(Posner et al) Accomodation of a scientific conception: toward a theory of conceptual change

8/3/2019 (Posner et al) Accomodation of a scientific conception: toward a theory of conceptual change

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Accommodationof a Scientific Conception:Toward a Theory of Conceptual Change*G E O R G E J. P O S N E R , K E N N E T H A . S T R IK E , P E T E R W . H E W S O N ,a n d W I L L I A M A . G E R T Z O GDepartment of Edu cation, Cornell Universi ty, I thaca, New Yo rk 14853

It has become a comm onplace belief th at learning is the result of th e interaction be-tween wh at the stude nt is taugh t and his cur ren t ideas or concepts. This is by no me ansa new view of learning. Its roots can be traced back to early Gestalt psychologists.How ever, Piagets (192 9, 1930) early studies of childrens explan ations of natu ral phe-nomen a and his more recent studies of causality (Piaget, 1974) have perhaps had th egreatest impa ct on the study of the interpretive framework s studen ts bring to learningsituations.Th is research has led to th e widespread stud y of stud ents scientific misconceptions.2From these studies and, particularly, from recent work by researchers such as Viennot( 1979) and Driver (1973), we have developed a more detailed understanding of someof these misconceptions and , more im portan tly, why they a re so highly robust andtypically outlive teaching which co ntradicts them (Viennot, 1979, p. 205 ).

But identifying m isconceptions or, mo re broadly speaking, alternative frameworks(Driver & Easley, 1978), and understanding some reasons for their persistence, falls shortof developing a reason able view of how a students curren t ideas interact with new, in-com patible ideas. Although Piaget (19 74) developed one such theory, there appears tobe a need for work which focuses mo re on th e actua l content of th e pupils ideas andless on th e supposed underlying logical structure s (Driver & Easley, 1978, p. 76). Severalresearch studies have been performed (N ussb aum , 1979; Nu ssbaum & Novak, 1976;Driver, 1973; Erickson, 1979) which have investigated the substance of the actu al beliefsand concepts held by children (Erickson, 1979, p. 221). However, there has been nowell-articulated theory explaining or describing the substantive dimensions of the processby w hich peoples central, organizing concepts change from one set of concepts to anotherset, incom patible with t he first. W e believe that a major source of hypotheses concerningthis issue is con tem po rary philosophy of science, since a ce ntra l ques tion of recent phi-losophy of science is how conce pts cha ng e under th e impact of new ideas or new infor-mation . In this article we first sketch a general model of conceptual change which islargely derived fro m cu rren t philosophy of science, but w hich we believe can illum inate

* This article is partly based on a paper entitled Learning Special Relativity: A Study of IntellectualProblems Faced by College Students, presented a t the International Conference Celebrating the 100th An-niversary of Albert Einstein, November 8-10, 1979 at Hofstra University.

See, for example, Au sube l(196 8).2 Se e Driver and Easley (1 978) for an excellent review of research in this area

Science Education 66(2): 21 1-227 (1982)0 982 John Wiley & Sons, Inc. CCC 0036-8326/82/020211-17SO2.70


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21 2 POSNER ET AL.

learning as well. We then illustrate some features of this model from interviews withstu den ts studying special relativity in physics. Finally, we derive some pedagogical im-plications.Ou r centra l comm itment in this study is that learning is a rational activity. Tha t is,learning is fundam entally com ing to comp rehend and accept ideas because they a re seenas intelligible and rational. L earning is thus a kind of inquiry. The student must makejud gm ent s on th e basis of availa ble evidence. It does not, of course, follow tha t motiva-tional or affective variables are unimportant to the learning process. The claim thatlearning is a rational activity is meant to focus attention on what learning is, not whatlearning depends on. Lea rning is concerned with ideas, their stru cture a nd the evidencefor them. I t is not simply th e acquisition of a set of corre ct responses, a verbal repertoireor a set of behaviors. W e believe it follows that learn ing, like inquiry, is best viewed a sa process of co nceptual chang e. T he basic question concerns how stud ents conceptionschan ge under the imp act of new ideas and new evidence.The Epistemological Base

Contem porary views in philosophy of science suggest tha t th ere a re two distinguishablephases of conceptual change in science. Usually scientific work is done against thebackground of central com mitm ents which organize research. T hese central commitmentsdefine problems, indicate strategies for dealing with them , and specify criteria for whatcounts as solutions. Tho ma s Kuhn ( 1 970) calls these central c omm itments3 paradigms,and paradigm-dominated research normal science. Irme Lakatos ( 1970) labels sci-entists central com mitm ents as their theoretical hard core and suggests tha t thesecommitments g enerate research programs designed to apply them to and defend themfrom experience.

T he second phase of conceptual chan ge occurs when these central com mitments requiremodification. He re the scientist is faced with a challenge to his basic assumptions. I finquiry is to procee d, the scientist m ust acq uir e new concep ts an d a new way of seeingthe world. Kuhn terms this kind of conceptual change a scientific revolution. ForLakatos it is a chan ge of research prog rams.

W e believe there a re analogo us patterns of conceptual change in learning. Som etimesstud ents use existing concepts to deal with new phenomen a. T his variant of the first phaseof conceptual change we call assimilation.Ofte n, however, the students current conceptsar e inade qua te to allow him to grasp some new phenom enon successfully. Then the stu-den t must replace or reorganize his centra l concepts. This more radical form of conceptualchange we call acc~mmodation.~Th is view of inquiry an d lea rning involves one addition al featu re. W e believe tha t in-quiry and learning occur against the background of the learners current concepts.Whenever the le arne r encounters a new phenomenon , he must rely on his current conceptsto orga nize his investigation. Wi tho ut suc h concepts it is impossible for the learner toask a question about the phenomenon, t o know what would count a s an answer to the

In this art icle the terms comm itments, concepts, and conceptions a re equivalent. Although theseterms (particular ly the latter two) refer to differing levels of conce ptualization , we do not distinguish amon gthe levels in this article .

