Producing Proofs and Counterexamples: Strategies of Undergraduate Students

• In Event: Poster Session 20
  In Poster Session: Mathematical Reasoning and Proof Across Grades

Abstract

To implement current reforms regarding proof and counterexample in secondary school mathematics and undergraduate mathematics successfully, undergraduate mathematics majors must have adequate understandings of concepts across mathematical domains for their future teaching. This paper examined the strategies that undergraduate mathematics majors had for producing proofs and counterexamples in the domains of algebra, analysis, geometry, and number theory. The results of the study suggest that most undergraduate students tend to apply important and useful facts when attempting to construct a proof or a counterexample. This study also suggests that some students who try to recall and copy similar proofs they have seen in the past with little mathematical reasoning often struggle to complete their proof and counterexample productions.

Author

• Yi-Yin Ko, Indiana State University