STUDENTS ’ PROOF SCHEMES: A CLOSER LOOK AT WHAT CHARACTERIZES STUDENTS ’ PROOF CONCEPTIONS

The guiding theoretical principle in this study is the notion that the process of producing a mathematical proof can be viewed as similar to the process of solving a mathematical problem. Undergraduate students with different proof schemes were interviewed while attempting to construct proofs and their protocols were analyzed to identify patterns in problem solving and possible relationships among students ’ proof schemes and these patterns. Our findings suggest that students within each proof scheme do follow some similar patterns in their attempts to construct proofs and these patterns impact their proof performance. Proof as a logical argument that one makes to justify a claim and to convince oneself and others assumes a central role in mathematics. As such there has been a growing research and policy effort to make proof central to school mathematics as well. To inform this interest in the teaching and learning of proof and mathematics, there is a substantial research base, mostly focusing on the difficulties students face when attempting to read and write proofs. (e.g.