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An interactionist perspective on mathematics learning: conditions of learning opportunities in mixed-ability groups within linguistic negotiation processes

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Abstract

This paper illustrates that focusing on processes of interaction is crucial to a closer understanding of mathematical learning processes in mixed-ability groups. In doing so, the paper’s focus is on expounding a theoretical-methodological framework of an interactionist perspective in mathematics education. This framework interlinks sociological and social-constructivist theories with subject-specific educational theories. As a result of two examples of analyses it becomes apparent that investigations on mathematics learning within linguistic negotiation processes, based on an interactionist-oriented theoretical frame, provide in-depth insights into individual learning possibilities of a diverse student body. These insights are made possible only by means of a detailed micro-sociological examination of collectively occurring learning processes within linguistic negotiation processes.

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Notes

  1. Both transcripts are included in the original language (German) in the electronic supplementary material of this paper. The rules for transcription are presented in the “Appendix”.

  2. Following Jensen (2003), subtractions can be done in two ways: “comparative subtraction” and “take-away subtraction”. In German references, there is a third category and the mental models (vom Hofe et al. 2006) of subtraction can be distinguished into: taking-away, supplementing and comparing (Wessel 2015). Thus, we use these terms. The mental models of taking-away and supplementing have a dynamic characteristic. Taking-away is characterized by taking away the subtrahend from the minuend. For supplementing, the gap between the minuend (or the sum) and the subtrahend (or the first summand) is determined by an (imaginary) action. On the contrary, comparing is static and is characterized by the gap between the two given items without performing the action of taking away or supplementing. According to the interactionist understanding at hand, these basic notions are used in analyses to differentiate the learners’ framings regarding subtraction, and to visualize modulations in framings.

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Authors and Affiliations

  1. Technical University of Dresden, Dresden, Germany

    Judith Jung & Marcus Schütte

Authors
  1. Judith Jung
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  2. Marcus Schütte
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Correspondence to Marcus Schütte.

Electronic supplementary material

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Supplementary material 1 (PDF 91 KB)

Appendix

Appendix

1.1 Transcript conventions

<

Overlapping/simultaneous speech

#

Interrupting, seamless transition between speakers

. / .. / ..

Pause for one to three seconds

smaller

Spoken quietly, whisper

n o w

Elongation

/

Strong rising intonation

(but)

Word not fully comprehensible

(incomprehensible)

Incomprehensible utterance

[stands up]

Actions, facial expressions, gestures, paralinguistic utterances

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Jung, J., Schütte, M. An interactionist perspective on mathematics learning: conditions of learning opportunities in mixed-ability groups within linguistic negotiation processes. ZDM Mathematics Education 50, 1089–1099 (2018). https://doi.org/10.1007/s11858-018-0999-0

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