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Mathematics Colloquium: What is Expertise in Mathematical Proving? A "Beginning" Examination
4:30 pm, Education Addition 216
Dr. Shiv Karunakaran
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" mathematician populations in the process of proving mathematical statements. The findings focus on the differences in the use of mathematical knowledge of the two populations. More importantly, with the findings of this study I hope to begin an ongoing examination of the nature of expertise in mathematical proving.