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Open peer commentary on the article “Coordination Dynamics of Semiotic Mediation: A Functional Dynamic Systems Perspective on Mathematics Teaching/Learning” by Anna Shvarts & Dor Abrahamson. Abstract: My present reflections will center on a point the authors present as an afterthought, but that seems pivotal: mathematical knowledge is not comprised of perception-action loops alone. Instead, “guided coordination of sensorimotor and semiotic activity” is held to be essential. Shvarts and Abrahamson do not elaborate on how this happens. My aim is to sketch what an account giving equal weight to semiotic and embodied facets might look like, and to clarify why paying attention to the details of their interplay is crucial for evaluating ontological claims such as the monist position defended by the authors. I will presently address four questions: (a) why failing to tackle the semiotic pole explicitly is a risky methodological choice, (b) what literature we can draw on to address the embodied-semiotic relationship, (c) what empirical criteria ontological claims might hinge on, and (d) why a dialectic (and non-dualist) approach offers a credible alternative to monism.
Kimmel M. (2023) Concepts, material anchors and interactivity: A dialectic perspective. Constructivist Foundations 18(2): 247–250. https://constructivist.info/18/2/247
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