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Expert and novice approaches to reading mathematical proofs
journal contribution
posted on 2012-06-25, 11:11 authored by Matthew InglisMatthew Inglis, Lara AlcockLara AlcockThis 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 MathematicsVersion
- NA (Not Applicable or Unknown)
Publication date
2012Notes
This article was published in the Journal for Research in Mathematics Education [© National Council of Teachers in Mathematics ]:http://www.nctm.org/publications/jrme.aspxISSN
0021-8251Publisher version
Language
- en