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What teachers do in their classroom makes a difference in what students learn. Many experts agree with this statement and suggest that professional develop- ment of teachers is central to sustaining and deepening efforts to provide quality mathematics education for all students (National Research Council [NRC], 1996; National Science Foundation, 19981. However, much professional development provides teachers with knowledge and skill but leaves them to make their own connections with their daily practice in the classroom. As the nation undertakes improvement of instruction in mathematics classrooms, there is a need to access the best information available and to create opportunities to learn to use this informa- tion universally to help teachers improve their practice. Learning from other countries can be a valuable source in efforts to develop a more coherent approach to mathematics teacher educa- tion issues in the Unite(1 States. The release of the Third International Mathematics and Science Study has heightened interest in the Japanese educational system as a resource for those thinking deeply about teacher preparation in the United States (Stigler and Hiebert, 19991. Results from international studies rTrS~ (Beaton et al., 1996; Husen, 1967; McKnight et al., 1987; Stevenson et al., 1986) consis- tently show that Japanese students outperform those in the United States in most content areas. Evidence from research (Lewis anti Tsuchi(la, 1997, 1998; National Center for Education Statistics, 1996; Shimaihara and Sakai, 1995; Stevenson and Stigler, 1992; Stigler et al., 1999; Yoshida, 1999) indicates that the Japanese have a highly (levelope(1 teach- ing culture where the acquisition of knowledge of teaching is significantly unlike that in the Unite(1 States. One factor in Japanese teacher (levelopment programs seems to revolve around careful (resign of lessons where teachers learn content anti teaching in the process of developing a common lesson done through a community of professionals in coordinated and deliberate effort to improve instruction. This approach also serves as a way to mentor those new to the profession. Recent work in the United States by researchers in professional development in mathematics education (Ball anti Cohen, 1999; NRC, 2001; Schifter et al., 1999; Shulman, 1992; Stein et al., 2000;) has begun to buil(1 experi- ence anti expertise with tools for profes- sional development based on tasks of

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teaching such as video, case studies, teacher reflection on practice, analysis of student work, and mathematicians' commentary. Mathematics educators from the United States and Japan have much to learn from each other by sharing their work and current thinking on the professional development of teachers. The Mathematical Sciences Education Board (MSEB) and the U.S. National Commission on Mathematics Instruction (USNCMD recognized and took advan- tage of a unique opportunity to bring these educators together. Following the Ninth International Congress on Math- ematics Education (ICME-9) held July 31- August 6, 2000, in Makuhari, Japan, MSEB and USNCMI held a two- and a half-day workshop on the professional development of mathematics teachers. The workshop was able to capitalize on the presence of mathematics educators from the United States and Japan attend- ing {CME-9, using the expertise of the participants from the two countries to develop a better, more flexible, and more useful understanding of the knowledge that is nee(le(1 to teach well anti of how to help teachers obtain this knowledge. The workshop provided an opportunity to learn about the structure of Japanese lesson study and enabled mathematics educators from the Unite(1 States to share with Japanese colleagues their recent thinking about some promising approaches to teacher development in the United States. Thus, a major focus of the work- shop was to discuss teachers' opportuni- ties to learn in both societies, using teaching practice as a medium for profes- sional development. The first part of the workshop a(l(lresse(1 practice by studying the preparation for anti enactment of an actual lesson. The secon(1 part of the workshop addressed practice by consider- ing the stu(ly of records of teaching, including videos of classroom lessons and cases describing teachers and their work. These proceedings reflect the activities anti (1iscussion of the workshop using both print and video to enable others to share in the workshop experiences. S T U D Y I N G C LA S S R O O M T E A C H I N G