The influence of ready-made tools on students’ learning by modelling with differential equations systems

Abstract

This article discusses the role played by the tool when students learn about differential equations systems (DE) by modelling. The discussion was based on a three-case sub-study of an ongoing study of group-reports from experienced mathematics teachers participating in a masters’ program in mathematics education. In the teaching sequences, setting the scene for the students’ modelling of authentic problems by DE, it was indispensable to include a variety of digital resources such as databanks and software for numerical solutions, graphical representations, and some sorts of simulations. Apps with simulations of commonly used DE models are widespread on the internet, some of them are user-friendly and elaborated to a degree that justify use of the term ready-made tools. The issue addressed in this article is whether such ready-made tools constitute shortcuts to the students’ modelling process and thereby obstacles in their learning of mathematics. For the analysis, the term direction of modelling was used to make a distinction between expressive and explorative modelling, respectively. Direction of modelling proved useful for the analysis of students’ learning not only with relation to the ready-made tool but also more generally. In line with the author’s previous research, students’ learning of mathematics by modelling was conceptualised in terms of emergent models and modelling and detected by textual analysis of students’ written reports. The study gave new insight into the students’ learning processes in the form of a variety of patterns for interplay between the tool use and the learning of mathematics. This variety seems to be pivotal for the designs of modelling sequences in general and particularly in the case of DE due to their dependence on digital resources.