The Role of Expository Writing in Mathematical Problem Solving

Abstract

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the effectiveness of using writing as a tool for deeper engagement with mathematical problems. Students’ claims about, and tutor observations of, problem-solving behaviour were analysed through the lens of Piaget's theory of cognitive development. Examples of enhanced problem-solving behaviour are presented as well as reports from student interviews that writing ‘forces’ deeper engagement. The analysis of students’ work and their reflections indicated that writing about problem-solving processes potentially resulted in a cognitive perturbation when students were forced to confront their incomplete understanding (and hence their unstable knowledge structures) and therefore had to achieve a deeper level of understanding in order to adequately describe the solution process.

Keywords:

• Problem solving
• writing
• mathematical understanding
• cognitive conflict

Acknowledgements

The larger study of which this article forms a part was funded by a Spencer Foundation Fellowship. I wish to acknowledge the advice on earlier versions of this work from Tim Dunne, John Webb, Alan Schoenfeld, Ed Dubinsky, Johann Engelbrecht and Saalih Allie. I am grateful to the anonymous reviewers for their valuable contributions to this article.

Disclosure Statement

No potential conflict of interest was reported by the author.