PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Calculus Students’ Understanding of Volume
Page: 2-498
Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students’ volume understanding volume. This study investigated calculus students’ understanding of volume. Clinical interview transcripts and written responses to volume problems were analyzed. One finding is that some calculus students, when asked to find volume, find surface area instead and others blend volume and surface area ideas. We categorize students’ formulae according to their volume and surface area elements. Clinical interviews were used to investigate why students might find surface area when asked for volume. We found that some students believe adding the areas of an object’s faces measures three-dimensional space. Findings from interviews also revealed that understanding volume as an array of cubes is connected to successfully solving volume problems. This finding and others are compared to those for elementary school students. Implications for calculus teaching and learning are discussed.