Sociomathematical Norms of Elementary School Classrooms: Crossnational Perspectives on the *Reform of Mathematics Teaching.

Mathematics education reform in the United States has marshaled large-scale support for instructional innovation, and enlisted the participation and allegiance of large numbers of mathematics teachers. However, there is concern that many teachers have not grasped the full implications of the reform ideals. This study explored the breakdown that may occur between teachers\u27 adoption of reform objectives and their successful incorporation of reform ideals by comparing and contrasting two reform-oriented classrooms. This study was an exploratory, qualitative, comparative case study using constant comparative analysis. Seven mathematics lessons were video-taped from each class, and intensive interviews conducted with the two teachers. The study provided a detailed description to explore how the participants in each class established a reform-oriented mathematics microculture. Then the two classes were compared and contrasted in terms of their general social norms and sociomathematical norms (Cobb & Yackel, 1996). The two classes established similar social participation patterns but very different mathematical microcultures. In both classes open-ended questioning, collaborative group work, and students\u27 own problem solving constituted the primary modes of classroom participation. However, in one class mathematical significance was constituted as using standard algorithm with accuracy, whereas the other class established a focus on providing reasonable and convincing arguments. Given these different mathematical foci, students\u27 learning opportunities were seen as unequal. The students in the latter class had more opportunities to develop conceptual understanding than their counterparts. This study was nested within a cross-national, collaborative project involving two reform-oriented Korean classrooms. This research report includes a brief joint analysis. As in the U.S., the two Korean classes were similar in their general social norms, but only one class reified mathematically significant distinctions among students\u27 contributions. However, the more successful Korean classroom was very different in character from its U.S. counterpart, with the former focusing on sophisticated conceptual distinctions whereas the latter focused on the social values of students\u27 active participation. A retheorization of sociomathematical norms is offered so as to highlight the importance of this construct in the analysis of reform-oriented classrooms, and to promote a more diverse conceptualization of the possibilities for viable mathematics teaching