Journal of Mathematics Teacher Education

, Volume 15, Issue 4, pp 271–291 | Cite as

Supporting children’s mathematical understanding: professional development focused on out-of-school practices

  • Edd V. Taylor


This study describes the Reflection Connection Cycle professional development designed to support teachers’ use and appreciation of students’ out-of-school practices related to school mathematics. The year-long program incorporated group lesson design, readings, and video analysis for 14 elementary school (ages 5–12) teachers. Analysis of lesson development, written reflections, and analysis of teacher talk revealed important patterns related to the difficulty in writing lessons that built on students’ informal understandings. While initial lessons focused solely on the context of practices like gardening and sports, subsequent lessons show a greater concern for the mathematics in which children were engaged within a practice. A Multi-approach Engagement Framework is presented both as a tool to support further professional development efforts and as a means to describe stability and change in teachers’ efforts to connect in-school and out-of-school mathematical understandings.


Math education Professional development Social context Informal learning 



The author would like to thank Anita Wager, the co-facilitator of the professional development program, and the assistance of student researchers Ruben Navarro, Lilia Vreeland, and Bradford Whitman. Miriam Sherin provided valuable feedback to an earlier draft of this manuscript. The material in this paper is based in part on work supported by the National Science Foundation under Grant No. ESI-0119732 to the Diversity in Mathematics Education Center for Learning and Teaching (DiME). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the position, policy, or endorsement of the National Science Foundation.


