Counter-examples in teaching/learning of calculus: students’ performance

This paper presents a case study which involved the first year science and engineering students of the Auckland University of Technology, New Zealand. After very favourable feedback received from the students in the international study on their attitudes towards usage of counter-examples in teaching/learning of Calculus (Gruenwald & Klymchuk, 2003) it was decided to investigate how usage of counterexamples affects students’ performance. The case study revealed that usage of counter-examples significantly improved students’ performance on a test question that required conceptual understanding but did not affect their performance on the other test questions (applying familiar rules and algorithms, calculations, applications, etc.).