PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Conditions for cognitive unity in the proving process
Page: 398
Although a mathematical proof is a syntactic product, the proving process often entails other reasoning types, such as semantic or intuitive, that contribute to the evaluation of conjectures and the construction of supporting arguments. Cognitive unity and rupture refer to the possible continuity or discontinuity, respectively, between various reasoning types, argumentation and mathematical proof, and the processes of evaluating and proving conjectures. Undergraduate students struggle with mathematical proof, but it is hypothesized that cognitive unity facilitates the proving process. In this study, task-based interviews were conducted with undergraduate students who completed three prove-or-disprove tasks. The goals are to determine conditions under which students experience cognitive unity or rupture when evaluating and proving the conjectures and conditions under which cognitive unity and rupture aided or hindered the proving process. Preliminary findings suggest that various factors affect cognitive unity, cognitive unity can hinder proving, and cognitive rupture can facilitate proving.