Title

Contrasting Cases of Calculus Students' Understanding of Derivative Graphs

Authors

Authors

E. S. Haciomeroglu; L. Aspinwall;N. C. Presmeg

Comments

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Abbreviated Journal Title

Math. Think. Learn.

Keywords

Education & Educational Research

Abstract

This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to sketch antiderivative graphs when presented with derivative graphs. These students constructed different and idiosyncratic images and representations leading to different understandings of derivative graphs. Our results suggest that the two students whose cognitive preferences were strongly visual or analytic and who did not synthesize visual and analytic thinking experienced different difficulties associated with their preferred modes for mathematical representation and thinking. Even the student who did synthesize these modes to some extent, to good effect, experienced difficulty when he did not do so. We discuss pedagogical implications for these results in a final section.

Journal Title

Mathematical Thinking and Learning

Volume

12

Issue/Number

2

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

152

Last Page

176

WOS Identifier

WOS:000293189400002

ISSN

1098-6065

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