The case of four classrooms analyzed in this study point to many commonalities in the challenges of reforming mathematics teaching in Korea and the U. S. In both national contexts we have seen the need fur a clear distinction between implementing new student-centered social practices in the classroom, and providing significant new loaming opportunities for students. In particular, there is an important need to distinguish between attending to the social practices of the classroom and attending to students conceptual development within those social practices. In both countries, teachers in the less successful student-centered classes tended to abdicate responsibility fur sense making to the students. They were more inclined to attend to the literal statements of their students without analyzing their conceptual understanding (Episodes KA5 and UP 2). This is easy to do when the rhetoric of reform emphasizes student-centered social practices without sufficient attention to psychological correlates of those social practices. The more successful teachers tended to monitor the understanding of the students and to take proactive measures to ensure the development of that understanding (Episodes KO5 and UN3). This suggests the usefulness of constructivism as a model (or successful student-centered instruction. As Simon(1995) observed, constructivist teachers envision a hypothetical learning trajectory that constitutes their plan and expectation for students learning from the particular if the trajectory is being followed. If not, the teacher adjusts or supplements the task to obtain a more satisfactory result, or reconsider her or his assumptions concerning the hypothetical learning trajectory. In this way, the teacher acts proactively to try to ensure that students are progressing in their understanding in particular ways. Thus the more successful student-centered teacher of this study can be seen as constructivist in their orientation to student conceptual development, in comparison to the less successful student-centered teachers. It is encumbant on the authors of reform in Korea and the U. S. to make sure that reform is not trivialized, or evaluated only on the surface of classroom practices. The commonalities of the two reform endeavores suggest that Korea and the U. S. have much to share with each other in the challenges of reforming mathematics teaching for the new millennium.