EDITORIAL

This October we will commemorate one yearsince the creation of the Reference Center forMathematical Modeling in Teaching CREMM,a daring idea that emerged from the mappingof Mathematical Modeling in Teaching that webegan in 2003. Our expectation is to turnCREMM into a Research Center withinternational cooperation, integrated withseveral other Research Centers in the area;making use of the largest national andinternational collection in the area; making asummary of materials and their respectiveauthors available on the CREMM electronicsite for consultation and requests forsupervision; orient students and teachers;with the support of teachers from Brazil andother countries, create didactic supportmaterials for various levels of education andmake them available to interested teachers;promote seminars and distance learningcourses and publish informative bulletins,magazines and books that include the resultsof work developed by collaborating teachers.During this first year, we've spent most of ourtime gathering and acquiring Brazilianproduction: doctoral dissertations, masters'theses, monographs, and articles published inthe annals of Congresses and in Magazines.Just to give an idea, we've already identified219 academic works (11 doctora ldissertations, 76 masters' theses, 105monographs, 15 works of scientific initiationand 12 end of course undergraduate works);503 articles (87 in specialized magazines and416 in annals issued from congresses); 35Teaching License courses that have adiscipline in Modeling and 47 disciplines inPost-Graduate courses. A part of thisproduction can already be found in theCREMM library and is available on theelectronic site. We hope to have the

Newsletter of Reference Center of Mathematical Modeling in Teaching - CREMM

Year I - N 1 - November of 20070

inform@cremm

rest available shortly.In order to consolidate CREMM, we havecounted on the support of several researchprofessors from Brazil and other countriesand have already sent projects to agenciesthat support research in order to promoteModeling Courses in distance learningprograms. The Regional University of

Blumenau has given complete support to thisproject. CREMM inhabits a physical space of90 m2, composed of 6 areas: a library with aModeling collection; support, meeting andstudy rooms; a kitchen and a bathroom. Workis conducted by 8 undergraduate students, 2masters' students and us Nelson, Salett andEmília.In the informative bulletin Inform@CREMM,which will be virtual and printed, we willpresent news and items from variouscountries about precursors, production,projects and events. In this first bulletin, wefocus more on activities in Brazil. A countrywith the continental dimensions of Brazil, andwhich has moved towards modeling inteaching significantly over the last threedecades, without a doubt has a lot to show. Wehope that this Inform@CREMM brings moreand more contributions, allowing for thefurther consolidation of CREMM.

General InformationUniversidade Regional de Blumenau (FURB)Antônio da Veiga, 140 - CEP 89010-971- Blumenau - Santa Catarina - BrasilTel.:(5547)3321 0282 - Fax: (5547) 3322 8818

E-mail: cremm@furb.br - www.furb.br/cremm

COORDINATION: Maria Salett BiembengutSECRETARY: Emilia de Mello VieiraEDITOR: Alex CarvalhoTIRAGE: 1000

Newsletter of Reference Center of Mathematical Modeling in Teaching - CREMM2

According to the registry, Aristides CamargosBarreto was the first Brazilian professor to usedidactic activities involving mathematicalmodeling in teaching and, moreover, the first torepresent Brazil at international congresses,presenting work related to the theme. Born inBelo Horizonte, Minas Gerais in 1935, hegraduated from UFMG in 1959 with a degree incivil engineering and completed his doctorate inMathematics from IMPA in 1964. He started as aprofessor at UFMG in 1960 and in 1969 beganteaching at PUC in Rio de Janeiro, where heworked until the early 1990's when he retired.For many years, he dedicated himself toresearch on , in the area ofApplied Mathematics, supervising 13 masters'theses in the areas of Analysis, DifferentialTopology, Foliations, Dynamic Systems,Singularities, Mathematics in Ecology andMathematical Models in non-exact sciences. I n1969, he published a collection of books forSecondary School teaching entitled

and anotherentitled , used in HigherEducation and published in 1971.

