric and synthetic approaches, 254metric and synthetic geometry, 254

metric approach, 258metric geometry, 259metric, synthetic, or traditional, 259Michael Matthews, 199, 200Michael Ruse, 118Michel Foucault, 42Michelson-Morley experiment, 42Micro-organisms, 312microwave and infrared spectroscopy, 281Middle Ages, 46Mill, 261Millar, 58Miller, 319Ming Antu, 237Ministry of Education, 40misconceptions, 165, 166, 171, 289, 291

about science, 133mixture, 206mixture and a compound, 206mixtures, 206model

Cognitive Science, 137statics, 180

models, 332current, 289

modernacademic chemistry, 283conceptual scheme, 175electron orbital theory, 283mathematics, 214, 225, 232, 251science, 48, 316, 317scientific discoveries, 315secondary chemistry, 283western science, 63

modern view, 175Mohapatra, 292Mohapatra and Bhattacharya, 292Mohini Mullick, 40mole concept, 280molecular motions, 280molecules, 334Molefi Asante, 116momenta, 303moral issues, 209Morris Kline, 220, 230MORST, 4motion, 289motions of celestial objects, 312Mueller, 261, 264Mullick, 41multicultural, 52, 53

communities, 51literature on science, 62materials, 53mathematics, 211

perspective, 56perspectives, 51, 58science, 53, 56science education, 13

multiculturalism, 55mathematics, 214

multiculturalists, 62, 63multisciences, 56Mutazilah, 257mysterious, 315

N.R. Hanson, 43naıve inductivism, 198Nadeau & Desautels, 118Nalanda, 252Nanda, 106Narayana, 226, 231NAS, 112Nasiruddin, 241Native American views, 57natives, 209natural

kinds, 160motion, 180phenomena, 59, 120philosopher, 120philosophy, 53, 120, 195resources, 202, 312sciences, 118, 195

naturalismQuinean, 75

naturalist, 58, 93naturalistic, 59, 93

conceptual system, 121observation, 52observation and insight, 63

nature, 122and method of science, 201and philosophy of science, 320and science, 48of chemical bonding, 281of electronic orbitals, 279of Indian mathematics, 237of knowledge, 89of light, 281of objectivity in science, 116of science, 15, 22, 27, 58, 85, 99, 283, 301,

302, 316, 319–322, 324–328, 330, 331of scientific activity, 43of scientific knowledge, 117, 154of scientific mode, 46of synthesis, 208

Nayyayika notion of proof, 255NCERT, 241, 252–254, 320, 323–330NCERT text, 253

Needham, 61Neils Bohr, 42Nelkin, 52Neoplatonic, 258Neoplatonic linkages, 260Neoplatonic principles, 257Neoplatonism, 244, 257, 258Neoplatonists, 244, 260Neugebauer, 213Neuhaus, 112Neurath, 94New Apollonians, 135new Dionysians, 135Newlands, 283Newton, 47, 98, 225, 301

inverse cube law, 95notebooks, 101

Newtonianmechanics, 302, 303, 306, 316notion, 249synthesis, 47, 48

Niels Bohr, 282night-sky, 312Nilakantha, 226, 227, 231nitric oxide, 198non-Euclidean, 266

geometry, 211non-European

mathematical traditions, 220mathematics, 235

non-living nature, 311non-science, 58, 195non-stoichiometry, 205Normal Dahl, 39Norman Levitt, 85Norris, 104, 106Norris-Tull & Norris-Tull, 52Norris-Tull, & Norris-Tull, 53notion

inequality, 261rapidity of convergence, 232space and time, 176

Novak, 165, 289NSTA, 112number system, 214

O.B. Hardison, 114Oakely, 39objective

education, 258knowledge, 75

objectivism, 59objectivity, 325

and precision, 202of science, 322

observation, 309, 316observational

astronomy, 167astronomy research project, 167

observing, 308of Research Programmes, 46of science, 286Ogawa, 56Ohm’s law, 291, 295omissions and appropriation, 214omnipotency of science, 331On Floating Bodies, 180one right answer, 282oneness, 305Ontario Board of Education, 279Ontario program, 284ontological, 43

presuppositions, 170realism, 117

ontology, 76optics, 281order and causality, 61organic or inorganic, 207organization, 320origin

alternative framework, 292origin of science, 24origins of modern science, 30Orwell, 104Osborne, 289outcomes of learning of science, 319Overton, 52Owens, 54oxygen, 198

and hydrogen, 198, 199discovery, 279

oxygene, 198

P.R.K. Rao, 41Pappus, 243, 265paracetamol, 305paradigm, 100, 199paradigmatic shifts, 46parallel postulate, 267parameters, 309parapsychology, 105partitioning, 305Passmore, 5pathological tests, 310pathshala-s, 252Paul Gross, 85Paul Saltman, 113Paulus Gerdes, 219pedagogical, 53pedagogoy

critical, 116pedagogy, 77

good, 285mathematics, 238

People’s science, 305People’s science movements, 47periodic law, 284, 286periodic table, 279, 280, 282–284, 313personal cleanliness, 307perspective on science, 55Perspectives

