Mathematical proof is an important topic in mathematics education research. Many researchers have addressed various aspects of proof. One aspect that has not been addressed is what common traits are shared by those who are successful at creating proof. This research investigates the common
Mathematical proof is an important topic in mathematics education research. Many researchers have addressed various aspects of proof. One aspect that has not been addressed is what common traits are shared by those who are successful at creating proof. This research investigates the common traits in the thought processes of undergraduate students who are considered successful by their professors at creating mathematical proof. A successful proof is defined as a proof that successfully accomplishes at least one of DeVilliers (2003) six roles of proof and demonstrates adequate mathematical content, knowledge, deduction and logical reasoning abilities. This will typically be present in a proof that fits Weber's (2004) semantic proof category, though some syntactic proofs may also qualify. Proof creation can be considered a type of problem, and Schoenfeld's (1985) categories of resources, heuristics, control and ability are used as a framework for reporting the results. The research involved a) finding volunteers based on professorial recommendations; b) administering a proof questionnaire and conducting a video recorded interview about the results; and then c) holding a second video recorded interview where new proofs were introduced to the subjects during the interviews. The researcher used Goldin's (2000) recommendations for making tas