In order to learn more about student understanding of the structure of proofs, we generated a novel genre of tasks called "Proof Without Claim" (PWC). Our work can be viewed as an extension of Selden and Selden's (1995) construct of "proof framework"; while Selden and Selden discuss how the structure of a proof can be discerned by the claim it proves, we leverage the consideration that one can discern a claim by the structure of its proof. In these PWC tasks, the student is presented with a proof with any explicit mention of its claim being proven removed and is instructed to discern the proof's claim. We introduce the construct of Personal Proof Framework (PPF) to describe the varied ways in which students relate the claim being proven to the content of the proof. [For the complete proceedings, see ED658295.]