Multicultural, 51Peru, 216pessimistic historical meta-induction, 22phenomenological, 302, 314

theory, 303phenomenology, 303–306, 316, 317

health, 310practical subjects, 306

Philippus, 242philosopher, 85, 118philosopher of science, 22philosophical, 41, 58

analysis, 206arguments, 197aspects of science, 41materialism, 117views, 58views about science, 204

philosophies, 202philosophy, 3, 42, 46, 54, 58, 76, 117, 195

of logical positivism, 117of Neoplatonism, 244of science, 9–11, 14, 23, 28, 40, 46, 71, 75,

176, 196, 203, 205science, 58

phlogistic chemistry, 29phrenology, 90physical

analogies, 181condition, 202particles, 206science, 309systems, 193

physics, 41, 185, 204, 206, 250, 261, 289, 303, 312,335

physiology, 309, 310Piaget, 71Pickering, 104Pierre Jartoux, 236Pierre Macquare, 206Pillars of health, 310Pinch, 21, 86, 99, 106Pinch and Collins, 105planetary motions, 303

Plato, 242, 243, 250, 254, 265Platonic idealism, 255Platonic philosophy, 247Platonic-Kantian, 251Platonic-Pythagorean Tradition, 149Platonism, 46Plotinus, 258political

philosophy, 14science, 219

Polymer substances, 335polymerase enzyme, 113Popper, 22, 98, 106Popperian

falsifiability, 72porphyry, 192, 243, 258positional

number system, 216system, 214

positivism, 117Posner, 289post colonialism, 55post modernism, 55post-epistemological, 76post-modernist, 71postmodernist philosophy, 14postulates, 265potential difference, 291, 295practical

applications of chemistry, 282mathematics, 258skills, 316

pragmaticconception of science education, 21view, 58

pragmatism, 200pragmatist, 104pre-scientific, 304

knowledge-systems, 302presocratics, 24primary

education, 307ontological reduction, 39–41, 43, 44school level, 316

prime numbers, 215Principe, 27Principia, 21, 98principle, 202, 286, 301, 317, 332

and theories, 306chemical elementarity, 199chemical simplicity, 199chemistry, 203, 279, 284conservation of mass, 199equilibrium, 179fundamental, 202

mechanics, 39unifying, 202

problem solving, 333, 334procedural knowledge, 292, 295process of enquiry, 327processes of science, 320, 332Proclus, 242–245, 251, 254, 257, 259professional CMS courses, 306, 316Proficiency Levels of Rural School, 301Project 2000+, 111proof, 253, 266

deductive, 251properties of elements, 280protagonists, 199pseudo-science, 58, 106pseudo-scientific, 26pseudoscience, 58Pseudoscientific and irrational world views, 5psychological form of constructivism, 71psychologism, 97psychologistic, 91psychologists, 165psychology, 98Ptolemy, 242, 243public

scientific literacy, 115square, 112, 117understanding of science, 111, 127

pure elements, 199pure hydrogen and pure oxygen, 199pure results, 199Putumana Somayajin, 226, 227Pythagoras, 48, 214, 244, 265

theorem, 253Pythagorean

theorem, 250, 251, 254viewpoint, 125

Pythagoreanism, 46Pythagoreans, 244

qualitativetest, 209visualisable models, 293

quantification and measurement, 263quantitative formulation of problems, 202quantum

mechanics, 31, 204, 279, 281, 303theory, 31, 53

questions, 322Quine, 94Quine-Duhem, 94Quinean

naturalism, 75underdetermination, 72

R. J. Gillespie, 203

racist history, 252radical

constructivism, 71, 72relativism, 119skepticism, 106social constructivist, 119social constructivists, 116, 117, 119sociologist of scientific knowledge, 121

radioactive properties, 282radioactivity, 280Ramanujan, 238rampant relativism, 86rare-earths, 282rarer media, 192rational, 56

