Proof Construction and Collaborative Revision in Undergraduate Mathematics

Although there is much research showing that proof serves more than just a verification function in mathematics, there is little research documenting which functions of proof undergraduate students understand. Additionally, the ability to construct or determine the validity of a proof is an important skill for mathematicians and mathematics educators alike yet research suggests that students have difficulties determining the validity of a given argument and constructing valid proofs. This study examines the effects of a teaching intervention using a process called collaborative revision on students’ beliefs regarding proof and on students’ proving skills. Collaborative revision refers to the process in which students present a proof they have constructed to their classmates and the other students are encouraged to provide feedback to aid in the revision of the proof. Student assessment data in the form of pre- and post-assessments was collected, as well as student interviews. Results indicate that students do understand many functions of proof identified in the literature and, although collaborative revision may not impact the ability to identify valid proofs, it does affect the way that students gain conviction about the proof of a statement. Additionally, this study demonstrates that collaborative revision does positively impact students’ proof construction abilities.