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On mathematicians' different standards when evaluating elementary proofs
journal contributionposted on 2013-04-19, 10:23 authored by Matthew InglisMatthew Inglis, Juan P. Mejia-Ramos, Keith Weber, Lara AlcockLara 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.
- Mathematics Education Centre
CitationINGLIS, M. ... et al., 2013. On mathematicians' different standards when evaluating elementary proofs. Topics in Cognitive Science, 5 (2), pp. 270 - 282.
PublisherJohn Wiley & Sons, Inc. © Cognitive Science Society, Inc.
- AM (Accepted Manuscript)
NotesClosed 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