Framing the structural role of mathematics in physics lectures: A case study on electromagnetism

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like) use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Figure 1

Videograph’s coding interface.

Figure 2

Timeline of the flux episode.

Figure 3

Timeline of the charged plate problem episode.

Figure 4

Timeline of the charge density episode.

Figure 5

Timeline of the Gauss’s law episode.

Figure 6

Timeline of the Ampère’s law episode.

Figure 7

Timeline of the flux through a disk problem episode.

Figure 8

Timeline of the electric field of an infinite wire problem episode.

Figure 9

Timeline of the magnetic field created by a finite wire problem episode.