An Improved Representation of Mathematical Modelling for Teaching, Learning and Research

Abstract

Modelling real-world physical or natural systems with mathematics is one of the cornerstones of scientific endeavour. A review of past works reveals significant differences and inconsistencies between the analysis and representations or images of mathematical modelling. New definitions are developed of a system, such as real-world problem, mathematical problem and mathematical solution; the process of relating and transforming one system to another, such as mathematising a real-world problem into a mathematical one, and modelling one system as another. The new definitions are then used to analyse and reconcile past images. To improve past images the following two new systems are introduced: the written-word description of a real-world problem, and the written-word description of the mathematical solution. The new systems provide a more realistic representation of what students experience in the classroom. The new definitions and systems are used to produce an improved image of mathematical modelling for pedagogy. This new image is a valuable tool for representing systems and processes of pedagogical modelling. This new image provides an anatomy of modelling that can be used to teach and identify different forms of learning, teaching and research modelling. The new image also provides a method of diagnosing students’ difficulties and targeting help.