Abstract
A successful practice grounded in the principles that guide the current mathematics education reform effort requires a qualitatively different and significantly richer understanding of mathematics than most teachers currently possess. However, it is not as clear how teachers' mathematical understandings develop and how those understandings affect instruction. This paper explores two avenues for K-6 teachers' mathematical development, (a) engagement in inquiry into mathematics itself, and (b) investigation of children's mathematical thinking, illustrating how the need for these two kinds of investigations arises in classroom situations and how they can be pursued in a professional development setting.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ball, D.L. (1989). Research on teaching mathematics: Making subject matter knowledge part of the equation. In J. Brophey (Ed.), Advances in research on teaching: Vol. 2. Teacher' subject matter knowledge and classroom instruction (1–48). Greenwich, CT: JAI Press.
Ball, D.L. (1990). Fractions: Excerpts from Deborah Ball' third-grade class, May 1990. East Lansing, MI: Mathematics and Teaching through Hypermedia.
Ball, D.L. (1992, summer). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(15–18), 46–47.
Ball, D.L. (1993). Halves, pieces, and twoths: Constructing representational contexts in teaching fractions. In T.P. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (157–196). Hillsdale, NJ: Lawrence Erlbaum Associates.
Ball, D.L. (1996). Connecting to mathematics as part of learning to teach. In D. Schifter (Ed.), What' happening in math class, Volume 2: Reconstructing professional identities (36–45). New York: Teachers College Press.
Cohen, D.K. & Ball, D.L. (1990). Policy and practice: An overview. In D.K. Cohen, P.L. Peterson, S. Wilson, D. Ball, R. Putnam, R. Prawat, R. Heaton, J. Remillard & N. Wiemers (Eds.), Effects of state-level reform of elementary school mathematics curriculum on classroom practice (Research Report 90-14), 1–8. East Lansing, MI: The National Center for Research on Teacher Education and The Center for the Learning and Teaching of Elementary Subjects, College of Education, Michigan State University.
Cohen, D.K. & Barnes, C.A. (1993). Conclusion: A new pedagogy for policy? In D.K. Cohen, M.W. McLaughlin & J.E. Talbert (Eds.), Teaching for understanding: Challenges for policy and practice (240–276). San Francisco: Jossey-Bass Publishers.
Cohen, D.K., McLaughlin, M.W. & Talbert, J.E. (Eds.) (1993). Teaching for understanding: Challenges for policy and practice. San Francisco: Jossey-Bass Publishers.
Confrey, J. (1990). What constructivism implies for teaching. In R.B. Davis, C.A. Maher & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics, Journal for Research in Mathematics Education Monograph No. 4 (107–124). Reston, VA: National Council of Teachers of Mathematics.
Even, R. & Lappan, G. (1994). Constructing meaningful understanding of mathematics content. In D. Aichele & A. Coxford (Eds.), Professional development for teachers of mathematics: 1994 Yearbook NCTM (128–143). Reston, VA: National Council of Teachers of Mathematics.
Featherstone, H., Smith, S.P., Beasley, K., Corbin, D. & Shank, C. (1993). Expanding the equation: Learning mathematics through teaching in new ways. Paper presented at the Annual Meeting of the American Educational Research Association, Atlanta, GA.
Fennema, E., Franke, M.L., Carpenter, T.P. & Carey, D.A. (1993). Using children' knowledge in instruction. American Educational Research Journal, 30, 555–583.
Fennema, E. & Nelson, B.S. (Eds.) (1997). Mathematics teachers in transition. Hillsdale, N.J.: Lawrence Erlbaum Associates.
Fosnot, C.T. (1989). Enquiring teachers enquiring learners: A constructivist approach for teaching. New York: Teachers College Press.
Friel, S. & Bright, G. (Eds.) (1997). Reflecting on our work: NSF teacher enhancement in K-6 mathematics. Lanham, MD: University Press of America, Inc.
Ginsburg, H. & Kaplan, R. (1988). Overview: Math video workshop. New York: Teachers College, Columbia University.
Heaton, R. (1996). Learning while doing: Understanding early efforts to create new practices of teaching and learning mathematics. In D. Schifter (Ed.), What' happening in math class, Volume 2: Reconstructing professional identities (74–80). New York: Teachers College Press.
