Seeking physical/mathematical coherence by recruiting and reconciling reasoning: A case study in E&M

Abstract

The entanglement between physical and mathematical reasoning can be exploited for problem solving, making physical/mathematical coherence seeking a desirable learning goal. Our research aim is to contribute an empirical example of physical/mathematical coherence seeking during physics problem solving. Drawing from a video corpus of 18 interviews with students solving qualitative E&M problems, we present a case study of how and why a student reasons coherently with physical entities/processes and mathematical equations across three lines of reasoning. We focus especially on the role of the student's attempt to seek coherence, which explains their serious consideration of a contradiction that arises between a physical and a mathematical line of reasoning. Even after reaching the correct conclusion, the student recruits a third line of reasoning involving ideas from outside the explicit problem statement to resolve the contradiction. We end by discussing hypotheses about how instruction in physical/mathematical coherence seeking could support students in problem solving.