PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Variation in successful mathematics majors proving
Page: 1086
We examined the proof-writing behaviors of six highly successful mathematics majors on proving tasks in calculus. We found that these students approached the proof writing tasks in two different ways. Three students, who we labeled as drillers, would develop a strong understanding of the statement they were proving, choose a plan based on this understanding, develop a graphical argument for why the statement is true, and formalize this graphical argument into a proof. The other three students, who we labeled as probers, would begin trying different proving approaches immediately after reading the statement and would abandon an approach at the first sign of difficulty. Despite being inconsistent with theories of effective problem solving in the mathematics literature, the probers were highly successful in their advanced mathematics courses and on the proving tasks in this study.