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

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

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

While structured as an autobiography, this memoir exemplifies ways in which classic contributions to cybernetics (e.g., by Wiener, McCulloch & Pitts, and von Neumann) have fed into a diversity of current research areas, including the mathematical theory of systems and computation, artificial intelligence and robotics, computational neuroscience, linguistics, and cognitive science. The challenges of brain theory receive special emphasis. Action-oriented perception and schema theory complement neural network modeling in analyzing cerebral cortex, cerebellum, hippocampus, and basal ganglia. Comparative studies of frog, rat, monkey, ape and human not only deepen insights into the human brain but also ground an EvoDevoSocio view of “how the brain got language.” The rapprochement between neuroscience and architecture provides a recent challenge. The essay also assesses some of the social and theological implications of this broad perspective.

Key words: action-oriented perception, ape, architecture, artificial intelligence, automata theory, basal ganglia, brain theory, cerebellum, cerebral cortex, cognitive science, computational neuroscience, cybernetics, frog, hippocampus, human, language evolution, li

A series of articles has recently appeared in which implications of second-order cybernetics for the practice of family therapy have been discussed. In this article, we attempt to advance the discussion by addressing ideas that we think have not been adequately emphasized thus far. Specifically proposed are ideas about conditions that might facilitate the emergence of consciously pragmatic strategy informed by the kind of systemic wisdom that delicately balances natural systems without the benefit of human planning. It is argued that a shift in the personal habits of knowing and acting that typically organize individual human experience is required. After attempting to specify what this shift might involve, implications of these ideas for the practice of family therapy and for human action in general are discussed.

We propose a methodological framework for developing and communicating academic knowledge relevant for practice: the dialogical model. This model of engaged scholarship comprises five activities: specifying a research question, elaborating local knowledge, developing conceptual knowledge, communicating knowledge, and activating knowledge. The current article focuses on the early stage of research question design and presents the epistemological framework in which the model was initially developed. It also offers guidance on how to maintain academic value and practical relevance in tension throughout the research process. Examples illustrate how to construct research questions relevant both for academia and practice, and how to justify validity in pragmatic constructivism. This model can likewise be mobilized in other epistemological frameworks, particularly for knowledge generation purposes. It enriches the researchers’ methodological toolbox by adding a new procedural tool that provides valuable guidelines from the very start of research projects. Relevance: The first part of this article is dedicated to presenting and discussing what internal validity, external validity, and reliability mean specifically in pragmatic constructivism, which is another name for radical constructivism. This naming is consistent with the radical constructivist view of the relationship between knowledge and action, and has the advantage of being free from all the misinterpretations associated with the term “radical.”

The author compares the development of constructivist approaches in two national communities of communication researches, France and Germany. Radical approches are nearly unvisible in the French community, here social constructivism relies mainly on action and speach theory.

This article presents a unifying theory of the embodied, situated human brain called the Hierarchically Mechanistic Mind (HMM). The HMM describes the brain as a complex adaptive system that actively minimises the decay of our sensory and physical states by producing self-fulfilling action-perception cycles via dynamical interactions between hierarchically organised neurocognitive mechanisms. This theory synthesises the free-energy principle (FEP) in neuroscience with an evolutionary systems theory of psychology that explains our brains, minds, and behaviour by appealing to Tinbergen’s four questions: adaptation, phylogeny, ontogeny, and mechanism. After leveraging the FEP to formally define the HMM across different spatiotemporal scales, we conclude by exploring its implications for theorising and research in the sciences of the mind and behaviour.

Key words: active inference, evolutionary systems theory, hierarchically mechanistic mind, free-energy principle, neuroscience, psychology

The paper looks at how a society having to deal with the introduction of the computer and its derivatives may differ from earlier societies which dealt with the introduction of language, writing, and the printing press. Each one of the introduction of these media of the dissemination of communication is regarded as a ‘catastrophe ’ forcing the society into new ways to selectively deal with new kinds of surplus meaning. The paper presents a sociological theory having to incorporate aspects of heterogeneous networks and of self-referential action in order to watch how the transformation of modern society into a next society may enfold. It draws a distinction between the structure of a society, ensuring the dissemination of communication, and the culture of the society, enabling it to condense the meaning of disseminated and distributed communication into a form which allows actors to focus on selections of it while taking account of the unmarked state as the other side of any one selection. Niklas Luhmann proposed to consider Aristotelian telos the ancient literal society’s culture form, and Cartesian self-referential restlessness or equilibrium as modern printing press society’s culture form. We add the culture form of boundaries for primitive oral society, and Spencer-Brownian form for the emerging next computer society. The paper will be

This is the second paper of a pair of two, the first one of which looked at a sociological theory of a computer-based future society distinct from earlier language-based ‘primitive’ society, writing-based ancient society, and printing press-based modern society. If the form of the next society’s culture will be the Spencer-Brownian form as we suggest, then sociological theory will have to reformulate itself in terms of an analysis of network synthesis. We look at possible reasons to do so, stemming above all from demands to be able to describe and understand how social actors are able to frame indeterminacy, present a possible model of social action, and advance the idea that it may be useful to base social analysis neither on subjects nor on objects but on a hypokeimon which we here propose to christen ‘catjects’. Catjects describe how a network synthesis comes about.