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

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.