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What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views

journal contribution
posted on 12.11.2020, 12:04 by Benjamin Davies, Lara AlcockLara Alcock, Ian JonesIan Jones
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.

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

The Journal of Mathematical Behavior

Volume

61

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal The Journal of Mathematical Behavior and the definitive published version is available at https://doi.org/10.1016/j.jmathb.2020.100824.

Acceptance date

09/11/2020

Publication date

2020-12-03

Copyright date

2020

ISSN

0732-3123

Language

en

Depositor

Dr Lara Alcock. Deposit date: 12 November 2020

Article number

100824