AlcockSimpson(2016)ESM_ACCEPTED.pdf (2.36 MB)

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

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journal contribution
posted on 16.05.2016, 12:28 by Lara Alcock, Adrian Simpson
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.

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Educational Studies in Mathematics

Citation

ALCOCK, L. and SIMPSON, A., 2017. Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences. Educational Studies in Mathematics, 94(1), pp.5-19.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

22/04/2016

Publication date

2017

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s10649-016-9709-4

ISSN

0013-1954

eISSN

1573-0816

Language

en

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