reconstruction, 96reconstruction of beliefs, 96theology, 243, 251, 257

rationalism, 72rationalist, 58, 91, 94, 97, 98

philosophers, 91, 96philosophy of science, 92theories, 92view, 91

rationality, 96, 99, 116African, 116and critical thinking, 24

Rayleigh-Jeans, 31reaction mechanism, 205reaction rates, 207real world experiments, 176realism, 22realism/instrumentalism, 28realist, 58, 61reason, 176reasoned thought, 96reasoning, 207, 307, 308, 316

mathematical, 193skills, 13students, 322

rediscovery of Greek thought, 46reducibility, 305reductionistic thinking, 125relative density, 177relativism, 66, 72, 93relativist, 21relativistic, 178Relativistic Analysis, 178Relativistic dethronement, 47relativity, 193

theory, 249representations of numbers and space, 215requirements, 314research

chemists in USA, 201

cognitive developmental, 165scientists, 204

resistance, 291resistances, 192Richard Dawkins, 51, 119Richard J. Merill, 281ritual geometry, 259Robert Boyle, 206Robertta Barba, 53Roger Penrose, 61role of

chemistry, 205history of chemistry, 200history of science, 200

Roth, 293Royal Asiatic Society, 226rules of categorisation, 332Ruse, 112, 118Russell, 248, 268

Sadratnamala, 227, 232Sagan, 60Salviati, 175Samarapungavan, Vosniadou, & Brewer, 167Samarkand Observatory, 235Sample examination paper, 47Sandra Harding, 116Sanitation, 312Sankara, 231Sankara Variyar, 226Sankara Varman, 227SAS postulate, 253Saxena, 289–293school

Alexandrian, 180chemistry textbooks, 279children, 211education, 197, 302high, 301Kerala, 225, 228, 230middle, 301primary, 301science, 51, 52science curriculum, 52science education, 315science textbook, 320

Schopenhauer, 250Schrodinger’s cat, 255science, 46, 51, 100, 195, 200, 209, 286, 301–306,

316, 322, 323, 331, 334popularization among housewives, 315wars, 21alternative, 47and philosophy, 14and society, 331

and technology, 39, 306, 311, 317, 323, 326,331, 334, 335

and technology for society, 323and technology with society, 326anti, 115antithetical, 117basic knowledge, 331burden, 301celebration, 111central, 204centrality, 125centres, 315cognitive enterprise, 39community, 62competencies, 327computer, 41concept, 301, 317curricula, 55, 136, 165, 301, 303, 316curriculum, 327curriculum frameworks, 112deconstruction, 121definition of, 51, 52dehumanises, 135development, 61, 279, 331discourse, 63educationists, 320educators, 24empirical, 93empirical nature, 322, 331, 334epistemology, 156ethnomethodology of, 100exclusivity, 62for all, 111, 114for common people, 301for painters, 303for physicians, 303good, 199, 285growth, 200, 201historical activity, 42historical aspects, 41history of, 199human activity, 201in daily-life situations, 301instruction, 200, 209interest, 122, 202Islamic, 62learning, 165, 166, 171, 200, 320, 328learning of, 165liking, 201literacy crisis, 3methodological dimension, 11nature, 331of pendulum motion, 7or scientific investigation, 196pedagogy, 164

philosophical aspects, 41philosophical dimension, 11popularization, 301, 302, 315principles, 301, 317purpose, 306society, 331Standard Account of, 53standard account of, 66teachers, 3teaching, 32technology, and society, 196, 203theory, 301thinking process, 331traditional, 302, 304, 305universal, 51, 52universality of, 51uses and abuses, 201utilitarian view, 21wars, 52, 71, 85wars in India, 106western, 51, 53, 63with society, 331

science and technologyuse, 319

science classrooms, 197science curricula

interdisciplinary, 123science education, 5, 6, 8, 9, 24, 43, 51, 52, 56, 71,

78, 86, 100, 112, 123, 135, 171, 195–197, 199, 200, 205, 209, 226, 301, 306

and logic, 10curriculum, 196general education, 302multicultural, 13programme, 164purpose, 302research, 165, 173

science, technology and society, 40, 323, 334curricula, 13, 123

science-technology-society, 14scientific, 209, 306

enlightenment, 316and epistemological relativism, 65and technological needs, 39antirealism, 32appreciation of nature, 306belief, 89, 98community, 40, 62, 111, 112, 117, 205concept, 5, 114, 168, 200, 295creativity, 306criteria, 202development and conceptual change, 13disciplines, 41enterprise, 333experiments, 135

ideas, 59, 111, 166, 196illiteracy, 101imagination, 175inquiry, 103, 293investigation, 304investigations, 113knowledge, 8–10, 14, 55, 62, 86, 89, 92, 104,

