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Undergraduates’ example use in proof construction: purposes and effectiveness

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journal contribution
posted on 2011-11-17, 13:09 authored by Lara AlcockLara Alcock, Keith Weber
In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully constructing proofs, and that these purposes are consistent with those described by mathematicians. We then examine other cases in which students used examples ineffectively. We note that in these cases, the purposes for which the students attempted to use examples are again appropriate, but the implementation of their strategies is inadequate in one of two specific ways. On this basis we identify points that should be borne in mind by a university teacher who wishes to teach students to use examples effectively in proof-based mathematics courses.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

ALCOCK, L. and WEBER,K., 2010. Undergraduates’ example use in proof construction: purposes and effectiveness. Investigations in Mathematics Learning, 3 (1), pp. 1-22

Publisher

© Research Council on Mathematics Learning

Version

  • AM (Accepted Manuscript)

Publication date

2010

Notes

This article was published in the journal, Investigations in Mathematics Learning [© Research Council on Mathematics Learning].

ISSN

1947-7503

Language

  • en

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