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Students constructing meaning for the number line in small-group discussions: negotiation of essential epistemological issues of visual representations

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In mathematics classroom interaction, the multiple meanings of mathematical visual diagrams are often ignored; instead, depending on the given situation, they are read in a well-defined and unitary way. Mathematical visual representations are thus used even less in their epistemological function for learning, but more as pre-given subject matter. The purpose of this paper is to elaborate opportunities for negotiating and clarifying differences, dealing with a great variety of ways of interpreting visual diagrams that are brought into focus in interaction. Theory-based qualitative analyses of two exemplifying video episodes of small-group discussions negotiating their ideas on the topic “number line” show differences of meaning and the importance of conventions followed by mathematical deductions. Two mutually exclusive teacher behaviors within the communicative acts, reconstructed as a dominating way of instruction and a moderating way of focusing, are identified.

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  1. The research reported in this paper is part of the project “Probing and Evaluating Focusing Interaction and Teaching Strategies (ProFIT)”.

  2. We decided to conduct the small-group discussions outside from the class in an experimental setting. The rules for transcription used in this paper can be found in the addendum (Sect. 7).

  3. Such a teaching behavior Bauersfeld (1978) called the “funneling pattern.” For the interested reader also cf. Wood (1994).


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Thank you to three anonymous reviewers for their ideas and helpful feedback and to a colleague and friend from Oxford University, UK, for editing the English version.

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Correspondence to Andrea Gellert.

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Gellert, A., Steinbring, H. Students constructing meaning for the number line in small-group discussions: negotiation of essential epistemological issues of visual representations. ZDM Mathematics Education 46, 15–27 (2014).

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