Advertisement

An Approach for Supporting Teachers’ Learning in Social Context

  • Paul Cobb
  • Kay Mcclain

Abstract

Our purpose in this chapter is to outline a general approach to collaborating with teachers in order to support the establishment of a professional teaching community. As will become apparent, our goal is to help teachers develop instructional practices in which they induct their students into the ways of reasoning of the discipline by building systematically on their current mathematical activity. We develop the rationale for the approach we propose by describing how our thinking about in-service teacher development has evolved over the last thirteen years or so. To this end, we first revisit work conducted in collaboration with Erna Yackel and Terry Wood between 1986 and 1992 in which we supported the development of American second- and third-grade teachers. In doing so, we tease out aspects of the approach we took that still appear viable and discuss two major lessons that we learned. In the next section of the chapter, we draw on a series of teaching experiments we have conducted over the past seven years in American elementary and middle-school classrooms both to critique our prior work and to develop three further aspects of the approach we propose. We conclude by highlighting broad features of the approach and by locating them in institutional context.

Keywords

Teaching Experiment Instructional Practice Mathematical Activity Instructional Activity Teacher Development 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8, 14.Google Scholar
  2. Barnett, C. (1991). Building a case-based curriculum to enhance the pedagogical content knowledge of mathematics teachers. Journal of Teacher Education. 42(4), 263–271.CrossRefGoogle Scholar
  3. Barron, L.C. & Goldman, E.S. (1994). Integrating technology with teacher preparation. In B. Means (Ed.), Technology and Education Reform. San Francisco: Jossey-Bass.Google Scholar
  4. Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In T. Cooney & D. Grouws (Eds.), Effective mathematics teaching (pp. 27–46). Reston, VA: National Council of Teachers of Mathematics and Erlbaum Associates.Google Scholar
  5. Bishop, A. (1985). The social construction of meaning—a significant development for mathematics education? For the Learning of Mathematics, 5(1), 24–28.Google Scholar
  6. Bowers, J., Barron, L., & Goldman, E. (1994). An interactive media environment to enhance mathematics teacher education. In J. Willis, B. Robin & D.A. Willis (Eds.), Technology and Teacher Education Annual (515–519). Washington, DC: Society for Technology and Teacher Education.Google Scholar
  7. Bowers, J. & Nickerson, S. (1998, April). Documenting the development of a collective conceptual orientation in a college-level mathematics course. Paper presented at the annual meeting of the American Education Research Association, San Diego.Google Scholar
  8. Carpenter, T., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. In W. Secada (Ed.), Curriculum reform: The case of mathematics in the United States. Special issue of International Journal of Educational Research (pp. 457–470). Elmsford, NY: Pergamon Press, Inc.Google Scholar
  9. Cobb, P., & McClain, K. (1999, May). Supporting teachers’ learning in social and institutional context. Paper presented at the 1999 International Conference on Mathematics Teacher Education, Teipei, Taiwan.Google Scholar
  10. Cobb, P. & Steffe, L.P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83–94.CrossRefGoogle Scholar
  11. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (in press). Participating in classroom mathematical practices. Journal of the Learning Sciences.Google Scholar
  12. Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In N. Minick, E. Forman, & A. Stone (Eds.), Education and mind: Institutional, social, and developmental processes (pp. 91–119). New York: Oxford University Press.Google Scholar
  13. Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–602.Google Scholar
  14. Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second grade mathematics project. Journal for Research in Mathematics Education, 22, 3–29.CrossRefGoogle Scholar
  15. Cobb, P., Wood, T., Yackel, E., & Perlwitz (1992). A follow-up assessment of a second-grade problem-centered mathematics project. Educational Studies in Mathematics, 23, 483–504.CrossRefGoogle Scholar
  16. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175–190.Google Scholar
  17. Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while doing mathematical problem solving. In D.B. McCleod & V.M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 117–148). New York: Springer-Verlag.CrossRefGoogle Scholar
  18. Cobb, P., Yackel, E., & Wood, T. (1991). Curriculum and teacher development: Psychological and anthropological perspectives. In E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds), Integrating research on teaching and learning mathematics (pp. 83–120). Albany, NY: SUNY Press.Google Scholar
  19. Cognition and Technology Group at Vanderbilt (1990). Anchored instruction and its relationship to situated cognition. Educational Researcher, 19(6), 2–10.CrossRefGoogle Scholar
  20. Cognition and Technology Group at Vanderbilt (1997). The Jasper Project: Lessons in Curriculum, instruction, assessment, and professional development. Mahwah, NJ: Erlbaum.Google Scholar
  21. Cohen, D.K., & Hill, H.C. (1998). Instructional policy and classroom performance: The mathematics reform in California. Ann Arbor, MI: University of Michigan.Google Scholar
