PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Bundles and associated intentions of expert and novice provers: The search for and use of counterexamples
Page: 646
The argument for the importance of proving and of proof in the teaching and learning of mathematics has been repeatedly made by mathematics education researchers and by policy documents. There is also considerable research examining the existence of a gap in the proving and proof-constructing abilities of “novices” and “experts” in mathematics. However, considerably less research examines the nature of what constitutes expertise in proving mathematical statements, specifically with regard to the use of the individuals’ mathematical knowledge. This study uses grounded theory methods to examine “expert” and “novice” mathematicians in the process of proving mathematical statements. The result reported here focuses on the differences in the use of and search for counterexamples by the two populations. More specifically expert provers seem to value the unsuccessful searches for counterexamples, as well as the finding of valid counterexamples.