Visualizing and finding volumes of solids of revolution : research on the conceptual-based difficulties experienced by calculus students

Author

Melinda S. Connon

Publication Date

1996

Document Type

Dissertation/Thesis

First Advisor

Khoury, Helen

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences

LCSH

Concepts; Calculus--Study and teaching (Higher)--Psychological aspects

Abstract

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.

Comments

Includes bibliographical references (pages [157]-164)

Recommended Citation

Connon, Melinda S., "Visualizing and finding volumes of solids of revolution : research on the conceptual-based difficulties experienced by calculus students" (1996). Graduate Research Theses & Dissertations. 6663.
https://huskiecommons.lib.niu.edu/allgraduate-thesesdissertations/6663

Extent

iv, 277 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text