Educational Studies in Mathematics

, Volume 70, Issue 1, pp 49–70 | Cite as

Constructing competence: an analysis of student participation in the activity systems of mathematics classrooms

  • Melissa Gresalfi
  • Taylor Martin
  • Victoria Hand
  • James Greeno
Article

Abstract

This paper investigates the construction of systems of competence in two middle school mathematics classrooms. Drawing on analyses of discourse from videotaped classroom sessions, this paper documents the ways that agency and accountability were distributed in the classrooms through interactions between the teachers and students as they worked on mathematical content. In doing so, we problematize the assumption that competencies are simply attributes of individuals that can be externally defined. Instead, we propose a concept of individual competence as an attribute of a person's participation in an activity system such as a classroom. In this perspective, what counts as “competent” gets constructed in particular classrooms, and can therefore look very different from setting to setting. The implications of the ways that competence can be defined are discussed in terms of future research and equitable learning outcomes.

Keywords

Classroom culture Discourse analysis Competence Middle school Urban schools 

References

  1. Amit, M., & Fried, M. N. (2005). Authority and authority relations in mathematics education: A view from an 8th grade classroom. Educational Studies in Mathematics, 58(2), 145–168, doi: 10.1007/s10649-005-3618-2.CrossRefGoogle Scholar
  2. Bauersfeld, H. (1992). Classroom cultures from a social constructivist’s perspective. Educational Studies in Mathematics, 23, 467–481, doi: 10.1007/BF00571468.CrossRefGoogle Scholar
  3. Bauersfeld, H. (1995). The structuring of the structures: Development and function of mathematizing as a social practice. In L. P. Steffe, & J. Gale (Eds.), Constructivism in education (pp. 137–159). Hillsdale, NJ: Erlbaum.Google Scholar
  4. Boaler, J. (1999). Participation, knowledge, and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40, 258–281, doi: 10.1023/A:1003880012282.CrossRefGoogle Scholar
  5. Brown, T. (1994). Creating and knowing mathematics through language and experience. Educational Studies in Mathematics, 27, 79–100, doi: 10.1007/BF01284529.CrossRefGoogle Scholar
  6. Brown, A. L., & Campione, J. C. (1994). Guided discovery in a community of learners. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice. Cambridge, MA: MIT Press.Google Scholar
  7. Cobb, P. (1999). Individual and collective mathematical learning: The case of statistical data analysis. Mathematical Thinking and Learning, 1, 5–44, doi: 10.1207/s15327833mtl0101_1.CrossRefGoogle Scholar
  8. Cobb, P. (2000). Accounting for mathematical development in the social context of the classroom. In L. P. Steffe, & P. Thompson (Eds.), Radical constructivism in action: Beyond the pioneering work of Ernst von Glasersfeld (pp. 152–178). London: Falmer.Google Scholar
  9. Cobb, P., Gresalfi, M. S., & Hodge, L. (2008). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education (in press).Google Scholar
  10. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10, 113–164, doi: 10.1207/S15327809JLS10-1-2_6.CrossRefGoogle Scholar
  11. Cobb, P., Wood, T., & Yackel, E. (1992). Learning and interaction in classroom situations. Educational Studies in Mathematics, 23, 99–122, doi: 10.1007/BF00302315.CrossRefGoogle Scholar
  12. Cobb, P., Wood, T., & Yackel, E. (1993). Discourse, mathematical thinking, and classroom practice. In N. Minick, E. A. Forman, & A. Stone (Eds.), Education and mind: Institutional, social, and developmental processes (pp. 91–119). Oxford: Oxford University Press.Google Scholar
  13. Cobb, P., Wood, T., Yackel, E., & McNeal, G. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–602.Google Scholar
  14. Cobb, P., & Yackel, E. (1998). A constructivist perspective on the culture of the mathematics classroom. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The culture of the mathematics classroom: Analysis and changes (pp. 158–190). New York: Cambridge University Press.Google Scholar
  15. Delpit, L. (1995). The silenced dialogue: Power and pedagogy in educating other peoples' children. In L. Delpit (Ed.), Other people's children (pp. 21–47, 186–186). New York, NY: The New Press.Google Scholar
  16. Engeström, Y. (1993). Developmental studies of work as a testbench of activity theory: The case of primary care medical practice. In S. Chaiklin, & J. Lave (Eds.), Understanding practice: Perspectives on activity and context (pp. 64–103). Cambridge: Cambridge University Press.Google Scholar
  17. Gee, J. P. (1999). An introduction to discourse analysis: Theory and method. London: Routledge.Google Scholar
  18. Goffman, E. (1981). Forms of talk. Philadelphia: University of Pennsylvania Press.Google Scholar