The se are Piagets words, but in using them we do not intend any com mitm ent to his theories.


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CONCEPTUAL CHANGE 213

question, or to distinguish relevant from irrelevant features of the phenomenon. Withoutconcep ts the world is and rem ains W illiam Jam es blooming buzzing confusion. Bor-rowing a phrase from Stephen Toulmin ( 1 972) , we refer to those concepts which governa conceptual change as a conceptual e~ o l o g y . ~O ur w ork has focused on the kinds of radical conc eptual changes which we describeas accommodations. H ow do accommodations take place? Recent work in philosophyof science suggests tha t this question be divided into two. The first concerns the conditionsunder which an accommodation is likely to take place. When will individuals find itreasonable to undertake a major reorganization of their current concepts or to replaceone set of central concepts with another? Even in a major conceptual reorganization,however, not all concepts are replaced. Individuals will retain many of their currentconcep ts, some of which will function to guide the process of conceptual change. Onecan then ask what kinds of concepts tend to govern the process of accommodation. Thisis, in effect, to ask for the fea tures of the conceptual ecologies which govern the processof m ajor conceptual changes. W e thus express our theory of accommodation in responseto two questions:

1 ) Under what conditions does one central concept come to be replaced by an-other?2) W ha t a re the featur es of a concep tual ecology which govern the selection of newconcepts?

Conditionsof AccommodationT he views of science on which this work is based differ from their em piricist prede-cessors i n ways th at a re suggestive concerning the conditions of accomm odation. Mostvarieties of empiricism tend to see the grounds for accepting a given scientific theory asthe capacity of the theory to generate confirmed predictions. More recent views, however,suggest th at an adequate view of the grounds for accepting a new theory must ta ke intoaccoun t the charac ter of the problems generated by its predecessor and th e natu re of thenew theorys competition.One rather common theme in recent literature is that central concepts rarely directlyentail anything about experience. Rather they suggest strategies and procedures wherebyphenomena may be assimilated. Central concepts a re thus not judged in terms of theirimm ediate capacity to generate correct predictions. They a re judged in terms of theirresources for solving current problems. In Lakatos terms (1970) research programs arenot confirmed o r refuted. Instead they are progressive or degenerative. Central conceptsar e likely to be rejected when they have generated a class of problems which they appearto lack the capacity to solve. A competing view will be accepted when it appears to havethe potential to solve these problems and to generate a fruitful line of further re-search.It is also important to note tha t a persons centra l concepts are the vehicle wherebya given range of phenomena become intelligible. Such concepts can be linked to prior5 W e understand this view in direct opposition to traditional empiricism. Empiricisms central com mitm ent,

tha t there is nothing in th e mind not first in the senses, requires people to be able to learn something in the totalabsence of any prior concepts. W e believe this to be impossible. A mind which began a s a blank tablet wouldremain so, fo r it would lack the m eans to investigate experience.


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214 POSNER ET AL

experience, images, or m odels which m ake them appear intuitively obvious and whichmake competing concepts seem not just wrong but virtually unintelligible. Often,therefore, the first hurdle a set of central concepts must face in gaining accep tance is toappear to make sense.These kinds of considerations suggest that there a re several important conditions whichmust be fulfilled before an accomm odation is likely to occur. T he following four seemto us to express conditions which a re common to m ost cases of accommodation.1 ) There m ust be dissatisfaction w ith existing conceptions. Scientists and studentsare unlikely to make m ajor changes in their concepts until they believe that less radicalchanges will not work. Thus, before an accomm odation will occur, it is reasonable tosuppose that an individual m ust have collected a store of unsolved puzzles or anomalies

an d lost faith in the capacity of his current concepts to solve these problems62) A new conception m us t be intelligible. T he individual must be able to gra sp howexperience can be structured by a new concept sufficiently to explore the possibilitiesinherent in it. Writers often stress the importance of analogies and metaphors in lendinginitial meaning and intelligibility to new concepts (O rtony , 1975; Belth, 1977; Black,1962).3 ) A new conception m us t appear initially plausible. Any new concept adopted mustat least appear to have the capacity to solve the problems generated by its predecessors.Otherwise it will not appear a p lausible choice. Plausibility is also a result of consistencyof th e concepts with oth er knowledge. A new idea in, say, astronom y is less likely to beaccepted i f i t is inconsistent w ith curren t physical knowledge or if it simply has no clearphysical account. Physical scientists prior to the 20th cen tury, for example, were reluctantto accept what geologists were claiming about the age of the world since they had notheory which would allow the sum to provide energy for th at period of time.4 ) A new concept should suggest the pos sibility of a fru it f ul research program. Itshould have th e potential to be extended, to open up new a reas of inquiry.Features of a Conceptual Ecology

An individuals curren t concepts, his conceptual ecology, will influence th e selectionof a new cen tral concept. Th e literature in philosophy of science and o ur own work (tobe d iscussed shortly) have suggested that the following kinds of concepts are particularlyimpo rtant d eterminants of the direction of an accomm odation.1 ) Anomalies: The character of the specific failures of a given idea are an im portantpart of the ecology which selects its successor.2) Analogies and metaphors: These can serve to suggest new ideas and to m ake themintelligible.The re is, of course, a sizeable body of literature in both psychology (Sm edslun d, 1961; Kuh n, 1972;Berlyne,

1965) and science education (Driver, 1973; Stavy & Berkowitz, 1980) on the use of conceptual or cognitiveconflict for the development of thought and con ceptual change. But m ost of this literature has been conductedwithin a strict ly Piagetian framework [though Berlyne (1965) reviews the broader use of conflict situationsin education]. However, none of this work app ears to be grounded in a theo ry of conceptual change of the sortdiscussed in this article. Th at is, none is focused on fu ndam ental ch anges in a persons central, orga nizingconcepts from one se t of concepts to another set incompatible with the first.