Aristides became familiar with MathematicalModeling during his Engineering course. Theidea to used modeling in MathematicsEducation began in the latter part of the 1970'sat PUC/Rio, arising from the

. In an attempt to get thestudents more motivated and interested,Aristides employed a strategy that combinedmodels with institutional modules in thedisciplines of Fundamentals of ElementaryMathematics and Teaching Practices forLicensing as a Mathematics Teacher, as well asin the Advanced Calculus course for engineers,in the Post-Graduate program. Together withthe students, he designed various models inspecific areas like Linguistics, Ecology, Biologyand Music, among others. One of his principalpedagogical experiences was realized in 1976, inthe Differential Calculus IV course withstudents from Engineering, Mathematics,Physics and Chemistry. A total of 215 studentssigned up for the course, divided into 4 classes.For each group, Aristides gave 2 classroomhours per week (90 minutes), elaborating thetheoretical part with examples, while in theanother two classroom hours, on another day,one of his assistants took care of solvingexercises with the students. The remainingclassroom hour was used for group discussionof proposed problems, under the guidance of twoassistant teachers.

“Dynamic Systems”

“FunctionalMathematics for Secondary School”

“Topics for Analysis”

“constant anddisturbing question: 'what use is this?' thatstudents would make when confronted withmathematical theories”

Aristides Camargos Barreto

During the course, various mathematical modelswere proposed, formulated and analyzed, along withclassical maxims and others adapted to classicmodels from Economics, Physics, Mechanics,Technology and Ecology. At the same time, Aristidessupervised the first two Masters' theses from thePost-Graduate program at PUC-RJ that dealt withModeling in teaching. The first was

, by Celso Braga Wilmer,defended in 1976, and the second

, Jorge de Pardo Sánchezof Costa Rica, defended in 1979.

The experiences and studies with and/or by meansof supervised students, led Aristides to defend hisproposal to teach mathematics by means of modelsand to offer definitions about models and modelingin teaching at various Events and Courses onMathematics Educationin Brazil and abroad.Among the internationalcongresses that heparticipated in, thefollowing stand out: theUNESCO meeting thattook place in Montevideo,Uruguay in 1974; the 3oand 4º InternationalC o n g r e s s e s o nMathematics EducationICME-III and ICME IV,that took place inKarlsruhe, Germany in1976 and in Berkeley,California in 1980; the 4ºCongress on Lat inMathematics in Palma de Mallorca, Spain in 1977and the 5a Inter-American Conference onMathematics Education V CIAEM, that occurred inCampinas (SP), Brazil in 1979. Aristides'participation in V CIAEM led Professor UbiratanD'Ambrosio, at that time director of IMECC atUNCAMP, to invite him to hold seminars on the useof mathematical models in the teaching ofDifferential and Integral Calculus and LinearAlgebra. Thus, in October 1979. Aristides came toUNICAMP, the time when Rodney Carlos Bassaneziand Eduardo Sebastiani Ferreira, for example,heard him talk about mathematical modeling.Aristides Camargos Barreto has made an immensecontribution not only to academic production, butmainly to the people that he has motivated who, as aresult, continuing spreading the seed ofMathematical Modeling throughout the BrazilianEducational System.

Models inMathematics Learning

CombinedSt ra tegy o f Ins t ruc t i ona l Modu les andInterdisciplinary Mathematical Models for teachingthe learning of mathematics at Secondary schoollevel: an exploratory study

A fragment extracted from a text about Aristides Camargos Barreto in thebook The History of Modeling in Brazilian Teaching (work in progress) byMaria Salett Biembengut.

Aristides Camargos Barreto

inform@cremm

Precursors:

ICTMA - International Community oFTeachers of Mathematical ModeLing

and Applications*

The beginning 'principles' of ICTMA took place inthe 1970's, at the same time in Brazil and for thesame reasons: discontent and criticism byteachers and businesspeople in relation to theeducation of undergraduates in areas thatrequire mathematical knowledge for problemsolving and decision making. For example, in areport published in 1973, R.R. Mclone statedthat a recent graduate in mathematics was goodat solving problems and had reasonableknowledge of mathematics literature andtechnique, but was not so good at formulating,planning and making a critical evaluation of theproblem he was dealing with.

Criticism like this was what possibly led DavidBurghes of England to liven up the schoolmathematics curriculum, working with teachersto produce interesting modeling with secondaryschool students. Burghes is considered the'father' of the ICTMA, since besides his activitieswith teachers at Cranfield University in 1978, hepublished various articles and three books onthe subject in 1981, 1982 and 1983. He was partof the , along with professors JohnBerry, from the Open University, and IanHuntley from Paisley College in Scotland. Otherpeople were involved in the movement towardsmathematical modeling in schools anduniversities, among them John McDonald fromPaisley College, Glynn James from ConventryPolytechnic, Hugh Burkhardt and George Hallfrom Nottingham University and Dick Clementsfrom Bristol. In their various initiatives,emphasis was placed on the teaching ofmathematical modeling.

