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Demonstrating mathematics learning as the emergence of eye–hand dynamic equilibrium

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Abstract

This paper combines recent developments in theories of knowledge (complex dynamic systems), technologies (embodied interactions), and research tools (multimodal data collection and analysis) to offer new insights into how conceptual mathematical understanding can emerge. A complex dynamic system view models mathematics learning in terms of a multimodal agent who encounters a set of task constraints. The learning process in this context includes destabilizing a systemic configuration (for example, coordination of eye and hand movements) and forming new dynamic stability adapted to the task constraints. To test this model empirically, we applied a method developed to study complex systems, recurrence quantification analysis (RQA), to investigate students’ eye–hand dynamics during a touchscreen mathematics activity for the concept of proportionality. We found that across participants (n = 32), fluently coordinated hand-movement solutions coincided with more stable and predictable gaze patterns. We present a case study of a prototypical participant’s hand–eye RQA and audio–video data to show how the student’s cognitive system transitioned out of prior coordination reflective of additive thinking into a new coordination that can ground multiplicative thinking. These findings constitute empirical substantiation in mathematics education research for cognition as a complex system transitioning among dynamic equilibria.

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Data availability

The data that support the findings of this study are available from the Freudenthal Institute at Utrecht University, but restrictions apply to the availability of these data, which were used under license for the current study and so are not publicly available. However, data are available from the authors upon reasonable request and with the permission of the Freudenthal Institute at Utrecht University.

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Authors and Affiliations

  1. David Yellin College of Education, Jerusalem, Israel

    Rotem Abdu

  2. University of California, Berkeley, CA, USA

    Sofia Tancredi & Dor Abrahamson

  3. San Francisco State University, San Francisco, CA, USA

    Sofia Tancredi

  4. University of California, Merced, CA, USA

    Ramesh Balasubramaniam

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Abdu, R., Tancredi, S., Abrahamson, D. et al. Demonstrating mathematics learning as the emergence of eye–hand dynamic equilibrium. Educ Stud Math (2023). https://doi.org/10.1007/s10649-023-10279-0

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