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

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

The paradox of scientific expertise is that the growth of science leads to a fragmentation of scientific expertise. To resolve this paradox, this paper probes three hypotheses: 1) All scientific knowledge is perspectival. 2) The perspectival structure of science leads to specific forms of knowledge asymmetries. 3) Such perspectival knowledge asymmetries must be handled through second order perspectives. We substantiate these hypotheses on the basis of a perspectivist philosophy of science grounded in Peircean semiotics and autopoietic systems theory. Perspectivism is an important elaboration of constructivist approaches to help overcome problems in cross-disciplinary collaboration and use of science, and thereby make society better able to solve complex, real-world problems.

Open peer commentary on the article “Social Autopoiesis?” by Hugo Urrestarazu. Upshot: We agree on the need to explore a concept of social autopoiesis that goes beyond a strictly human-centered concept of social systems as autopoietic communicative systems. But both Hugo Urrestarazu and Niklas Luhmann neglect the importance of semiosis in understanding communication, and this has important implications for the question of a more general approach to social systems.

Context: The problems that are most in need of interdisciplinary collaboration are “wicked problems,” such as food crises, climate change mitigation, and sustainable development, with many relevant aspects, disagreement on what the problem is, and contradicting solutions. Such complex problems both require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order science in domains where there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem, 4. rely on first-order perspectives to see themselves as perspectives, and 5. be based on other rules than first-order research. Implications: The perspectivist insights of second-order science provide a new way of understanding interdisciplinary research that leads to new polyocular methods and research designs. It also points to more reflexive ways of dealing with scientific expertise in democratic processes. The main challenge is that this is a paradigmatic shift, which demands that the involved disciplines, at least to some degree, subscribe to a perspectivist view. Constructivist content: Our perspectivist approach to science is based on the second-order cybernetics and systems theories of von Foerster, Maruyama, Maturana & Varela, and Luhmann, coupled with embodied theories of cognition and semiotics as a general theory of meaning from von Uexküll and Peirce.

Key words: Perspectivism, semiotics, complex phenomena, social systems theory, differentiation of science, perspectival knowledge asymmetries.