The Cognition of Counterexample in Mathematics Students

TL;DR

This study investigates how students' logical reasoning skills relate to their success in university mathematics courses, highlighting the importance of logical preparedness for academic achievement.

Contribution

It provides empirical evidence that logical reasoning ability before and after intervention predicts student success in first-year university mathematics.

Findings

Logical skills significantly correlate with course success

Pre- and post-intervention logical abilities predict outcomes

Logical preparedness is crucial for mathematics achievement

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.