STUDENT USE OF MATHEMATICAL CONTENT KNOWLEDGE DURING PROOF PRODUCTION

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STUDENT USE OF MATHEMATICAL CONTENT KNOWLEDGE DURING PROOF PRODUCTION

Abstract

Proof is an important component of advanced mathematical activity. Nevertheless, undergraduates struggle to write valid proofs. Research identifies many of the struggles students experience with the logical nature and structure of proofs. Little research examines the role mathematical content knowledge plays in proof production. This study begins to fill this gap in the research by analyzing what role mathematical content knowledge plays in the success of a proof and how undergraduates use mathematical content knowledge during proofs. Four undergraduates participated in a series of task-based interviews wherein they completed several proofs. The interviews were analyzed to determine how the students used mathematical content knowledge and how mathematical content knowledge affected a proof’s validity. The results show that using mathematical content knowledge during a proof is nontrivial for students. Several of the proofs attempted by the students were unsuccessful due to issues with mathematical content knowledge. The data also show that students use mathematical content knowledge in a variety of ways. Some student use of mathematical content is productive and efficient, while other student practices are less efficient in formal proofs.

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