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

Davies, B; Alcock, L; Jones, I; (2021) What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views. The Journal of Mathematical Behavior , 61 , Article 100824. 10.1016/j.jmathb.2020.100824. (In press).

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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.

Type: Article
Title: What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views
DOI: 10.1016/j.jmathb.2020.100824
Publisher version: https://doi.org/10.1016/j.jmathb.2020.100824
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Comparative judgement, Beliefs, Proof, Reliability, Validity, Mathematicians
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10119188
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