Visual and Analytic Thinking in Calculus

A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts. The National Council of Teachers of Mathematics, for instance claims that "different representations support different ways of thinking about and manipulating mathematical o...

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Bibliographic Details
Published in:The Mathematics teacher 2009-09, Vol.103 (2), p.140-145
Main Authors: Haciomeroglu, Erhan Selcuk, Aspinwall, Leslie, Presmeg, Norma C., Knott, Libby
Format: Article
Language:English
Subjects:
Antiderivatives
Art sketches
Calculus
College students
Connecting Research to Teaching
Critical thinking
Inflection points
Line graphs
Mathematical analysis
Mathematics education
Mathematics teachers
Reasoning
Slope of a line
Tangents
Visualization
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Summary:A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts. The National Council of Teachers of Mathematics, for instance claims that "different representations support different ways of thinking about and manipulating mathematical objects." Here, Haciomeroglu, Aspinwall, and Presmeg feature their developed case-study approach to gain an understanding of the thinking process of two college students who had completed an elementary calculus sequence. They also offer here an in-depth discussion regarding visual and analytic thinking in calculus.
ISSN:0025-5769
2330-0582