In 1983, Burghes (who had transferred to ExeterUniversity), John Berry, Huntley, Glynn andAlfredo Moscardini (Sunderland Polytechnic)organized the 1ª and 2ª InternationalConferences on Mathematical Modeling inteaching at Exeter University, England. The firsthad 125 participants from 23 countries. Therewere two featured presentations and more than39 parallel sessions. Most of these presentationsdealt with modeling in Higher Education, whileonly 5 were related to Primary Education. Thisdifference was justified by the fact it would beeasier to change a curriculum in PolytechnicSchool that in Primary School, or even at aUniversity.

Spode Group

Many of the presentations were about teachingmodeling or describing models, although fewdescr ibed research or phi losophica lperspectives. Thus every two years there takesplace a Conference with a significant number ofparticipants and representatives from differentcountries: ICTMA (1987) under a coordination of

Werner Blum at Kassel University, Germany;ICTMA 4 (1989) chaired by Mogens Niss, atRoskilde University Denmark; ICTMA 5 (1991)by Jan de Lange at Freudenthal Institute,Utrecht University Holland; ICTMA 6 (1993) byCliff Sloyer at the University of Delaware USA;ICTMA 7 (1995) by Ken Houston at theJordanstown Campus of the University of UlsterNorthern Ireland; ICTMA 8 (1997) by PeterGalbraith at the University of QueenslandAustralia; ICTMA 9 (1999) by João Felipe Matosat the Universidade de Lisboa Portugal; ICTMA10 (2001) by Qi-Yuan Jiang at TsinghuaUniversity, Beijing China; ICTMA 11 (2003) atthe University of Milwaukee USA; ICTMA 12(2005) by Christopher Haines at the CityUniversity, London, England; ICTMA 13 (2007)took place by Satellite Meeting at KathmanduUniversity Nepal and at Indiana University,Bloomington USA under the coordination ofRichard Lesh. It should be noted that the bestworks presented at each ICTMA are published inbook form. The term 'Applications” was onlyincluded in the title of the Conference in thethird edition, leading to the title InternationalConference on the Teaching of MathematicalModeling and Applications. In the first twoConferences, the organizing commission of theevents was the Committee of the ICTMA.Starting with ICTMA 3, some changes were madeand in 1998 a regulation was designed that alsoincluded the election of the Executive Committeeof ICTMA.

Currently, the Executive Committee is made upof a president, the two organizers from the lasttwo Conferences and by three elected membersand another four indicated members whorepresent countries. The Committee puts on theConferences, publishes the annals in book formand puts out a periodical (that began this year,in 2007). It also makes use of space within theICME-

; recognized as "The InternationalStudy Group for Mathematical Modeling andApplications ICTMA" in the InternationalCommission on Mathematical Instruction ICMI.The current Executive Committee, elected onJuly 26th of this year during ICTMA 13 inBloomington, Indiana, USA, is made up of:President: Gabriele Kaiser (Germany);organizers from the two previous Conferences:Chris Haines (England) Secretary and RichardLesh (USA); members: Toshikazu Ikeda (Japan),Thomas Lingefjärd (Sweden) Gloria Stillman(Australia) Editor of the Newsletter and co-optedMembers: the Brazilian Jonei Barbosa, KatjaMaaß (Germany), Bhadra Tuladhar (Nepal) andJinxing Xie (China). The next Conference -ICTMA 14, will be at the University of Hamburg,Germany in 2009.

M o r e i n f o r m a t i o n : w w w . i c t m a . n e t .

International Congress on MathematicalEducation

Part of this synthesis was taken from the article: “ICTMA:the first twenty years” Written by Ken Houston from theUniversity of Ulster, Northern Ireland

inform@cremm

Newsletter of Reference Center of Mathematical Modeling in Teaching - CREMM3

http://www.furb.br/cremm SENDING COLLABORATIONS

I f your have any academic work(Undergraduate monograph, Thesis,Dissertation, Monograph, Research Report)article, report on experience or some news orinformation that you think is pertinent, pleasesend it to CREMM and we'll put it on theelectronic site; send it to us at any time.