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3 ) Epistemological comm itments:a) Explanatory ideals: Most fields have som e subject matter-specific views con-cerning what counts as a successful explanation in t he field.b) General views about the character of knowledge: So m e standard s for successful

knowledge such as elegance, economy, parsimony, and not being ad hoc seem subjectmat ter neutra l.4) Metaphysical beliefs and concepts:a) Metaphysicial beliefs about science: Beliefs concerning t he exte nt of orderliness,symmetry , or nonrando mness of the universe are often imp ortan t in scientific workand ca n result in epistemological views which in turn can select or reject particularkind s of expla natio ns. Su ch beliefs played a large role in Einsteins th oug ht. Beliefsabout the relations between science and commonplace experience are also importanthere.

b) Metaphysical concepts of science: Specific scientific concepts often have ametap hysical quality in that they are beliefs abou t the ultima te natu re of the universeand ar e imm une from direct em pirical refutation. A belief in absolute space or t imeis an exam ple.5 ) Other knowledge:a) Knowledge in other fields.

b) Competing concepts: On e condition for the selection of a new conce pt is tha tit should appear t o have more promise tha n its competitors.W e will see in this study how the se five features of a conc eptu al ecology relate to thefou r conditions of a conceptua l change in accou nting for the difficulties students facein learning science. W e thus turn to a study of the conceptual chang e required of physics

stude nts in the context of a specific topic: Einsteins special theory of relativity. Th is topicwas chosen b ecau se it has been comm only viewed a s a proto type of a scientific revolu-tion.

The MethodIn order to study students attem pts in coming to terms with th e special theory, we

con du cte d interviews in a noncalculus, self-study, self-paced intro duc tory college physicscourse with students who had completed a unit on special relativity, and with severalphysics instructors. In t he interviews, two problems were presented to the intervieweeswho were requested to solve the problems while thinking aloud. At each sta ge they wereaske d to give reasons for their answers, but no attempts were ma de to teach them in thosecases whe re their a nswers were inconsistent with the special theory. Th e first problemconsidered the workings of a light clock and th e implications it has for the concept of time.T h e second problem involved simultaneity and th e synchroniz ation of distant clocks andwas followed by the presentation of written explanations from two different points ofview which the interviewee was asked to read, and subsequently to repeat back, as acomprehension exercise. ee Posner et al . (1979) fo r a full description of the problems.


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216 POSNER ET ALThe Theory with Illustrations from Interviews

W e now explore in gr eater d etail the conditions governing assimilation and accom -modation by relating them to th e different feat ures of a conceptual ecology listed above.Th e application to the special theory of relativity is illum inate d by examp les take n fromthe interviews with physics students and instructors.Intelligibility of a N e w Conception

In order for a stu dent to consider a n alterna tive concep tion, he m ust find it intelligible.It should be clear that intelligibility is necessary for but not equivalent to or sufficientfor accom mod ation. Intelligibility a t a superficial level requires an understand ing of thecom ponent term s and sym bols used and th e syntax of the m ode of expression. For somenew conceptions, th is aspe ct of intelligibility is easily me t. T he special theo ry is one suchcase in which this aspect is not particularly problematic for college students with anadequate background in algebra.

However, as recent research on language comprehension dem onstrates, finding dis-course (o r for that ma tter, theories) intelligible requires more than just knowing whatthc w ords and symbols mean. Intelligibility also requires constructing or identifying acoherent representation of what a passage or theory is saying (Bransford & Johnson,1973). In fact, we would claim th at n o theo ry can func tion psychologically a t all unlessit is internally represented by the individual.

In general, representations may be in the form of propositions or images, or networksof interrelated propositions and/or images. One might, for example, represent traveldistances between New York S ta te cities as a series: Ithaca-Albany, 165 miles; Al-bany-Syracuse, 60 miles; Albany-New York City, 150 miles, etc. O r, th e same infor-mation could be represented by a ma trix formed by writing each city on both th e hori-zontal and vertical axes of the matrix, w here each mat rix cell contains the distance be-tween the two cities intersecting a t the cell.Or, the sa m e information could be representedeven m ore econom ically by a New York S ta te ma p with lines connecting pairs of citiesand distanc e written on each line. Similarly, a tru th tab le and a Venn diagr am can rep-resent th e sa me information as propositions and a s images, respectively.x

Representations function both passively and actively. They function passively as afor ma t into which in formation m ust be fit. In paragrap h com prehension tasks, for ex-ample, a nom alous sentences ar e confusing (i.e., unintelligible) because they ca nnot befit into the representations being built an d, thus, ar e not easily entered into the readersmemory (Bransford & Johnson, 1973). Represe ntations also function actively a s a planfor directing ones attention and conducting purposeful searches (Neisser, 1976). T h einability of read ers to remember an anomalous sentence in a n otherwise coherent para-graph may be attr ibuted to the readers inattention to i t .The different fun ctions of a representation showed up dram atica lly in the comparisonbetween the responses of a student, O N facing relativity for the first time, and an in-

struct or, ET , who had taug ht physics, but not relativity, for a num ber of years. Both readthe written explanation of the simultaneity problem, part of which follows:When E passed A , they both set their clocks to zero and sent me a synchronization signal. Since1 was a distance d A B / c from A when the signal arrived I set my clock to read r = d,+,B/c.So Es

Th ese examples were all adapted from Je rom e Bruner (1966).


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clock and my clock were correctly synchronized when E was at A , but since moving clocks run slow,when E reached me, his clock had fallen behind mine.ONS ecollection of this section ca m e without hesitation a s follows:(B said) that when E reached point A , they synchronized the clocks to read zero, and at that pointhe sends a signal to B, and B synchronized his clock with t equal to th e distance AB over th e velocityand thats how B stated tha t he did it-because moving clocks run slow, E was behind.

There was no indication of a ny active functioning. Sh e was intent on giving th e writtenexplanation without comm ent. She had already at tem pted her own solution to theproblem , but there is no comparison between th e written explanation a nd her own previousatt em pt . This, in contras t, is ETs recollection of precisely the s am e section:(E said) th at he sent a synchron ization signal to B, and that differs from approach which was tohave B look at them visually. And apparen tly heres B considering that (E ) sent out a synchroni-zation signal and that the distance t ha t it travelled (pause) yes, see, thats where hes getting hi svelocity, relative velocity.

