Experienced provers’ operative logical principles for evaluating proofs of conditional claims

Introduction to proof courses often teach mathematics majors logical principles to support their later interactions with proof. Prior research tells us little about how students draw upon these principles or their justifications in subsequent processes of comprehending proofs. This study investigates what logical principles thirteen experienced undergraduates employ while reading proofs of conditional claims. We also consider whether and how they justify any of those principles. Asking students to read various proofs related to a given conditional statement helped reveal their attention to and reasoning about logical principles. We found that student judgments were almost always logically normative, but their readiness to justify those principles varied more widely. Furthermore, we observe that students interpreted proofs in terms of inferences rather than truth-values showing some disconnect between their operative logic and the ways logic is generally taught in introduction to proof courses.