Teaching proof to undergraduates: semantic and syntactic approaches

This paper contrast the rationales behind semantic and syntactic approaches to teaching an undergraduate transition-to-proof course, using data from interviews with two mathematicians. It addresses the ICMI theme of teachers’ views and beliefs, with particular focus on (1) instructors’ expectations in proofbased courses and (2) both example-based and logical structure-based skills that we would like students to develop before arriving at university.