Ball, D.L. (1988). *The subject-matter preparation of prospective mathematics teachers: Challenging the myths*. Issue paper *88*-*3*. East Lansing, MI: National Center for Research on Teacher Education.

Ball, D.L. (1988). *Unlearning to teach mathematics*. Issue paper *88*-*1*. East Lansing, MI: National Center for Research on Teacher Education.

Ball, D.L. (1990). Breaking with experience in learning to teach mathematics: The role of a pre-service methods course. *For the Learning of Mathematics*, 10(2), 10–16.

Ball, D.L. (1992). The mathematical understandings that prospective teachers bring to teacher education. In J. Brophy (Ed.), *Advances in research on teaching* (Volume 2, 1–48). Greenwich, CT: JAI.

Ball, D.L. & McDiarmid, G.W. (1990). The subject-matter preparation of teachers. In W. Robert Houston (Ed.), *Handbook of research on teacher education: A project of the Association of Teacher Educators*. New York: Macmillan.

Brown, H.I. (1977). *Perception, theory and commitment: The new philosophy of science*. Chicago: University of Chicago Press.

Dewey, J. (1916/1944). *Democracy and education*. New York: The Free Press.

Donald, J.G. (1991). *Knowledge and the university curriculum*. In C.F. Conrad & J.G. Haworth (Eds.), *Curriculum in transition: Perspectives on the undergraduate experience* (295–307). Needham Heights, MA: Ginn Publishing.

Glaser, B. & Strauss, A. (1967). *The discovery of grounded theory*. New York: Aldine.

Hershkowitz, R., Baruch, B.S. & Dreyfus, T. (2001). Abstraction in context: Epistemic actions.

*Journal for Research in Mathematics Education*, 32(2), 195–222.

CrossRefHiebert, J. (1986). *Conceptual and procedural knowledge: The case of mathematics*.Hillsdale, NJ: Lawrence Erlbaum.

Kinach, B.M. (1996). Logical trick or mathematical explanation? Re-negotiating the epistemological stumbling blocks of pre-service teachers in the secondary mathematics methods course. *Proceedings of the eighteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*, Volume *2* (414–420). Columbus, OH: Ohio State University.

Kinach, B.M. (2001). Assessing, challenging, and developing prospective teachers' pedagogical content knowledge and beliefs: A role for instructional explanations. In T. Ariav, A. Keinan & R. Zuzovsky (Eds.), *The ongoing development of teacher education: Exchange of ideas*. Tel Aviv, Israel: The Mofet Institute.

Kinach, B.M. (2002). A cognitive strategy for developing prospective teachers' pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice.

*Teaching and Teacher Education*,

*18*(1), 51–71.

CrossRefMa, L. (1999). *Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States*. Mahwah, NJ: Lawrence Erlbaum Associates.

Martin, J.R. (1970). *Explaining, understanding and teaching*. New York: McGraw Hill.

McDiarmid, G.W. (1990). Challenging prospective teachers' beliefs during an early field experience: A quixotic undertaking?

*Journal of Teacher Education*,

*41*(3), 12–20.

CrossRefNational Council of Teachers of Mathematics. (1989). *Curriculum and evaluation standards for mathematics*. Reston,VA: author.

National Council of Teachers of Mathematics. (2000). *Principles and standards for school mathematics*. Reston,VA: author.

Pape, S.J. & Tchoshanov, M.A. (2001). The role of representation(s) in developing mathematical understanding.

*Theory into Practice*, 40(2), 118–127.

CrossRefPerkins, D.N. (1992). *Smart schools: Better thinking and learning for every child*.New York: Free Press.

Perkins, D.N. & Simmons, R. (1988). Patterns of misunderstanding: An integrative model for science, math, and programming. *Review of Educational Research*, 58(3), 303–326.

Pimm, D. (1995).

*Symbols and meanings in school mathematics*. New York: University of Oxford Press.

CrossRefSchwab, J.J. (1978). Education and the structure of the disciplines. In I. Westbury & N.J. Wilkof (Eds.), *Science, curriculum and liberal education: Selected essays* (229–272). Chicago: University of Chicago Press.

Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform. *Harvard Educational Review*, 57(1), 1–22.

Sierpinska, A. (1990). Some remarks on understanding in mathematics. *For the Learning of Mathematics*, 10(3), 24–41.

Skemp, R.R. (1976). Relational understanding and instrumental understanding. *Mathematics Teaching*, *77*, 20–26a.

Skemp, R.R. (1978). Relational understanding and instrumental understanding. *Arithmetic Teacher*, 26(3), 9–15.

Stodolsky, S.S. (1985). Telling math: Origins of math aversion and anxiety.

*Educational Psychologist*, 20(3), 125–133.

CrossRefSteinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers.

*Journal of Mathematics Teacher Education*, 1, 157–189.

CrossRefTall, D. (1978). The dynamics of understanding mathematics. *Mathematics Teaching*, 84, 50–52.

Thompson, A.G. (1984). The relationship of teachers' conceptions of mathematics teaching to instructional practice.

*Educational Studies in Mathematics*, 15, 105–127.

CrossRefThompson, A.G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. InDouglas A. Grouws (Ed.), *Handbook of research on mathematics teaching and learning* (127–146). New York: Macmillan.

Watanabe, T. & Kinach, B. (1997). Creating a community of inquiry in an undergraduate mathematics course for prospective middle grade teachers: Voices from MCTP. Paper presented at the American Educational Research Association, Chicago.

Winicki-Landman, G. & Leikin, R. (2000). On equivalent and non-equivalent definitions: Part 1. *For the Learning of Mathematics*, 20(1), 17–21.

Wiske, M.S. (Ed.) (1998). *Teaching for understanding: Linking research with practice*. San Francisco, CA: Jossey-Bass.