How mathematicians assign points to student proofs

In this paper, we present an exploratory study on the important but under-researched area in undergraduate mathematics education: How do mathematics professors assign points to the proofs that their students submit? We interviewed nine mathematicians while they assigned points to three student-generated proofs from a transition-to-proof course. We observed that (i) One proof that contained a generic sub-proof was evaluated as correct by all nine participants and was given full credit by six participants, (ii) there were ten instances in which a mathematician did not assign full credit to a proof that she evaluated as correct, (iii) there was substantial variation in the points assigned to one proof, and (iv) mathematicians assigned points based not primarily on the correctness of the written artifact that they were given, but rather based on their models of students' understanding. We discuss the importance of these observations and how they can inform future research.