Journal of Mathematics Teacher Education

, Volume 6, Issue 3, pp 201–222 | Cite as

Learning to Learn to Teach: An ``Experiment'' Model for Teaching and Teacher Preparation in Mathematics

  • James Hiebert
  • Anne K. Morris
  • Brad Glass


This paper describes a model for generating and accumulating knowledge for both teaching and teacher education. The model is applied first to prepare prospective teachers to learn to teach mathematics when they enter the classroom. The concept of treating lessons as experiments is used to explicate the intentional, rigorous, and systematic process of learning to teach through studying one's ownpractice. The concept of planning teaching experiences so that others can learn from one's experience is used to put into practice the notion of contributing to a shared professional knowledge base for teaching mathematics. The same model is then applied to the work of improving teacher preparation programs in mathematics. Parallels are drawn between the concepts emphasized for prospective teachers and those that are employed by instructors who study and improve teacher preparation experiences. In this way, parallels also are seen in the processes used to generate an accumulating knowledge base for teaching and for teacher education.

knowledge for mathematics teaching knowledge for mathematics teacher education learning to teach lesson study 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Artzt, A.F. (1999). A structure to enable preservice teachers of mathematics to reflect on their teaching. Journal of Mathematics Teacher Education, 2, 143–166.CrossRefGoogle Scholar
  2. Ball, D.L. & Cohen, D.K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco: Jossey-Bass.Google Scholar
  3. Bereiter, C. & Scardamalia,M. (1989). Intentional learning as a goal of instruction. In L.B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 361–392). Hillsdale, NJ: Erlbaum.Google Scholar
  4. Borko, H., Eisenhart, M. Brown, C.A., Underhill, R.G., Jones, D. & Agard, P.C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194–222.CrossRefGoogle Scholar
  5. Britt, M.S., Irwin, K.C. & Ritchie, G. (2001). Professional conversations and professional growth. Journal of Mathematics Teacher Education, 4, 29–53.CrossRefGoogle Scholar
  6. Brown, A.L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the Learning Sciences, 2, 141–178.CrossRefGoogle Scholar
  7. Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College Press.Google Scholar
  8. Clark, C.M. (Ed.) (2001). Talking shop: Authentic conversation and teacher learning. New York: Teachers College Press.Google Scholar
  9. Cobb, P., Confrey, J., diSessa, A., Lehrer, R. & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  10. Cooney, T.J. (1985). A beginning teacher's view of problem solving. Journal for Research in Mathematics Education, 16, 324–336.CrossRefGoogle Scholar
  11. Cooney, T.J. (1994). Teacher education as an exercise in adaptation. In D. Aichele & A. Coxford (Eds.), Professional development for teachers of mathematics (pp. 9–22). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  12. Darling-Hammond, L. (1997). The right to learn: A blueprint for creating schools that work. San Francisco: Jossey-Bass.Google Scholar
  13. Darling-Hammond, L. & Sykes, G. (Eds.) (1999). Teaching as the learning profession: Handbook of policy and practice. San Francisco: Jossey-Bass.Google Scholar
  14. Design-Based Research Collective (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.CrossRefGoogle Scholar
  15. Ebby, C.B. (2000). Learning to teach mathematics differently: The interaction between coursework and fieldwork for preservice teachers. Journal of Mathematics Teacher Education, 3, 69–97.CrossRefGoogle Scholar
  16. Fernandez, C., Chokshi, S., Cannon, J. & Yoshida, M. (2001). Learning about lesson study in the United States. In New and old voices on Japanese education. Amonk, New York: M. E. Sharpe.Google Scholar
  17. Fey, J.T. (1979). Mathematics teaching today: Perspectives from three national surveys. Arithmetic Teacher, 27(2), 10–14.Google Scholar
  18. Gagné, R.M. (1985). The conditions of learning and theory of instruction, 4th ed. New York: Holt, Rinehart & Winston.Google Scholar
  19. Gallimore, R.G. (1996). Classrooms are just another cultural activity. In D.L. Speece & B.K. Keough (Eds.), Research on classroom ecologies: Implications for inclusion of children with learning disabilities (pp. 229–250). Mahwah, NJ: Erlbaum.Google Scholar
  20. Grimmett, P.P. & MacKinnon, A.M. (1992). Craft knowledge and the education of teachers. Review of Research in Education, 18, 385–456.Google Scholar
  21. Gonzales, P., Calsyn, C., Jocelyn, L., Mak, K., Kastberg, D., Arafeh, S., Williams, T. & Tsen, W. (2000). Pursuing excellence: Comparisons of international eighthgrade mathematics and science achievement from a U.S. perspective, 1995 and 1999 (NCES 2001-028). U.S. Department of Education.Washington, DC: National Center for Education Statistics.Google Scholar
  22. Hiebert, J. (1999). Relationships between research and the NCTM Standards. Journal for Research in Mathematics Education, 30, 3–19.CrossRefGoogle Scholar
  23. Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A. & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4), 12–21.CrossRefGoogle Scholar
