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Title: Doctoral students’ use of examples in evaluating and proving conjectures
Authors: Alcock, Lara
Inglis, Matthew
Keywords: Examples
Generic examples
Number theory
Proof
Reasoning
Strategies
Issue Date: 2008
Publisher: © Springer
Citation: ALCOCK, L. and INGLIS, M., 2008. Doctoral students’ use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69 (2), pp. 111-129.
Abstract: This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and semantic reasoning strategies relative to a representation system of proof. We then use this conceptualisation as a basis for contrasting the behaviour of two successful mathematics research students whilst they evaluated and proved number theory conjectures. We observe that the students exhibited strikingly different degrees of example use, and argue that previously observed individual differences in reasoning strategies may exist at the expert level. We conclude by discussing implications for pedagogy and for future research.
Description: The final publication is available at: www.springerlink.com
Version: Accepted for publication
DOI: 10.1007/s10649-008-9149-x
URI: https://dspace.lboro.ac.uk/2134/8575
Publisher Link: http://dx.doi.org/10.1007/s10649-008-9149-x
ISSN: 0013-1954
1573-0816
Appears in Collections:Published Articles (Mathematics Education Centre)

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