Journal of Mathematics Teacher Education

, Volume 11, Issue 5, pp 349–371 | Cite as

Promoting student collaboration in a detracked, heterogeneous secondary mathematics classroom

Article

Abstract

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one teacher’s role in creating a classroom system that supported student collaboration within groups in a detracked, heterogeneous geometry classroom. The analysis focuses on four categories of the teacher’s work that created a set of affordances to support within group collaborative practices and links the teacher’s work with principles of complex systems.

Keywords

Heterogeneous groups Detracking Secondary mathematics Teacher’s role 

Notes

Acknowledgments

I would like to thank Melissa Gresalfi for her insightful and generative feedback on earlier drafts of this manuscript. I would also like to thank Jo Boaler for her guidance in the design of this project. Finally, I extend my deep appreciation to Linda McClure and her geometry class for allowing me to be a part of their classroom community.

References

  1. Ball, D., & Bass, H. (2000). Using mathematics in practice: What does it take to help students work collectively? Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  2. Barab, S. A., Cherkes-Julkowski, M., Swenson, R., Garrett, S., Shaw, R. E., & Young, M. (1999). Principles of self-organization: Learning as participation in autocatakinetic systems. The Journal of the Learning Sciences, 8(3&4), 349–390.CrossRefGoogle Scholar
  3. Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. (Revised and expanded edition). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  4. Boaler, J. (2006). How a detracked mathematics approach promoted respect, responsibility, and high achievement. Theory into Practice, 45(1), 40–46.CrossRefGoogle Scholar
  5. Boaler, J. (2007). Promoting ‘relational equity’ and high mathematics achievement through an innovative mixed ability approach. British Educational Research Journal, 1–28.Google Scholar
  6. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608–645.Google Scholar
  7. Burris, C. C., Heubert, J., & Levin, H. (2006). Accelerating mathematics achievement using heterogeneous grouping. American Educational Research Journal, 43(1), 105–126.CrossRefGoogle Scholar
  8. Carey, N., Farris, E., & Carpenter, J. (1994). Curricular differentiation in public high schools (NCES 95–360). U.S. Department of Education, National Center for Education Statistics.Google Scholar
  9. Cohen, E. (1994a). Restructuring the classroom: Conditions for productive small groups. Review of Educational Research, 64(1), 1–35.Google Scholar
  10. Cohen, E. (1994b). Designing groupwork: Strategies for the heterogeneous classroom. New York: Teachers College Press.Google Scholar
  11. Cohen, E. (1997). Equity in heterogeneous classrooms: A challenges for teachers, sociologists. In E. Cohen & R. Lotan (Eds.), Working for equity in heterogeneous classrooms: Sociological theory in practice (pp. 3–14). New York: Teachers College Press.Google Scholar
  12. Cohen, E. G., Brody, C. M., & Sapon-Shevin, M. (2004). Teaching cooperative learning: The challenge for teacher education. Albany, NY: State University of New York Press.Google Scholar
  13. Cohen, E., & Lotan, R. (1997). Working for equity in heterogeneous classrooms: Sociological theory in practice. New York: Teachers College Press.Google Scholar
  14. Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.CrossRefGoogle Scholar
  15. Dweck, C. S., & Leggett, E. (1988). A social cognitive approach to motivation and personality. Psychological Review, 95, 256–273.CrossRefGoogle Scholar
  16. Elliott, E. S., & Dweck, C. S. (1988). Goal: An approach to motivation and achievement. Journal of Personality and Social Psychology, 54, 5–12.CrossRefGoogle Scholar
  17. Forsyth, D. (1999). Group dynamics. Boston, MA: Brooks/Cole.Google Scholar
  18. Gamoran, A. (1993). Alternative uses of ability grouping in secondary schools: Can we bring high quality instruction to low-ability classes? American Journal of Education, 102, 1–22.CrossRefGoogle Scholar
  19. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. London: Weidenfeld & Nicholson.Google Scholar
  20. Greeno, J., & MMAP (1997). Theories and practices of thinking and learning to think. American Journal of Education, 106, 85–126.Google Scholar
  21. Guitiérrez, R. (1996). Practices, beliefs and cultures of high school mathematics departments: Understanding their influence on student advancement. Journal of Curriculum Studies, 28(5), 495–529.CrossRefGoogle Scholar
  22. Horn, I. (2005). Learning on the job: A situated account of teacher learning in two high school mathematics departments. Cognition & Instruction, 23(2), 207–236.CrossRefGoogle Scholar
  23. Linchevski, L., & Kutscher, B. (1998). Tell me with whom you’re learning, and I’ll tell you how much you’ve learned: Mixed-ability versus same-ability grouping in mathematics. Journal for Research in Mathematics Education, 29(5), 533–554.CrossRefGoogle Scholar
  24. Lou, Y., Abrami, P., Spence, J., Poulsen, C., Chambers, B., & d’Apollonia, S. (1996). Within-class grouping: A meta-analysis. Review of Educational Research, 66(4), 423–458.Google Scholar
  25. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.Google Scholar
  26. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.Google Scholar
  27. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  28. National Research Council. (2001). Adding it up: Helping children learn mathematics. Mathematics Learning Study Committee. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Division of behavioral and social sciences and education. Washington, DC: National Academy Press.Google Scholar
  29. Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven, CT: Yale University Press.Google Scholar
  30. Oakes, J. (1990). Multiplying inequalities: The effects of face, social class and tracking on opportunities to learn mathematics and science. Santa Monica, CA: RAND.Google Scholar
  31. Perry, S. M. (2007). Shaping self-concepts: Ability grouping and middle school students. Unpublished doctoral dissertation. Stanford University, Stanford, CA.Google Scholar
  32. Schroeder, T., & Lester, F. (1989). Developing understanding in mathematics via problem solving. In P. Trafton, & A. Shulte (Eds.), New directions for elementary school mathematics (pp. 31–42). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  33. Schwartz, D. (1999). The productive agency that drives collaborative learning. In P. Dillenbourg (Ed.), Collaborative learning: Cognitive and computational approaches (pp. 197–218). New York: Pergamon.Google Scholar
  34. Staples, M., & Colonis, M. (2006). Sustaining mathematical discussions: A comparative analysis of two secondary mathematics teachers. Paper presentation at the annual meeting of the American Education Research Association Annual Conference, San Francisco, CA.Google Scholar
  35. Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory. Thousand Oaks, CA: Sage Publications, Inc.Google Scholar
  36. Webb, N. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal of Research in Mathematics Education, 22, 366–389.CrossRefGoogle Scholar
  37. Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge: Cambridge University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.University of ConnecticutStorrsUSA

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