Mathematical applications and modelling in the teaching and learning of mathematics

Organizing team composition

Papers and discussion documents

Morten Blomhoej (Denmark)

Susana Carreira (Portugal)

Swapna Mukhopadhyay (USA)

Ramiro Ávila Godoy (Mexico)

ravilag@gauss.mat.uson.mx

The aim of the study group is to present and discuss recent research within the area of teaching and learning mathematical modelling and applications and its role in mathematics education. The scope of this endeavour includes all levels and branches of mathematics teaching – elementary school, secondary or high school, college and university level as well as the transitions between levels.

In particular we welcome contributions that

? survey the current state of our knowledge concerning students development of modelling competency through the teaching of application and modelling

? review our knowledge of if and how the students’ learning of mathematics can be enhanced through the teaching of applications and modelling

? discuss mathematical modelling and its role in mathematics teaching from various perspectives such as mathematical, epistemological, learning, pedagogical-didactical perspectives and critical-societal perspectives.

? report recent research or developmental projects with thought provoking findings within the realm of our topic.

Some notes on the demarcation of TSG 21 in relation to closely related TSGs might be helpful for guiding potential contributors. First of all in TSG 21 our common focus of interest is the teaching and learning of modelling and the applications of models understood as the use of mathematics as a tool to understand, formulate, structure, and solve non-mathematical problems or situations occurring in the real world. Hereby TSG 21 distinguishes itself from TSG 19 that focuses on problem solving. It is no doubt that mathematical modelling often involves mathematical problem solving but in our understanding modelling also involves other types of processes with specific aspects of teaching and learning.

The inclusion of modelling is perhaps, together with the integration of information technology, the most wide spread and common feature in recent curriculum developments especially at secondary level. Therefore it is relevant to consider the demarcation to TSG 35. Research on the implementation of mathematical modelling in curricula and its effects is of interest to TSG 21 only if it includes analyses of specific cases of teaching and learning mathematical modelling.

Despite this attempt to clarify the demarcation of TSG 21 we expect to receive quite a few contributions that could be submitted to other TSGs with the same right, and in cases of doubt we will communicate with the organisers of the relevant TSGs in order to suggest the best placement of the contribution.

In a TSG there are three different types of contributions suggested by the IPC of ICME-11. Papers published on the web page of the TSG before the congress to be used as a basis for surveys and discussions during the congress, papers distributed to the participants as printed handouts at the congress prior to a TSG session and papers presented orally and discussed in one of the four TSG sessions during the congress. All three last types of papers will be made available on the web before the congress.

The OT of TSG21 has accepted fifteen papers as contributions to our group. Below, you find the final versions of thirteen of these papers listed in the order they appear in the programme. The remaining two papers will be uploaded as soon as we have the final versions.

During our four TSG sessions the presentation and discussion of papers will be structured according to the following three themes:

1. Conceptualizations of mathematical modelling in different theoretical frameworks and for different purposes.

2. Cultural differences and the importance of international co-operation in research and development on the teaching and learning of mathematical modelling.

3. Design of curricular experiments and didactical reflections on the teaching of mathematical modelling.

For each theme there will be a short introduction, oral presentations of a few selected papers and a short general discussion to round off the theme. Papers introducing each of the three themes will be uploaded only shortly before the congress, intentionally on July 1.

The paper presentations will have the format of 15 minutes presentation followed by 5 minutes for questions. The presenters should assume that all participants have read the papers beforehand and the participants are urged to fulfil their part of this assumption and be prepared to discuss all the papers published on the web-page.

Tuesday, July 8, 12.00-13.00: Introduction and Theme 1

12.00-12.15 Introduction to the programme for TSG21 (Morten Blomhøj and Susana Carreira)

12.15-12.35 Introduction to theme 1. Different perspectives on mathematical modelling in educational research – categorising the TSG21 papers, Morten Blomhøj.

12.40-13.00 Mathematical modelling, the socio-critical perspective and the reflexive discussion. Jonei Cerqueira Barbosa, Brazil

Wednesday, July 9, 12.00-13.30: Theme 1, continued

12.00-12.20 Mathematical models in the context of sciences. Patrica Camarena Gallardo, Mexico

12.20-12.40 Differential equations as a tool for mathematical modelling in physics and mathematics courses. Ruth Rodríguez Gallegos, France/Mexico

12.40-13.00 On the development of mathematical modelling competencies – The PALMA longitudinal study. Rudolf vom Hofe & Alexander Jordan et al., Germany

13.00-13.20 Reinforced bonds between modelling and reflecting. Mette Andresen, Denmark

13.20-13.30 Closing discussion on theme 1.

Friday, July 11, 12.30-13.30: Theme 2

12.30-12.50 Introduction to theme 2. Challenges with international collaboration regarding teaching of mathematical modeling. Thomas Lingefjärd, Sweden.

12.50-13.10 A comparative study on mathematical modelling competences with German and Chinese students. Matthias Ludwig, Germany & Binyan Xu, China

13.10-13.30 Mathematical modelling in a European context – A European network-project. Stefanie Meier, Germany.

Saturday, July 12, 12.00-13.30: Conclusion of Theme 2 and Theme 3

12.00-12.15 Closing discussion on theme 2.

12.15-12.35 Introduction to theme 3. Didactical Reflections on the teaching of mathematical modelling – Suggestions from concepts of “time” and “place”.

12.35-12.55 Formatting real data in mathematical modelling projects. Jussara de Loiola Araújo, Brazil

12.55-13.15 Simple spreadsheet modelling by first-year business undergraduate students: Difficulties in the transition from real world problem statement to mathematical model. Djordje Kadijevich, Serbia

13.15-13.30 Closing discussion on theme 3 and what did we accomplish in TSG21? Closing remarks by Susana Carreira.

