Counterexamples and refutations in undergraduate mathematics

How do undergraduate mathematics students interpret refutations? We investigated this question by asking participants to 1) decide whether statements are true or false and provide refutations, 2) evaluate counterexamples and ‘correct versions’ of the statements as valid or invalid refutations, and 3) judge which potential refutations are better, explaining why. We report a study in which 173 undergraduate mathematics students completed this task. Results reveal that participants did largely understand the logic of counterexamples but did not reliably understand the broader logic of refutations.