Visualizing and finding volumes of solids of revolution : research on the conceptual-based difficulties experienced by calculus students
Connon, Melinda S.
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Teaching experiments on finding volumes of solids of revolution were conducted with five student volunteers who were selected from three sections of second-semester calculus. As measured by the Paper Folding Test (of the Factor- Referenced Cognitive Tests) and the Space Relations Test (of the Differential Aptitude Test), these five students had average- to above-average visualization skills. The researcher worked individually with the students for three to four 50- minute sessions regarding finding volumes of solids of revolution. Physical models were used and visual explanations were stressed during the instructional interactions. Initially, the students? selections of the methods for finding the volumes were based on their images of the whole solids rather than on the slices needed for the models which the specific calculus methods required. Various geometric and algebraic misconceptions which prevented the students from consistently setting up correct volume integrals were identified. After instruction, the visualization of the five students improved and they began to form images of the appropriate slicing necessary for each particular method in order to find the volumes of the solids of revolution. Students also improved their ability to express the geometric situations algebraically, but misconceptions remained. Based on the findings of this research, suggestions for future instruction about finding volumes of solids of revolution were made.