Simple yet Hidden Counterexamples in Undergraduate Real Analysis

Abstract

We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more complex) counterexamples daily in class. We provide perspective on these observations in the context of an informative body of related work in undergraduate mathematics studies.

Keywords:

• Analysis
• counterexample
• logic
• proof
• transition course

Acknowledgements

This material is based upon work supported in part by the National Science Foundation under grant No. 0837810. We thank Dr. Nancy Rowe, Manager of Statistical Services at UT Arlington, for statistical analysis of students' responses to the true/false questions.