Abstract
In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's engagement with children's thinking changed dramatically in a period of only a few months; observations and interviews several years later confirm she sustained this change. Our analysis focuses on the mathematical discussions she had with her students, and suggests this talk with children about their thinking in instruction served both as an index of change, and, in combination with other factors, as a mechanism for change. We identified four phases in Ms. Statz's growth toward practical inquiry, distinguished by her use of interactive talk with children. Motivating the evolution of phases were two sorts of mechanisms: scaffolded examination of her students' thinking; and asking and answering questions about individual students' thinking. Processes for generating and testing knowledge about children's thinking ultimately became integrated into Ms. Statz's instructional practices as she created opportunities for herself, and then students, to hear and respond to children's thinking.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Baker, S., Carpenter, T.P., Fennema, E. & Franke, M.L. (1992). Cognitively Guided Instruction: Fractions. Wisconsin Center for Education Research.
Ball, D. (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. Phi Delta Kappa, 77(7), 500–508.
Baek, J. (1998). Children's invented algorithms for multidigit multiplication problems. In L. Morrow & M. Kenney (Eds.), it NCTM yearbook: The teaching and learning of algorithms in school mathematics (pp. 151–160). Reston, VA: NCTM.
Carpenter, T.P. & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. In W. Secada (Ed.), Researching educational reform: The case of school mathematics in the United States (pp. 457–470). Special Issue of International Journal of Educational Research.
Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L. & Empson, S.B. (1999). Children's mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.
Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L. & Empson, S.B. (2002). Cognitively guided instruction: A research based teacher professional development program for elementary school mathematics. Research Report 00-3. Madison, WI: Wisconsin Center for Education Research. Downloaded from http://www.wcer.wisc.edu/ncisla/publications/index.html, June 27, 2003.
Carpenter, T.P., Fennema, E. & Franke, M. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. Elementary School Journal, 97(1), 3–20.
Carpenter, T.P., Fennema, E., Peterson, P.L., Chaing, C. & Loef, M. (1989). Using knowledge of children's mathematical thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499–532.
Carpenter, T.P., Franke, M. & Levi, L. (2003). Thinking mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann.
Cobb, P. & McClain, K. (2001). An approach for supporting teachers' learning in social context. In F. L Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 207–231). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Cobb, P., Wood, T. & Yackel, E. (1990). Classrooms as learning environments for teachers and researchers. In R.B. Davis, C.A. Maher & N. Noddings (Eds.), Constructivist views on teaching and learning mathematics (Journal for Research in Mathematics Education Monograph No. 4, pp. 125–146). Reston, VA: National Council of Teachers of Mathematics.
Denzin, N.K. & Lincoln, Y.S. (Eds.) (2000). Handbook of qualitative research. Thousand Oaks, CA: Sage.
Empson, S.B. (1999). Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17(3), 283–342.
Empson, S.B. (2002). Using sharing situations to help children learn fractions. In D.L. Chambers (Ed.), Putting research into practice in the elementary grades (pp. 122–127). Reston, VA: NCTM.
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.
Franke, M.L., Carpenter, T.P., Levi, L. & Fennema, E. (2001). Capturing teachers' generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38, 653–689.
Hammer, D. & Schifter, D. (2001). Practices of inquiry in teaching and research. Cognition and Instruction, 19, 441–478.
Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A. & Human, P. (1997). Making sense: teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30, 393–425.
Jacobs, V. & Ambrose, R. (2003). Individual interviews as a window into teachers' practice: A framework for understanding teacher-student interactions during mathematical problem solving. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.
Jaworski, B. (1988). Mathematics teacher research: Process, practice, and the development of teaching. Journal of Mathematics Teacher Education, 1, 3–31.
Jaworski, B. (1994). Investigating mathematics teaching. A constructivist enquiry. London: Falmer Press.
Jaworski, B. (2001). Developing mathematics teaching: Teachers, teacher educators, and researchers as co-learners. In F.L. Lin & T.J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 295–321). Dordrecht, The Netherlands: Kluwer Academic Publisher.
