What do mathematicians mean by proof? A comparative-judgement study of students’ and mathematicians’ views

We present a study in which mathematicians and undergraduate students were asked to explain writing what mean by proof. The 175 responses evaluated using comparative judgement: compared pairs of their judgements used construct scaled rank order. provide evidence establishing the reliability, divergent validity content this approach investigating individuals’ written conceptions mathematical In doing so, we compare quality student mathematician identify features judges collectively valued. Substantively, our findings reveal that despite variety views literature, broadly agree on people should say when Methodologically, judgement could have an important role play ideas, conjecture similar methods be productive evaluating more general (mathematical) beliefs.