A longitudinal study on students' development and transfer of the concept of integration

We present results from the first two years of a project investigating how engineering students develop problem solving skills through their academic career. The project consists of a longitudinal study as well as cross-sectional studies in multiple courses in mathematics, physics and engineering. In this article, we focus on the transfer of knowledge from mathematics to physics courses. We track how students' understanding of function and integration evolves as they progress through the Calculus courses using individual semi-structured interviews. Most students develop a solid understanding of the mathematical concepts of function and integration. However, they are unable to access different representations (for example, use geometric reasoning) when solving a similar problem in the physics interviews. Transfer of knowledge depends upon students recognizing a connection between the different subjects.