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Doctoral students’ use of examples in evaluating and proving conjectures

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journal contribution
posted on 05.07.2011, 15:37 by Lara Alcock, Matthew Inglis
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.

History

School

  • Science

Department

  • Mathematics Education Centre

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.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publication date

2008

Notes

The final publication is available at: www.springerlink.com

ISSN

0013-1954;1573-0816

Language

en

Exports

Loughborough Publications

Categories

Exports