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The Enactive Roots of STEM: Rethinking Educational Design in Mathematics

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Abstract

New and radically reformative thinking about the enactive and embodied basis of cognition holds out the promise of moving forward age-old debates about whether we learn and how we learn. The radical enactive, embodied view of cognition (REC) poses a direct, and unmitigated, challenge to the trademark assumptions of traditional cognitivist theories of mind—those that characterize cognition as always and everywhere grounded in the manipulation of contentful representations of some kind. REC has had some success in understanding how sports skills and expertise are acquired. But, REC approaches appear to encounter a natural obstacle when it comes to understanding skill acquisition in knowledge-rich, conceptually based domains like the hard sciences and mathematics. This paper offers a proof of concept that REC’s reach can be usefully extended into the domain of science, technology, engineering, and mathematics (STEM) learning, especially when it comes to understanding the deep roots of such learning. In making this case, this paper has five main parts. The section “Ancient Intellectualism and the REC Challenge” briefly introduces REC and situates it with respect to rival views about the cognitive basis of learning. The “Learning REConceived: from Sports to STEM?” section outlines the substantive contribution REC makes to understanding skill acquisition in the domain of sports and identifies reasons for doubting that it will be possible to apply the same approach to knowledge-rich STEM domains. The “Mathematics as Embodied Practice” section gives the general layout for how to understand mathematics as an embodied practice. The section “The Importance of Attentional Anchors” introduces the concept “attentional anchor” and establishes why attentional anchors are important to educational design in STEM domains like mathematics. Finally, drawing on some exciting new empirical studies, the section “Seeing Attentional Anchors” demonstrates how REC can contribute to understanding the roots of STEM learning and inform its learning design, focusing on the case of mathematics.

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Notes

  1. For a compelling critique of the need to invoke this Fodorian hypothesis-formation assumption, see Shea’s (2011) commentary on Carey (2011).

  2. Borrowing from Fodor, again, the assumption is that representing as necessarily involves concepts: “To represent (e.g., mentally) Mr. James as a cat is to represent him falling under the concept CAT” (Fodor 2007, p. 105). This line of thought motivates and (apparently) justifies believing in atomistic conceptual primitives. Carruthers (2011) articulates this working assumption well and makes his commitment to it indelibly clear: “many mental states are realized discretely in the brain and possess causally relevant component structure … they possess a discrete existence and are structured out of component concepts” (Carruthers 2011, p. xiv; see the preface of Fodor and Pylyshyn 2015 for similar view and an expanded list of related working assumptions).

  3. Here “content” is understood designating representational content—where, canonically, the notion of representation content assumes the existence of some kind of correctness condition such that the world is taken (“said,” “represented,” or “claimed”) to be in a certain way that it might not be in.

  4. See (Hutto et al. 2014) for an elaborated account of the notion extensive, including how the idea of an extensive mind differs from that of an extended mind.

  5. Other publications explain the critical role that the interval plays in fostering mathematical learning through the MIT-P activity, and in particular its mediating function in students’ micro-actions of adopting the mathematical frames of reference (i.e., the grid and numerals; see (Abrahamson and Trninic 2015); (Abrahamson et al. 2011)) and linking among competing visualizations of the bimanual “green” enactment (Abrahamson et al. 2014).

  6. At the Embodied Design Research Laboratory (EDRL), we are particularly excited by the opportunities created by these new intellectual perspectives and research designs for revisiting and corroborating the construct of reflective abstraction (Piaget 1968). Piaget implicated sensorimotor coordination as a critical achievement in the development of a new conceptual schema. Attentional anchors enable us to underscore Piaget’s revolutionary adoption of structuralism (Piaget 1970) as the systemic alternative to cognitivism.

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  1. Philosophy, University of Wollongong, Wollongong, Australia

    Daniel D. Hutto & Michael D. Kirchhoff

  2. Graduate School of Education, Berkeley University of California, Berkeley, CA, USA

    Dor Abrahamson

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Hutto, D.D., Kirchhoff, M.D. & Abrahamson, D. The Enactive Roots of STEM: Rethinking Educational Design in Mathematics. Educ Psychol Rev 27, 371–389 (2015). https://doi.org/10.1007/s10648-015-9326-2

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