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ERIC Number: EJ809618
Record Type: Journal
Publication Date: 2008-Oct
Pages: 19
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0013-1954
Doctoral Students' Use of Examples in Evaluating and Proving Conjectures
Alcock, Lara; Inglis, Matthew
Educational Studies in Mathematics, v69 n2 p111-129 Oct 2008
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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: Teachers; Researchers
Language: English
Sponsor: N/A
Authoring Institution: N/A