Date of Award


Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)




Natasha M. Speer

Second Committee Member

Eric Pandiscio

Third Committee Member

Robert Franzosa


Researchers have documented difficulties that elementary school students have in understanding area and volume. Although area and volume show up in various ways later in the curriculum, we know very little about older students' understanding of these concepts. The goal of this study is to develop descriptions of calculus students' understanding of area and volume concepts in non-calculus contexts. Participants included 255 introductory calculus students and 43 multivariable calculus students. Clinical interview transcripts and students' written responses to area and volume problems (computational and short answer) were analyzed. Findings from the study indicate that multivariable calculus students struggle with neither the computations nor the units of area and volume problems. In contrast, some differential calculus students struggle with the units associated with various spatial measures. In addition, some differential calculus students mistakenly find surface area when directed to find volume.