Mathematical applications and modelling in the teaching ...

1 Mathematical applications andmodelling in the teaching andlearning of mathematicsProceedings from Topic Study Group 21 at the 11thInternational Congress on Mathematical ducation inMonterrey, Mexico, July 6-13, 2008 Editors:Morten Blomh j, NSM, Roskilde University, DenmarkSusana Carreira, University of Algave, PortugalJune 2009nr. 461 - 2009- I, OM OG MED MATEMATIK OG FYSIK Roskilde University, Department of Science, Systems and Models, IMFUFA Box 260, DK - 4000 Roskilde Tel: 4674 2263 Fax: 4674 3020 Mathematical applications and modelling in the teaching and learning of mathematics Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematical Education in Monterrey, Mexico, July 6-13, 2008 IMFUFA tekst nr.

2 461/ 2009 252 pages ISSN: 0106-6242 These proceedings contain the papers reviewed and accepted for Topic Study Group 21 (TSG21) at ICME-11. Prior to acceptance all papers were reviewed by at least two reviewers and revised on the basis of the review reports. Preliminary versions of all the papers were published at the congress web-site before the congress so as to form a common basis for the work of the TSG. The papers presented during the TSG sessions are all marked with a * in the table of contents found below. After the congress revised versions of the papers have been submitted for the proceedings.

3 During the TSG21 sessions the papers were presented and discussed according to a thematic organisation in three themes, namely: Theme 1: Different perspectives on Mathematical modelling in educational research; Theme 2: Challenges in international collaboration on the teaching of Mathematical modelling , and Theme 3: Didactical reflections on the teaching of Mathematical modelling . The intentions of theme 1 were to present and discuss an overall view on different perspectives found in the field of educational research on the teaching and learning of Mathematical modelling , and to use this overview to characterise and discuss the research presented in the TSG.

4 The two other themes are more particular foci on the teaching and learning of Mathematical modelling dealt with in the papers submitted for TSG21. In these proceedings the papers are presented according to the theme under which they were presented or discussed during the congress. Morten Blomh j, July 2009 Roskilde University, Department of Science, Systems and Models, IMFUFA Box 260, DK - 4000 Roskilde Tel: 4674 2263 Fax: 4674 3020 IITable of contents Theme 1: Different perspectives on Mathematical modelling in educational research Different perspectives in research on the teaching and learning Mathematical modelling 1 Categorising the TSG21 papers * Morten Blomh j Differential equations as a tool for Mathematical modelling in physics and 19 mathematics courses A study of high school textbooks and the modelling processes of senior high students * Ruth Rodr guez Gallegos Mathematical modelling .

5 From Classroom to the real world 35 Denise Helena Lombardo Ferreira & Otavio Roberto Jacobini On the development of Mathematical modelling competencies 47 The PALMA longitudinal study * Rudolf vom Hofe, Alexander Jordan, Thomas Hafner, Pascal St lting, Werner Blum & Reinhard Pekrun The teachers tensions in Mathematical modelling practice 61 Andr ia Maria Pereira de Oliveira & Jonei Cerqueira Barbosa teaching to reinforced bonds between modelling and reflecting * 73 Mette Andresen Applying pastoral metamatism or re-applying grounded mathematics 85 Allan Tarp A new type of diagram to support functional modelling PROGRAPH diagrams 101 Hans-Stefan Siller Mathematical models in the context of sciences * 117 Patrica Camarena Gallardo Mathematical modelling .

6 The socio-critical perspective and the reflexive discussions * 133 Jonei Cerqueira Barbosa Mathematical modelling and environmental education 145 Ademir Donizeti Caldeira Mathematical models in the secondary Chilean education 159 Mar a D. Aravena & Carlos E. Caama o III IVTheme 2: Challenges in international collaboration on the teaching of Mathematical modelling Challenges with international collaboration regarding teaching of Mathematical modelling * 177 Thomas Lingefj rd A comparative study on Mathematical modelling competences 197 with German and Chinese students.* Matthias Ludwig & Binyan Xu Mathematical modelling in a European context 207 A European network-project.

7 * Stefanie Meier Theme 3: Didactical reflections on the teaching of Mathematical modelling Didactical reflections on the teaching of Mathematical modelling 217 Suggestions from concepts of time and place * Toshikazu Ikeda Formatting real data in Mathematical modelling projects * 229 Jussara de Loiola Ara jo Simple spreadsheet modelling by first-year business undergraduate students: 241 Difficulties in the transition from real world problem statement to Mathematical model * Djordje Kadijevich *) Papers presented orally during the TSG21 sessions at ICME-11. DIFFERENT PERSPECTIVES IN RESEARCH ON THE teaching AND LEARNING Mathematical modelling - CATEGORISING THE TSG21 PAPERS Morten Blomh j NSM, Roskilde University, Denmark Introduction We have a large and growing collection of didactical research on Mathematical modelling .

8 Moreover this research even seems to have had a serious impact on the practices of mathematics teaching at least on curricula level. During the last couple of decades the introduction of Mathematical modelling and applications is probably - together with the introduction of information technology - the most prominent common features in mathematics curricula reforms around the world (Kaiser, Blomh j and Sriraman, 2006, p. 82). Curricula reforms in many western countries, especially at secondary level have emphasised Mathematical model-ling as an important element in an up-to date mathematics secondary curricula preparing generally for further education.

9 Didactical research has undoubtedly played an important role in this development. The fundamental goals in the teaching of Mathematical modelling and the reasons for pursuing these goals developed and analysed in research can be pinpointed in the guidelines for mathematics teaching in many countries. Also, the general understanding of the model concept and of a modelling process expressed in many mathematics curricula is clearly influenced by didactical research. (Blum et al, 2007) and (Haines et al, 2006). However, the way Mathematical modelling and applications is organised in curricula and, especially, how these parts of the curricula are assessed reveal only a very limited influence from research.

10 And when it comes to the level of teaching practice in the classroom it is still a pending question to which degree the many developmental modelling projects carried out and analysed in research have actually influenced the practices of teaching Mathematical modelling . Influencing practices of mathematics teaching are not the only criteria for progress in the didactical research on Mathematical modelling . It is also relevant to try to evaluate the coherency of the theories developed. In the editorial Towards a didactical theory for Mathematical modelling of ZDM (2, vol. 38), we argued that at a general level it is possible to identify in the field of research.