Benefits of using context while teaching differential equations

Abstract

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret differential equations. We use a pretest posttest quasi-experimental design with an experimental and a control group. The experimental group is offered context-rich problems in which the construction of a differential equation and the interpretation of its solution in the given context is emphasized, while the control group is offered problems that mostly lack context and focus on procedural knowledge and skills only. The study shows that offering context-rich problems results in students being more skilled in the construction and interpretation of differential equations. Furthermore, it seems that the progress of students in these skills is not at the expense of procedural knowledge. According to our results, high performing students benefit the most from an approach that does not only focus on procedures. Finally, this approach seems to be effective in eliminating the misconception concerning the interpretation of the derivative in a differential equation as a change of amount instead of a rate of change.

Keywords:

• Mathematics education
• teaching differential equations
• ODEs
• conceptual understanding
• context-rich problems

Acknowledgments

First of all, we would like to thank the student teachers Hanne Lambrichts, Egon Patteeuw, and Lies Van den Eynde for their collaboration in setting up and conducting this study. Moreover, we want to acknowledge the professors of ‘Calculus, part 2’ for supporting this study in the context of their course. Furthermore, we would like to thank the TAs and the master students involved in the course for their cooperation in the study while guiding the recitation sessions. At last, we are grateful to the engineering students at KU Leuven who participated in the pre- and posttests.

Disclosure statement

No potential conflict of interest was reported by the authors.