PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Students’ views of the relationship between integration and volume when solving second-semester calculus volume problems
Page: 1081
Volume problems are a typical first type of integral application problem that students encounter in second-semester calculus. We will present students’ responses to the question, “Why does integration give a volume?” Participants were Calculus 2 and Calculus 3 students enrolled in summer classes at a large, public university. Task-based interviews consisted of students working on and discussing second-semester volume problems. Students had varied and interesting responses that included formula-, units-, and derivative/antiderivative-based reasoning. These results are part of a larger study on how students understand the underlying structure of the definite integral, and how they use pictures and visualizations when solving volume problems.