If you have used some activity or have had anexperience using Modeling with your students,or if some of them have done interesting workthat you'd like to be known, send us a report,the text or the work. We can put in the virtualJournal summary and the work in PDF will bein the Pedagogical Practices section ofCREMM's electronic site. Together with thework, we ask that you send along an abstractof a maximum of 100 words. If possible,translate the abstract to English and Spanish.

Universidade Estadual de Feira de Santana (UEFS)http://www.uefs.br/nupemm

This year, the National Conference on Modeling inMathematics Education (CNMEM) will have its 5th edition,in Ouro Preto (MG). The appearance of this event in 1999can be seen as one of the signs of maturity in the Modelingmovement in this country, creating in this way a specificspace in which teachers, researchers and students cancome together to discuss the subject.

In mid-1999, Prof. Rodney Bassanezi spoke about puttingon an event with this purpose. At that time, Jussara Araújoand I were students in the Post-Graduate Program inMathematics Education at the Universidade EstadualPaulista (Unesp), Rio Claro campus (SP), and hadparticipates along with other Braziliansin the

(ICTMA9), in July1999, in Lisbon. When we returned toBrazil, we presented the idea of anational event on Modeling, as ananalog to the international event, andbegan to discuss the idea at the Post-Graduate Program at Unesp. Thecoordinator at that time, Prof. AltairPolettini, also got behind and supportedthe proposal. Thus on November 19thand 20th 1999 the I CNMEM took placein Rio Claro, with a total of about 200participants. In a discussion that tookplace during the event, those present decided that theCNMEM should be bi-annual, which has ended up as one ofits characteristics.

9th International Conference onthe Teaching of Mathematical Modelingand Applications

The II CNMEM occurred in 2001 on theItatiba (SP) campus of the Universidade São Francisco(USF), and was coordinated by Prof. Alexandrina Monteiro.Once again we enjoyed the coming together of researchers,teachers and students from the area.

The success of the event left participants certain of the needto guarantee a permanent place for CNMEM on thecalendar of Brazilian Mathematics Education. The IIICNMEM was held in 2003 in Piracicaba (SP) atUniversidade Metodista (UNIMEP) and was coordinated byProf. Regina Franchi. At this event, we made a substantialachievement publication of the Annals. This was animportant step in structuring and consolidating the event

Jonei Cerqueira Barbosa since starting then we have had submission andevaluation of complete works, which are published in theAnnals. There was another important bit of progress at IIICNMEM: it was supported by both CAPES and FAPESP.The financial support of these research fosteringagencies symbolized the consolidation and recognition ofthe event.

The IV CNMEM brought the opportunity of coordinatingits organization at the Universidade Estadual de Feira deSantana (UEFS). Here it is worth pointing out the factthat it was the first time that the event occurred outsideof São Paulo State, in fact taking on a nationaldimension. With about 400 participants from 9 differentStates, we maintained the progress we had already madein previous events (publication of the Annals andfinancing from the agencies, for example).

In the organization for IV CNMEM, theproposal was made to have a distinctionbetween the organizing commission andthe scientific commission, clearlyseparating the roles of each. TheMathematical Modeling Work Group ofSBEM (GTMM/SBEM) assumed the taskof indicating the members of the scientificcommission. In my view, this was animportant step in the scientificstructuring of the event, besides settingout a move towards a strong relationshipwith GTMM/SBEM. For the V CNMEMthis year, I think that we have arrived at avery well-structured event, a result of the

advances made in previous events. Beyond maintainingthose advances, one more important step has been takenextending an invitation to Prof. Gabriele Kaiser,President of the International Study Group forMathematical Modeling and Applications (ICTMA), torealize the opening of the conference, as this inauguratesthe international scope of the event.

In summarizing the trajectory and progress of this event,I can say that CNMEM is well established on the nationalcalendar of Mathematics Education. I had the privilege ofparticipating in every event and can testify to the gradualadvances that have culminated in this rich space fordebate on Mathematical Modeling. Its continued supportand reinforcement must be a shared commitment for allof us!

inform@cremm

On the progress of CNMEM

Jonei Cerqueira Barbosa