Contrasting Cases of Calculus Students' Understanding of Derivative Graphs

    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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