The representat ion which ET builds, functions act ively to direct his at tention incommenting on the w ritten explanation and t o conduct a search for any information whichcould be used to clear up difficulties in his own solution to the problem. As he sayslater:Look, 1dont remember what he said, I wasnt really trying to recall it, but to sort out my own ideas. . . I suppose I was selective in my reading, trying only to take from (th e written explanation) whatwould clarify my own ideas.

Ho w o ne represents knowledge an d theories determines ones ability to mak e senseof an d use th e new ideas. On ly if the stud ent can psychologically construct a coherent,meaningful representation of a theory can it becom e an object of assessmen t and a toolof thought. Only an intelligible theory can be a candidate for a new conception in aconceptual change.

Ho w difficult is this task for special relativity? Einstein ( 1 954) describes th e two basicpos tulates of special relativity as follows:. . . Every universal law of nature which is valid in relation to a coordinate system C, must also bevalid, as it stands, in relation to a coordinate system C, which is in uniform translatory motionrelatively to C . . .

Th e second principle, on which th e special theory of relativity rests, is th e principleof the co nstan t velocity of light in uucuo. This principle asserts tha t ligh t in uacuo alwayshas a definite velocity of propag ation (indepen dent of th e sta te of motion of th e observeror of the source of the l ight) (pp. 224-225).

Constructing a coherent representation of the theorys two postulates individually is notparticularly problematic. O ne can imagine a state of affairs in which each in turn is true,al though th e more one accepts Newtonian mechanics the harder i t will be to imaginea world in which the p ostulate about con stancy of the speed of light is true. But in b alance,intelligibility of each of Einsteins two po stulates is not pa rticularly problem atic.

Th e intelligibility of th e theory a s a whole, however, is a differe nt ma tte r. Findin g itintelligible entails imagining a world in which both of Einsteins postulates a re true, to-


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218 POSNER ET AL .

geth er with the logical imp lications of the postula tes for notions of spac e an d time. Thistask is a demand ing one. To ma ke m atte rs even more diffic ult, it is possible to apply thepostulates an d for mu las of special relativity in a superficial way witho ut those necessaryrevisions in ones con ceptions of space and tim e which ar e in accord with th e theory; orwith out even having understood th e full implic ation s of its principles. Th us, both lea rnerand instruc tor can m istake the intelligibility of th e parts-the postu lates of th e specialtheory-for th e intel ligibi lity of th e whole.Initial Plausibility of a N ew Conception

One source of difficulty in learning special relativity stems from its lack of initialplausibility to physics students. Regardless of how intelligible one finds the theory, itmay s ti ll appea r counterintuit ive. W ha t makes a theory like special relativity counter-intuitive?Initial plausibility c an be th oug ht of as the anticipated deg ree of fit of a new conceptioninto an existing conceptual ecology. Th ere ap pear to be a t least five ways by which aconception can become initially plausible.

1) On e finds it consistent with ones curre nt m etap hysic al beliefs and epistemologicalcomm itments, i.e., ones fund am ental assum ptions.

2) One finds the conception to be consistent with other the ories or knowledge.3 ) One finds the conception t o be consistent with past experience.4) One finds or ca n cre ate images for th e conception, w hich m atc h ones sense of what

th e world is or could be like.5 ) On e finds the new concep tion capa ble of solving problem s of which one is aw are(i.e ., re so lv ing an ~ m a l i e s ) .~

Of these five factors the first appea rs to offer the greate st explanatory power withregard to the difficulties faced by st uden ts attem pting to learn Einsteins special theory.Let us then look at fundamental assumptions as they bear on this learning task.One set of f unda me ntal assum ptions is the individuals epistemological com mitm ents.Einstein ( 1949) was comm itted to two funda me ntal epistemological principles:

1 ) A theory must not con tradic t empirical facts; and2) The premises of the theory must be characterized by naturalness or logicalsimplicity, a kind of inner perfection of the theory. H e was com mitt ed so fully to thesetwo principles tha t he was able to apply them ruthlessly, even if tha t app lication mean ta rejection of our comm on sense notions of space and tim e.

Needless to say, stude nts do not always sh are Einsteins epistemological comm itments,but the ir own com mitm ents a re likely to be highly significant in determining what theyfind initially plausible and , thus, in shap ing thei r concep tual changes. There fore, it isimportan t to find ou t jus t wh at epistemological co mm itm ents studen ts have, if one wantsto understand what they a re likely t o find initially plausible or implausible and moregenerally, to understand their processes of conceptual chang e. W h at is their theory oftheories? W ha t is their the ory of knowing? W ha t is their view of the relation of disci-plinary knowledge to everyday knowledge?

Th e present discussion will focus only on the first of these five ways, tha t is, on th e individuals fund ame ntalassumptiona. In the next sect ion we e la borat e on t he last of these ways . Th ere w e discuss th e dual function ofanomalies .


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Scientific metaphysica l beliefs, like epistemological comm itments, ar e central to aConception. The central scientific metap hysical belief tha t contrasts special relativitywith its immediate predecessors is its rejection of an absolute space and absolute timein favor of an interpretation which considers space and t ime relative to any given inertialsystem. So long as s tudents ar e f irmly committed to absolute space and t ime, they willfind the special theory counterintuitive.A good exa mple of such a co mm itment is provided by stu dent C P , who outlines herbelief in absolute time explicitly a nd repeatedly. In response to a portion of the simul-tane ity problem (for which the special theory predicts tha t two clocks read different times)she responds:After she has read the written explanation showing the derivation of the relativisticprediction, the interviewer (1) questions her further:

( C P ) I mean, how could they change?Tim e only goes at one rate, r ig ht?