Hammer, D. (in press). Discovery learning and discovery teaching. Newton, MA: Center for the Development of Teaching, Education Development Center, Inc.
Hiebert, J. & Behr, M. (1988). Introduction: Capturing the major themes. In M. Behr & J. Hiebert (Eds.), Number concepts and operations in the middle grades (1–18). Reston, VA: National Council of Mathematics.
Knapp, N.F. & Peterson, P.L. (1995). Teachers' interpretations of “CGI” after four years: Meanings and practices. Journal for Research in Mathematics Education, 26, 40-65.
Lamon, S. (1993). Ratio and proportion: Children' cognition and metacognition. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (131–156). Hillsdale, NJ: Erlbaum.
Lampert, M. (1988). The teacher' role in reinventing the meaning of mathematics knowing in the classroom. In M.J. Behr, C.B. Lacampagne & M.M. Wheeler (Eds.), Proceedings of the tenth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (433–480). DeKalb, IL: Northern Illinois University.
Mack, N. (1993). Learning rational numbers with understanding: The case of informal knowledge. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (85–105). Hillsdale, NJ: Lawrence Erlbaum Associates.
Mokros, J., Russell, S.J. & Economopoulos, K. (1995). Beyond arithmetic: Changing mathematics in the elementary classroom. Palo Alto, CA: Dale Seymour Publications.
Moynahan, J. (1996). Of-ing fractions. In D. Schifter (Ed.), What' happening in math class, Volume 1: Reshaping practice through teacher narratives (24–36). New York: Teachers College Press.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for 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 mathematics. Reston, VA: Author.
Nelson, B.S. (Ed.) (1995). Inquiry and the development of teaching: Issues in the transformation of mathematics teaching. Newton, MA: Center for the Development of Teaching, Education Development Center, Inc.
O'Reilly, A.M. (1996). Understanding teaching/teaching for understanding. In D. Schifter (Ed.), What' happening in math class?, Volume 2: Reconstructing professional identities (65–73). New York: Teachers College Press.
Russell, S.J. & Corwin, R.B. (1993). Talking mathematics: “Going slow” and “letting go.” Phi Delta Kappan, 74, 12.
Russell, S.J., Schifter, D., Bastable, V., Yaffee, L, Lester, J.B. & Cohen, S. (1995). Learning mathematics while teaching. In B.S. Nelson (Ed.), Inquiry and the development of teaching: Issues in the transformation of mathematics teaching (9–16). Newton, MA: Center for the Development of Teaching, Education Development Center, Inc.
Schifter, D. (1993). Mathematics process as mathematics content: A course for teachers. Journal of Mathematical Behavior, 12, 271–283.
Schifter, D. & Fosnot, C.T. (1993). Reconstructing mathematics education: Stories of teachers meeting the challenge of reform. New York: Teachers College Press.
Schifter, D., Russell, S.J. & Bastable, V. (in press). Teaching to the big ideas. In M. Solomon (Ed.), The diagnostic teacher: Revitalizing professional development. New York: Teachers College Press.
Schifter, D. & Simon, M.A. (1992). Assessing teachers' development of a constructivist view of mathematics learning. Teaching and Teacher Education, 8, 187–197.
Simon, M.A. & Schifter, D.E. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22, 309–331.
Thompson, A., Phillipp, R., Thompson, P. & Boyd, B. (1994). Calculational and conceptual orientations in teaching mathematics. In D. Aichele & A. Coxford (Eds.), Professional development for teachers of mathematics: 1994 Yearbook NCTM (79–92). Reston, VA: National Council of Teachers of Mathematics.
Wood, T., Cobb, P. & Yackel, E. (1991). Change in teaching mathematics: A case study. ?? ??
Rights and permissions
About this article
Cite this article
Schifter, D. Learning Mathematics for Teaching: From a Teachers' Seminar to the Classroom. Journal of Mathematics Teacher Education 1, 55–87 (1998). https://doi.org/10.1023/A:1009911200478
Issue Date:
DOI: https://doi.org/10.1023/A:1009911200478