The Cognition of Counterexample in Mathematics Students

Abstract: Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university mathematics courses and also the effectiveness of using logical facility to predict successful course outcomes. We analyze data collected from students enrolled at the University of Winnipeg in a pre-service course for high school teachers. We do find that, being able to successfully answer logical questions, both before and after intervention, are significant in relation to improved student outcomes.