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.

Key words: mathematics, education, motor learning, conceptual learning, motor problem, conceptual metaphor

Enactivism theorizes thinking as situated doing. Mathematical thinking, specifically, is handling imaginary objects, and learning is coming to perceive objects and reflecting on this activity. Putting theory to practice, Abrahamson’s embodied-design collaborative interdisciplinary research program has been designing and evaluating interactive tablet applications centered on motor-control tasks whose perceptual solutions then form the basis for understanding mathematical ideas (e.g., proportion). Analysis of multimodal data of students’ handand eyemovement as well as their linguistic and gestural expressions has pointed to the key role of emergent perceptual structures that form the developmental interface between motor coordination and conceptual articulation. Through timely tutorial intervention or peer interaction, these perceptual structures rise to the students’ discursive consciousness as “things” they can describe, measure, analyze, model, and symbolize with culturally accepted words, diagrams, and signs – they become mathematical entities with enactive meanings. We explain the theoretical background of enactivist mathematics pedagogy, demonstrate its technological implementation, list its principles, and then present a case study of a mathematics teacher who applied her graduate-school experiences in enactivist inquiry to create spontaneous classroom activities promoting student insight into challenging concepts. Students’ enactment of coordinated movement forms gave rise to new perceptual structures modeled as mathematical content.

A rising epistemological paradigm in the cognitive sciences – embodied cognition – has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students’ physical movements, eye-gaze paths, and verbal–gestural utterance so as to track and evaluate emerging conceptual capacity. We – a cohort of cognitive scientists and design-based researchers of embodied mathematics – survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.

In this article we analyze the methodological commitments of a radical embodied cognition (REC) approach to social interaction and social cognition, specifically with respect to the explanatory framework it adopts. According to many representatives of REC, such as enactivists and the proponents of dynamical and ecological psychology, sociality is to be explained by (1) focusing on the social unit rather than the individuals that comprise it and (2) establishing the regularities that hold on this level rather than modeling the sub-personal mechanisms that could be said to underlie social phenomena. We point out that, despite explicit commitment, such a view implies an implicit rejection of the mechanistic explanation framework widely adopted in traditional cognitive science (TCS), which, in our view, hinders comparability between REC and these approaches. We further argue that such a position is unnecessary and that enactive mechanistic explanation of sociality is both possible and desirable. We examine three distinct objections from REC against mechanistic explanation, which we dub the decomposability, causality and extended cognition worries. In each case we show that these complaints can be alleviated by either appreciation of the full scope of the mechanistic account or adjustments on both mechanistic and REC sides of the debate.

Key words: enactivism, mechanistic explanation, social cognition

In this paper we examine an enactive approach to social cog- nition, a species of radical embodied cognition typically pro- posed as an alternative to traditional cognitive science. Ac- cording to enactivists, social cognition is best explained by reference to the social unit rather than the individuals that par- ticipate in it. We identify a methodological problem in this approach, namely a lack of clarity with respect to the model of explanation it adopts. We review two complaints about a mechanistic explanatory framework, popular in traditional cognitive science, that prevent enactivists from embracing it. We argue that these complaints are unfounded and propose a conceptual model of enactive mechanistic explanation of so- cial cognition.

Key words: enactivism, social cognition, mechanistic expla- nation

Open peer commentary on the article “Decentering the Brain: Embodied Cognition and the Critique of Neurocentrism and Narrow-Minded Philosophy of Mind” by Shaun Gallagher. Abstract: Simulation theory and theory theory are interaction accounts of theory of mind that have been neurocentrically characterized. A hybrid of these theories approximates the interaction theory of social cognition, and can be described in an indexical-symbolic processing framework.

This paper examines the shared roots and crossed paths between Jean Piaget’s constructivism, what Seymour Paper refers to as “constructionism,” and socio-cultural theories as epitomized by Lev Vygotsky. We do so in the light of more situated, pragmatic, and ecological approaches to human cognition. All these views are developmental (stressing the genesis children’s interests and abilities over time), experiential (in the sense that knowledge is rooted in sensori-motor activity) and interactionist (people are seen as constructing their knowledge by transforming the world). Yet, the views also differ, each highlighting some aspects of how children grow and learn, while leaving other questions unanswered. Piaget’s main contribution was to flesh out what is common in children’s ways of thinking at different stages of their cognitive development and, more important, how consistent, robust, and generally “adapted” their views are. The theory stresses the progressive de-contextualization of knowledge (from here-and-now to then-and-there) and identifies some of the hidden mechanisms (internal reorganizations) that drive human cognitive development. Papert, in contrast, stresses how individuals learn in context and how they use their own – and other people’s – externalizations as objects to think with, especially as their convictions break down. His approach is more situated. Papert is particularly interested the role of new media in human learning. Both Papert and Vygotsky shed light on the articulations between direct and mediated experience (from action and tool-use to enactments, language, and symbol-use). Yet Vygotsky and the Russian school have paid much closer attention to the role of caring adults and peers in a child’s initiation to her culture. They remind us that it takes a whole village to raise a child. Integrating the views helps rethink how children come to make sense of their experiences, and how they find their own places – and voices – in the world. At once world-makers, world-readers, and dwellers in the world, human infants are granted from birth with the abilities to optimize exchanges with people and things by moving in and out of contexts, by shifting perspectives, and by switching roles or standpoint. They are extraordinary learners, and much can be learned from them. Lastly, while mostly inner-driven and curious, children need caring adults, secure grounds, and engaging peers and props to thrive and grow. Tools, media, and cultural artifacts are the tangible forms through which they explore their surrounds, express their thoughts, and share the fun with others – and the traces left by those who came before (cultural heritage) become a terrain for newcomers to create their paths.

Key words: Constructivism, Piaget, Papert, Vygotsky, situated learning, embodied cognition, ecology of mind

“Are living beings extended autopoietic systems? An embodied reply,” makes the case for grounding the autopoietic definition of living beings to the discrete bodies of organisms rather than to autopoietic systems that extend beyond the organisms into their environments. They attempt this grounding by amending a clause to the original formulation of autopoiesis that identifies living beings with their bodies, and then they explicitly define “bodies”. This commentary makes the case that bodily grounding can be derived from molecular autopoiesis by taking the molecular domain seriously, and no new amendment is required.

Key words: autopoiesis, embodiment, organisms.

This special issue focuses on the theoretical, empirical and practical integrations between embodied cognition theory (EC) and educational science. The key question is: Can EC constitute a new theoretical framework for educational science and practice? The papers of the special issue support the efforts of those interested in the role of EC in education and in the epistemological convergence of EC and educational science. They deal with a variety of relevant topics in education and offer a focus on the role of the body and embodied experience in learning and educational settings. In conclusion, some further topics are suggested that will need to be investigated in the future, such as a critical evaluation of the possibility for an epistemological alliance between educational theory and embodied cognition, and the contribution that enactive cognition can provide to educational systems, organizations, institutions and policies.

Key words: embodied cognition, education, educational theory, phenomenology, phenomenological pedagogy.

Excerpt: Obviously perception is embodied. After all, if creatures were entirely disembodied, how could physical processes in the environment, such as the propagation of light or sound, be transduced into a neurobiological currency capable of generating experience? Is there, however, any deeper, more subtle sense in which perception is embodied?