Mathematical Modelling in Teacher Education – Overview

Abstract

Within ICTMA and beyond, it is essential that authors clearly present their understanding of the term mathematical modelling. There are multiple interpretations and associated understandings, which contribute to fruitful discourse, but at times, it is left to the reader to identify the views of the author. The same is true of the term teacher education, but here the differences relate to practices rather than interpretation. Firstly, the meaning of mathematical modelling is examined. With respect to purposes for teaching, Julie and Mudaly (2007, p. 504) identified modelling as vehicle and modelling as content. For the former, real world problems are used for both motivation and the development of specific mathematical content. For the latter, the focus shifts to ‘developing the capacity of students to address problems located in the external world, and to evaluate the quality of their solutions’ (Galbraith 2007, p. 181). These approaches are not dichotomous, whilst the emphasis may be different the goals may intersect as, in order to solve a genuine problem, the need for new mathematical content may emerge (Stillman et al. 2008, p. 145). In addition, what distinguishes a modelling task from an application task? Stillman positions applications tasks ‘between structured word problems and open modelling problems’ (2000, p. 334) such that the problem must be embedded in a real world context. Moreover, ‘in an applications task, the primary sources of information that are external to the task solver are the problem statement and any accompanying visual representations’ (p. 335).