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Expert and novice approaches to reading mathematical proofs

journal contribution
posted on 25.06.2012 by Matthew Inglis, Lara Alcock
This article presents a comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians. Participants’ eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short purported proofs; (b) compared with mathematicians, undergraduate students spend proportionately more time focusing on “surface features” of arguments, suggesting that they attend less to logical structure; and (c) compared with undergraduates, mathematicians are more inclined to shift their attention back and forth between consecutive lines of purported proofs, suggesting that they devote more effort to inferring implicit warrants. Pedagogical implications of these results are discussed, taking into account students’ apparent difficulties with proof validation and the importance of this activity in both school- and university-level mathematics education.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

INGLIS, M.J. and ALCOCK, L., 2012. Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43 (4), pp. 358-390.

Publisher

© National Council of Teachers in Mathematics

Version

NA (Not Applicable or Unknown)

Publication date

2012

Notes

This article was published in the Journal for Research in Mathematics Education [© National Council of Teachers in Mathematics ]:http://www.nctm.org/publications/jrme.aspx

ISSN

0021-8251

Language

en

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