24 SES 03 B, Mathematical Discourse
Mathematics learning can be conceptualised in terms of participation in forms of social practice, where discourses form key components of that practice. Language plays a central role in mediating and constituting this participation, which is performed as classroom discourse. Traditionally regarded as only auxiliary to thinking, active mathematical communication is nevertheless believed to enhance mathematical learning. It is a useful exercise, however, to conceptualise mathematics as a special form of communication. From this perspective, the expression “learning mathematics” becomes tantamount to developing mathematical discourse (Sfard, 2008).
The research reported in this paper revealed significant differences in both the public mathematical discourse practised in various classrooms around the world and in the priority attached to the promotion of student-student mathematical speech. The 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 even whole class choral response. Such diversity in classroom discourse patterns and in the goals and methods of promoting student speech associated with measurable success in achieving a range of learning outcomes raise issues for generalized conceptions of quality mathematics teaching.
The role of language in learning has been widely researched and variously conceived. Different theories attend to different aspects of language and the learning process. The adoption of a cognitive perspective towards learning directs the researcher’s attention to the content represented by the language used. The assumption seems to be that the learner’s language use can be taken to reflect their thought processes. In studies with a socio-cultural emphasis, the focus tends to be on the discursive functions of spoken and written language (e.g., Inagaki, Hatano, & Morita, 1998). From this perspective, language is a cultural resource through which the learner is initiated into a particular community of practice. Studies adopting a sociolinguistic perspective address the distinctive linguistic features of specialised or technical language and facility with language is taken to be prerequisite to effective communication and consequently to any learning.
The Asian classrooms in this study varied in their practice from no spoken mathematics by students (Seoul), through almost entirely public spoken mathematics by students (Shanghai), to spoken mathematics by students in both public and private classroom settings (Tokyo and Singapore). Differences in outcome in terms of facility with spoken mathematics (as displayed in interviews) may reflect differences in aspiration (rather than simply differences in success) - different cultures valuing different types of mathematical performance. What is essential is that our theories of learning and instruction should not unwittingly incorporate culturally-specific assumptions about valued outcomes and quality teaching practice. It is our hope that research in the classrooms of competent mathematics teachers around the world might lead to an expansion in the instructional repertoire of all teachers and to a more inclusive reconstruction of the theories by which accomplished mathematics teaching and learning are conceived.
Clarke, D.J. (2006). The LPS Research Design. Chapter 2 in D.J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics Classrooms in Twelve Countries: The Insider’s Perspective. Rotterdam: Sense Publishers, 15-37. Inagaki, K., Hatano, G., & Morita, E. (1998). Construction of mathematical knowledge through whole-class discussion. Learning and Instruction, 8(6), 503–526. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press. Wang, T. (2010). Teaching Mathematics through Choral Responses: A Study of Two Sixth Grade Classrooms in China. NY: The Edwin Mellen Press.
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