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