AlcockSimpson(2016)ESM_ACCEPTED.pdf (2.36 MB)
Interactions between defining, explaining and classifying: The case of increasing and decreasing sequences
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 MathematicsCitation
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
© SpringerVersion
- 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
2016-04-22Publication date
2017Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s10649-016-9709-4ISSN
0013-1954eISSN
1573-0816Publisher version
Language
- en
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