Using clickers in the statistics classroom can help students identify and understand common errors and misconceptions through a combination of surprise and discussion. Students are presented with multiple-choice questions that they discuss with each other and then vote on; a class-wide discussion follows. Questions for which many students vote for…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

This paper describes a framework for identifying, classifying, and coding student proofs, modified from existing proof-grading rubrics. The framework includes 20 common errors, as well as categories for interpreting the severity of the error. The coding scheme is intended for use in a classroom context, for providing effective student feedback. In…

Teachers often promote care in doing calculations, but for most students a single mistake rarely has major consequences. This article presents several real-life events in which relatively minor mathematical errors led to situations that ranged from public embarrassment to the loss of millions of dollars' worth of equipment. The stories here…

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

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…