Calculus Students’ Understanding of Volume

Abstract

Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students’ understanding of 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 elements. We found that some of these 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 what has been documented for elementary school students. Implications for calculus teaching and learning are discussed.