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Enactivism and the study of collectivity

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Abstract

In this paper, we trace the development of our theorizing about students’ mathematical understanding, showing how the adoption of an enactivist perspective has transformed our gaze in terms of the objects of our studies and occasioned for us new methods of data analysis. Drawing on elements of Pirie–Kieren (P–K) Theory for the Dynamical Growth of Mathematical Understanding, together with aspects of improvisational theory and the associated notion of coactions, we describe the ways in which we have moved from a focus on the individual learner to that of the collective. In particular, we identify how our research methods and methodology have evolved to enable us to transform our data in ways that allow us to identify, consider, and discuss collective mathematical action. Using a brief transcription of an extract of video-recorded data in which three Grade 6 students work together to find the area of a parallelogram, we share and discuss successive iterations of our data analysis process. We identify the ways in which we manipulate and rework transcriptions of group discourse to reveal the relationship between enactivist thought and processes of engagement with data involving groups of mathematics learners.

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Acknowledgments

This research was funded in part by the Social Sciences and Humanities Council of Canada (Grant # 410-2009-0383) and the University of Calgary Research Grants Committee. Neither organization exercised any oversight in the design of the research, the collection, analysis, and interpretation of data, or the writing of this report.

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Authors and Affiliations

  1. University of Calgary, Calgary, Canada

    Jo Towers

  2. York University, Toronto, Canada

    Lyndon C. Martin

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  1. Jo Towers
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  2. Lyndon C. Martin
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Correspondence to Jo Towers.

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Towers, J., Martin, L.C. Enactivism and the study of collectivity. ZDM Mathematics Education 47, 247–256 (2015). https://doi.org/10.1007/s11858-014-0643-6

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