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Students discussing mathematics in small-group interactions: opportunities for discursive negotiation processes focused on contentious mathematical issues

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Abstract

Small-group discussions involving students and their teacher that focus on meanings constructed during the mathematics lessons or solutions to problems produced in these lessons offer great potential for debate and argument. An analysis of the epistemological nature of knowledge can give deeper insight, to gain a better understanding of the emerging discontinuities in argumentations, negotiations, and clarifications about contentious meaning differences that arise. In most cases mathematical interactions between students and a teacher about contentions are very fragile and seem to be handled more or less directly—by side-stepping to another topic or by resolving via the teacher’s authority, for example. Therefore, the maintenance of such negotiation processes in mathematics teaching is a specific challenge for students and the teacher. The type of closure of these processes seems to be related to the emerging maintenance processes. In this paper, small-group discussions are interpretatively analyzed in the three steps “Initiation—Maintenance—Closing” with the focus on fundamental (dialogical) learning.

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Notes

  1. A discussion of classroom talk about this diagram can be found in Gellert and Steinbring (2012).

  2. Named after Zoltan Paul Dienes.

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Acknowledgments

I would like to thank the working group ‘EInmaL’ (Professor H. Steinbring) for the profound discussions within the project and especially the examples used in this paper. Also many thanks to the reviewers for their advice, and to Professor C. Morgan and PhD J. Ingram for editing the English version.

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  1. Department of Mathematics, University of Duisburg-Essen, Thea-Leymann-Str. 9, 45127, Essen, Germany

    Andrea Gellert

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  1. Andrea Gellert
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Correspondence to Andrea Gellert.

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Gellert, A. Students discussing mathematics in small-group interactions: opportunities for discursive negotiation processes focused on contentious mathematical issues. ZDM Mathematics Education 46, 855–869 (2014). https://doi.org/10.1007/s11858-014-0594-y

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