Dissertations

12-1988

Degree Name

Doctor of Philosophy

Department

Mathematics

Dr. Dwayne Channell

Dr. M. Kathleen Heid

Dr. Paul Eenigenburg

Dr. Robert Laing

Abstract

Student understanding of selected calculus concepts as developed through use of a Cartesian coordinate graphical representation system were investigated. Subjects (N = 163) enrolled in first-semester calculus sections at Western Michigan University participated in one of four treatment conditions: Graphics (G), exposure to a computer-graphically-developed conceptual course; Graphics Plus (G+), exposure to the same course as G subjects plus provision of computer graphics software and related supplemental assignments; Standard 1 (S1), exposure to a graphically-developed, conceptual course; and Standard 2 (S2), exposure to a traditional skill-oriented course.

Two investigations were undertaken. In Investigation 1, comparisons were made between G and G+ sections on student: (a) understanding of Cartesian graphs, including the ability to use graphs in understanding calculus concepts, and (b) attitudes toward the use of graphs. In Investigation 2, comparisons were made between G, G+, S1, and S2 sections on student: (a) performance on routine applied, routine symbolic, and nonroutine symbolic questions; (b) performance on the departmental final exam and its subscales: (c) changes in attitudes toward mathematics; and (d) attitudes toward the course. Prior calculus experience was used as a blocking variable for cognitive measures on two levels, prior and no prior experience. Multivariate analysis with covariates, precalculus competency and attitudes toward mathematics, were performed for cognitive variables. $\chi\sp2$ tests were conducted for affective variables.

For Investigation 1, no significant differences (p <.05) were detected between the G and G+ sections. G+ subjects' scores on cognitive variables were slightly higher than those of G subjects, suggesting that further study is warranted. Attitudes pertaining to the use of graphs were overwhelmingly positive.

For Investigation 2, significant differences favored G subjects over S2 subjects on nonroutine symbolic questions. Questionable significant differences were detected for routine questions. Attitudes toward the course and mathematics were generally positive. Retention rates were much higher for the conceptually-developed sections than for the technique-oriented section.

Results suggest that developing calculus concepts through the use of a graphic representation system, especially as presented through computer graphics, can positively affect student understanding and interest without necessarily, negatively influencing skill acquisition.