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

Context: Seventeen years ago Francisco Varela introduced neurophenomenology. He proposed the integration of phenomenological approaches to first-person experience – in the tradition of Husserl, Heidegger and Merleau-Ponty – with a neuro-dynamical, scientific approach to the study of the situated brain and body. Problem: It is time for a re-appraisal of this field. Has neurophenomenology already contributed to the sciences of the mind? If so, how? How should it best do so in future? Additionally, can neurophenomenology really help to resolve or dissolve the “hard problem” of the relation between mind and body, as Varela claimed? Method: The papers in this special issue arose out of a conference organised by the Consciousness and Experiential Psychology Section of the British Psychological Society in Bristol, UK, in September 2012. We have invited a representative sample of the speakers at that conference to present their work here. Results: Various papers argue that the first-person methods of phenomenology are distinct from, and more robust than, the failed “introspectionist” methods of early modern psychology. The “elicitation interview” emerges as a successful and widely adopted method to have emerged from this field. Phenomenological techniques are already being successfully applied to neuroscientific problems. Various specific proposals for new techniques and applications are made. Implications: It is time to take neurophenomenology seriously. It has proven its worth, and it is ripe with the potential for further immediate, successful applications. Constructivist content: Varela’s key aim was to develop a non-dualising approach to the science of consciousness. The papers in this special issue look at the philosophical and practical details of successfully putting such an approach into practice.

Key words: Phenomenology, neuroscience, dynamical systems, first-person methods, second-person methods, the elicitation interview, introspection, consciousness

This is a major departure from traditional approaches to team and social group dynamics and is based firmly in Maturana and Varela’s explanation of language, (languaging and conversing). The obvious audience is academics and practitioners involved in team working and team work theory. However, for proponents of Maturana and Varela, the paper shows how the biology of cognition can be a foundation of a multidisciplinary theory of social group dynamics. Somewhat controversially, I suspect, I believe I have found a point of agreement between the “complexity scientist,” Stuart Kauffman, and Maturana and Varela. The result is a concept of supracritical conversational networks that are nonlinear dynamical systems and hence the source of “complexity” in social systems.

According to the sensorimotor approach, perception is a form of embodied know-how, constituted by lawful regularities in the sensorimotor flow or in sensorimotor contingencies (SMCs) in an active and situated agent. Despite the attention that this approach has attracted, there have been few attempts to define its core concepts formally. In this paper, we examine the idea of SMCs and argue that its use involves notions that need to be distinguished. We introduce four distinct kinds of SMCs, which we define operationally. These are the notions of sensorimotor environment (open-loop motor-induced sensory variations), sensorimotor habitat (closed-loop sensorimotor trajectories), sensorimotor coordination (reliable sensorimotor patterns playing a functional role), and sensorimotor strategy (normative organization of sensorimotor coordinations). We make use of a minimal dynamical model of visually guided categorization to test the explanatory value of the different kinds of SMCs. Finally, we discuss the impact of our definitions on the conceptual development and empirical as well as model-based testing of the claims of the sensorimotor approach.

Key words: embodied cognition, sensorimotor contingencies, dynamical systems, sensorimotor approach to perception, minimal cognition

The work of physicist and theoretical biologist Howard Pattee has focused on the roles that symbols and dynamics play in biological systems. Symbols, as discrete functional switching-states, are seen at the heart of all biological systems in the form of genetic codes, and at the core of all neural systems in the form of informational mechanisms that switch behavior. They also appear in one form or another in all epistemic systems, from informational processes embedded in primitive organisms to individual human beings to public scientific models. Over its course, Pattee’s work has explored (1) the physical basis of informational functions (dynamical vs. rule-based descriptions, switching mechanisms, memory, symbols), (2) the functional organization of the observer (measurement, computation), (3) the means by which information can be embedded in biological organisms for purposes of self-construction and representation (as codes, modeling relations, memory, symbols), and (4) the processes by which new structures and functions can emerge over time. We discuss how these concepts can be applied to a high-level understanding of the brain. Biological organisms constantly reproduce themselves as well as their relations with their environs. The brain similarly can be seen as a self-producing, self-regenerating neural signaling system and as an adaptive informational system that interacts with its surrounds in order to steer behavior.

Key words: Adaptive systems, biological cybernetics, biological semiotics, dynamical systems, emergence, epistemology, evolutionary robotics, genetic code, neural code, neurocomputation, self-organization, symbols.

Open peer commentary on the article “Exploration of the Functional Properties of Interaction: Computer Models and Pointers for Theory” by Etienne B. Roesch, Matthew Spencer, Slawomir J. Nasuto, Thomas Tanay & J. Mark Bishop. Upshot: Artificial life computer simulations hold the potential for demonstrating the kinds of bottom-up, cooperative, self-organizing processes that underlie the self-construction of observer-actors. This is a worthwhile, if limited, attempt to use such simulations to address this set of core constructivist concerns. Although we concur with much of the philosophical perspective in the target article, we take issue with some of the implied positions related to dynamical systems, sensorimotor contingency theory, and neural information processing. Ideally, we would like to see computational approaches more directly address adaptive, constructive processes and mechanisms operant in minds and brains. This would entail using tasks that are more relevant to the psychology of human and animal learning than performing digit sums or sorts. It also could involve relating the dynamics of agents more explicitly to ensembles of communicating neural assemblies.

Functional brain imaging studies reveal the complexity of brain activity during pain. The marked explanatory gaps that separate such research from classical neurophysiology and perceptual psychology raise the challenge of integrating knowledge gleaned at multiple levels of investigation into a coherent multidisciplinary account of pain. A conceptual framework from consciousness research, grounded in the concept of self-organization, can address this challenge through nonlinear dynamical systems and related models. We propose a constructivist model that construes pain, not as the passive registration of sensory information that traditional research would presume, but rather an active process of generating and shaping awareness. If pain is a dynamic product of a self-organizing brain, then pain research needs a theoretical framework to address the observations that functional brain imaging yields.

Key words: consciousness, pain, nonlinear dynamical systems, constructivism, functional brain imaging.

Review of: Andy Clark (1997) Being There: Putting Brain, Body and World Together Again. MIT Press: Cambridge, Massachusetts. xiii+267pp. ISBN 0-262-03240-6. Price: $US12 pbk.

Key words: artificial intelligence, dynamical systems theory, embodiment, autonomous agents, artificial life, mental repesentation, metaphysics.

This paper outlines an interactivist-constructivist theory of autonomy as the basic organisational form of life, and the role we see it playing in a theory of embodied cognition. We distinguish our concept of autonomy from autopoiesis, which does not emphasise interaction and openness. We then present the basic conceptual framework of the I-C approach to intelligence, including an account of directed processes, dynamical anticipation, normative evaluation, and selfdirectedness as the basis of intelligence and learning, and use this to briefly reflect on other contemporary dynamical systems approaches.

The last ten years have seen an increasing interest, within cognitive science, in issues concerning the physical body, the local environment, and the complex interplay between neural systems and the wider world in which they function. Yet many unanswered questions remain, and the shape of a genuinely physically embodied, environmentally embedded science of the mind is still unclear. In this article I will raise a number of critical questions concerning the nature and scope of this approach, drawing a distinction between two kinds of appeal to embodiment: (1) ‘Simple’ cases, in which bodily and environmental properties merely constrain accounts that retain the focus on inner organization and processing; and (2) More radical appeals, in which attention to bodily and environmental features is meant to transform both the subject matter and the theoretical framework of cognitive science.

Key words: embodiment, environment, computational models, internal representation, dynamical systems.