Students’ personal proof approaches: how students determine what a proof proves

To learn more about students' conceptualisations of the relationships between proofs and the claims they prove, we created a genre of tasks called Proof Without Claim (PWC). In these PWC tasks, the student is given a proof in which explicit mention of the statement being proven is omitted. They are then tasked with identifying this omitted statement. We introduce the construct of Personal Proof Approach (PPA), which parallels Selden, J., and Selden, A.'s (1995. Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29, 123–151) proof framework construct, to characterise the various ways in which students relate the statement being proven to the content of the proof. Analysing PPAs can reveal how students conceptualise the relationship between a proof and what it proves.