STUDENT UNDERSTANDING OF DEFINITE INTEGRALS WITH RELEVANCE TO PHYSICS USING GRAPHICAL REPRESENTATIONS

Learning physics concepts often requires fluency with the underlying mathematics concepts. Mathematics not only serves as a representational tool in physics (e.g. equations, graphs and diagrams), but it also provides logical paths to solve complex physics problems. The broad scope of this research is to understand the extent to which students’ mathematical knowledge and understanding influence their responses to physics questions. One mathematical concept that is widely used across a broad spectrum of contexts in physics is the definite integral. We studied students’ conceptual understanding of definite integrals that are relevant in physics contexts. We also identified specific difficulties that students have with definite integrals, particularly with graphical representations. One strong focus of this work was how students reasoned about integrals that yield a negative result.

In this study, two written surveys were administered in introductory calculus-based physics and multivariable calculus classes, and seven individual interviews were conducted with students from the physics survey population. In the first survey, students were asked to determine the signs and compare the magnitudes of two integrals. In interviews, students' deep understanding of integrals was probed by varying representational features of the graphs from the first written survey. The second survey was administered in the following semester to test some of the interview results in a larger population.

Overall, our results serve as one example that the connections between mathematics and physics are not trivial for students to make, and need to be explicitly pointed out. Implications for additional research as well as for instruction are discussed.