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Matthew Inglis and 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 schooland university-level mathematics education.

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Matthew Inglis and Lara Alcock

We recently reported a study in which undergraduate students and research mathematicians were asked to read and validate purported proofs (Inglis & Alcock, 2012). In our eye-movement data, we found no evidence of the initial skimming strategy hypothesized by Weber (2008). Weber and Mejía-Ramos (2013) argued that this was due to a flawed analysis of eye-movement data and that a more fine-grained analysis led to the opposite conclusion. Here we demonstrate that this is not the case, and show that their analysis is based on an invalid assumption.