Classroom sociomathematical norms for proof presentation in undergraduate in abstract algebra

This paper is a case study of the teaching of an undergraduate abstract algebra course with a particular focus on the manner in which the students presented proofs and the class engaged in a subsequent discussion of those proofs that included validating the work. This study describes norms for classroom work that include a set of norms that the presenter of a proof was responsible for enacting, including only using previously agreed upon results, as well as a separate set that the audience was to enact related to developing their understanding of the presented proof and validating the work. The study suggests that the students developed a sense of communal and individual responsibility for contributing to growing the body of mathematical knowledge known by the class, with an implied responsibility for knowing the already developed mathematics. Moreover, the behaviors that norms prompted the students to engage were those that literature suggests leads to increased comprehension of proofs.

► I describe classroom sociomathematical norms in an abstract algebra class.
► I explain how those norms promote behaviors that support proof comprehension.
► I describe beliefs students hold about activities related to proofs and proving.