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National Center for Education Statistics. (1996~. Pa~rs?`ing excellence: A study of U.S. eighth-grade mathematics and science teaching, learning, ca~rric?`l?`m, and achievement in international context. Washington, DC: U.S. Department of Education. National Center for Education Statistics. (2000~. The condition of education 2000. Washington, DC: U.S. Department of Education. National Council of Teachers of Mathematics. (1989~. Ca~rric?`l?`m and evaluation standards for teaching school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics. (1991~. Professional standards for teaching mathematics. Reston, VA: Author. National Council of Teachers of Mathematics. (1995~. Assessment standards for school math- ematics. Reston, VA: Author. National Council of Teachers of Mathematics. (2000~. Principles and standards for school mathematics. Reston, VA: Author. National Research Council. (1996~. From analysis to action: Undergraduate education in science, mathematics, engineering, and technology. Center for Science, Mathematics, and Engineering Education. Washington, DC: National Academy Press. National Research Council. (2001~. Knowing and learning mathematics for teaching. Mathematics Teacher Preparation Content Workshop Steering Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. National Science Foundation. (1998). Shaping the future. Arlington, VA: Author. National Science Foundation. (2000~. Observations on science and mathematics teacher education in Japan. Tokyo, Japan: National Science Founda- tion Tokyo Regional Office. Okabe, T. (1999~. The university student who can't do fractions. Tokyo, Japan: Toyo Keizai Shinpo Sha. Okabe, T. (2000~. The university student who can't do decimals. Tokyo, Japan: Toyo Keizai Shinpo Sha. A P P E N D I X M Polya, G. (1952~. How to solve it. Princeton, NJ: Princeton University Press. Polya, G. (1963~. On learning, teaching, and learning teaching. American Mathematical Monthly, 70, 605-619. Porter, R., Desimone, L, Herman, R., and Yoon, K.S. (1999~. Designing effective professional develop- ment: Lessons from the Eisenhower Program. Washington, DC: U.S. Department of Education. Post, T. R., Harel, G., Behr, M. J., and Lesh, R. (1991~. Intermediate teachers' knowledge of rational number concepts. In E. Fennema, T. P. Carpenter, and S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp.194-21n. New York: SUNY Press. Riley, R. W. (2000, February). Setting new expecta- tions. Paper presented at the Seventh Annual State of American Education address, Southern High School, Durham, NC. Schifter, D. (1998~. Learning mathematics for teaching: From a teachers' seminar to the classroom. .Ioa~rnal of Mathematics Teacher Education, 1(1) 55-87. Schifter, D., Bastable, V., and Russell, S. J. (with Yaffe, L, Lester, J. B., and Cohen, S.) (1999~. Developing mathematical ideas, number and operations part 2: Making meaning for operations casebook. Parsippany, NJ: Dale Seymour. Shields, P.M., Esch, C.E., Humphrey, D.C., Young, V.M., Gaston, M., and Hunt, H. (1999~. The status of the teaching profession: Research findings and policy recommendations. Santa Cruz, CA The Center for the Future of Teaching and Learning. Shimahara, N., and Sakai, A. (1995~. Learning to teach in two ca~lt?`res. New York: Garland. Shimizu, Y. (2000, August). Discussing multiple solutions for a problem: How do.lapanese teachers capitalize on the diversity of students' thinking in their lessons? Paper presented at the meeting of The Study of Teaching Practice as a Medium for Professional Development U.S. - Japan Teacher Preparation Workshop, Maruhari, Japan. Shulman,J. (1992~. Case methodsin teacher education. New York: Teachers College Press.