116, 118, 121, 124, 125, 133, 135, 136,209, 213, 261, 332

literacy, 115, 334method, 39, 46, 197, 333, 334methods of investigation, 202model of current, 290organizations, 301outlook, 301, 306pipeline, 122positivism, 111, 117, 119, 121positivists, 120progress, 63, 114rationality, 106realism, 32research, 325revolution, 30, 46, 97skills, 316skills of observation, 307text, 121themes and concepts, 125theory, 23, 60, 93, 94, 96, 102, 154, 167, 283,

285thinking, 125, 322, 325, 326, 334truths, 44understanding, 315view of the earth, 168ways of thinking, 112world, 292description, 51investigation, 302knowledge, 66, 154method, 286theory, 93theory construction, 269theory profile, 58

scientifically educated men and women, 126scientifically literate, 317scientificity of science, 101scientism, 63, 64, 136scientist, 42, 200, 201, 207, 303, 306, 315, 323,

326, 333Scott, 58second law of thermodynamics, 196secondary, 306, 309, 316

school science textbooks, 320education, 307

semiconductors, 204senior secondary, 306, 316

sequence model, 290Settle, 118Shakespeare, 42shape of the earth, 167, 173Shepardson and Pizzini, 321Shipstone, 289–291, 293Side-Angle-Side, 248, 251Signals, 310Silver Chloride, 203Simplicio, 175, 192sixth and seventh-row rare earths, 282Sjφberg, 111Skinner, 97Skinnerian, 97, 98Sky-watching, 313Slezak, 97, 98slowness of motion, 183Smith, 289Smith, Blakeslee and Anderson, 294Smith, Siegel & McInerney, 5Smolicz & Nunan, 118Snively & Corsiglia, 56, 59, 63, 65Snivley & Corsiglia, 53social, 41

constructivist view, 116activity, 296application, 205constructivism, 21, 85–87, 91–95, 97–99, 106,

117constructivist doctrines, 87, 91, 104, 106constructivist ideas, 104constructivist programme, 97constructivist writings, 104constructivists, 94, 104justice, 317nature of chemical discovery, 205

social sciences, 195socio-cultural mileu, 319sociogical constructivist, 77sociological, 58

form of constructivism, 71, 86programme, 91relativism, 95relativist views, 21

sociologies of science, 14sociologist, 85, 94, 95

of science, 117, 287sociology, 95sociology of knowledge, 88, 89, 96, 97sociology of science, 99sociology of scientific knowledge, 87, 90, 91, 98,

104Socratic dialogue, 293sodium atom, 209sodium chloride, 281

sodium metal, 209Sokal, 119Sokal Hoax, 85solar, 313Solomon, 292solving problems of physics, 184Sophism, 46sources, 302South America, 216South Bihar, 301Spain, 213specific empirical statements, 178specific-theories, 170speed, 192spherical shape of the earth, 171spiritual phenomena, 59spiritualism, 115Srinivas Ramanujan, 221stages of learning, 286stagnation, 317standard account, 51–53, 55, 56, 58, 61–64standard units, 312Stanley & Brickhouse, 55, 59Stanley Fish, 116Stanley Miller, 113state of equilibrium, 179statics, 180, 193stellar aberration, 303Stephen Hawking, 61stereochemistry, 207Steve Fuller, 116Steven Brush, 200Sthananga Sutra, 226stoichiometry, 205, 280, 281stories of scientific success, 114strategy

achieve conceptual change, 293conceptual change, 293

strict objectivity, 117Strike, Hewson and Gertzog, 292strong cultural aspect, 209strong programme, 88, 89, 91, 96–98structure, 205

atom, 279periodic table, 279

structured curriculum, 293STS, 201

education, 14student’s

motivation and social maturity, 202understanding of science, 202understanding of technology, 202

students’concept of current, 289own bias, 324

reasoning in electrokinetics, 291study

of chemistry, 205of science and epistemology, 91

sub-atomic particles, 284sub-divided into disciplines, 303subject matter of CMS, 304sulbasutra, 259sulbasutra-s, 259, 260sulbasutras, 225, 230, 253Summers, 294Summers, Kruger and Mant, 289super conductors, 208superstition, 305, 312, 314, 317Sutton, 332swiftness of motion, 183syllabi, 307symbolic models, 159Symptoms of health, 310synthesis, 207, 208synthetic, 255

