PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Student Understanding of Integration When Applied to Finding Volumes of Solids
Page: 2-581
Past research has shown that students struggle when solving definite integral application problems, but little has been done to examine the sources of their difficulties. This study aims to more thoroughly examine student misconceptions about definite integrals and develop new curricula to address these issues. Participants were second-semester calculus students enrolled in a large, public university. Exam problems required students to sketch approximating slices of given solids, and set up a corresponding volume integral. Students’ written work was analyzed for common mistakes and misconceptions. Although some students solved the problems correctly, a majority exhibited major deficiencies in their understanding of how to apply the definite integral. Most surprising was students’ widespread failure to make a connection between the sketch and the set up of the integral. Further research is currently under way that aims to expose sources of students’ faulty thought processes when using definite integrals to solve volume problems.