## Two Aspects of Proof: Examining the Amount of Logic in Student-Constructed Proofs and Mathematicians’ Actions in Recovering From Proving Impasses

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##### Abstract

To obtain a Master’s or PhD in mathematics, or even to succeed in proof-based courses in an undergraduate mathematics major, one must often be able to construct original proofs, a common difficulty for students [18, 30]. This process of proof construction is usually explicitly taught, if at all, to U.S. undergraduates as a small part of a course, such as linear algebra, whose stated goal is something else, or in a transition-to-proof or “bridge” course. Students might also get discouraged when attempting a proof, perhaps due to the differences between proving and prior exercises [15] asked of them. Students may often complain about “getting stuck.” In this article, I attempt to address two questions in proving: what extent does logic appear on the surface of student-constructed proofs, and what do mathematicians do when they “get stuck.”