PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
The equation has particles! How calculus students construct definite integral models
Page: 418
This research characterizes the cognitive challenges that students encounter while constructing definite integrals to model physical quantities and relationships, how students resolve those challenges, and the resulting conceptual artifacts. We video-recorded four groups of second- semester calculus students working with definite integral models during two 50-minute labs. This paper focuses on how two groups of students that worked on the same problem reasoned about and constructed an integral representing the gravitational attraction between a co-linear thin rod and point mass. Prior research on students’ understanding of definite integrals posits the multiplicative structure f (x)x in a Riemann sum as an essential component in conceiving an integral. Our findings indicate that in many contexts, other symbolic forms subsume the simple product in this essential conceptual role and that they interact significantly with students’ symbolic forms for the definite integral.