(1 ) And so what a bou t this idea of absolute time?( C P ) I cant say thats not t r u e . . .C P not only sta tes her belief in absolutc time but a t a later sta ge shows how she defends

it in a discussion of the troublesome resu lts of the sim ultan eity problem which she assi-milates into an existing conception:(I ) Im just asking you wha t you feel abo ut results like th at .

(CP) Yeah, 1 mea n, absolute time, it just seems to go on a t a certain rate everywhere.It just seems natural that its constant everywhere. I mean, even though yousee these results.

(I) . . . i t seems these ar e s trange results . W ha t att i tud e do you ta ke of these re-sults?( C P ) I say they dont re ally mean all th at m uch; it just depend s on what your fram e

is. Its sort of like potential en ergy de pen ds on the way you defin e zero to be?(I ) T h e amou nt of potential energy youve got?(CP) Rig ht, all relative to whats going on.CPs reference to potential energy is significant in pinpointing a conception whichenables her to reg ard t he values given to a variable as arbitr ary, being d ependen t solely

on th e observers point of view. Sh e attem pts to resolve som e counterintuitive results ofEinsteins view of time by drawing an analogy between time and potential energy. N oma tter th at the analogy might break down with further analysis-it serves her belief inabsolute t ime.I t is appropriate at this point to note the importance of the s trength a nd depth of ametaphysical belief in determining whether assimilation or accommodation occurs.Because CPs com mitm ent to absolute tim e is so stron g, accomm odation is a less attractiveoption th an assimilation, and as a result she needs to be a ble to m ake h er belief in absolutetime and her und erstanding of special relativity consistent. Sh e succeeds, to her satis-faction, by using the potential energy ana logy.

A tutor in the course, SL, provides ano ther exam ple of an a ttem pt t o assimilate thefindings of th e special theory into an e xisting conception, in this case in a rathe r moresophis ticated a nd detailed fashion. H e shows a f irm N ewtonian com mitment to amec hanistic view of the world which re quires t ha t objects have fixed properties such aslength, mass, etc., and tha t explanation s of phenom ena should be given in term s of these


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220 POSNER ET AL

objects and their interactions. In talking ab ou t the question of shrinking rods and slowingclocks, he says:(SL) I see them a s being-as changing their length, or changin g their time. But I cant

talk t o the person whos moving a t the sa me velocity a s the stick and the clock.Hes tel ling me that they dont cha ng e. . . I feel they havent chan ged , but th eway Im looking at them h as cha nge d. .. 1 guess Im allowing for the fac t tha tperson whos seeing these thing s a t rest, who has his clock at rest, his me ter stickat rest, has (pause) a little more right to say what is really happening to thesticks.

A little later he continues:(SL) But Im not a t all uncom fortable w ith the idea of foreshortening. I do say, I dofeel it is a percep tion. I will say it is a shortening. I know in the back of my min dtha t my friend whos riding along with tha t m eter stick is telling me all the timethat as far as he can tell, its the sam e length a nd 1 believe wha t hes saying, whichis 0.k.

(1) Its not a conflict?(SL) N o, because th e fact th at i ts moving makes i t app ear to m e as if it were fore-

Here SL insists on treatin g length as constant, ind ependen t of fram es of reference. H eis, thus, led to tre at the special theorys claims concerning th e relativity of length a s simplya distortion of perception .

Wh at is of interest to us at this point is that SL reveals this comm itme nt by using itas the conception to which he assimilates the findings of special relativity. In order todo this he has to make two auxiliary assumptions: that a shrinking rod co nstitutes aperceptual problem, an d doesnt actu ally shrink (I feel they [rods and clocks] haventchanged , but the way Im looking a t them has chang ed) , and tha t in principle a mech-anistic interpretation in terms of objects and their m otion is needed in order to explainwhy clocks run slower (I dont see how in de pt h. . .bu t 1 believe it can be done). Ne itherof these assumptions is necessary or even consistent with an Einsteinian perspective basedon a reanalysis of space an d tim e. The y do, however, play a n integral p art in protectingSLs metaphysical commitments.Dissatisfaction with Existing Conceptions

Genera lly, a new con ception is unlikely to displace an old one, unless the old one en-counters difficulties, and a new intelligible and initially plausible conception is availablethat resolves these difficulties. T ha t is, th e individual must first view an existing conceptionwith so me dissatisfaction before he will seriously consider a new on e.On e ma jor sou rce of dissatisfaction is th e anom aly. Eac h tim e a person unsuccessfullyattem pts to assim ilate an experience or a new conception into his existing network ofconceptions, tha t person experiences a n anom aly. An anom aly exists when one is unableto assimilate somethin g th at is presum ed assimilable-or (in othe r words), one simplycannot make sense of som ething.

IThe reader should note that this section builds on some of the points raised in the two previous sections.Therefore, fo r purposes or clarity and succinctness, this section is placed out of order in relation to the list ofconditions presented earlier.

shortened.

I Lakatoa ( 1 970) terms these difficulties recalcitrant data.


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Wh en faced with an anomaly, the individual (scientist or student) has several alter-natives. One may come to the conclusion that ones existing conceptions require somefundam ental revisions (i.e., an accomm odation) in order to eliminate the conflict. Butthis is the most difficult and, therefore, the m ost unlikely approach, especially when therear e other possibilities:1) rejection of the observ ational theory I2;2) a lack of concern with exp erimental findings on the grounds th at they ar e irrelevant to ones3) a co mp artmen talization of knowledge to prevent the new information from conflicting with4) an at tem pt to assimilate the new information into existing conceptions (e.g., Newtonizing

curre nt conception;existing belief (Science doesnt have anyth ing to do with th e real wo rld ); andrelativistic pheno men a).

This analysis suggests that th e presentation of anom alies will produce dissatisfactionwith an existing conception only if:1) Students understand why t he experimental finding represents an anomaly;2) Students believe that it is necessary to reconcile the findings with their existing concep-3) Students are commit ted to the reduction of inconsistencies among the beliefs they hold;4) Atte mp ts to assim ilate the findings into the students existing conceptions a re seen not to

tions;an dwork.

