Didactic and pragmatic approaches to mathematical modelling

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Abstract
The teaching of mathematical modelling is a growing industry. Ten years ago few, if any, institutes of higher education taught mathematical modelling as such. Today it is a subject in its own right and its advocates suggest that it might even have a place in the primary school, such has been its increase in popularity. This paper suggests that now is the time to reflect on this growth and to consider the subject from a pedagogical point of view. It is argued that in most of the literature, scant regard is given as to why we are teaching mathematical modelling and, where this is perhaps not the case, we do not make it clear to those who are being taught what they are actually doing. A classification of models into true, didactic and pragmatic is suggested so as to help define aims and objectives for the modelling activity. The paper argues that it is only when this classification is done and when a clear set of learning objectives is presented that the activity of modelling mathematically is worthwhile. Two models, one didactic on rolling resistance, and one pragmatic on comminution of particulate solids, are developed to highlight the differences between these two types of models.

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