Metadiscursive Rules in Three “East Asian Classrooms”: Case Studies of Mathematics Classroom Discourse From Shanghai, Seoul, and Tokyo

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

Abstract

The benefits of engaging students in mathematics classroom dialogues have been highlighted in a number of recent publications (e.g. Alexander, 2008; Walshaw & Anthony, 2008). While there seems to be an universal assumption about the significance of student mathematical talk in learning mathematics, our studies of spoken mathematics in 22 well-taught classrooms internationally (Clarke & Xu, 2008; Clarke et al., 2010) revealed significant differences among those classrooms characterised as “Asian” in the opportunities that each classroom afforded for the students to employ relatively sophisticated mathematical terms in both public discussion and private student interactions.

Extending our previous studies, this study seeks to compare the ways in which classroom talk was conducted in three cultural settings: Seoul, Shanghai, and Tokyo. The analysis reported in this paper centres on the events in which “Linear Equation in Two Unknowns” was introduced. The key question of this paper is “what are the similarities and differences in the ways in which a new topic was introduced in the three classrooms”. The similarities and differences will be illustrated through the data obtained from the Learner’s Perspective Study (LPS) (Clarke, 2006). The data analysis was conducted in two phases. In the first phase, lessons from each of the three classrooms were analysed to reveal the forms and functions of the activities involved in introducing the new content. In the second phase, classroom dialogue was examined in detail to uncover not only the content of the exchanges between classroom participants, but also the meta-rules (Sfard, 2001) governing those exchanges.

The results of the analysis demonstrate several significant differences of the three classrooms. The Shanghai teacher introduced the topic by helping the students to establish connections with their prior knowledge, and emphasized the definitions of key concepts and the application of these definitions. The same topic was introduced in the Seoul classroom, but through activities of solving equations conducted in the form of teacher demonstration with minimal student contribution. In the Japanese classroom, this topic was introduced through a series of mathematical modelling activities that centred on “a stair problem”. Differences were also evident in the meta-rules governing the public classroom discourse. While the students in the Shanghai classroom were “enculturated” into a form of mathematical discourse in which the students were expected to employ appropriate mathematical terms, the interactions in the Seoul classroom did not provide the students with many opportunities to exercise the use of terms. The Tokyo students were invited to brainstorm about the “stair problem”, and to contribute their mathematics knowledge in a way that helped to shape the teaching of the topic. The similarities and differences of the three classrooms suggest that while the shared macrocultural values and beliefs frame the social activity of the three classrooms in similar ways, the meta-rules of discursive practice determine the opportunities for student learning in mathematics. This paper argues for a culturally situated theory of learning and pedagogy that takes into account both the local institutional norms and the cultural specificities of the classroom practice.

Authors

• Li Hua Xu, The University of Melbourne

• David J. Clarke, University of Melbourne