Supporting Students in Exploring, Developing, and Formalizing Mathematical Arguments

The difficulties students encounter writing proofs have been heavily documented in the last several decades of research conducted on undergraduate proof writing. These difficulties have often been attributed to difficulties related to getting started in exploring a claim and generating initial strategies for proving. Our goal in this paper is to present an adaptation of Stylianides’ reasoning-and-proving framework as a lens to view students’ proof-writing as a multi-step process and how teaching sessions designed through this lens can support students learning and progression in reasoning, developing, and formalizing mathematical arguments. Our paper first describes our conceptualization of the proof-writing process in three stages, which is an adaptation of Stylianides’ reasoning-and-proving framework. We then describe the teaching sessions we designed alongside the different proof-writing activities we incorporated into each session. Additionally, we critique the effectiveness of the sessions at elucidating students’ challenges in the stages of the proof-writing process and at promoting their meta-knowledge of the processes involved in writing a proof.