Pedagogical Reflections on the Role of Modelling in Mathematics Instruction

Abstract

From a broad perspective, there are two categories of pedagogical aims of modelling. The first is where modelling itself is treated as an objective. The second is mathematical knowledge construction, where modelling is treated as a means to an end. For the first aim three key questions are considered: (1) How can the teacher set an appropriate situation so that students realise the necessity of solving a real-world problem? (2) How can the teacher assist students’ abstraction processes? (3) How can the teacher show students the necessity of controlling various assumptions? For the second aim, three principles are suggested: (1) expanding and clarifying real-world situations satisfying a developed original model, (2) expanding and integrating mathematical knowledge by setting up a concrete situation so that students can consider it, and (3) refining and clarifying the developed mathematical methods by treating instances of the same contexts repeatedly.