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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 authored 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.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

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.

Publisher

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

Version

AM (Accepted Manuscript)

Publication date

2014

Notes

This is a conference paper.

Language

en