Given th e improbability that all these conditions will be met, it is no wonder tha t fewstudents find their cur rent conceptions weakened by anom alies. W hy consider alternativesto a New tonian view (or whatever view they ho ld) when they ar e unconvinced of the in-adequacy of their conceptions? The search for instructionally viable and effectiveanom alies is of primary importance if accom modation is to be taken seriously as a goal.Recounting historical anomalies (such as the M ichelson-M orley experiment) wont alwaysdo!Assuming this formidable instructional problem is solved, the process of accommo-dation can proceed. If t he dissatisfaction w ith the existing conception created by its in-ability t o mak e sense of experience is followed by learning of an intelligible alternativewhich resolves or promises to resolve some of the anom alies of its predecessor, then th enew conception m ay be plausible.Th ere is little evidence in the interviews that students were aware of anom alies, eventhough videotapes of two experiments formed part of the study material in the course.It is significant that the clearest example of a students awareness of anomalous behavioroccurs along with a statem ent of his epistemological comm itme nt.HU has derived a m istaken result from his view of the relativity principle which impliesth at p ictures taken by two cameras m oving past one another a t the same instant and of

l 2 Reports of observation ar e not theory neutra l. Rathe r. observations are described and inter pretcd by meansof concepts taken from some theory, or some theory is assumed in treating the observations as dat a. Treatingobservations of the red shift as a measure of dis tance assumes a wave theory of light and , in som e cases, relativity.Even the use of a telescope assumes a theory of optics. Theo ries which function to describe or interpret datawe refer to as observation theories.


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the s am e two clocks will show differe nt things. Th e interviewe r looks for confirma tionof this view:

( I ) So wh at youre saying is th at the y wouldnt agr ee, they couldnt agre e, th attheyd ac tually see differen t things.( H U ) Right .(H U ) I t did at f irs t , but when you think about i t and hash i t out, there really is no

reason why we should limit ourselves to one fra m e of mind. I like to think ab-stractly and I can see that . 1 had trouble realizing th at lengths would change,too, but you know, Im gam e! N o, it doesnt both er m e. Its jus t th at we dontrealize i t du e to our slow speeds. I tend to a gree with scientif ic da ta thatsbrou ght up an d when they say th at an electron-what was that-a meson,actually goes with the predictions, what c an you do ? An d once you see the facts,you can stretc h your im agination.HUs stated epistemology is simple and empiricist : Theories a re derived from experi-

me ntal evidence. It also appea rs to exhibit a d egree of tole rance for theoretical incon-sistencies, which tolerance precludes him from seeing that he has made a mistake.However, H U has pinpointed one anomaly: Newtonian mechanics calculates the lifetimeof a m eson to be mu chsh orter than t ha t which is observed expe rimentally. H e has,however, seen tha t special relativitys prediction agre es with expe rim ent. Thu s, H U seesan anomaly, he sees the alternative conception, and his epis temological com mitm entallows for its plausib ility.Fruitfulness of a New Conception

On ce awa re of an intelligible, plausible alterna tive to a n existing conception tha t re-solves app aren t anomalies, students m ay actively atte m pt to ma p their new conceptionsonto the world; tha t is , they m ay a ttem pt to interpret experience with i t . I f the new con-ception not only resolves its predecessors anom alies bu t also leads to new insights anddiscoveries, then th e new conception will app ear fruitfu l and th e accom mod ation of itwill seem persuasive.A brief ex am inatio n of t he fruitfulness of th e special theory for professional scientistsmay suggest some of th e theorys potential. It is this potential of which stude nts shouldbe made aware, if they ar e to sha re in the view th at the theory is indeed fruitful, and, thus,worth accommodating:

1 ) As an engineering tool in t he design of acc elerato rs (relativistic mec hanics);2) As a technological tool in th e developme nt of nuclear weapons and nuc lear reac-tors;3 ) As a theoretical and technological tool in nuclear chemistry for predicting theproducts of n uclear rea ctions;4) As a theoretical and mathematical tool in astronomy for calculating life expec-

tancies of stars , for explaining astronomical phen ome na (e.g. supernov ae), an d for makingcalculations of astronom ical distances;5 ) As a theoretical basis (along with quantum physics) for the development of modern

physics.To the extent that the s tudent can understand these contr ibutions and trace them backto the basic postulates of the special theory, they may begin to app rec iate the fruitfulnessof the theory .

( I ) Th at doesnt bother you?


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The Character of AccommodationO ur description of the four conditions of a successful accom modation may have sug-gested a fairly straig htfo rwar d linear process: students dissatisfaction with New tonianphysics; followed by the students finding special relativity intelligible; leading to an initialbelief in its plausibility; and concluding with the belief that the theory is ultimatelyfruitful.However, it should be clear th at this accoun t is oversimplified, since many basic con-ceptions, including relativity, a re so complex th at at a particular time one is likely toaccommodate certain aspects but not others. We have, of course, described accommo-dation as a radical change in a persons conceptual system. Th at an accom modation is

a radical change does not, however, entail that it is abrupt. Indeed, there are good reasonsto suppose that for students accommodation will be a gradual and piecemeal affair.Stu de nts ar e unlikely to have at th e outset a clear or well-developed grasp of any giventheory and w hat it entails about the world. For them, accommo dation may be a processof taking an initial step toward a new conception by accepting some of its claims and thengradually modifying other ideas, as they more fully realize the meaning and implicationof these new c omm itments. Accommodation, particularly for the novice, is best thoughtof as a gradual adjustment in ones conception, each new adjustment laying thegroundwork for further adjustm ents but where the end result is a sub stantial reorgani-zation or c han ge in ones centra l concepts.O ur interviews also indicate that w hat m ay initially appear as an accommodation m ayturn out to be something less than tha t. As the interview with SL indicates, people whoaccept Einsteins two postulates may understand them in a rather non-Einsteinian fashion.Often it appears that as students, who have accepted the two postulates, begin to realizetheir counterintuitive implications or their conflicts with Newtonian notions of spaceand time, the com mitment to the two postulates weakens. Typically, students will attem ptvarious strategies to escape the fu ll implication of the two postulates or to reconcile themwith Newtonian assumptions. Accomm odation may, thus, have to wait until some un-fruitful atte mp ts a t assimilation are worked throug h. It rarely seems characterized byeither a flash of insigh t, in which old ideas fall away to be replaced by new v isions, or as

a steady logical progression from one commitm ent to ano ther. Ra the r, it involves muchfumb ling abou t, many false star ts and mistakes, and frequent reversals of direction.

