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

Hutto and Satne, Philosophia (2014) propose to redefine the problem of naturalizing semantic content as searching for the origin of content instead of attempting to reduce it to some natural phenomenon. The search is to proceed within the framework of Relaxed Naturalism and under the banner of teleosemiotics which places Ur-intentionality at the source of content. We support the proposed redefinition of the problem but object to the proposed solution. In particular, we call for adherence to Strict Naturalism and replace teleosemiotics with autopoietic theory of living beings. Our argument for these adjustments stems from our analysis of the flagship properties of Ur-intentionality: specificity and directedness. We attempt to show that the first property is not unique to living systems and therefore poses a problem of where to place a demarcation line for the origin of content. We then argue that the second property is a feature ascribed to living systems, not their intrinsic part and therefore does not form a good foundation for the game of naturalizing content. In conclusion we suggest that autopoietic theory can not only provide a competitive explanation of the basic responding of pre-contentful organisms but also clarify why Ur-intentionality is attributed to them in such an intuitive manner.

Context: The idea for this article sprang from a desire to revive a conversation with the late Ernst von Glasersfeld on the heuristic function - and epistemological status - of forms of ideations that resist linguistic or empirical scrutiny. A close look into the uses of humor seemed a thread worth pursuing, albeit tenuous, to further explore some of the controversies surrounding the evocative power of the imaginal and other oblique forms of knowing characteristic of creative individuals. Problem: People generally respond to humor, i.e., they are inclined to smile at things they find funny. People like to crack jokes, make puns, and, starting at age two, human infants engage in pretense or fantasy play. Research on creativity, on the other hand, has mostly scorned the trickster within. Cognitivists in particular are quick to relegate wit, whimsy, and even playfulness to the ranks of artful or poetic frivolities. Method: We use the emblems of the craftsman, the trickster, and the poet to highlight some of the oblique ways of knowing by which creative thinkers bring forth new insights. Each epitomizes dimensions intrinsic to the art of “possibilizing.” Taken together, they help us better understand what it means to be playful beyond curious, rigorous beyond reasonable, and why this should matter, even to constructivists! Results: The musings characteristic of creative individuals (artists, scientists, children) speak to intelligent beings’ ability to use glitches intentionally or serendipitously as a means to open up possibilities; to hold on to a thought before spelling it out; and to resist treating words or images as conventional and arbitrary signs regardless of their evocative power. To fall into nominalism, Bachelard insisted, is a poet’s nightmare! Implications: Psyche is image, said Jung, and when we feel alive we rely on the imaginal to guide our reason. Note that image is not here to be understood as a picture in the head or a photographic snapshot of the world. The imaginal does not represent, it brings forth what we understand beyond words. It does not lock us into a single mode. Instead, it is a call to be mindful, in Ellen Langer’s sense: in the present, mentally alert, and on the outlook for our psyche’s own surprising wisdom (sagacity. Constructivist content: Debates on the heuristic function and epistemological status of oblique ways of knowing have long occupied constructivist scholars. I can only guess whether my uses of Jung’s imaginal or Bachelard’s anti-nominalism would have amused or exasperated Ernst! I do know that, on occasion, Ernst the connoisseur, bricoleur, and translator allowed the rationalist-within to include the poet’s power to evoke as a legitimate form of rationality. He himself has written about oblique knowing as legit!

Key words: Incongruity, playfulness, mindfulness, trickster, craftsman, poet, glitches.

Upshot: In view of Kenny’s clinical insights, Hug’s notes on the intricacies of rational vs. a-rational “knowing” in the design sciences, and Chronaki & Kynigos’s notice of mathematics teachers’ meta-communication on experiences of change, this response reframes the heuristic power of bisociation and suspension of disbelief in the light of Kelly’s notion of “as-if-ism” (constructive alternativism. Doing as-if and playing what-if, I reiterate, are critical to mitigating intra-and inter-personal relations, or meta-communicating. Their epistemic status within the radical constructivist framework is cast in the context of mutually enriching conversational techniques, or language-games, inspired by Maturana’s concepts of “objectivity in parenthesis” and the multiverse.

Purpose: Complexity is the real beast that baffles everybody. Though there are increasing inter-disciplinary discussions on it, yet it is scantly explored. The purpose of this paper is to bring a new and unique dimension to the discourse assimilating the important ideas of two towering scientists of their time, Newton and Heinz von Foerster. In the tradition of Foersterian second-order cybernetics the paper attempts to build a bridge from a cause-effect thinking to a thinking oriented towards “understanding understanding” and in the process presents a model of “Cybernetics of Simplification” indicating a path to simplicity from complexity. Design/methodology/approach – The design of research in the paper is exploratory and the paper takes a multidisciplinary approach. The model presented in the paper builds on analytics and systemics at the same time. Findings: Simplicity can be seen in complex systems or situations if one can construct the reality (be that the current one that is being experienced or perceived or the future one that is being desired or envisaged) through the Cybernetics of Simplification model, establishing the effect-cause-and-effect and simultaneously following the frame of iterate and infer as a circular feedback loop; in the tradition of cybernetics of cybernetics. Research limitations/implications – It is yet to be applied. Practical implications: The model in the paper seems to have far reaching implications for complex problem solving and enhancing understanding of complex situations and systems. Social implications – The paper has potential to provoke new ideas and new thinking among scholars of complexity. Originality/value – The paper presents an original idea in terms of Cybernetics of Simplification building on the cybernetics of the self-observing system. The value lies in the unique perspective that it brings to the cybernetics discussions on complexity and simplification.

