Development of Teachers’ Conceptions Through Learning and Teaching: The Meaning and Potential of Multiple-Solution Tasks

Abstract

This study analyzes development of teachers’ mathematical and pedagogical conceptions in systematic (through learning) and craft (through teaching) modes and the relationships between them. We focus on teachers’ conceptions of the meaning and potential of multiple-solution connecting tasks in school mathematics. We found that in systematic mode teachers increase primarily their shared conceptions and that the development of mathematical conceptions precedes that of pedagogical conceptions. Only in craft mode do they develop new understandings while their mathematical and pedagogical conceptions become integrated and advance each other mutually.

Résumé

Cette étude analyse le développement des conceptions mathématiques et pédagogiques chez les enseignants pour ce qui est des aspects systématiques (par le biais de l'apprentissage) et pratiques (par le biais de l'enseignement), ainsi que les rapports qui existent entre ces deux modalités. Nous centrons notre attention sur les idées des enseignants à propos du sens et du potentiel des tâches à solutions multiples en enseignement des mathématiques à l'école. Nos résultats montrent que, pour les aspects systématiques, les enseignants développent principalement leurs conceptions partagées, et que le développement des conceptions mathématiques précède le développement des conceptions pédagogiques. C'est seulement pour ce qui est des modalités pratiques que les enseignants approfondissent leurs connaissances, au fur et à mesure que leurs conceptions mathématiques et pédagogiques s'intègrent les unes aux autres et se favorisent mutuellement.

ACKNOWLEDGMENTS

The authors thank Irena Gurevich for her assistance in data collection and management of the course. They are indebted to the teachers who participated in the study for their collaboration and goodwill.

This research was made possible by grant #891/03 from the Israel Science Foundation.

Notes

1. All the teachers’ names are pseudonyms.

2. For the other five teachers the collected data are incomplete due to their unwillingness to participate in the last interview (two teachers) and unwillingness to record their implementation (three teachers).

3. We use the term description of a mathematical situation to contrast specific examples of mathematical problems with general accounts of various types of problems (e.g., mathematical topics) that teachers use to solve problems in different ways.