Barbara Clarke,, Doug M. Clarke, Göran Emanuelsson, Bengt Johansson, Diana V. Lester, Anders Wallby, Karin Wallby
1 The Department of Science, Systems and Models, Roskilde University2 IMFUFA, Department of Science and Environment, Roskilde University
a theory for practice
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical framework, which has been used for designing modelling courses, analysing students’ modelling activities, identifying learning obstacles in the modelling process and to guide the teachers interaction with the students during their work. This will be illustrated with an example from a developmental project where 8. graders have worked with modelling real life phenomena related to their own experiences. In the chapter xx in part two of this book, two different ways of setting the scene for mathematical modelling activities at lower secondary level are presented.
International Perspectives on Learning and Teaching Mathematics, 2004, p. 145-159