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Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences

Alcock, L.; Simpson, A.

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Authors

L. Alcock



Abstract

This paper describes a study in which we investigated relationships between defining mathematical concepts — increasing and decreasing infinite sequences — explaining their meanings and classifying consistently with formal definitions. We explored the effect of defining, explaining or studying a definition on subsequent classification, and the effect of classifying on subsequent explaining and defining. We report that (1) student-generated definitions and explanations were highly variable in content and quality; (2) explicitly considering the meaning of the concept facilitated subsequent classification, and giving a personal definition or explanation had a greater effect than studying a given definition; (3) classifying before defining or explaining resulted in significantly poorer definitions and explanations. We discuss the implications of these results for the teaching of abstract pure mathematics, relating our discussion to existing work on the concept image/concept definition distinction and on working with examples.

Citation

Alcock, L., & Simpson, A. (2017). Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences. Educational Studies in Mathematics, 94(1), 5-19. https://doi.org/10.1007/s10649-016-9709-4

Journal Article Type Article
Acceptance Date Apr 22, 2016
Online Publication Date Jun 30, 2016
Publication Date Jan 1, 2017
Deposit Date May 4, 2016
Publicly Available Date Jun 30, 2017
Journal Educational Studies in Mathematics
Print ISSN 0013-1954
Electronic ISSN 1573-0816
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 94
Issue 1
Pages 5-19
DOI https://doi.org/10.1007/s10649-016-9709-4

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