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On mathematicians' different standards when evaluating elementary proofs

journal contribution
posted on 19.04.2013, 10:23 by Matthew Inglis, Juan P. Mejia-Ramos, Keith Weber, Lara Alcock
In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

INGLIS, M. ... et al., 2013. On mathematicians' different standards when evaluating elementary proofs. Topics in Cognitive Science, 5 (2), pp. 270 - 282.

Publisher

John Wiley & Sons, Inc. © Cognitive Science Society, Inc.

Version

AM (Accepted Manuscript)

Publication date

2013

Notes

Closed access. This article was published in the journal, Topics in Cognitive Science [John Wiley & Sons, Inc. © Cognitive Science Society, Inc.] and the definitive version is available at: http://dx.doi.org/10.1111/tops.12019

ISSN

1756-8757

Language

en

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