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

Education has institutionalized a process that reifies cultures, ecological communities, and ultimately evolution itself. This enclosure has lessened our sensitivity to the pedagogical (eteragogical) nature of our lived relations with other people and with other living beings. By acknowledging that learning and teaching go on between species, humans can regain an eteragogical sense of the interspecies curricula within which they exist. This article explores interspecies lived curricula through a selection of ideas from ecopragmatist Anthony Weston, and cybernetician Gregory Bateson, and through lived experiences with shorebirds of Lake Ontario. Some gulls and a tern teach the author to enrich and diversify, rather than constrict, the potentiality of life. In so doing, being ecological and being educative become unified concepts. Relevance: The publication is concerned with the relational implications between humans and other species of Bateson’s cybernetic theory of learning.

For millennia people have wondered what makes the living different from the non-living. Beginning in the mid-1980s, artificial life has studied living systems using a synthetic approach: build life in order to understand it better, be it by means of software, hardware, or wetware. This review provides a summary of the advances that led to the development of artificial life, its current research topics, and open problems and opportunities. We classify artificial life research into 14 themes: origins of life, autonomy, self-organization, adaptation (including evolution, development, and learning), ecology, artificial societies, behavior, computational biology, artificial chemistries, information, living technology, art, and philosophy. Being interdisciplinary, artificial life seems to be losing its boundaries and merging with other fields. Relevance: Artificial life has contributed to philosophy of biology and of cognitive science, thus making it an important field related to constructivism.

The aim of this paper is to reconsider some of the stakes involved in the dialogue between sciences and between scientists, considering it as a complex and critical learning process. Dialogue – as conversation, expression, performance and negotiation – can be conceived in several ways. It carries both an epistemic and an experiential side. It involves simultaneously heterogeneous theories and identities. Because it involves fragmented scientific languages, it also requires a shared vision. But above all, what seems critical to acknowledge is that dialogue is a matter of transformation. And because transformation is also a matter of learning, the promotion of dialogue between sciences should be perceived as a virtuous spiral involving: instrumental learning (to dialogue), communicational learning (what we mean by dialoguing) and emancipatory learning (to challenge our core assumptions about dialogue and sciences). Considering the evolution of sciences as a double process embedded in the production of knowledge and the self-development of researchers raises the question of how to conceive simultaneously the relationships between these two major stakes. From a practical point of view, considering scientific dialogue as a lifelong learning process would finally suggest the management of forums like the World Knowledge Dialogue (WKD) as a privileged educational opportunity to be designed following what is known about science as a social practice and about researchers as adult learners. Based on the first edition of this forum, four suggestions are finally considered: favoring heterogeneity; valorizing formal knowledge as well as lived experience; acknowledging the learning dimension involved in the process of sharing; and confronting professional experience with knowledge produced about sciences. Inspired by Edgar Morin’s constructivist and non-dualistic position, this paper explores its practical stakes by revisiting the practice of transdisciplinary research and by considering the relationships between the process of knowledge construction and researchers’ self-development as a lifelong learning process.

Living systems are characterized as self-generating and self-maintaining systems. This type of characterization allows integration of a wide variety of detailed knowledge in biology. The paper clarifies general notions such as processes, systems, and interactions. Basic properties of self-generating systems, i.e. systems which produce their own parts and hence themselves, are discussed and exemplified. This makes possible a clear distinction between living beings and ordinary machines. Stronger conditions are summarized under the concept of self-maintenance as an almost unique character of living systems. Finally, we discuss the far-reaching consequences that the principles of self-generation and self-maintenance have for the organization, structure, function, and evolution of singleand multi-cellular organisms.

This bibliometric review covers the scientific production with or about the repertory grid technique between 1998 and 2007. The analysis of previous reviews suggests the need for a more careful and broad process of bibliographic research. With this aim, 24 bibliographic sources were used to cover a wide range of specialties. We began with the drawing up of an explicit protocol in which the research terms were detailed. Then the bibliographic sources were consulted, taking into account a specification of inclusion and exclusion criteria. As a result of this process, 973 references were obtained: 468 were journal papers, 335 book chapters, 108 doctoral theses and 62 books. The review also evaluates the types of documents found, the evolution of the number of works published, the repertory grid’s fields of application and the degree of openness to other disciplines. The most relevant authors, their affiliations, their countries and the publication language are also revealed in this article, as well as the major journals contributing to disseminate the work done with this technique. Relevance: Since Kelly created his personal construct theory (PCT), the repertory grid technique (RGT) has been the most well-known instrument used not only by researchers and practitioners within PCT but also across a variety of disciplines and approaches. In the present work, we try to portray a recent picture of the status of the RGT using bibliometric analysis.

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

This paper attempts to provide the basis for a broader naturalized account of agency. Naturalization is considered as the need for an ongoing and open-ended process of scientific inquiry driven by the continuous formulation of questions regarding a phenomenon. The naturalization of agency is focused around the interrelation of the fundamental notions of autonomy, functionality, intentionality and meaning. Certain naturalized frameworks of agency are criti¬cally considered in an attempt to bring together all the charac¬teristic properties that constitute an autonomous agent, as well as to indicate the shaping of these notions/properties during the development and the evolution of its agential capacity. Autonomy and interaction are proved to be key concepts in this endeavor.

Key words: Autonomy, agency, naturalization, functionality, meaning, interactive representations.

Already in the romantic it has been assumed, that there is an existential interrelation between nature, human being and mind. According to this idea, there is a narrow interrelation of creation between literature, science, dream and reality, which should be expressed in a progressive universal poetry. Gestalt theory and the concept of autopoiesis, developed by Maturana and Varela, could be regarded as a scientific enhancement of this approach and are united in that sense. By analyses of dreams, it becomes evident, that neurobiological and mental processes are determined by the same principles of self-constitution and gestalt production. They are attending in equal measures to homeostatic conditions. The interaction of living systems with their environment as well as their evolution base on recursive reorganisation. Following this principle, imagination, speech and self-reflection are developed. The observer comes to existence by his own distinctions. Phenomenal appearance and real existence, poetry and scientific findings are results of the autopoietic organisation of living, of which we form a part.

Key words: universal poetry, autopoiesis, imagination, gestalt psychology, systems theory.

The book uses the method and categories of systems theory (inspired by Niklas Luhmann) in a scrutiny of the evolution of the main semantic trends of modern society and its influence in the formation of the systemic boundaries of the social systems of society. The book is an investigation of the meaning of the functional differentiation according to its semantic symptoms and evolution. In order to reconstruct the semantic evolution of basic modern socio-economic categories the book is divided according to the three classic branches of the political philosophy of the classic tradition, the Aristotelian division also conserved in Hegel’s own distribution of the themes of his “Sittlichkeit” – family, civil society and the state. Thus, in “The Individuation of Modern Society” the author explores the classic notion of oikós and its opposition to the pólis, the evolution of the concept of utility in modern times and its importance to the formation of the modern political economy and the economic system as an autonomous functional system, the idea of “civil society,” its meaning in the Hegelian description of the social modernity, the fragmentation of XVIIIth century civil society according to the use of the term “Entzweiung” in the Hegelian philosophical vocabulary, and the formation of the concept of the nation as a self-referential condition of the political system. The book finishes with a discussion of Niklas Luhmann’s theory of functional differentiation and his concept of the political system. Relevance: The book applies second-order cybernetics to the analysis of the evolution of modern social systems, especially in the case of the formation of self-referential conditions for the observation and reproduction of the systems.