Mathematical Modelling: Can It Be Taught And Learnt?
Mathematical modelling (the process of translating between the real world and mathematics in both directions) is one of the topics in mathematics education that has been discussed and propagated most intensely during the last few decades. In classroom practice all over the world, however, modelling still has a far less prominent role than is desirable. The main reason for this gap between the goals of the educational debate and everyday school practice is that modelling is difficult both for students' and for teachers. In our paper, we will show examples of how students and teachers deal with demanding modelling tasks. We will refer both to results from our own projects DISUM and COM² as well as to empirical findings from various other research studies. First, we will present some examples of students' difficulties with modelling tasks and of students' specific modelling routes when solving such tasks (also dependent on their mathematical thinking styles), and try to explain these difficulties by the cognitive demands of these tasks. We will emphasise that mathematical modelling has to be learnt specifically by students, and that modelling can indeed be learned if teaching obeys certain quality criteria, in particular maintaining a permanent balance between teacher's guidance and students' independence. We will then show some examples of how teachers have successfully realised this subtle balance, and we will present interesting differences between individual teachers' handling of modelling tasks. In the final part of our paper, we will draw some consequences from the reported empirical findings and formulate corresponding implications for teaching mathematical modelling. Eventually, we will present some encouraging results from a recent intervention study in the context of the DISUM project where it is demonstrated that appropriate learning environments may indeed lead to a higher and more enduring progress concerning students' modelling competency.
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