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

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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.

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Notes

  1. Our framework captures the teacher’s actions in support of mathematical arguments in classrooms. It does not distinguish actions that might be mathematically productive from those that might not be. Nor does it distinguish actions that encourage more productive argumentation from others that might limit students’ participation. However, it does point out the potential actions and contributions of the teacher and allows users of the framework to draw conclusions about the mathematical and pedagogical potential of such actions.

  2. Toulmin (1958/2003) called these preliminary arguments or lemmas (p. 90). We use subargument to indicate that these may not come temporally before the other argument and to avoid lemma, which has a specific mathematical meaning.

  3. All participant names are pseudonyms.

  4. Note that a move did not have to be productive, nor did it have to be part of a productive or mathematically correct argument to be supportive. We interpreted a move as supporting collective argumentation if it elicited or responded to a component of an argument.

  5. The three types of support comprise the actual framework. We make the assumption that in order to use the framework most robustly, a user would diagram the episode(s) of argumentation of interest prior to applying the categories of the framework.

  6. This statement and the preceding eight lines did not add to the argument but are included here in the transcript for the sake of completeness and to illustrate that when diagramming arguments, there are decisions that must be made concerning what actually contributed to the argument.

  7. Although this statement was made by a student, Ms. Bell’s preceding question suggested only one possible answer. Therefore, the component was attributed to both student and teacher.

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Acknowledgments

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.

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Authors and Affiliations

  1. Department of Mathematics and Science Education, University of Georgia, 105 Aderhold Hall, Athens, GA, 30602, USA

    AnnaMarie Conner, Ryan C. Smith, Patty Anne Wagner & Richard T. Francisco

  2. Department of Natural Sciences and Mathematics, Lee University, Cleveland, TN, 37311, USA

    Laura M. Singletary

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  1. AnnaMarie Conner
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Correspondence to AnnaMarie Conner.

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Conner, A., Singletary, L.M., Smith, R.C. et al. Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educ Stud Math 86, 401–429 (2014). https://doi.org/10.1007/s10649-014-9532-8

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