Modelling labs for a course on differential equations

Abstract

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential. However, students often struggle to create and understand these models in the course. The purpose of this article is to share and examine a scaffolded sequence of labs implemented at regular intervals throughout a semester intended to train students in construction and analysis of mathematical models using differential equations. In these labs students learn basic principles of modelling that better prepare them for many of the high-quality modelling projects already available in differential equations. The course in which these activities were developed is taught using the SIMIODE text, Differential Equations: A Toolbox for Modelling the World, by Kurt Bryan. The labs are split into two components, with the first completed during class time and the second as out of class assignments. Furthermore, the course was re-organised to allow for the time needed to introduce the labs in class. We include classroom materials for labs, analysis, results on student perceptions and pedagogical recommendations.