Explanations in Mathematics Classrooms: A Discourse Analysis

Abstract

This article focuses on student explanations as a discourse practice central to mathematics teaching and learning. I discuss classrooms as hybrid discourse spaces and focus on how talk is used to accomplish social action. In doing so, I contrast several different social and sociomathematical norms for explanation and suggest that students’ choices of discourse practices position them within the classroom. Further, I caution educators against assuming that complete and detailed explanations are always best to support student learning. I discuss how explanations that are coconstructed by several students can actually support joint engagement in mathematical work and help peers stay “on the same page” while avoiding hierarchical positioning.

Résumé

Cet article se penche sur les explications fournies par les étudiants comme pratique du discours essentielle en enseignement et apprentissage des mathématiques. Je présente la salle de classe comme un espace hybride de discours, et j'analyse les façons dont on se sert du discours comme acte social. Je compare ainsi plusieurs normes sociales et socio-mathématiques dans les explications, et je postule que les pratiques du discours choisies par les étudiants positionnent ces étudiants au sein de la classe. De plus, je suggère aux enseignants de ne pas présumer que les explications complètes et détaillées soient toujours celles qui sont le mieux en mesure de favoriser l'apprentissage des élèves. Au contraire, les explications construites en collaboration avec d'autres élèves semblent favoriser l'engagement en groupe lorsqu'il s'agit du travail mathématique, et aider les pairs à partager les mêmes connaissances tout en évitant les positionnements hiérarchiques.

ACKNOWLEDGEMENTS

The author thanks Mariana Levin, Shiuli Mukhopadhyay, Jennifer Langer-Osuna, Roland S. Coloma, Joseph Flessa, Ruben Gaztambide-Fernandez, Lance McCready, and editors and anonymous reviewers of the Canadian Journal for Science, Mathematics and Technology Education for their critical feedback on earlier versions of the article.

This work was supported by the National Science Foundation under Grant No. ESI-0119732 to the Diversity in Mathematics Education Center for Learning and Teaching; a Graduate Student Fellowship from the Institute for Human Development at the University of California, Berkeley; and a Connaught Grant from the University of Toronto. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the position, policy, or endorsement of the funding agencies.

Notes

1. Linear programming problems in two variables include a set of constraints on the variables and a quantity to be maximized or minimized. In the jigsaw activity, this group was supposed to provide general guidelines for finding the feasible region of any linear programming problem. This can be done by first graphing the set of constraints (linear inequalities) and then determining the region of the coordinate plane that satisfies all of the constraints.

2. To find the point(s) of highest profit for a two-variable linear programming problem, students could graph a set of profit lines. This can be done by setting the profit equal to some (arbitrary) value and graphing the resulting line. If one does this repeatedly for different values, one will obtain a set of parallel lines. Students could then visually determine where the line of highest profit would cross the feasible region—always at a boundary point or line for the feasible region.