Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research.
Educators must understand two opposing traditions in education, the mimetic and the transformative. Whereas traditional lesson structuring stresses concept introduction, constructivism emphasizes exploration. To constructivists, teachers strike the delicate balance between teaching for fact and skill acquisition and teaching for independent and expert thinking.
de Zeeuw G. (2013) Quality and Qualifications. Constructivist Foundations 9(1): 138–139. https://constructivist.info/9/1/138
Open peer commentary on the article “A Cybernetic Computational Model for Learning and Skill Acquisition” by Bernard Scott & Abhinav Bansal. Upshot: The paper is an admirable example of first-order cybernetics. It does not appear to be developed as part of the constructivist paradigm and of second-order cybernetics. It neglects research as the context that generates problems of observation.
Dreyfus H. (1996) The current relevance of Merleau-Ponty’s phenomenology of embodiment. Electronic Journal of Analytic Philosophy 4(Spring): 1. https://cepa.info/2901
In this paper I would like to explain, defend, and draw out the implications of this claim. Since the intentional arc is supposed to embody the interconnection of skillful action and perception, I will first lay out an account of skill acquisition that makes explicit what Merleau-Ponty’s claim presupposes. I will then show how his account of skill and the intentional arc it establishes allows Merleau-Ponty to criticize cognitivism and introduce a new account of the relation of perception and action. Finally, I will suggest that neural-network theory supports Merleau-Ponty’s phenomenology, but that it still has a long way to go before it can instantiate an intentional arc.
Dreyfus H. (2002) Intelligence without representations – Merleau-Ponty’s critique of mental representation: The relevance of phenomenology to scientific explanation. Phenomenology and the Cognitive Sciences 1(4): 367–383.
Existential phenomenologists hold that the two most basic forms of intelligent behavior, learning, and skillful action, can be described and explained without recourse to mind or brain representations. This claim is expressed in two central notions in Merleau-Ponty’s Phenomenology of Perception: the intentional arc and the tendency to achieve a maximal grip. The intentional arc names the tight connection between body and world, such that, as the active body acquires skills, those skills are “stored”, not as representations in the mind, but as dispositions to respond to the solicitations of situations in the world. A phenomenology of skill acquisition confirms that, as one acquires expertise, the acquired know-how is experienced as finer and finer discriminations of situations paired with the appropriate response to each. Maximal grip names the body’s tendency to refine its responses so as to bring the current situation closer to an optimal gestalt. Thus, successful learning and action do not require propositional mental representations. They do not require semantically interpretable brain representations either. Simulated neural networks exhibit crucial structural features of the intentional arc, and Walter Freeman’s account of the brain dynamics underlying perception and action is structurally isomorphic with Merleau-Ponty’s account of the way a skilled agent is led by the situation to move towards obtaining a maximal grip.
Dreyfus H. L. (2002) Intelligence without representation – Merleau-Ponty’s critique of mental representation: The relevance of phenomenology to scientific explanation. Phenomenology and the Cognitive Sciences 1(4): 367–383. https://cepa.info/4592
Existential phenomenologists hold that the two most basic forms of intelligent behavior, learning, and skillful action, can be described and explained without recourse to mind or brain representations. This claim is expressed in two central notions in Merleau-Ponty’s Phenomenology of Perception: the intentional arc and the tendency to achieve a maximal grip. The intentional arc names the tight connection between body and world, such that, as the active body acquires skills, those skills are “stored,” not as representations in the mind, but as dispositions to respond to the solicitations of situations in the world. A phenomenology of skill acquisition confirms that, as one acquires expertise, the acquired know-how is experienced as finer and finer discriminations of situations paired with the appropriate response to each. Maximal grip names the body’s tendency to refine its responses so as to bring the current situation closer to an optimal gestalt. Thus, successful learning and action do not require propositional mental representations. They do not require semantically interpretable brain representations either. Simulated neural networks exhibit crucial structural features of the intentional arc, and Walter Freeman’s account of the brain dynamics underlying perception and action is structurally isomorphic with Merleau-Ponty’s account of the way a skilled agent is led by the situation to move towards obtaining a maximal grip.
Franchi S. (2013) On Models, Simulations, and the Relevancy of Biochemistry to Cognitive Functions. Constructivist Foundations 9(1): 141–142. https://constructivist.info/9/1/141
Open peer commentary on the article “A Cybernetic Computational Model for Learning and Skill Acquisition” by Bernard Scott & Abhinav Bansal. Upshot: Scott and Bansal’s assessment of the limitations of their work relies on a concept of simulation that I find problematic. It assumes that the ultimate goal of a model is a replication of the phenomena it applies, whereas a limited model produces only simulations. I argue that this position leads to unfortunate epistemological results, and it ends up assigning an unduly exclusive role to the study of the biochemical substrate of cognition.
Hutto D. D. & Sánchez-García R. (2015) Choking RECtified: Embodied expertise beyond Dreyfus. Phenomenology and the Cognitive Sciences 14(2): 309–331. https://cepa.info/5802
On a Dreyfusian account performers choke when they reflect upon and interfere with established routines of purely embodied expertise. This basic explanation of choking remains popular even today and apparently enjoys empirical support. Its driving insight can be understood through the lens of diverse philosophical visions of the embodied basis of expertise. These range from accounts of embodied cognition that are ultra conservative with respect to representational theories of cognition to those that are more radically embodied. This paper provides an account of the acquisition of embodied expertise, and explanation of the choking effect, from the most radically enactive, embodied perspective, spelling out some of its practical implications and addressing some possible philosophical challenges. Specifically, we propose: (i) an explanation of how skills can be acquired on the basis of ecological dynamics; and (ii) a non-linear pedagogy that takes into account how contentful representations might scaffold skill acquisition from a radically enactive perspective.
Hutto D. D., Kirchhoff M. D. & Abrahamson D. (2015) The enactive roots of STEM: Rethinking educational design in mathematics. Educational Psychology Review 27(3): 371–389. https://cepa.info/5075
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.
Jonassen D., Mayes T. & McAleese R. (1993) A manifesto for a constructivist approach to uses of technology in higher education. In: Duffy T. M., Lowyck J. & Jonassen D. H. (eds.) Designing Environments for Constructive Learning. Springer, Berlin: 231–247.
Excerpt: This paper will describe our assumptions about advanced knowledge and skill acquisition in higher education and our assumptions about environments and tools that should support this phase of learning.