  1. Ball, D. L. (1996). Teacher learning and the mathematics reforms: What we think we know and what we need to learn. Phi Delta Kappa, 77, 500–508.Google 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. Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M. E. (2008). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24, 417–436.CrossRefGoogle Scholar
  4. Bottge, B. A. (2001). Reconceptualizing math problem solving for low-achieving students. Remedial and Special Education, 22, 102–112.CrossRefGoogle Scholar
  5. Brenner, M. E. (1998). Meaning and money. Educational Studies in Mathematics, 36, 123–155.CrossRefGoogle Scholar
  6. Brophy, J. (Ed.). (2004). Advances in research on teaching: Vol. 1. Using video in teacher education. Oxford, UK: Elsevier.Google Scholar
  7. Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. International Journal of Educational Research, 17, 457–470.CrossRefGoogle Scholar
  8. Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20.CrossRefGoogle Scholar
  9. Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.Google Scholar
  10. Chamberlin, M. T. (2005). Teacher discussions of students’ thinking: Meeting the challenge of attending to students’ thinking. Journal of Mathematics Teacher Education, 8(2), 141–170.CrossRefGoogle Scholar
  11. Cole, M. (1996). Cultural psychology: A once and future discipline. Cambridge, MA: Belknap/Harvard University Press.Google Scholar
  12. Cole, M., & Bruner, J. S. (1971). Cultural differences and inferences about psychological processes. American Psychologist, 26, 867–876.CrossRefGoogle Scholar
  13. Diversity in Mathematics Education Center for Learning, Teaching. (2007). Culture, race, power, and mathematics education. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 405–434). Charlotte, NC: Information Age Publishing.Google Scholar
  14. Foote, M. Q. (2010). The power of one: Teachers examine their mathematics teaching practice by studying a single child. In M. Q. Foote (Ed.), Mathematics teaching and learning K-12: Equity and professional development (pp. 41–58). New York: Palgrave.CrossRefGoogle Scholar
  15. Fuson, K. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). New York: Macmillan.Google Scholar
  16. Gearhart, M., & Wolf, S. A. (1997). Issues in portfolio assessment: Assessing writing processes from their products. Educational Assessment, 4, 265–296.CrossRefGoogle Scholar
  17. Gonzalez, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging funds of distributed knowledge: Creating zones of practices in mathematics. Journal of Education for Students Placed at Risk, 6(1), 115–132.CrossRefGoogle Scholar
  18. Guberman, S. R. (1996). The development of everyday mathematics in Brazilian children with limited formal education. Child Development, 67, 1609–1623.CrossRefGoogle Scholar
  19. Gutstein, E., & Peterson, B. (Eds.). (2005). Rethinking mathematics: Teaching social justice by the numbers. Milwaukee, WI: Rethinking Schools.Google Scholar
  20. Hawley, W. D., & Valli, L. (1999). The essentials of effective professional development: A new consensus. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 127–150). San Francisco, CA: Jossey-Bass.Google Scholar
  21. Hiebert, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction, 14, 251–283.CrossRefGoogle Scholar
  22. Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203–235.CrossRefGoogle Scholar
  23. Labov, W. (1972). Language in the inner city: Studies in the Black English vernacular. Philadelphia: University of Pennsylvania Press.Google Scholar
  24. Ladson-Billings, G. (1995). Making mathematics meaningful in a multicultural context. In W. G. Secada, E. Fennema, & L. B. Adajian (Eds.), New directions for equity in mathematics education (pp. 126–145). New York: Cambridge University Press.Google Scholar
  25. Lampert, M., & Ball, D. (1990). Using hypermedia technology to support a new pedagogy of teacher education. National Center for Research on Teacher Education, Michigan State University.Google Scholar
  26. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  27. Lipka, J. (1994). Culturally negotiated schooling: Toward a Yup’ik mathematics. Journal of American Indian Education, 33(3), 14–30.Google Scholar
  28. Little, J. W. (2002). Locating learning in teachers’ professional community: Opening up problems of analysis in records of everyday work. Teaching and Teacher Education, 18(8), 917–946.CrossRefGoogle Scholar
  29. McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2–8.Google Scholar
  30. Moschkovich, J. (2002). An introduction to examining everyday and academic mathematical practices. In M. Brenner, & J. Moschkovich (Eds.), Everyday and academic mathematics in the classroom. Journal for Research in Mathematics Education, Monograph Number 11, 1–11.Google Scholar
  31. Moses, R. P., & Cobb, C. E. (2001). Radical equations: Math literacy and civil rights. Boston: Beacon Press.Google Scholar
  32. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  33. National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academic Press.Google Scholar
  34. Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Mathematics in the streets and in schools. Cambridge, U.K: Cambridge University Press.Google Scholar
  35. Putnam, R. T., & Borko, H. (1997). Teacher learning: Implications of new views of cognition. In B. J. Biddle, T. L. Good, & I. F. Goodson (Eds.), International handbook of teachers and teaching (2nd ed., pp. 1223–1296). Dordrecht, The Netherlands: Kluwer.Google Scholar
  36. Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.Google Scholar
  37. Reys, R. E., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth and eighth grade students in Taiwan. Journal for Research in Mathematics Education, 2(2), 225–227.CrossRefGoogle Scholar
  38. Rogoff, B. (2003). The cultural nature of human development. New York: Oxford University Press.Google Scholar
  39. Saxe, G. B. (1988). The mathematics of child street vendors. Child Development, 59, 1415–1425.CrossRefGoogle Scholar
  40. Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical development. Hillsdale NJ: Lawrence Erlbaum Associates.Google Scholar
  41. Sherin, M. G., & Han, S. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20, 163–183.CrossRefGoogle Scholar
  42. Smith, M. S. (2002). Practice-based professional development for mathematics teachers. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  43. Taylor, E. V. (2000, April). Multi-unit conceptual understanding in low-income African-American first and second grade students: The influence of currency knowledge. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  44. Taylor, E. V. (2009). Purchasing practice of low-income students: The relation to mathematical development. Journal of the Learning Sciences, 18(3), 370–415.CrossRefGoogle Scholar
  45. Taylor, E. V., & Kitchen, R. (2008). Doctoral programs in mathematics education: Diversity and equity. In R. E. Reys & J. A. Dossey (Eds.), U. S. Doctorates in mathematics education: Developing stewards of the discipline (Vol. 15, pp. 111–116). Washington, DC: American Mathematical Society.Google Scholar
  46. Watanabe, T. (1996). Ben’s understanding of one-half. Teaching Children Mathematics, 2(8), 460–464.Google Scholar
  47. Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of research and education, 24 (pp. 173–209). Washington, DC: American Educational Research Association.Google Scholar
  48. Zeichner, K., & Liston, D. (1990). Traditions of reform in US teacher education. Journal of Teacher Education, 41, 3–20.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Learning SciencesNorthwestern UniversityEvanstonUSA

Personalised recommendations