Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities
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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.
KeywordsArgumentation Reasoning Questioning Teaching Discussions
This paper is based on work supported by the University of Georgia Research Foundation under grant no. FRG772 and the National Science Foundation through the Center for Proficiency in Teaching Mathematics under grant no. 0227586. Opinions, findings, and conclusions in this paper are those of the authors and do not necessarily reflect the views of the funding agencies. The authors would like to thank Jeremy Kilpatrick and Denise Spangler for their helpful comments on earlier versions of this manuscript.
- Advisory Committee on Mathematics Education. (2011). Mathematical needs: Mathematical needs of learners. London, UK: Advisory Committee on Mathematics Education.Google Scholar
- 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
- 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
- Chazan, D., & Ball, D. L. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2–10.Google Scholar
- 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
- 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
- Herbel-Eisenmann, B., & Breyfogle, M. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484–489.Google Scholar
- 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
- 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
- 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
- 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
- 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
- Martin, T. S. (Ed.). (2007). Mathematics teaching today: Improving practice, improving student learning. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
- National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: Author.Google Scholar
- 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.
- 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
- Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25, 161–217.Google Scholar
- 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