What evolutionary account explains our capacity to reason mathematically? Identifying the biological provenance of mathematical thinking would bear on education, because we could then design learning environments that simulate ecologically authentic conditions for leveraging this universal phylogenetic inclination. The ancient mechanism coopted for mathematical activity, I propose, is our fundamental organismic capacity to improve our sensorimotor engagement with the environment by detecting, generating, and maintaining goal-oriented perceptual structures regulating action, whether actual or imaginary. As such, the phenomenology of grasping a mathematical notion is literally that – gripping the environment in a new way that promotes interaction. To argue for the plausibility of my thesis, I first survey embodiment literature to implicate cognition as constituted in perceptuomotor engagement. Then, I summarize findings from a design-based research project investigating relations between learning to move in new ways and learning to reason mathematically about these conceptual choreographies. As such, the project proposes educational implications of enactivist evolutionary biology.

Key words: constructivism, design, education, enactivism, mathematics

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.

Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants’ multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device.

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

This article presents the design and analysis of a polysensory listening experience of different languages. Combining sensory design, phenomenology and language education, this research draws on the enaction paradigm. The objective of the authors is twofold: to understand the nature and structures of transmodal perception of unknown languages and to prepare a novel educational approach to sensory awareness to foreign languages. The article will explain the origin of the project as well as its theoretical framework and the foundations that dictated the aesthetic and didactic choices for the video used as a primer within the experiment. Finally, the authors share findings that suggest that inhabitual ways of listening to familiar and unfamiliar languages result in emotional filters as well as cognitive and attentional oscillations.

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).