Expert and Novice Approaches to Reading Mathematical Proofs

By Matthew Inglis, Lara Alcock. 2012

78 citations recorded by the source corpus.

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 schooland university-level mathematics education.

Subfields: Education, Experimental and Cognitive Psychology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/494e7981ee892d500139708e53901d6260bd83b1

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Citations in the corpus

Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey. (2016, background): “Students' propensity to focus on calculation rather than the overarching ideas of the proof has been documented in the proof reading literature (e.g., Inglis & Alcock, 2012; Selden & Selden, 2003).”
Why and how mathematicians read proofs: further evidence from a survey study (2014, methodology): “Based on their data from an eye-tracking study, Inglis and Alcock (2012) questioned Weber’s (2008) finding that mathematicians skimmed a proof at the beginning of a proof validation attempt.”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “…of the 20 mathematicians judged “the real thing” to be valid and only 12 judged “the gap” to be 18Whether mathematicians actually read a proof for its high-level ideas is currently under debate in the mathematics education community (e.g., Inglis & Alcock, 2012, 2013; Weber & Mejia-Ramos, 2013b).”