Towards a didactical theory for mathematical modelling

Abstract

Mathematics education research has been somewhat short of its own paradigmatic theories (see ZDM, 2005, issue 6 and ZDM 2006, issue 1 for an ongoing discussion). Theories are often borrowed from the background sciences and applied to the field of mathematics education e.g. general learning theories from pedagogy, sociology, psychology etc. This has led to our field being a subject to a host of criticisms (e,g., Lerman, 2006; Lester, 2005; Sriraman & English, 2005, 2006; Steen, 1999). Therefore it is relevant to look for areas in mathematics education where theories may emerge from studying the processes of teaching and learning mathematics. In this issue of ZDM we present and discuss what we consider to be an example of a developing theory within the field of mathematics education research, namely a theory for the teaching and learning of mathematical modelling. During the last decades a coherent theoretical understanding of mathematical modelling processes and connected teaching and learning processes has been emerging. This has happened through a close interplay between the development of curricula, teaching practices, experimental teaching, theoretical reflections and research. Together with the use of information technology, the introduction of mathematical modelling and applications is a prominent general feature of the recent developments in the practice of mathematics teaching, especially with regard to secondary level teaching. In this development, didactical research has already played an important role and we find it of general interest for mathematics education research to examine the development of a theory for mathematical modelling as a paradigmatic case for developing theory in close interplay with teaching practice.