Students Speaking Mathematics: Practices and Consequences for Mathematics Classrooms in Different Countries

• In Event: What Is the Value of Classroom Talk?

Abstract

Objectives
This paper analyses the orchestrated use of mathematical language in 22 eighth-grade classrooms in eight countries. The focus is the role of spoken mathematics in both instruction and learning. Since the data set included some classrooms where student-student mathematical conversations were encouraged and some where they were not, it was possible to address the question: “What differences in practice exist between classrooms where student-student mathematical talk is encouraged and those where it is not and what appear to be the consequences for learning of those differences in practice?”

Perspective
Classroom practice is inevitably framed by local pedagogical histories of practice and of discourse. The distinctive character of classrooms situated in different cultural traditions has been the subject of several substantial publications (Author, 2006; Fan, Wong, Cai & Li, 2004; and Leung, Graf, & Lopez-Real, 2004). The analyses reported in this presentation suggest that the instructional practices of the teachers in the various classrooms were predicated on pedagogies that assign student speech a very different function in the learning process.

Methods
This project employed three video cameras in the classroom (teacher camera, student camera and whole class camera) to document the practices in the classrooms of mathematics teachers judged competent by local standards over sequences of at least ten lessons. Three types of oral classroom interactions were recorded: whole class interactions, teacher-student interactions, and student-student interactions. All whole class and teacher-student interactions were documented and transcribed, but student-student interactions could only be recorded for selected pairs of focus students in each lesson. Each focus student then participated in a post-lesson video-stimulated interview.

Data sources
The findings are based on analyses of 110 lessons documented in 22 classrooms in Shanghai, Seoul, Hong Kong, Tokyo, Singapore, Berlin, San Diego and Melbourne, and on 191 post-lesson student interviews. Transcripts were analyzed of both public and private utterances by teacher and students and of the post-lesson interviews with two focus students per lesson. Analysis focused on the spoken use of those “key mathematical terms” that constituted the content-focus of each lesson.

Findings and implications
Across the classrooms studied, almost all teachers explicitly valued and promoted student spoken use of mathematical terminology. However, constrained by the conventions of Chinese classroom practice, the Shanghai teachers enacted this prioritization in the public domain only, employing choral response extensively, in sharp contrast to the pedagogies employed in those other classrooms where student-student spoken mathematics was prioritized. The findings suggest that if student facility with technical mathematical vocabulary is a valued outcome, then the public scaffolding (and explicit valuing) of student technical fluency can be as effective as the encouragement of student-student spoken mathematics in developing this facility.

Scholarly Significance
The research revealed significant differences in the public mathematical discourse practised in various classrooms around the world. Our analyses suggest that at least some of the goals of those advocating student-student mathematical conversations in the classroom may be met by other instructional strategies, such as whole class public discussion and choral response.

Authors

• David J. Clarke, University of Melbourne

• Lihua Xu, Deakin University

• Vivien Wan, University of Melbourne