Conceptual understanding of solutions to differential equations: How do assessment tasks promote it?

Overview & Synopsis

Differential equations (DEs) are used for modelling real-life phenomena in economics, engineering, natural and social sciences. Courses in DEs constitute an important part of engineering curricula at many universities but educational research on teaching DEs is rather scarce. Recent empirical studies point towards students' difficulties with the conceptual understanding of DEs and solutions to DEs. We use Conceptual Change Theory to analyse five tasks suggested in the literature for assessing students conceptual understanding of solutions to DEs arguing that only one problem contributes to the goal. The task on the Existence and Uniqueness Theorem for first-order linear DEs designed by the authors for engineering students revealed gaps in their conceptual understanding of the general solution to a DE. Our analysis emphases the role of rigour and nonstandard tasks for students' conceptual thinking.