Educational Studies in Mathematics

, Volume 86, Issue 3, pp 401–429 | Cite as

Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities

  • AnnaMarie Conner
  • Laura M. Singletary
  • Ryan C. Smith
  • Patty Anne Wagner
  • Richard T. Francisco
Article

Abstract

We propose a framework for examining how teachers may support collective argumentation in secondary mathematics classrooms, including teachers’ direct contributions to arguments, the kinds of questions teachers ask, and teachers’ other supportive actions. We illustrate our framework with examples from episodes of collective argumentation occurring across 2 days in a teacher’s classroom. Following from these examples, we discuss how the framework can be used to examine mathematical aspects of conversations in mathematics classrooms. We propose that the framework is useful for investigating and possibly enhancing how teachers support students’ reasoning and argumentation as fundamentally mathematical activities.

Keywords

Argumentation Reasoning Questioning Teaching Discussions 

References

  1. Advisory Committee on Mathematics Education. (2011). Mathematical needs: Mathematical needs of learners. London, UK: Advisory Committee on Mathematics Education.Google Scholar
  2. Baxter, J. A., & Williams, S. (2009). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26. doi:10.1007/s10857-009-9121-4.CrossRefGoogle Scholar
  3. Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the twenty-sixth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 773–781). Toronto, Canada: Ontario Institute for Studies in Education/University of Toronto.Google Scholar
  4. Brodie, K. (2010). Pressing dilemmas: Meaning-making and justification in mathematics teaching. Journal of Curriculum Studies, 42(1), 27–50.CrossRefGoogle Scholar
  5. Chapin, S. H., O’Connor, C., & Anderson, N. C. (2003). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions.Google Scholar
  6. Chazan, D., & Ball, D. L. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2–10.Google Scholar
  7. Conner, A. (2012). Warrants as indications of reasoning patterns in secondary mathematics classes. In Proceedings of the 12 th International Congress on Mathematical Education (ICME-12), Topic Study Group 14 (pp. 2819–2827). Seoul, Korea.Google Scholar
  8. Conner, A. (2008). Expanded Toulmin diagrams: A tool for investigating complex activity in classrooms. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (Vol. 2, pp. 361–368). Morelia, Mexico: Cinvestav-UMSNH.Google Scholar
  9. Conner, A., Edenfield, K., Gleason, B., & Ersoz, F. (2011). Impact of a content and methods course sequence on prospective secondary mathematics teachers’ beliefs. Journal of Mathematics Teacher Education, 14, 483–504. doi:10.1007/s10857-011-9186-8.CrossRefGoogle Scholar
  10. Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Brown, C. A. (1998). “You’re going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8, 527–548.CrossRefGoogle Scholar
  11. Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60, 380–392. doi:10.1177/0022487109339906.CrossRefGoogle Scholar
  12. Herbel-Eisenmann, B., & Breyfogle, M. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484–489.Google Scholar
  13. Hollebrands, K. F., Conner, A., & Smith, R. C. (2010). The nature of arguments provided by college geometry students with access to technology while solving problems. Journal for Research in Mathematics Education, 41, 324–350.Google Scholar
  14. Hufferd-Ackles, K., Fuson, K., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81–116.CrossRefGoogle Scholar
  15. Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66, 3–21. doi:10.1007/s10649-006-9059-8.CrossRefGoogle Scholar
  16. Knipping, C. (2003). Argumentation structures in classroom proving situations. Paper presented at the Third Congress of the European Society for Research in Mathematics Education. Italy: Bellaria.Google Scholar
  17. Knipping, C. (2008). A method for revealing structures of argumentations in classroom proving processes. ZDM: The International Journal on Mathematics Education, 40(3), 427–441. doi:10.1007/s11858-008-0095-y.CrossRefGoogle Scholar
  18. Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229–269). Hillsdale, NJ: Erlbaum.Google Scholar
  19. Krummheuer, G. (2000). Mathematics learning in narrative classroom cultures: Studies of argumentation in primary mathematics education. For the Learning of Mathematics, 20(1), 22–32.Google Scholar
  20. Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom: Two episodes and related theoretical abductions. Journal of Mathematical Behavior, 26, 60–82. doi:10.1016/j.jmathb.2007.02.001.CrossRefGoogle Scholar
  21. Lobato, J., Clarke, D., & Ellis, A. B. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education, 36, 101–136.Google Scholar
  22. Martin, T. S. (Ed.). (2007). Mathematics teaching today: Improving practice, improving student learning. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  23. McClain, K. (2002). Teacher’s and students’ understanding: The role of tools and inscriptions in supporting effective communication. Journal of the Learning Sciences, 11(2–3), 217–249.CrossRefGoogle Scholar
  24. McCrone, S. S. (2005). The development of mathematical discussions: An investigation in a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.CrossRefGoogle Scholar
  25. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  26. National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: Author.Google Scholar
  27. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards: Mathematics standards. Washington, DC: National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/the-standards/mathematics.
  28. Rasmussen, C. L., & Stephan, M. (2008). A methodology for documenting collective activity. In A. Kelly, R. Lesh, & J. Baek (Eds.), Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics teaching and learning (pp. 195–215). New York, NY: Routledge.Google Scholar
  29. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  30. Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25, 161–217.Google Scholar
  31. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10, 313–340.CrossRefGoogle Scholar
  32. Toulmin, S. E. (2003). The uses of argument (updated ed.). New York: Cambridge University Press. Original work published 1958.CrossRefGoogle Scholar
  33. Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Education Studies in Mathematics, 68, 247–261.CrossRefGoogle Scholar
  34. Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing? In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167–178). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  35. Wood, T. (1999). Creating a context for argument in mathematics class. Journal for Research in Mathematics Education, 30(2), 171–191.CrossRefGoogle Scholar
  36. Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation? Journal of Mathematical Behavior, 21, 423–440.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • AnnaMarie Conner
    • 1
  • Laura M. Singletary
    • 2
  • Ryan C. Smith
    • 1
  • Patty Anne Wagner
    • 1
  • Richard T. Francisco
    • 1
  1. 1.Department of Mathematics and Science EducationUniversity of GeorgiaAthensUSA
  2. 2.Department of Natural Sciences and MathematicsLee UniversityClevelandUSA

Personalised recommendations