PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Expert Performance on Routine and Novel Integral Application (Volume) Problems
Page: 2-647
Past research has shown that students struggle when applying the definite integral concept, and these difficulties stem from incomplete understanding of the integral’s underlying structure. This study aims to provide insight into the construction of effective mental structures for integrals by examining experts’ solutions to volume problems. Seven mathematics faculty members from a large, public university solved three volume problems (two routine, one novel) in videotaped interview sessions. Preliminary analysis shows that the experts have a rich understanding of definite integrals, and the few instances of errors seemed to be a result of inattention as opposed to a deficit in understanding. Their problem-solving process was highly structured and detailed. The experts’ visual representations varied from sparse and static to fully 3-dimensional and dynamic. We hope to use this and past student data to construct a framework for analyzing student understanding of integral volume problems.