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.

“Are living beings extended autopoietic systems? An embodied reply,” makes the case for grounding the autopoietic definition of living beings to the discrete bodies of organisms rather than to autopoietic systems that extend beyond the organisms into their environments. They attempt this grounding by amending a clause to the original formulation of autopoiesis that identifies living beings with their bodies, and then they explicitly define “bodies”. This commentary makes the case that bodily grounding can be derived from molecular autopoiesis by taking the molecular domain seriously, and no new amendment is required.

Key words: autopoiesis, embodiment, organisms.

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

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.

Personal construct and family systems theories can profit from an exchange of ideas concerning the relationship between their personal and interpersonal aspects of construction. This article examines three possible points of contact between the two orientations. First, we suggest that personal construct psychology could profit from addressing the important contributions of the family context to the development of each individual’s system. Second, we address the impact of the person’s constructions on the larger family system. Third, we suggest that the family system itself develops a system of shared constructions that define and bind its identity and interactions. Each of these areas of interface carries implications for therapy, and specific intervention techniques corresponding to each of these are discussed.

This paper defines a theoretical framework aiming to support the actions and reflections of researchers looking for a “method” in order to critically conceive the complexity of a scientific process of research. First, it starts with a brief overview of the core assumptions framing Morin’s “paradigm of complexity” and Le Moigne’s “general system theory.” Distinguishing “methodology” and “method,” the framework is conceived based on three moments, which represent recurring stages of the spiraling development of research. The first moment focuses on the definition of the research process and its sub-systems (author, system of ideas, object of study and method) understood as a complex form of organization finalized in a specific environment. The second moment introduces a matrix aiming to model the research process and nine core methodological issues, according to a programmatic and critical approach. Using the matrix previously modeled, the third moment suggests conceiving of the research process following a strategic mindset that focuses on contingencies, in order to locate, share and communicate the path followed throughout the inquiry. Relevance: This paper provides the readers with a constructivist methodology of research inspired by Morin’s paradigm of complexity and Le Moigne’s general system theory.

This paper undertakes a theoretical investigation of the “learning” aspect of science as opposed to the “knowledge” aspect. The practical background of the paper is in agricultural systems research – an area of science that can be characterised as “systemic” because it is involved in the development of its own subject area, agriculture. And the practical purpose of the theoretical investigation is to contribute to a more adequate understanding of science in such areas, which can form a basis for developing and evaluating systemic research methods, and for determining appropriate criteria of scientific quality. Two main perspectives on science as a learning process are explored: research as the learning process of a cognitive system, and science as a social, communicational system. A simple model of a cognitive system is suggested, which integrates both semiotic and cybernetic aspects, as well as a model of self-reflective learning in research, which entails moving from an inside “actor” stance to an outside “observer” stance, and back. This leads to a view of scientific knowledge as inherently contextual and to the suggestion of reflexive objectivity and relevance as two related key criteria of good science.

Key words: Agriculture, cognition, communication, experiential, learning, research, science, self-reflective, systemic

Upshot: In our response we focus on how different types of systems are related from a constructivist perspective, and specifically on the relation between communicational social systems and embodied agency.

Context: Society is faced with “wicked” problems of environmental sustainability, which are inherently multiperspectival, and there is a need for explicitly constructivist and perspectivist theories to address them. Problem: However, different constructivist theories construe the environment in different ways. The aim of this paper is to clarify the conceptions of environment in constructivist approaches, and thereby to assist the sciences of complex systems and complex environmental problems. Method: We describe the terms used for “the environment” in von Uexküll, Maturana & Varela, and Luhmann, and analyse how their conceptions of environment are connected to differences of perspective and observation. Results: We show the need to distinguish between inside and outside perspectives on the environment, and identify two very different and complementary logics of observation, the logic of distinction and the logic of representation, in the three constructivist theories. Implications: Luhmann’s theory of social systems can be a helpful perspective on the wicked environmental problems of society if we consider carefully the theory’s own blind spots: that it confines itself to systems of communication, and that it is based fully on the conception of observation as indication by means of distinction.

Key words: Umwelt, phenomenology, biosemiotics, autopoiesis, perspectivism, Peirce, environment, observing, Luhmann, Uexküll, Maturana , Varela, observer