approach, 258aspect of chemistry, 204geometry, 253, 259models, 167, 168, 170

T.L. Heath, 180Tusı, 241Takebe Katahiro, 237Takshashila, 252Tantrasamgraha, 226Tasmania, 215taxonomically ordered, 42Taxonomy, 286Taylor series, 232teacher education, 289, 295teaching

and history, 39history and philosophy of science, 39classroom, 211geometry, 252physics, 296science, 165, 279, 319

technicalparameters, 311terms, 309

technology, 306, 309and scientific positivism, 118agricultural, 316industrial, 316

teleological, 91, 97, 98teleological model, 96teleological view, 96tempels, 54terminology, 315

tertiary, 306textbook, 284Thabit Ibn Qurra, 241Thales, 214Theaetetus, 242theistic traditions, 120Theocharis & Psimopoulos, 112theological curriculum, 260theology, 48, 58, 252, 257Theon, 243, 245Theonine, 248–250theorem of Menelaus, 243theoretical

basis, 305consistency, 59construction, 176constructions, 193framework, 165, 166imagination, 176, 178model, 193analysis, 206

theories, 202, 324, 332scientific, 93

theory, 165knowledge, 104electromagnetic, 44knowledge, 22

theory of evolution, 4thermodynamic, 207thermodynamics, 204

caloric, 29second law, 196

think logically, 202thinking

processes, 324, 329processes of science, 322, 325convergent, 24divergent, 24lateral, 24

third planet, 282third world women’s science, 106Thomas Fuller, 218, 219Thomas Kuhn, 199Thomist philosophy, 257Thompson, 284Thorley and Woods, 289Thorndike’s Law of Effect, 98Thornton, 295thought

activity, 324experiment, 176, 185, 321, 324, 333experiment, 31

tidal action, 52TIMSS, 111Tobias, 126

Tobin & Tippins, 78Todhunter, 241, 248Toldeo, 213total vacuum, 192totalitarian, 99totality of science, 303tradition of geometry, 260traditional, 255, 316

ecological knowledge, 56geometry, 254, 259notion of proof, 254parameter, 309, 315representationalist theories, 76science, 302, 304, 305understanding, 316wisdom, 317

traditionsBuddhist and Jaina, 255

transcendentalidealism, 73philosophy, 74

transfer of the learning, 329Treagust, Harrison and Venville, 294treatment of data, 202triads or octaves, 283Truesdell, 41truth-functional logic, 255

Uclides, 242, 257, 259, 260ultra-violet catastrophe, 31unacceptable biasedness, 201unbiased observation, 201underdetermination

Quinean,, 72understand the phenomena in chemistry, 204understanding, 304

nature, 305chemistry, 203nature and knowledge, 304the universe, 202

understandingscience concept, 165

UNESCO, 111uniformity, 122unifying

principles, 202unilinear trajectory, 212, 213unity of science, 305universal

concept of science, 62science, 62

universalist, 52perspective, 52perspective on science, 51

universality, 51, 62

science, 62concept of, 52science, 51, 62

university science textbooks, 112Upapatti, 222use of science and technology, 319uses and abuses of science, 201utilitarian, 86

view of science, 21

V.K. Jairath, 41vacuum, 186valence electrons, 284validity of knowledge, 106van Fraassen, 71varieties of constructivism, 71, 86vast generalizations, 302verbal behaviour, 97Victor Katz, 239Vidal Abarca and San Joze, 328Vidal-Abraca and Sanzose, 327view

equality, 295hierarchy, 295of nature, 47

vigesimal, 216Vikrami, 312, 313Vine DeLoria, 53visual impact, 328vital resources of the common man, 315vocabularly, 331void, 176, 192voltage and current, 291von Glasersfeld, 77Vosniadou, 167Vosniadou & Brewer, 167, 168

W.H. Freeman, 281Wallis, 225Walsh, 117warnings given by the body, 310water as a compound, 199Watson and Crick, 332Watts and Gilbert, 289Western science, 63western science, 63William Brewer, 167witch-craft, 305Wittgenstein, 97Wolfgang Pauli, 282woman mathematician, 217Woolgar, 99–101working knowledge, 202world view, 111, 177, 178, 196, 201

Galilean, 177

Aristotelian, 176, 177Galilean, 178

X-ray crystallographic patterns, 332X-ray diffraction, 281

Yager, 115Yang Guangxian, 236Yash Pal Committee, 317Yesudas Ramchandra, 237Yoruba method of multiplication, 220YuktiBhasa, 254, 260Yuktibhasa, 226, 227

Zaire, 215Zambia, 215zero, 216

introduction, 214Zij al-Arjabhar, 226Ziman, 112zoology, 286