Teachers Constructing Concepts of Mathematics for Teaching and Learning: “It's like the roots beneath the surface, not a bigger garden”

Abstract

Conceptually rich classroom learning environments can only be supported by teachers with appropriate mathematical knowledge. A lack of clarity exists as to whether or how such teacher knowledge might go beyond knowledge of the relevant curriculum. This study contributes to the field by investigating further examples of what appropriate teacher mathematical knowledge might be, as rooted and contextualized in teachers’ daily classroom practices. Teacher journaling, individual meetings, and teacher focus-group discussions were used to identify relevant examples, and ultimately continue to collectively describe, in a specific, contextually based and practitioner-developed manner, the mathematical knowledge required for elementary teaching.

Résumé

Un environnement d’apprentissage riche en concepts doit se fonder avant tout sur des enseignants qui possèdent des connaissances mathématiques appropriées. Cependant, il n’est pas clair si ou comment ce niveau de connaissance peut aller au-delà des connaissances pertinentes pour le curriculum. Cette étude analyse certains exemples de ce qui pourrait constituer des connaissances mathématiques appropriées, telles que contextualisées dans les pratiques quotidiennes des enseignants dans leur classe. Des comptes-rendus sous forme de journal, des rencontres individuelles et des discussions de groupe ont permis de définir nombre d’exemples pertinents, et continuent de contribuer à une description collective, fondée sur le contexte et l’expérience dans la classe, des connaissances mathématiques requises pour l’enseignement au primaire.

ACKNOWLEDGMENTS

The author is indebted to Ralph Mason for his advice and support in the development of the project as well as the writing of this article. The contributions of Jennifer Holm in supporting the research are also acknowledged with thanks. The author is also grateful to Rina Zazkis, Dan Jarvis, Peter Taylor, Wes Maciejewski, Tom Boland, and Maria Casasola for their helpful comments on drafts of this article.

This work was funded by the National Science and Engineering Research Council of Canada University of Manitoba CRYSTAL grant Understanding the Dynamics of Risk and Protective Factors in Promoting Success in Science and Mathematics Education.

Notes

1. To this end, the author is most grateful to Ralph Mason of the University of Manitoba.