What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views
What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views
We present a study in which mathematicians and undergraduate students were asked to explain in writing what mathematicians mean by proof. The 175 responses were evaluated using comparative judgement: mathematicians compared pairs of responses and their judgements were used to construct a scaled rank order. We provide evidence establishing the reliability, divergent validity and content validity of this approach to investigating individuals’ written conceptions of mathematical proof. In doing so, we compare the quality of student and mathematician responses and identify which features the judges collectively valued. Substantively, our findings reveal that despite the variety of views in the literature, mathematicians broadly agree on what people should say when asked what mathematicians mean by proof. Methodologically, we provide evidence that comparative judgement could have an important role to play in investigating conceptions of mathematical ideas, and conjecture that similar methods could be productive in evaluating individuals’ more general (mathematical) beliefs.
Davies, Ben
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Alcock, Lara
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Jones, Ian
57f5005d-e071-4140-b95c-4953d7b40ae5
Davies, Ben
aa12efcd-c8a4-4abc-9f2a-469afaff2770
Alcock, Lara
f4c0d07f-0fde-4a10-b893-28b49c980613
Jones, Ian
57f5005d-e071-4140-b95c-4953d7b40ae5
Davies, Ben, Alcock, Lara and Jones, Ian
(2020)
What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views.
Journal of Mathematical Behavior, [100824].
(doi:10.1016/j.jmathb.2020.100824).
Abstract
We present a study in which mathematicians and undergraduate students were asked to explain in writing what mathematicians mean by proof. The 175 responses were evaluated using comparative judgement: mathematicians compared pairs of responses and their judgements were used to construct a scaled rank order. We provide evidence establishing the reliability, divergent validity and content validity of this approach to investigating individuals’ written conceptions of mathematical proof. In doing so, we compare the quality of student and mathematician responses and identify which features the judges collectively valued. Substantively, our findings reveal that despite the variety of views in the literature, mathematicians broadly agree on what people should say when asked what mathematicians mean by proof. Methodologically, we provide evidence that comparative judgement could have an important role to play in investigating conceptions of mathematical ideas, and conjecture that similar methods could be productive in evaluating individuals’ more general (mathematical) beliefs.
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Davies, Alcock and Jones (2021) - preprint
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Accepted/In Press date: 9 November 2020
e-pub ahead of print date: 3 December 2020
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Local EPrints ID: 470676
URI: http://eprints.soton.ac.uk/id/eprint/470676
ISSN: 0732-3123
PURE UUID: e9acdaba-4c73-4c53-9103-8279dfdf0ad5
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Date deposited: 17 Oct 2022 17:04
Last modified: 17 Mar 2024 07:31
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Author:
Ben Davies
Author:
Lara Alcock
Author:
Ian Jones
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