Proof is an essential practice of the discipline of mathematics and, as such, has a critical importance in mathematics education. For mathematicians, proof carries a special meaning as a heart of mathematical endeavors; for learners, developing productive dispositions towards proof and becoming proficient in proof writing is challenging. Geometry for Teachers (GeT) courses provide unique opportunities for undergraduate students to hone their proof-writing skills, take ownership of proving, and make connections to secondary teaching. This chapter focuses on students’ ability to “derive and explain geometric arguments and proofs,” one of the key student learning objectives (SLOs) of a GeT course. We unpack the dual meaning of the concept of proof as a creative process of exploration and meaning-making and as a formalized product of this process. Concurrently, we describe different ways in which instructors of GeT courses can support students’ developing mathematical habits of mind and proficiency with proof, and point to connections to other SLOs.