  22. Cole, M. (1996). Cultural psychology. Cambridge, MA: Belknap Press of Harvard University Press.Google Scholar
  23. Confrey, J. (1990). How compatible are radical constructivism, sociocultural approaches, and social constructivism? In L. P. Steffe & J. Gale (Eds.), Constructivism in education. (pp. 185–225). Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  24. Dillon, D. R. (1993). The wider social context of innovation in mathematics education. In T. Wood, P. Cobb, E. Yackel, & D. Dillon (Eds.), Rethinking elementary school mathematics: Insights and issues. (pp. 71–96.) Journal for Research in Mathematics Education Monograph No. 6. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  25. Engestrom, Y. (1998). Reorganizing the motivational sphere of classroom culture: An activity theoretical analysis of planning in a teacher team. In F. Seeger, J. Voight & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 76–103). New York: Cambridge University Press.CrossRefGoogle Scholar
  26. Erickson, F. (1986). Qualitative methods in research on teaching. In M.C. Wittrock (Ed.), The handbook of research on teaching (3rd. ed., pp. 119–161). New York: Macmillan.Google Scholar
  27. Fennema, E., Carpenter, T.P., Franke, M.L., Levi, L., Jacobs, V.R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403–434.CrossRefGoogle Scholar
  28. Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (1993). Using children’s mathematical knowledge in instruction. American Educational Research Journal, 30, 555–583.Google Scholar
  29. Franke, M.L., Carpenter, T.P., Levi, L., & Fennema, E. (1998, April). Capturing teachers’ generative change: A follow-up study of teachers’ professional development in mathematics. Paper presented at the annual meeting of the American Educational Research Association, San Diego.Google Scholar
  30. Franke, M.L., & Kazemi, E. (in press). Teaching as learning within a community of practice: Characterizing generative growth. In T. Wood, B. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy in elementaiy mathematics: The nature of facilitative teaching. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  31. Gamoran, A., Secada, W.G., & Marrett, C.B. (in press). The organizational context of teaching and learning: Changing theoretical perspectives. In M.T. Hallinan (Ed.), Handbook of sociology.Google Scholar
  32. Gearhart, M, Saxe, G. B., Seltzer, M. Schlackman, J., Fall, R., Ching, C. C., Nasir, N., Bennett, T., Rhine, S., & Sloan, T. (1999). When can educational reforms make a difference? Opportunities to learn fractions in elementary mathematics classrooms. Journal for Research in Mathematics Education, 30, 206–315.CrossRefGoogle Scholar
  33. Goodlad, J.I. (1983). A place called school. New York: McGraw-Hill.Google Scholar
  34. Gravemeijer, K. E. P. (1994). Developing realistic mathematics education. Utrecht, Netherlands: CD-β Press.Google Scholar
  35. Gravemeijer, K. (1994). Educational development and developmental research. Journal for Research in Mathematics Education, 25(5), 443–471.CrossRefGoogle Scholar
  36. Hiebert, J., & Wearne, D. (1992). Instructional tasks, classroom discourse, and students’ learning in second grade arithmetic. American Educational Research Journal. 30,(2), 393–425.Google Scholar
  37. Jackson, P. (1968). Life in Classrooms. New York: Holt, Rinehart, and Winston.Google Scholar
  38. Kaput, J. J. (1987). The body in the mind: The bodily basis of reason and imagination. Chicago: University of Chicago Press.Google Scholar
  39. 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.CrossRefGoogle Scholar
  40. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.Google Scholar
  41. Lampert, M. & Ball, D. (1990). Using hypermedia to support a new pedagogy of teacher education. Issue Paper 90-5. East Lansing, MI: Michigan State University, National Center for Research on Teacher Education.Google Scholar
  42. Lazerson, M., McLaughlin, J. B., McPherson, B., & Bailey, S. K. (1985). New curriculum, old issues. In An education of value: The purpose and practices of schools, (pp. 23–46). Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
  43. Lehrer, R., & Schauble, L. (1998, April). Developing a community of practice for reform of mathematics and science. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.Google Scholar
  44. Lehrer, R., & Shumow, L. (1997). Aligning the construction zones of parents and teachers for mathematics reform. Cognition and instruction, 15(1), 41–83.CrossRefGoogle Scholar
  45. Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
  46. Lesh, R. & Akerstrom, M. (1982). Applied problem solving: Priorities for mathematics education research. In F. K. Lester & J. Garofalo (Eds.), Mathematical problem solving: Issues in research. Philadelphia: Franklin Institute Press.Google Scholar
  47. Little, J.W. (1993). Teachers’ professional development in a climate of educational reform. Educational Evaluation and Policy Analysis, 15, 129–151.Google Scholar
  48. McClain, K. & Cobb, P. (1995, April). An analysis of the teacher’s proactive role in initiating and guiding the development of productive mathematical discourse. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.Google Scholar
  49. McClain, K. & Cobb, P. (1998). The role of imagery and discourse in supporting students’ mathematical development. In M. Lampert (Ed.) Mathematical talk and school learning: Where, what, and how (pp. 56–81). New York: Cambridge University Press.Google Scholar
