Improving formal reasoning in mathematics through tutorials

Introduction

Although many students view mathematics as being about numbers and formulas, for mathematicians the subject is about abstract reasoning and formal logic. A primary goal in math courses then is for students to learn to approach mathematics rigourously, learning the formal tools of theorems and proofs. Only when these formal techniques are mastered can their applicability in solving real world problems be understood and appreciated.

Many mathematics courses, however, tend to emphasize the numerical and formulaic aspects of mathematics rather than the abstract reasoning, in part because it is difficult to teach and assess abstract reasoning. The settings in which students learn and solve coursework problems – via lectures and independent problem solving – do not correspond with how mathematicians solve research problems – through discussion and collaboration. The value of peer teaching and groupwork has long been known in the education literature, but it has been difficult to integrate these pedagogical techniques into traditional mathematics lecture-style courses.

In this paper, I propose the use of student-led presentations of solutions to abstract reasoning problems in tutorials as a technique to improve student skills in abstract reasoning. The proposal is motivated by the reported benefits of various peer teaching and groupwork scenarios, and encourages the use of comprehension tests and proof validation to improve formal reasoning.

Reference

Douglas Stebila. Improving formal reasoning in mathematics through tutorials. University of Waterloo, 2008. Submitted as part of the Certificate in University Teaching.

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