Shvarts, A., & Abrahamson, D. (2023). Coordination dynamics of semiotic mediation: A functional dynamic systems perspective on mathematics teaching/learning.

In T. Veloz, R. Videla, & A. Riegler (Eds.), Education in the 21st century [Special issue]. Constructivist Foundations, 18(2), 220–234.

ABSTRACT: Context: Radical embodied approaches to cognition propose a drastic alternative to representation-based models of the mind by way of theorizing and empirically demonstrating the constitutive roles of perception–action loops in human behavior. However, applying those approaches to higher-order processes – such as mathematical thinking and learning – remains one of the hottest debates within contemporary cognitive science. Problem: How might a radical embodied perspective theoretically explain semiotic mediation? For example, how can we theorize the understanding of trigonometric relations expressed through the symbolic form of “sin 2a = sin a”? Method: Revisiting the nature of semiotic mediation, we pursue a historically grounded theoretical analysis that integrates perspectives from Lev Vygotsky and Nikolai Bernstein; to make the theoretical proposal accessible, we illustrate it by empirical data from a dual-eye-tracking study on teaching/learning trigonometry. Results: We show how semiotic mediation of mathematical ideas is constituted as direct intercorporeal sensorimotor coordination between interlocutors. We treat semiotic actions as directly transforming an environment for the interlocutor, inviting new sensorimotor processes. New sensorimotor routines potentially lead to the emergence of pedagogically desired perception and action orientations, that is, new enactive capacity as the cognitive vehicle of mathematical reasoning. As such, Vygotskian cultural– historical ideas of semiotic mediation become a natural continuation of a radical embodied project developed by Bernstein, Kelso, Turvey, and others. Semiotic actions do not represent mind-independent reality as standalone tokens – rather, they present the environment itself, for the interlocutor, in a new way. Implications: The proposed perspective avoids ontologically problematic views of pedagogical discourse as the negotiation of minds, instead focusing educators’ attention on transformations of the students’ environment that foster desired perceptions and actions. Constructivist content: We develop an alternative to a social-constructivist reading of cultural-historical ideas, thus contributing to the understanding of higher-order cognition as direct extension of perception and action.

Key words: Bernstein, complex dynamic systems, coordination dynamics, functional systems, intercorporeal systems, mathematics education, multimodal joint attention, semiotic mediation, Vygotsky.

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