  19. Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22, 170–218, doi: 10.2307/749074.CrossRefGoogle Scholar
  20. Greeno, J. G. (2006). Learning in activity. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 79–96). Cambridge: Cambridge University Press.Google Scholar
  21. Greeno, J. G., & Gresalfi, M. S. (2008). Opportunities to learn in practice and identity. In P. A. Moss, D. C. Pullin, J. P. Gee, E. H. Haertel, & L. J. Young (Eds.), Assessment, Equity, and Opportunity to Learn. New York: Cambridge University Press.Google Scholar
  22. Greeno, J. G., & MMAP (1998). The situativity of knowing, learning, and research. The American Psychologist, 53, 5–26, doi: 10.1037/0003-066X.53.1.5.CrossRefGoogle Scholar
  23. Gresalfi, M. S. (2004). Taking up opportunities to learn: Examining the construction of participatory mathematical identities in middle school students. Dissertation, Stanford University.Google Scholar
  24. Gutiérrez, R. (2004). The complex nature of practice for urban (mathematics) teachers. Paper presented at the Rockefeller Symposium on the Practice of School Improvement: Theory, Methodology, and Relevance, Bellagio, Italy, AugustGoogle Scholar
  25. Hand, V. (2003). Reframing participation: How mathematics classrooms afford opportunities for mathematical activity that is meaningful to students from diverse social and cultural backgrounds. Dissertation, Stanford University.Google Scholar
  26. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549, doi: 10.2307/749690.CrossRefGoogle Scholar
  27. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. Portmouth, NH: Heinemann.Google Scholar
  28. Holland, D., Skinner, D., Lachicotte Jr, W., & Cain, C. (1998). Identity in cultural worlds. Cambridge, MA: Harvard University Press.Google Scholar
  29. Horn, I. S. (2008). Turnaround students in high school mathematics: Constructing identities of competence through mathematical worlds. Mathematical Thinking and Learning (in press).Google Scholar
  30. Jungwirth, H. (1991). Interaction and gender—Findings of a microethnographical approach to a classroom discourse. Educational Studies in Mathematics, 22, 263–284, doi: 10.1007/BF00368341.CrossRefGoogle Scholar
  31. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.Google Scholar
  32. Ladson-Billings, G. (1997). It doesn’t add up: African American students’ mathematical achievement. Journal for Research in Mathematics Education, 28(6), 697–708, doi: 10.2307/749638.CrossRefGoogle Scholar
  33. 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, 29–63.Google Scholar
  34. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.Google Scholar
  35. Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. New York: Cambridge University Press.Google Scholar
  36. Lave, J. (1991). Situating learning in communities of practice. In L. B. Resnick, J. M. Levine, & S. D. Teasley (Eds.), Perspectives on socially shared cognition (pp. 63–82). Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  37. Lemke, J. L. (1990). Talking science. Norwood, NJ: Ablex.Google Scholar
  38. Lemke, J. L. (2000). Across the scales of time: Artifacts, activities, and meanings in ecosocial systems. Mind, Culture, and Activity, 7(4), 273–290, doi: 10.1207/S15327884MCA0704_03.CrossRefGoogle Scholar
  39. McDermott, R. (1993). The acquisition of a child by a learning disability. In S. Chaiklin, & J. Lave (Eds.), Understanding Practice. Cambridge: Cambridge University Press.Google Scholar
  40. Moses, R. P., & Cobb, C. E. (2001). Radical equations: Math literacy and civil rights. Boston: Beacon Press.Google Scholar
  41. National Council of Teachers of Mathematics.(2000). Principles and standards for school mathematics. Retrieved September 26, 2002, from http://standards.nctm.org/document/index.htm.
  42. National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: US Department of Education.Google Scholar
  43. Pickering, A. (1995). The mangle of practice: Time, agency, and science. Chicago, IL: University of Chicago Press.Google Scholar
  44. Pope, D. (2001). Doing School: how we are creating a generation of stressed out, materialistic, and miseducated students. New Haven, CT: Yale University Press.Google Scholar
  45. Schoenfeld, A. H. (1999). Looking toward the twenty-first century: Challenges of educational theory and practice. Educational Researcher, 28(7), 4–14.Google Scholar
  46. Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teacher College Press.Google Scholar
  47. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477, doi: 10.2307/749877.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Melissa Gresalfi
    • 1
  • Taylor Martin
    • 2
  • Victoria Hand
    • 3
  • James Greeno
    • 4
  1. 1.Indiana UniversityBloomingtonUSA
  2. 2.University of TexasAustinUSA
  3. 3.University of ColoradoBoulderUSA
  4. 4.University of PittsburghPittsburghUSA

Personalised recommendations