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Sourcing mathematical meaning as a dialogic process: meaning-focused and language-focused repairs

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Abstract

I report the results of an analysis of an episode of elementary school second language mathematics classroom talk focused on the classification of geometric forms, drawing on a dialogic, sources of meaning perspective. The episode was selected because participants make use of a variety of features of language, including vocabulary, gestures and diagrams. The analysis drew on methods and principles from conversation analysis and revealed that interactional repair was a key feature in the organisation of the episode. Repair sequences are stretches of interaction in which participants deal with explicitly signalled ‘trouble’ in participants’ working assumption of shared understanding. The results include a distinction between meaning-focused and language-focused repair, with some repair sequences embedded within others. This layered organisation is important in the emergence of meaning for participants’ utterances and mediates the tension between centripetal and centrifugal language forces. The findings highlight the complexity of mathematics classroom interaction and suggest possibilities for the careful management of focusing on language and on mathematical meaning in classroom interaction.

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Data availability

The data generated during the study referred to in this paper are confidential to protect the identity of the participants. The anonymised transcript of the lesson that is the focus of this paper may be requested from the author with reasonable justication.

Notes

  1. This finding is consistent with work in second language education based on Swain and Lapkin’s (1998) definition of ‘language-related episodes’. In a recent study in the context of content-language integrated learning (CLIL) classrooms, Smit and Finker (2022) found that the presence of regular language related episodes was linked to teachers’ explicit language-related goals.

  2. Transcription conventions: Student names are pseudonyms. Bold denotes emphasis. (.) indicates a short pause. (1) indicates a one-second pause.:: indicates phoneme extension. [ indicates overlapping speech, vertically aligned. ^ ^ encloses quiet speech. () encloses uncertain transcription. (…) indicates inaudible utterances. <  > encloses English translation, shown in italics after each turn.

  3. References to mutual understanding should be taken to mean that the participants display an assumption of mutual understanding or mutually agreed interpretations sufficient to close the repair sequence and continue the interaction. They do not refer to some supposed internal mental state.

  4. Observant readers will notice an incongruity in the teacher’s groupings. Later in the class, she realised that she had made an error: she had coloured two pentagons purple rather than white. In accordance with the principles of conversation analysis, this later revelation cannot be used to interpret the episode as presented.

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Acknowledgements

I am indebted to the school, teacher and students who kindly participated in this research. I am grateful to Maya Shrestra, Maha Sinno, Adil Dsousa, Jennifer Chew Leung and Élysée Cadet for their work on different aspects of the project.

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Social Sciences and Humanities Research Council of Canada, 410-2008-0544, Richard Barwell.

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  1. University of Ottawa, Ottawa, Canada

    Richard Barwell

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Barwell, R. Sourcing mathematical meaning as a dialogic process: meaning-focused and language-focused repairs. ZDM Mathematics Education 55, 535–550 (2023). https://doi.org/10.1007/s11858-023-01467-6

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