Educational ImplicationsTeaching science involves providing a ration al basis for a conceptual change. W e have

also seen tha t fun dame ntal conceptual changes, termed accommodations, may involvechanges in ones fundam ental assumptions abo ut the world, about knowledge, and a boutknowing and th at such changes can be strenuous and potentially threatening, particularlywhen the individual is firmly committed to p rior assumptions. We have seen th at peopleresist mak ing such chan ges, unless they a re dissatisfied w ith their curren t concepts andfind an intelligible and plausible alternative that appears fruitful for further inquiry.Tw o features of a conceptual ecology, in particular, w ere shown to guide the changeprocess from one conception to ano ther: 1) anomalies, and 2) fundamental assumptionsabout science and about knowledge.


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22 4 POSNER ET AL.

I f taken seriously by stud ents, anom alies provide the sort of cognitive conflict (likea Kuhnian state of crisis) that prepares the students conceptual ecology for an ac-commodation. The m ore students consider the anomaly to be serious, the more dissatisfiedthey will be with current concepts, and the more likely they may be ready u ltimately toaccommodate new ones.Metaphysical beliefs and epistemological commitments form the basis on whichjudgments ar e made about new knowledge. Thu s, a conceptual change will be rationalto the extent tha t stud ents have a t their disposal the requisite st an dar ds of judgmentnecessary for th e chan ge. If a chang e to special relativity requires a com mitment to theparsimony and symmetry of physical theories (as i t did for Einstein), then studentswithout these commitments will have no rational basis for such a change. Faced withsuch a situation students, if they are to accept the theory, will be forced to d o so on non-rational bases, for example, because the book or the instructors says it is true.O ur study of the history of science reveals that many conceptual changes in sciencehave been driven by the scientists fundam ental assumptions rather than by the awarenessof empirical an0ma1ies.I~Einsteins special relativity can be seen as such a case.I4However, since it is unlikely that s tude nts in an introductory physics course can be suc-cessfully taught the requisite standards of judgment for an accommodation of specialrelativity, physics teachers must rely on anomalies to prepare th e student for the ac-commodation.Our problem remains unsolved, however. Most of the anomalies will not be readilyseen as anomalies by students without a thorough understanding of the observationaltheory in which th e experiment was embedded. Th at is, most of th e experiments are farfrom being transpa rent. Does this problem m ean th at the special theory can realisticallybe made at best only intelligible and partially plausible, but never fully persuasive tostudents who are firmly comm itted to a set of conflicting m etaphysical beliefs and epis-temological com mitm ents? It is one thing to educate physicists over a course of four tosix years into a given set of sta nd ards of judg ment. It is qu ite another thing to accom plishthis goal in an introd uctory physics course, along with covering a great deal of content.And further, how is one to demonstrate the theorys fruitfulness in the limited timeavailable?Accepting, then, that accom mod ation of the special theory runs th e risk of being dif-ficult if not impossible, is there anything we as educators can do to enable physics studentsto accommodate new conceptions on a rational basis? Let us examine the implicationsof our research for science education . W e shall fram e these implications in the form ofquestions and suggestions raised by our research thus far.Curricular Objectives

O u r discussion of the critical role played by the students fundamental assumptionsabout the world and about their knowledge of the world raises serious questions aboutthe objectives of science courses. If the conceptual change process is to be rationally based ,then students will need to be immunized against the kind of inevitable indoctrination

l 3 See Burtts (1962, pp. 36-62) accoun t of Copernicus, whose theory was no t a response to anomalies, butl 4 Emp irical findings anom alous with respect to New tonian physics bu t consistent with Einsteinian theory

was only p resented as a simpler and more harmonious interpretation.developed many years af ter the special theory of relativity was proposed.


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that occurs when neither the teacher nor the student is aware of his own fundamentalassumptions, much less those implied by the science he is teaching and learning.The primary question which must be raised about curriculum objectives as a resultof our discussion in this article is the following: Is it realistic to expect science instructionto produce accommodation in students, rather than merely to help students make senseof new theories? And secondarily, should this be an expectation for all students, or onlyfor certain groups, such as science majors?In the event that an affirmative answer is given to the primary question, the contentsof the previous sections suggest we aim at developing in students:1 ) An awareness of their fundamental assumptions and of those implicit in scientifictheory;2) A demand for consistency among their beliefs about the world;3) An awareness of the epistemological and historical foundations of modern4) Some sense of the fruitfulness of new conceptions.The extent to which any of the above should be considered is a matter for future in-

science;

vestigation.Content

If we aim to produce rationally based conceptual change in students, then accordingto what we have said thus far, the content of science courses should be such that it rendersscientific theory intelligible, plausible, and fruitful. In order to give expression to thisgeneral requirement, the following conditions appear to be necessary:1) More emphasis should be given to assimilation and accommodation by studentsof that content than to content coverage.2) Retrospective anomalies should be included, particularly if historically validanomalies are difficult to comprehend,or, as with the special theory, were not responsiblefor driving the conceptual change in the first p1 a ~ e . l ~3) Sufficient observational theory should be taught for students to understand theanomalies employed.4) Any available metaphors, models, and analogies should be used to make a newconception more intelligible and plausible.Teaching Strategies

Teaching is typically thought of as clarifying content presented in texts, explainingsolutions to problems, demonstrating principles, providing laboratory exercises, andtesting for recall of facts and ability to apply knowledge to problems. That is, teachingis for recall and assimilation. For teaching aimed at accommodation the following possiblechanges in this approach are implied by our research:1) Develop lectures, demonstrations, problems, and labs which can be used to create

cognitive conflicts in students. Among other things, one might consider what types ofhomework problems would create the kind of cognitive conflict necessary as preparationfor an accommodation, and whether labs could be used to help students experienceanomalies (Stavy & Berkowitz, 1980).l 5 Se e Anthony P. French ( 1 968, pp. 6-29), for an example of the use of retrospective anom alies in teaching

special relativity.


