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.

Excerpt: This essay has two parts. In the first, I advance the main theses of the enactivist approach to perception and experience. Moreover, embracing Alvin Goldman’s concept of “enactment imagination,” I argue that the imagination works by simulating (or enacting) a hypothetical perceptual experience, and that this accounts for its experiential quality. In the second part, I develop an enactivist model of the reader’s imagination, suggesting that narrative texts are sets of instructions for the enactment of a storyworld. I also question the view that fictional consciousnesses are represented in narrative texts, adding some remarks concerning the relationship between narrative and qualia (defined as the intrinsic, ineffable qualities of our experience). The analogy that steers me through this argument is that, in their imaginative engagement with narratives, readers are like blind people tapping their way around with a cane. Every tap of the cane corresponds to the reader’s being invited to imagine a nonexistent object.

The ubiquitous human practice of spontaneously gesturing while speaking demonstrates the embodiment, embeddedness, and sociality of cognition. Spontaneous co-speech gesture confirms embodied aspects of linguistic meaning-making that formalist and linguistic turn-type philosophical approaches fail to appreciate, while also forefronting intersubjectivity as an inherent and normative dimension of communicative action. Co-speech hand gestures, as linguistically meaningful speech acts, demonstrate sedimentation and spontaneity (in the sense of Maurice Merleau-Ponty’s dialectic of linguistic expression), or features of convention and nonconvention in a Gricean sense. Yet neither pragmatic nor classic phenomenological approaches to communication can accommodate the practice of co-speech hand gesturing without some rehabilitation and reorientation. Pragmatic criteria of intersubjectivity, normativity, and rationality need to confront the nonpropositional and nonverbal meaning-making of embodied encounters. Phenomenological treatments of expression and intersubjectivity must consider the normative nature of high-order social practices like language use. Reciprocally critical exchanges between these traditions and gesture studies yield an improved philosophy that treats language as a multi-modal medium for collaborative meaning achievement. The proper paradigm for these discussions is found in enactive approaches to social cognition. Relevance: The view in this paper is constructivist as it argues for a middle-way understanding of meaning co-construction as neither internal nor external, but rather as multimodal and multi-body enacting.

Open peer commentary on the article “Enacting Enaction: A Dialectic Between Knowing and Being” by Sebastjan Vörös & Michel Bitbol. Upshot: In general agreement with the target article, I relate Vörös and Bitbol’s elucidation of Varelian philosophical roots of enaction to a discussion of enaction put forward by Varela’s co-authors Rosch and Thompson in their introductions to the revised edition of The Embodied Mind. I align Vörös and Bitbol’s multi-layered understanding of enaction to Rosch’s distinction between its “phase 1” and “phase 2” accounts. I consider the implications of the relationship between the pseudo-subject and the meta-subject of the enactive account of mind for the general enactivist conception of science and scientific knowledge.

Epistemology is often presented as an abstract body of knowledge accessible only to a small minority of intellectually capable individuals. In this paper, we elaborate the educational possibilities that present themselves when we question this prejudice and consider epistemology as a social practice. We argue that epistemology looses its air of divine mystery and becomes one of many language games they learn to play. We provide illustrations for this argument from high school students” conversations conducted in the context of their physics course. Enacting epistemological practice in the educational context is therefore not only possible but also desirable. It triggers a recursive self-organizing process that transforms pedagogical practice itself and thus brings to the foreground the socio-political and ethical character of the educational endeavor. Our brief argument is written in the form of a reflexive text and is presented as the starting point for the readers to begin a conversation about the problematic subjects raised.

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the “laws” of sensorimotor contingencies (SMCs) In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget’s theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget’s theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level.

