Teaching Practices That Can Promote the Authoritative Proof Scheme

Abstract

This article presents case studies of the classroom teaching practices of two algebra teachers. Our data consist of videotaped classroom observations during a single academic year. We identify and characterize specific teaching practices that establish the norm that the teacher is the sole arbiter of mathematical correctness in the classroom. We suggest that these practices are likely to promote the development of the authoritative proof scheme in students. Our results can provide a basis for future research investigating the prevalence of these teaching practices and their impact on student learning and can be used as parameters to investigate teacher change.

Résumé

Cet article présente deux études de cas sur les pratiques d’enseignement de deux enseignants d’algèbre. Nos données sont constituées d’observations de classe filmées au cours d’une même année scolaire. Nous définissons et analysons certaines pratiques d’enseignement qui imposent une norme selon laquelle l’enseignant est le seul arbitre de la véracité mathématique dans la salle de classe. Nous estimons que de telles pratiques sont susceptibles de promouvoir les arguments d’autorité dans les démonstrations formelles. Nos résultats pourraient servir de base pour des recherches ultérieures sur la prévalence de ces pratiques d’enseignement et leur impact sur l’apprentissage des étudiants, et pourraient également servir de paramètres pour analyser les possibilités de changement chez les enseignants.

ACKNOWLEDGMENTS

The authors are grateful to Alfred Manaster and Evan Fuller for their valuable comments on a draft of this article. The authors deeply appreciate the participation of both teachers in this study. They are dedicated professionals using the best teaching practices they know to ensure that their students learn and understand mathematics, notwithstanding our conclusions as to the relation of these practices to the authoritative proof scheme.

A brief report on this work has appeared separately (Harel & Rabin, 2010).

This work is supported, in part, by the National Science Foundation (REC 0310128, G. Harel PI). Opinions expressed herein are those of the authors and are not necessarily those of the Foundation.