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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/9087

Title: Undergraduates’ example use in proof construction: purposes and effectiveness
Authors: Alcock, Lara
Weber, Keith
Keywords: Advanced mathematical thinking
College counterexamples
Definitions
Equivalence relations
Examples
Functions
Mathematics education
Proof
Transition-to-proof courses
Undergraduates
Issue Date: 2010
Publisher: © Research Council on Mathematics Learning
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
Abstract: 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.
Description: This article was published in the journal, Investigations in Mathematics Learning [© Research Council on Mathematics Learning].
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/9087
ISSN: 1947-7503
Appears in Collections:Published Articles (Mathematics Education Centre)

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