Understanding Student Use of Differentials in Physics Integration Problems

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this paper we aim to explore students' reasoning about the differential concept in physics problems. We conducted group teaching or learning interviews with 13 engineering students enrolled in a second-semester calculus-based physics course. We amalgamated two frameworks--the resources framework and the conceptual metaphor framework--to analyze students' reasoning about differential concept. Categorizing the mathematical resources involved in students' mathematical thinking in physics provides us deeper insights into how students use mathematics in physics. Identifying the conceptual metaphors in students' discourse illustrates the role of concrete experiential notions in students' construction of mathematical reasoning. These two frameworks serve different purposes, and we illustrate how they can be pieced together to provide a better understanding of students' mathematical thinking in physics. (Contains 2 tables and 3 figures.)