1. x = ax= b f(x) Calculus students’ understanding of area and volume in calculus- and non-calculus contexts Allison Dorko Masters of Science in Teaching University of Maine Abstract Calculus students… Tasks & Subjects Results Researchers have documented difficulties that elementary school students have in understanding area and volume. We know very little about older students’ understanding of these concepts. This study develops descriptions of calculus students’ understanding of area and volume concepts in non-calculus contexts. Knowing what calculus students understand about area and volume will help us understand student difficulties with calculus applications such as integrals and Volumes of Revolution. Research questions: What do calculus students understand about area in non-calc contexts? What do calculus students understand about volume in non-calc contexts? Multivariable calculus students do calculations correctly and have expert-level conceptions of area and volume Introductory calculus students are relatively adept at area calculations but struggle with both volume computations and the conceptual aspects Consistent with findings from about elementary school students’ understanding of area and volume Not all students excel at calculus. Calculus courses have low enrollment rates; low retention rates; and some students demonstrate a less- than-ideal understanding of calculus topics (Steen 1987), sometimes getting by with just memorization. There are a few core ideas of integration that some students do not understand, among them (1) taking a limit of Riemann sums to find area under a curve and (2) volume of revolution (Orton 1993). Elementary school students struggle with computations, conceptual understanding, and units associated with various spatial measures (Lehrer 2003). 198 introductory calc students 43 multivariate calc students Written tasks: Computation Short answer Area under the curve = What is the volume of the object?

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