Jaworski, B., Wood, T. & Dawson, S. (1999). Mathematics teacher education: Critical international perspectives. London: Falmer Press.
Lampert, M. (1985). How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 5(2), 178–194.
Lave, J. & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge.
Little, J.W. (1999). Organizing schools for teacher learning. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 233–262). San Francisco: Jossey-Bass.
Loucks-Horsley, S. & Steigelbauer, S. (1991). Using knowledge of change to guide staff development. In A. Liberman & L. Miller (Eds.), Staff development for education in the 90's (pp. 15–36). New York, NY: Teachers College Press.
Mewborn, D. (1999). Reflective thinking among preservice elementary mathematics teachers. Journal for Research in Mathematics Education, 30, 316–341.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Richardson, V. (1990). Significant and worthwhile change in teaching practice. Educational Researcher, 19(7), 10–18.
Richardson, V. (1994). Conducting research on practice. Educational Researcher, 23(5), 5–10.
Richardson, V. & Placier, P. (2001). Teacher change. In V. Richardson (Ed.), Handbook of research on teaching, 4th edition (pp. 905–950). Washington, DC: American Educational Research Association.
Schifter, D. (2001). Learning to see the invisible: What skills and knowledge are needed to engage with students' mathematical ideas? In T. Wood, B.S. Nelson & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 109–134). Mahwah, NJ: Lawrence Erlbaum Associates.
Schifter, D. & Fosnot, C.T. (1993). Reconstructing mathematics education: Stories of teachers meeting the challenge of reform. New York: Teachers College.
Schön, D. (1983). The reflective practitioner. New York: Basic Books.
Schön, D. (1987). Educating the reflective practitioner. San Francisco: Jossey-Bass, Inc.
Sherin, M.G. (2002). When teaching becomes learning. Cognition and Instruction, 20(2), 119–150.
Simon, M. & Schifter, D. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22, 309–331.
Stein, M.K., Silver, E. & Smith, M.S. (1998). Mathematics reform and teacher development: A community of practice perspective. In J.G. Greeno & S. Goldman (Eds.), Thinking practices in mathematics and science learning (pp. 17–52). Mahwah, NJ: Lawrence Erlbaum Associates.
Steinberg, R., Carpenter, T.P. & Fennema, E. (1994). Children's invented strategies and algorithms in division. In J. Pedro de Ponte, & J.F. Matos (Eds.), Proceedings of the 18th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 305–312). University of Lisbon, Portugal: Psychology of Mathematics Education.
Streefland, L. (1991). Fractions in realistic mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Sullivan, P. & Mousley, J. (2001). Thinking teaching: Seeing mathematics teachers as active decision makers. In F.L. Lin & T.J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 147–163). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Tabachnick, B.R. & Zeichner, K.M. (1991). Issues and practices in inquiry-oriented teacher education. New York: Palmer Press.
Tom, A. (1985). Inquiring into inquiry-oriented teacher education. Journal of Teacher Education, 36(5), 35–44.
Tzur, R. (1999). An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. Journal for Research in Mathematics Education, 30, 390–416.
Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. New York: Cambridge.
Wilson, S. & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. Review of Research in Education, 24, 173–209.
Wood, T. (2001). Learning to teach mathematics differently: Reflection matters. In M.V. Heuvel-Panhizen (Ed.), Proceedings of the 25th conference of the International Group for the Psychology of Mathematics Education (pp. 431–438). Utrecht, The Netherlands: Psychology of Mathematics Education.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Steinberg, R.M., Empson, S.B. & Carpenter, T.P. Inquiry into Children's Mathematical Thinking as a Means to Teacher Change. Journal of Mathematics Teacher Education 7, 237–267 (2004). https://doi.org/10.1023/B:JMTE.0000033083.04005.d3
Issue Date:
DOI: https://doi.org/10.1023/B:JMTE.0000033083.04005.d3