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’ hand- and eye- movement 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.

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

Among the many ideas that go by the name of “enactivism” there is the idea that by “cognition” we should understand what is more commonly taken to be behavior. For clarity, label such forms of enactivism “enactivismb.” This terminology requires some care in evaluating enactivistb claims. There is a genu-ine risk of enactivist and non-enactivist cognitive scientists talking past one another. So, for example, when enactivistsb write that “cognition does not require representations” they are not necessarily denying what cognitivists claim when they write that “cognition requires representations.” This paper will draw attention to instances of some of these unnecessary confusions.

An important question in the debate over embodied, enactive, and extended cognition has been what has been meant by “cognition”. What is this cognition that is supposed to be embodied, enactive, or extended? Rather than undertake a frontal assault on this question, however, this paper will take a different approach. In particular, we may ask how cognition is supposed to be related to behavior. First, we could ask whether cognition is supposed to be (a type of) behavior. Second, we could ask whether we should attempt to understand cognitive processes in terms of antecedently understood cognitive behaviors. This paper will survey some of the answers that have been (implicitly or explicitly) given in the embodied, enactive, and extended cognition literature, then suggest reasons to believe that we should answer both questions in the negative.

Excerpt: In Radicalizing Enactivism (RE), Hutto and Myin present compelling arguments for why basic minds do not have content. In particular, they introduce the Hard Problem of Content (HPC), which states that ‘informational content is incompatible with explanatory naturalism’ (xv). By reviewing a range of theories, the pair demonstrate the futility of attempts to distinguish content from covariance (content is information within a system, whereas a covariant system can be explained purely by way of causal interactions).

Despite its short historical moment in the sun, behaviorism has become something akin to a theoria non grata, a position that dare not be explicitly endorsed. The reasons for this are complex, of course, and they include sociological factors which we cannot consider here, but to put it briefly: many have doubted the ambition to establish law-like relationships between mental states and behavior that dispense with any sort of mentalistic or intentional idiom, judging that explanations of intelligent behavior require reference to qualia and/or mental events. Today, when behaviorism is discussed at all, it is usually in a negative manner, either as an attempt to discredit an opponent’s view via a reductio, or by enabling a position to distinguish its identity and positive claims by reference to what it is (allegedly) not. In this paper, however, we argue that the ghost of behaviorism is present in influential, contemporary work in the field of embodied and enactive cognition, and even in aspects of the phenomenological tradition that these theorists draw on. Rather than take this to be a problem for these views as some have (e.g. Block, J Philos 102:259–272, 2005; Jacob, Rev Philos Psychol 2(3):519–540, 2011; O’Brien and Opie, Philos 43:723–729, 2015), we argue that once the behaviorist dimensions are clarified and distinguished from the straw-man version of the view, it is in fact an asset, one which will help with task of setting forth a scientifically reputable version of enactivism and/or philosophical behaviorism that is nonetheless not brain-centric but behavior-centric. While this is a bit like “the enemy of my enemy is my friend” strategy, as Shaun Gallagher notes (in Philos Stud 176(3):839–8512019), with the shared enemy of behaviorism and enactivism being classical Cartesian views and/or orthodox cognitivism in its various guises, the task of this paper is to render this alliance philosophically plausible.

Proponents of enactivism should be interested in exploring what notion of action best captures the type of action–perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because it has no traction on socially dependent perceptions (SDPs), which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, and music. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and intermodal perceptible material. I argue that perceptual practices explain three central features of SDP: attentional focus, aspects’ salience, and modal-specific harmony-like relations.

Key words: enactivism, perception, practices, culture, intersubjectivity, pragmatism

Proponents of enactivism should be interested in exploring what notion of action best captures the type of action–perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because it has no traction on socially dependent perceptions (SDPs), which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, and music. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and intermodal perceptible material. I argue that perceptual practices explain three central features of SDP: attentional focus, aspects’ salience, and modal-specific harmony-like relations.

Key words: enactivism, perception, practices, culture, intersubjectivity, pragmatism.