Key words: causality, complexity, second-order cybernetics, cybernetics of simplification, self-observing system, simplification

The concept of autonomy is of crucial importance for understanding life and cognition. Whereas cellular and organismic autonomy is based in the self-production of the material infrastructure sustaining the existence of living beings as such, we are interested in how biological autonomy can be expanded into forms of autonomous agency, where autonomy as a form of organization is extended into the behaviour of an agent in interaction with its environment (and not its material self-production) In this thesis, we focus on the development of operational models of sensorimotor agency, exploring the construction of a domain of interactions creating a dynamical interface between agent and environment. We present two main contributions to the study of autonomous agency: First, we contribute to the development of a modelling route for testing, comparing and validating hypotheses about neurocognitive autonomy. Through the design and analysis of specific neurodynamical models embedded in robotic agents, we explore how an agent is constituted in a sensorimotor space as an autonomous entity able to adaptively sustain its own organization. Using two simulation models and different dynamical analysis and measurement of complex patterns in their behaviour, we are able to tackle some theoretical obstacles preventing the understanding of sensorimotor autonomy, and to generate new predictions about the nature of autonomous agency in the neurocognitive domain. Second, we explore the extension of sensorimotor forms of autonomy into the social realm. We analyse two cases from an experimental perspective: the constitution of a collective subject in a sensorimotor social interactive task, and the emergence of an autonomous social identity in a large-scale technologically-mediated social system. Through the analysis of coordination mechanisms and emergent complex patterns, we are able to gather experimental evidence indicating that in some cases social autonomy might emerge based on mechanisms of coordinated sensorimotor activity and interaction, constituting forms of collective autonomous agency.

Many cognitive scientists have recently championed the thesis that cognition is embodied. In principle, explicating this thesis should be relatively simple. There are, essentially, only two concepts involved: cognition and embodiment. After articulating what will here be meant by ‘embodiment’, this paper will draw attention to cases in which some advocates of embodied cognition apparently do not mean by ‘cognition’ what has typically been meant by ‘cognition’. Some advocates apparently mean to use ‘cognition’ not as a term for one, among many, causes of behavior, but for what has more often been called “behavior.” Some consequences for this proposal are considered.

Key words: Behavior, Chemero, Chomsky, Clark, Cognition, Dennett, Embodied Cognition, Haugeland, Maturana, Skinner

Excerpt: Ecology is an eminently practical discipline, but the practical dilemmas of the ecological movement – and arguably of the environmental crisis itself – are the consequences of our failure to comprehend the complexity and unity of nature theoretically. The ecological crisis is first and foremost an epistemological crisis. 1 As Thomas Kuhn has taught us, such crises are potentially revolutionary episodes out of which new paradigms can emerge. 2 We have also learned from Kuhn that paradigm shifts are rarely sudden events; usually they unfold over decades or even centuries. So it has been with the search for a new paradigm that was inaugurated by Goethe’s scientific work. 3 As a practicing scientist and as a philosopher of science, Goethe both foresaw the crisis of mechanistic explanation and laid foundations for a new paradigm that might replace it. 4 In doing so, he also laid foundations for a future, alternative science of ecology. Although the term “ecology” did not exist until Ernst Haeckel coined it in 1866, Goethe was a profound ecologist in principle and practice if not yet in name. 5 This essay on four major “Goethean ecologists” seeks to add a brief chapter to the history of the reception of Goethe’s scientific work6 and also to Donald Worster’s now standard history of ecology, 7 which barely mentions Goethe in passing.

The intended study is to reveal the importance of values in the process of constructing our implicit knowledge. There is a strong connection between emotions and knowledge and this relationship appears especially in the process of evaluation. Our approach describes knowledge as more intuitive and emotional and unconscious than is traditionally proclaimed. It serves especially practical and useful purpose and our former experience is its foundation. As we evaluate the world which we get to know, our system of knowledge contains also its meaning for us, our value system is hidden in it and it influences our further conduct. Our activity is the aim of our life, through which we cause changes in the world as well as in us.

Key words: value, evaluation, implicit knowledge, constructivism, emotions, knowledge, activity.

In this part of our work about a comparison between Kelly’s personal construct theory and phenomenology, we enter the fields of psychotherapy and research. The topic of intersubjectivity, meant as original recognition of the other’s subjectivity, provides a backdrop for both phenomenological clinic and Kellyan psychotherapy. Though Kelly never used the term “intersubjectivity,” his theory and the corollary of sociality in particular, reveals a view of interpersonal relationships as intercorporeality, which is much closer to phenomenological ideas than to the cognitive ones. Depending on such commonality, in either cases clinical relationship is not viewed as an “aspecific factor” of psychotherapy, but as the essential tool for the care of other. Furthermore, the core role of intersubjectivity in scientific knowledge implies a radical revision of the criteria of research. Consistently with the intent of a science of experience, it is no more a matter of collecting data, as of accepting meanings. Psychological research has to refound itself in continuity with life and recognize the need for a real involvement and real interaction with the subjects, as far as to reverse the traditional relation between clinic and research. It is nonsense to conceive clinic as an applicative sector of a pure science because clinic, on the contrary, is the place where one can know, in first-person, those meaningful realities which take shape in the intersubjective exchange of ideas, in order to make them comprehensible and controllable. Relevance: The publication explores the dimension of intersubjectivity in phenomenology (starting from Husserl) and personal construct theory, and its relevance in psychotherapy and research.