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2) Organize instruction so that teachers can spend a subs tantia l portion of their timein diagnosing errors in stud ent thinking a nd identifying defensive moves used by studentsto resist accom moda tion.

3 ) Develop the kinds of strateg ies which teachers could include in their repertoire todeal with stude nt errors and moves that interfere with accom moda tion.4) Help stud ents ma ke sense of science content by representing c ontent in mu ltiplemodes (e.g., verbal, math em atica l, concrete-practical, pictorial), and by helping stud entstranslate from one mode of representation to another (Clem ent, 1977).

5 ) Develop evaluation techniques to help th e teacher track the process of conceptualchange in students (e.g., the Piagetian clinical interview) (Posn er & Gertzog, 1982).Teacher Role

Th e teacher a s clarifier of ideas an d presenter of information is clearly not ade quatefor helping students accommodate new conceptions. Our research suggests that theteacher m ight have to assume two further roles in order to facil itate s tudent accommo-dation. In these roles the teac her would become:

1 ) An adversary in th e sense of a Soc ratic tutor. In this role, the teacher confrontsthe students with th e problem arising from their atte mp ts to assimilate new conceptions.( A point of concern is the need to avoid estab lishin g an ad versa rial role with regar d tostudents as persons while developing and maintainin g it with regard to conceptions.)

2) A model of scientific think ing. Asp ects of such a model migh t include a ruthlessdem and for consistency am ong beliefs an d between th eory an d em pirical evidence, apursuit of parsimony among beliefs, a skepticism for excessive ad hoc-ness in theoriesand a critical appreciation of w hether discrepancies between results may be in reasonableagreement with theory. 6

W heth er any of the above changes could be implemen ted, and t he exte nt to which theywould prove effective in facilitating accommodation in students, are questions whichwe have not as yet add ressed .ReferencesAusubel, D. P. Educational psychology: A cognitive viewp oint. New York: Holt, Rinehart &Belth, M . Th e process of thinking. New York: David McKay, 1977.Berlyne, D. E. Curiosity and education. I n Learning and th e educational process , J. D. Krum boltzBlack, M. Models and metaphors. Ithac a, NY : Cornell University Press, 1962.Bransford, J. D., & Johnson, M . K . Considerations of some problems of comprehension. In VisualBruner, J. S . Toward a theory of instruction. Cambridge: Harvard University Press, 1966.Burtt, E. A. T he nletaphysical founda tions of mod ern science (rev. ed.). Garden City, N Y :Clement, .I . J . Som e typcs of knowledg e used in understanding physics. University of Massachusetts,

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instruction, J . Lockhead & J. J . Clem ent (Eds.). Philadelphia: Th e Franklin Press, 1979.Driver, R . Th e representation of conceptual frameworks in young adolescent science students.Unp ublish ed Ph.D . dissertation , University of Illinois, Ur ban a, Illinois, 1973.Driver, R., & Easley, J. Pupils and paradigms: A review of literature related to concept development

in adolescent science students. S t u d . S c i . Ed . , 1978, 5,61-84 .Einstein, A. Autobiographical notes. In Albert Einstein: Philosopher-scien tist, P. A. Schilpp (Ed.).Evanston, IL: Library of Living Philosophers, 1949 .Erickson, G . L. Childrens conceptions of heat and temperature. Sci . Educ . , 1979, 63, 221-230.French, A. P. Spec ial relativity. New York: W. W . Nor ton , 1968.Kuh n, D. M echanisms of chan ge in the development of cognitive structu re. Child Dev., 1972, 43,

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Lakatos, I . Falsification and the methodology of scientific research programmes. In Criticismand the growth of knowledge, I. Lakatos & A. Musgrave (Eds.). Cambridge: CambridgeUniversity Press, 1970.Neisser, U . Cognition and reality. San Francisco: W. H. Freeman, 1976.Nussbaum, J . Childrens conceptions of th e E arth as a cosmic body: A cross ag e study. Sci. Educ.,

Nussbaum, J., & Novak, J . D. An assessment of childrens concepts of the e arth utilizing structuredOrton y, A. Why metaphors a re necessary and not just nice. Educ. Theory, 1975, 25,45-53.Piaget, J . Understanding causality. New York: W. W. Norton, 1974.Piaget, J . The childs conceptiono f th e world. New York: Harcourt Brace, 1929.Piaget, J . Th e childs conception ofp hy sic al causality. London: Kegan Paul, 1930.Posner, G. J., Strike, K. A,, Hewson, P. W., & Gert zog, W . A. Learning special relativity: A studyof intellectual problems faced by college stude nts. Paper presented a t the 100th Anniversaryof the Birth of Albert Einstein, Hofstra University, 1979.

Posner, G. J. , & Gertzog, W . A. Th e clinical interview and the m easurement of conceptual change.Sci . Educ . , 198 2,66 , 195-209.Smedslund, J. The acquisition of conservation of substance and weight in children: V . Practicein conflict situation s without external reinforcement. Scand. J . Psycho / . , 19 61 ,2, 156-160.Stavy , R., & Berkowitz, 8 . Cognitive conflict as a basis for teaching quanti tative aspects of theconcept of temperature. Sci . Educ . , 1980 ,64 ,679-692 .Toulmin, S. Human understanding. Princeton: Princeton University Press, 1972.Viennot, L. Sp ontaneous reasoning in elementary dynamics. Eur. J . Sci . Educ. , 1979, I , 205-

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