  24. Hiebert, J., Gallimore, R. & Stigler, J.W. (2002). A knowledge base for the teaching profession: What would it look like and how can we get one? Educational Researcher, 31(5), 3–15.CrossRefGoogle Scholar
  25. Holmes Group (1986). Tomorrow's teachers: A report of the Holmes Group. East Lansing, MI: Author.Google Scholar
  26. Huberman, M. (1985). What knowledge is of most worth to teachers? A knowledge-use perspective. Teaching and Teacher Education, 1, 251–262.CrossRefGoogle Scholar
  27. Jaworski, B. (1998). Mathematics teacher research: Process, practice, and the development of teaching. Journal of Mathematics Teacher Education, 1, 3–31.Google Scholar
  28. Kelly, A.E. & Lesh, R.A. (Eds.) (2000). Handbook of research design in mathematics and science education.Mahwah, NJ: Erlbaum.Google Scholar
  29. Kilpatrick, J. (1997). Confronting reform. American Mathematical Monthly, 103, 955–962.CrossRefGoogle Scholar
  30. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale University Press.Google Scholar
  31. Lewis, C.C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for Better Schools, Inc.Google Scholar
  32. Lewis, C.C. & Tsuchida, I. (1998). A lesson is like a swiftly flowing river. American Educator, 22(4), 12–17; 50–52.Google Scholar
  33. Lortie, D.C. (1975). Schoolteacher: A sociological study. Chicago: University of Chicago Press.Google Scholar
  34. Loucks-Horsley, S., Hewson, P.W., Love, N. & Stiles, K.E. (1998). Designing professional development for teachers of science and mathematics. Thousands Oaks, CA: Corwin Press.Google Scholar
  35. Masingila, J.O. & Doerr, H.M. (2002). Understanding pre-service teachers' emerging practices through their analyses of a multimedia case study of practice. Journal of Mathematics Teacher Education, 5, 235–263.CrossRefGoogle Scholar
  36. Moyer, P.S. & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293–315.CrossRefGoogle Scholar
  37. National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.Google Scholar
  38. National Research Council (2002). Studying classroom teaching as a medium for professional development. Proceedings of a U.S.-Japan workshop. H. Bass, Z.P. Usiskin & G. Burrill (Eds.). Mathematical Sciences Education Board, Division of Behavioral and Social Sciences and Education, and U.S. Commission on Mathematics Instruction, International Organizations Board. Washington, DC: National Academy Press.Google Scholar
  39. Raths, J.D. & McAninch, A.C. (Eds.) (1999). Advances in teacher education: Vol. 5. What counts as knowledge in teacher education?Stamford, CT: Ablex.Google Scholar
  40. Sack, J.L. (2002, October 25). Research bill, after stall, sails to passage. Education Week, 22(8). Retrieved November 5, 2002 from Scholar
  41. Schoenfeld, A.H. (1985). Mathematical problem solving.Orlando, FL: Academic Press.Google Scholar
  42. Schön, D.A. (Ed.) (1991). The reflective turn: Case studies in and on educational practice. New York: Teachers College Press.Google Scholar
  43. Shulman, L. (2000). From Minsk to Pinsk: Why a scholarship of teaching and learning? Journal of Scholarship of Teaching and Learning, 1(1), 48–53.Google Scholar
  44. Silver, E.A. (Ed.) (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale, NJ: Erlbaum.Google Scholar
  45. Silver, E.A. & Kenney, P.A. (Eds.) (2000). Results from the seventh mathematics assessment of the National Assessment of Educational Progress. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  46. Simon, J. (Producer/Writer/Director) (1995). The art of discussion leading: A class with Chris Christensen (VHS tape). Cambridge, MA: Harvard University, Derek Bok Center for Teaching and Learning.Google Scholar
  47. Simon, M.A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.CrossRefGoogle Scholar
  48. Simon, M., Tzur, R., Heinz, K., Smith, M. & Kinzel, M. (1999). On formulating the teacher's role in promoting mathematics learning. In O. Zaslavsky (Ed.), Proceedings of the 23rd conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 201–208). Haifa, Israel.Google Scholar
  49. Stigler, J.W. & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom.New York: Free Press.Google Scholar
  50. Stodolsky, S.S. (1988). The subject matters: Classroom activity in math and social studies. Chicago: University of Chicago Press.Google Scholar
  51. Sullivan, P. (2002). Editorial: Using the study of practice as a learning strategy within mathematics teacher education programs. Journal of Mathematics Teacher Education, 5, 289–292.CrossRefGoogle Scholar
  52. Welch, W. (1978). Science education in Urbanville: A case study. In R. Stake & J. Easley (Eds.), Case studies in science education (pp. 5-1–5-33). Urbana, IL: University of Illinois.Google Scholar
  53. Wittrock, M.C. (1986). Students' thought processes. In M.C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 297–314). New York: Macmillan.Google Scholar
  54. Yinger, R. (1999). The role of standards in teaching and teacher education. In G. Griffin (Ed.), The education of teachers: Ninety-eighth yearbook of the National Society for the Study of Education (pp. 85–113). Chicago: University of Chicago Press.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • James Hiebert
    • 1
  • Anne K. Morris
    • 1
  • Brad Glass
    • 1
  1. 1.School of EducationUniversity of DelawareNewarkUSA

Personalised recommendations