Student-Student Classroom Discourse: Practices and Consequences for Mathematics Classrooms in Different Countries

• In Event: Discursive Practice and Knowledge Construction in Mathematics Classrooms in Widely Different Cultural Settings

Abstract

Research was conducted into the nature of mathematical discourse in well-taught classrooms in Berlin, Hong Kong, Melbourne, San Diego, Seoul, Shanghai, Singapore and Tokyo and into the associated learning outcomes arising from such discursive practices. Analysis was undertaken of classroom utterances occurring in a sequence of five lessons from each of the 22 classrooms studied (110 lessons). Specific emphasis is given in this paper to utterances and embedded spoken mathematical terms in the context of student-student (rather than public) interactions. Also analyzed was student use of technical mathematical terms in 191 post-lesson interviews.

Student-student spoken interactions were evident in the mathematics classrooms in Tokyo, frequent in the classrooms studied in San Diego, Singapore and Melbourne, and almost non-existent in Shanghai and Seoul, and student use of mathematical terminology varied significantly.

A focus of the analysis reported here is the mathematical sophistication of student-student spoken interactions. This sophistication was reflected in both the mathematical vocabulary employed by the students and the argumentative skills by which student capacity for mathematical reasoning was made visible. Fine-grained analyses were undertaken of student-student discursive practice in one Japanese and one American classroom.

In conducting the post-lesson interviews, students were asked to comment on what they had learned or felt was important from that day\'s lesson. Further comments were elicited from students after viewing a video recording of the lesson. Together with recorded classroom dialogue, the interviews documented student proficiency with mathematical discourse.

As a result of this research, we were able to compare the discursive practices of the twenty-two different mathematics classrooms. Several hypotheses emerged and these have been variously investigated.
• If student facility with technical mathematical vocabulary is the targeted outcome, then the analysis of the post-lesson interviews suggests that the public scaffolding of student technical fluency (eg Shanghai 1) can be as effective as the encouragement of student-student spoken mathematics (eg San Diego 2) in developing this facility.
• Where the classroom provided students with no opportunity for spoken mathematics (Seoul), there appeared to be little inclination (and possibly capacity) to do so, even in interview situations where the invitation to use spoken mathematics was explicit (“Tell me what the lesson was about”).
• Student inclination to employ other mathematical terms (‘other terms’) in addition to those specific to the lesson could indicate a form of interconnected knowing (San Diego 2).
• The level of student participation in the social modelling of particular forms of argumentation affords or constrains individual’s development of particular reasoning capabilities.
• Student-student interactions offer a window into the development of such reasoning capabilities.
• Student facility with mathematical discourse, in the broadest sense, may be enhanced or restricted by cultural contingencies.

Our work suggests that the theories of teaching/learning by which contemporary (largely Western) instructional advocacies are rationalized may themselves be culturally-specific. Fine-grained analysis of the discursive practices of mathematics classrooms in contrasting cultures may hold the key to connecting social discursive practice with specific forms of individual performative capability.

Authors

• Robert Hunting, La Trobe University

• David J. Clarke, University of Melbourne

• Li Hua Xu, The University of Melbourne

• May Ee Vivien Wan, University of Melbourne