  50. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.Google Scholar
  51. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.Google Scholar
  52. Newman & Associates (Eds.). (1996). Authentic achievement: Restructuring schools for intellectual quality. San Francisco, CA: Josey-Bass.Google Scholar
  53. O’Connor, M.C. & Michaels, S. (1996). Shifting participant frameworks: Orchestrating thinking practices in group discussions. In D. Hicks (Ed.), Discourse, Learning, and Schooling (pp. 63–103). New York: Cambridge University Press.CrossRefGoogle Scholar
  54. Pirie, S. & Kieren, T. (1989). A recursive theory of mathematical understanding. For the learning of mathematics, 9(3), pp. 7–11.Google Scholar
  55. Price, J. N. & Ball, D. L. (1997). ‘There’s always another agenda’: Marshaling resources for mathematics reform. Journal of Curriculum Studies, 29(6), 637–666.CrossRefGoogle Scholar
  56. Schifter, D. (1990). Mathematics process as mathematics content: A course for teachers. In G. Booker, P. Cobb, & T. deMendicuti (Eds.), Proceedings of the 14 annual meeting of the Psychology of Mathematics Education (pp. 191–198). Mexico City, Mexico.Google Scholar
  57. Schifter, D., & Fosnot, C. T. (1993). Reconstructing mathematics education: Stories of teachers meeting the challenge of reform. New York: Teachers College Press.Google Scholar
  58. Simon, M.A. (in press). Research in mathematics teacher development: The teacher development experiment. In R. Lesh & E. Kelly (Eds.) New Methodologies in Mathematics and Science Education. Dordrecht, Netherlands: Kluwer.Google Scholar
  59. Simon, M. A. (1993). Context for change: Themes related to mathematical education reform. In T. Wood, P. Cobb, E. Yackel, & D. Dillon (Eds.), Rethinking elementary school mathematics: Insights and issues. (pp. 109–114.) Journal for Research in Mathematics Education Monograph No. 6. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  60. Simon, M.A. & Blume, G.W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3–31.CrossRefGoogle Scholar
  61. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.CrossRefGoogle Scholar
  62. Simon, M. A., & Schifter, D. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22, 309–331.CrossRefGoogle Scholar
  63. Steffe, L. P. (1983). The teaching experiment methodology in a constructivist research program. In M. Zweng, T. Green, J. Kilpatrick, H. Pollak, & M. Suydam (Eds.), Proceedings of the Fourth International Congress on Mathematical Education (pp. 469–471). Boston: Birkhauser.Google Scholar
  64. Stein, M.K. & Brown, CA. (1997). Teacher learning in a social context: Integrating collaborative and institutional processes with the study of teacher change. In E. Fennema & B. Scott Nelson (Eds.), Mathematics teachers in transition (pp. 155–192). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  65. Stein, M.K., Silver, E.A., & Smith, M.S. (1998). Mathematics reform and teacher development: A community of practice perspective. In J. Greeno & S. Goldman (Eds.), Thinking practices: A symposium on mathematics and science learning (pp. 17–52). Mahwah, N.J.: Erlbaum.Google Scholar
  66. Stigler, J.W., & Hiebert, J. (1999). The teaching gap. New York: Free Press.Google Scholar
  67. Tharp, R. G., & Gallimore, R. (1988). Rousing minds to life. New York: Cambridge University Press.Google Scholar
  68. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning, (pp. 127–146). New York: Macmillan.Google Scholar
  69. Thompson, A. G., & Thompson, P. W. (1996). Talking about rates conceptually, part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27, 2–24.CrossRefGoogle Scholar
  70. Thompson, A. G., Philipp, R., Thompson, P. W., & Boyd, B. (1994). Calculational and conceptual orientations in teaching mathematics. In 1994 Yearbook of the National Council of Teachers of Mathematics (pp. 79–92). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  71. Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, part I: A teacher’s struggle. Journal for Research in Mathematics Education, 25, 279–303.CrossRefGoogle Scholar
  72. Thompson, P. W. (1992). Notations, principles, and constraints: Contributions to the effective use of concrete manipulatives in elementary education. Journal for Research in Mathematics Education, 23, 123–147.CrossRefGoogle Scholar
  73. Thompson, P. W. (1996). Imagery and the development of mathematical reasoning. In L. P. Steffe, B. Greer, P. Nesher, & G. Goldin (Eds.), Theories of learning mathematics. Hillsdale, NJ: Erlbaum, p. 167–184.Google Scholar
  74. Varela, F.J., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge: MIT Press.Google Scholar
  75. Voigt, J. (1985). Patterns and routines in classroom interaction. Recherches en Didactique des Mathematiques, 6, 69–118.Google Scholar
  76. Warren, B., & Rosebery, A. S. (1995). Equity in the future tense: Redefining relationships among teachers, students, and science in linguistic minority classrooms. In W. Secada, E. Fennema, & L. Byrd (Eds.), New directions in equity for mathematics education. New York: Cambridge University Press.Google Scholar
  77. Wenger, E. (1998). Communities of practice. New York: Cambridge University Press.Google Scholar
  78. Wood, T., & Sellers, P. (1996.) Assessment of a problem-centered mathematics program: Third grade. Journal for Research in Mathematics Education, 27, 337–353.CrossRefGoogle Scholar
  79. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Paul Cobb
    • 1
  • Kay Mcclain
    • 1
  1. 1.Vanderbuilt UniversityNashvilleUSA

Personalised recommendations