All the papers accepted for publication on the TSG21 web-page are organised according to their relations to the three themes. Supplementary to the papers presented orally and mentioned in the programme above the following papers will be published at the web-page:

Papers related to theme 1: Conceptualizations of mathematical modelling in different theoretical frameworks and for different purposes.

Applying mathematics: Metamatics or Mathematism?

The teachers’ tensions in the practice of mathematical modelling.

Andréia Maria Pereira de Oliveira & Jonei Cerqueira Barbosa, Brazil

Papers related to theme 2: Cultural differences and the importance of international co-operation in research and development on the teaching and learning of mathematical modelling.

Papers related to theme 3: Design of curricular experiments and didactical reflections on the teaching of mathematical modelling.

Mathematical modelling: From classroom to the real world.

Denise Ferreira & Otavio R. Jacobini, Brazil

Prograph Diagrams – a new old system for teaching functional modelling.

Hans-Stefan Siller, Austria

Mathematical models in secondary Chilean education.

Maria Aravena Díaz & Carlos Caamaño Espinoza, Chile

Mathematical modelling and environmantal education.

Ademir Donizeti Caldeira, Brazil

Below you find pdf of the papers accepted for TSG21 in the order of their appearance in the programme and related to the three themes of the study group. The last three papers are the papers that introduced each of the three themes in the programme.

After the papers, also you find pdf of the power point presentations given orally at the TSG sessions during ICME-11 in the order of their appearance in the programme.

Papers and discussion documents

Call for Papers (38.00 KB)

Programme for TSG21 (13.00 KB)

Mathematical modelling, the socio-critical perspective and the reflexive discussion, Jonei Cerqueira Barbosa, Brazil (36.00 KB)

Mathematical models in the context of sciences, Patrica Camarena Gallardo, Mexico (77.00 KB)

Differential equations as a tool for mathematical modelling in physics and mathematics courses, Ruth Rodríguez Gallegos, France/Mexico (199.00 KB)

On the development of mathematical modelling competencies – The PALMA longitudinal study, Rudolf vom Hofe, Alexander Jordan, et al., Germany (516.00 KB)

Reinforced bonds between modelling and reflecting, Mette Andresen, Denmark (146.00 KB)

Applying mathematics: Metamatics or Mathematism?, Allan Tarp, Denmark (89.00 KB)

The teachers’ tensions in the practice of mathematical modelling, Andréia Maria Pereira de Oliveira and Jonei Cerqueira Barbosa, Brazil (56.00 KB)

A comparative study on mathematical modelling competences with German and Chinese students, Matthias Ludwig, Germany and Binyan Xu, China (246.00 KB)

Mathematical modelling in a European context – A European network-project, Stefanie Meier, Germany (125.00 KB)

Formatting real data in mathematical modelling projects, Jussara de Loiola Araújo, Brazil (58.00 KB)

Simple spreadsheet modelling by first-year business undergraduate students: Difficulties in the transition from real world problem statement to mathematical model, Djordje Kadijevich, Serbia (252.00 KB)

Mathematical modelling: From classroom to the real world, Denise Ferreira & Otavio R. Jacobini, Brazil (65.00 KB)

Prograph Diagrams - a new old system for teaching functional modelling, Hans-Stefan Siller, Austria (254.00 KB)

Mathematical modelling and environmental education, Ademir Donizeti Caldeira, Brazil (65.00 KB)

Challenges with international collaboration regarding teaching of mathematical modeling, Thomas Lingefjärd, Sweden (69.00 KB)

Didactical Reflections on the teaching of mathematical modelling, Toshikazu Ikeda, Japan (79.00 KB)

Different perspectives on mathematical modelling in educational research - categorising the TSG21 papers, Morten Blomhøj, Denmark (115.00 KB)

Presentation: Different perspectives on mathematical modelling in mathematics education research, Morten Blomhøj, Denmark (43.00 KB)

Presentation: Different perspectives on mathematical modelling in mathematics educational research - categorising the TSG21 papers, Morten Blomhøj, Denmark (48.00 KB)

Presentation: Mathematical modelling, the socio-crital perspective and the reflexive discussions. Jonei Cerqueira Barbosa, Brazil (368.00 KB)

Mathematical models in the context of science. Patricia Camarena Gallardo (112.00 KB)

Differential equations as a tool for mathematical modeling in physics and mathematics courses. Ruth Rodríguez Gallegos, Mexico (767.00 KB)

Presentation: On the development of mathematical modelling competencies - the The PALMA longitudinal study. Rudolf vom Hofe & Alexander Jordan, Germany (1.00 MB)

Presentation: Teaching to reinforce the bonds between modelling and reflecting. Mette Andresen, Denmark (143.00 KB)

Presentation: Challenges with international collaboration regarding teaching of mathematical modeling. Thomas Lingefjärd, Sweden (33.00 KB)

Presentation: Comparative study on mathematical modelling competence with German and Chinese students. Binyan Xu, China & Matthias Ludwig, Germany (525.00 KB)

Mathematical modelling in a European context - A EU network project. Stefanie Meier, Germany (431.00 KB)

Presentation: Didactical reflections on the teaching of mathematical modelling. Toshikazu Ikeda, Japan (482.00 KB)

Presentation: Formatting real data in mathematical modelling projects. Jussara de Loiola Araùjo, Brazil (97.00 KB)

Simple spreadsheet modeling by first-year business undergraduate students. Djordje Kadijevich, Serbia (100.00 KB)

Closing: What did we accomplished in TSG21? Susana Carriera, Portugal (21.00 KB)