Educational Studies in Mathematics

, Volume 92, Issue 3, pp 331–345 | Cite as

Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic

  • Richard BarwellEmail author


The importance of the role of language/discourse in the learning and teaching of mathematics is noted in many mathematics curricula and standards documents. In the research literature, this role has been widely theorised from a Vygotskian perspective. This perspective is limited by some of its underlying assumptions, including an instrumental and systemic view of language as tool and its basis in dialectic. In this paper, I propose a Bakhtinian, dialogic perspective as an alternative. I focus my discussion on the long-standing issue of the relationship between formal and informal mathematical language in the learning and teaching of mathematics. I illustrate this discussion with an examination of interaction in an elementary school mathematics classroom in Québec, Canada. Based on Bakhtin’s ideas, I argue that mathematical meaning emerges through locally produced, situated dialogic relations between multiple discourses, voices and languages in mathematics classroom interaction. From this perspective, students do not follow a linear path from informal to formal mathematical discourse; rather, they work with the teacher to expand the repertoire of possible ways to make meaning in mathematics.


Mathematical language Mathematical discourse Dialogue Dialectic Bakhtin Vygotsky 



This research was funded by SSHRC, grant 410-2008-0544. Thanks to Élysée Cadet, Marc Prud’homme and Adil Dsousa for their work on this section of the project, and to the teacher and students who kindly participated. I am grateful to Anna Sfard and two anonymous reviewers for the comments on earlier versions of this work.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of OttawaOttawaCanada

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