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. |
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| 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] |
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| Database: | Education Research Complete |
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