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Investigating insight and rigour as separate constructs in mathematical proof.

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Title: Investigating insight and rigour as separate constructs in mathematical proof.
Authors: Sangwin, C. J.1 (AUTHOR) C.J.Sangwin@ed.ac.uk, Kinnear, George1 (AUTHOR)
Source: Research in Mathematics Education. Apr2026, Vol. 28 Issue 1, p25-53. 29p.
Subject Terms: *Mathematics education, *Comparative studies, Mathematical proofs, Awareness, Statistical reliability
Abstract: We investigate undergraduate mathematics students' conceptions of rigour and insight. We conducted comparative judgement experiments in which students were asked to judge different proofs of the same theorem with five separate criteria: rigour, insight, understanding, simplicity and assessment marks. We predicted, and our experiment found, that rigour is a reliable construct. We predicted that insight is also a reliable construct but asking students to judge on the basis of "which proof gives you more insight into why a theorem is true" did not result in a reliable judging scale. Our analysis suggests two distinct dimensions: rigour and marks contribute to one factor whereas simplicity and personal understanding relate to a second factor. We suggest reasons why insight was related almost equally to both factors. First, students may not have developed an aesthetic sense in which they appreciate insight in ways that are regularly discussed by mathematics educators. Second, insight may not be a coherent and well-defined construct after all. [ABSTRACT FROM AUTHOR]
Copyright of Research in Mathematics Education is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Investigating insight and rigour as separate constructs in mathematical proof.
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  Data: We investigate undergraduate mathematics students' conceptions of rigour and insight. We conducted comparative judgement experiments in which students were asked to judge different proofs of the same theorem with five separate criteria: rigour, insight, understanding, simplicity and assessment marks. We predicted, and our experiment found, that rigour is a reliable construct. We predicted that insight is also a reliable construct but asking students to judge on the basis of "which proof gives you more insight into why a theorem is true" did not result in a reliable judging scale. Our analysis suggests two distinct dimensions: rigour and marks contribute to one factor whereas simplicity and personal understanding relate to a second factor. We suggest reasons why insight was related almost equally to both factors. First, students may not have developed an aesthetic sense in which they appreciate insight in ways that are regularly discussed by mathematics educators. Second, insight may not be a coherent and well-defined construct after all. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Research in Mathematics Education is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/14794802.2024.2379301
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        Text: English
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      – SubjectFull: Mathematical proofs
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      – SubjectFull: Awareness
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      – SubjectFull: Statistical reliability
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              Text: Apr2026
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