Context: How can an enactive approach to the teaching and learning of mathematics be implemented, which fosters mathematical thinking, making intensive use of metaphorizing and taking into account the learner’s experience? Method: Using in-person and remote ethnographic participant observation, we observe students engaged in mathematical activities suggested by our theoretical approach. We focus on their idiosyncratic metaphorizing and affective reactions while tackling mathematical problems, which we interpret from our theoretical perspective. We use these observations to illustrate our theoretical approach. Results: Our didactic examples show that alternative pathways are possible to access mathematical thinking, which bifurcate from the metaphors prevailing in most of our classrooms, like teaching as “transmission of knowledge” and learning as “climbing a staircase.” Our participant observations suggest that enacting and metaphorizing may indeed afford a new and more meaningful kind of experience for mathematics learners. Implications: Our observations highlight the relevance of leaving the learners room to ask questions, co-construct their problems, explore, and so on, instead of just learning in a prescriptive way the method to solve each type of problem. Consequently, one kind of solution to the current grim situation regarding mathematics teaching and learning would be to aim at relaxing the prevailing didactic contract that thwarts natural sense-making mechanisms of our species. Our conclusions suggest a possible re-shaping of traditional teaching practice, although we refrain from trying to implement this in a prescriptive way. A limitation of our didactic experience might be that it exhibits just a couple of illustrative examples of the application of our theoretical perspective, which show that some non-traditional learning pathways are possible. A full fledged ethnomethodological and micro-phenomenological study would be commendable. Constructivist content: We adhere to the enactive approach to cognition initiated by Francisco Varela, and to the embodied perspective as developed by Shaun Gallagher. We emphasize the cognitive role of metaphorization as a key neural mechanism evolved in humans, deeply intertwined with enaction and most relevant in our “hallucinatory construction of reality,” in the sense of Anil Seth.

Key words: Metaphor, enaction, embodiment, mathematical experience, participant observation, emotional anesthesia, negative emotions, Francisco Varela, Shaun Gallagher

Excerpt: My focus is this essay will be somewhat different than in How We Became Posthuman. Whereas there I emphasized connecting embodiment with information, here I will be concerned with the role of metaphor and constraint in re-envisioning agency within posthuman contexts. If the posthuman implies distributed cognition, then it must imply distributed agency as well, for multiplying the sites at which cognizing can take place also multiplies the entities who can count as agents. I will take as my tutor texts Richard Dawkins’s The Selfish Gene and Deleuze and Guattari’s A Thousand Plateaus. Enacting the posthuman primarily through speech acts, these two texts mirror each other. One is a work of popular science that occasionally looks as if it is trying to do philosophy, the other a work of philosophy that occasionally looks as if it is trying to do popular science. Both propose radical reconfigurations of agency, Dawkins through the selfish gene and Deleuze and Guattari through “desiring machines” that engage in a ceaseless play of deterritorialization and reterritorialization. What can their mobilizations of metaphor tell us about the cultural significance of the posthuman, and what does their use or neglect of constraints imply about the viability of their respective projects? What is at stake in redefining agency, and how do these redefinitions of agency fit together with distributed cognition? Perhaps most significantly, what do these projects imply about our ability to exercise agency? Should we count as conscious human subjects capable of meaningful action, or are we rather assemblages of selfish genes and mutating desiring machines?

Open peer commentary on the article “Enacting Enaction: A Dialectic Between Knowing and Being” by Sebastjan Vörös & Michel Bitbol. Upshot: I consider the lack of clear guidelines for groundless non-dualist research proposed by Vörös and Bitbol’s interpretation of Varela’s programme. I attempt to clarify a mode of being that this kind of research calls for, and propose that understanding such a research-oriented existential attitude might replace the need for a detailed research “technique.” I reflect upon the ethical implications of research-oriented being.

Upshot: We begin our response by restating and clarifying the principal argument of the target article. We go on to focus on four main themes addressed by the commentators: (a) the question of the inevitability of a horizon in enacting beliefs about experience; (b) the consequences of our epistemological position for second-person research methodologies; (c) the importance of distinguishing between the feeling of veracity of what is observed and the unquestioned realistic intuitions of the natural attitude; and finally (d) the implications of our discussion for first-person science. We conclude by addressing the question about the relationship between inferred and apprehended experience.