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The ability to reject invalid logical inferences predicts proof comprehension and mathematics performance

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conference contribution
posted on 13.05.2014, 12:10 by Lara AlcockLara Alcock, Toby Bailey, Matthew InglisMatthew Inglis, Pamela Docherty
In this paper we report a study designed to investigate the impact of logical reasoning ability on proof comprehension. Undergraduates beginning their study of proof-based mathematics were asked to complete a conditional reasoning task that involved deciding whether a stated conclusion follows necessarily from a statement of the form “if p then q”; they were then asked to read a previously unseen proof and to complete an associated comprehension test. To investigate the broader impact of their conditional reasoning skills, we also constructed a composite measure of the participants’ performance in their mathematics courses. Analyses revealed that the ability to reject invalid denial-of-the-antecedent and affirmation-of-theconsequent inferences predicted both proof comprehension and course performance, but the ability to endorse valid modus tollens inferences did not. This result adds to a growing body of research indicating that success in advanced mathematics does not require a normatively correct material interpretation of conditional statements.



  • Science


  • Mathematics Education Centre


ALCOCK, L. ... et al, 2014. The ability to reject invalid logical inferences predicts proof comprehension and mathematics performance. Presented at: 17th Conference on Research in Undergraduate Mathematics Education, Denver, CO, USA, 27th February - 1st March 2014.


Special Interest Group of the Mathematical Association of American on Research in Undergraduate Mathematics Education (SIGMAA on RUME)


AM (Accepted Manuscript)

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This is a conference paper.