Enactivism theorizes thinking as situated doing. Mathematical thinking, specifically, is handling imaginary objects, and learning is coming to perceive objects and reflecting on this activity. Putting theory to practice, Abrahamson’s embodied-design collaborative interdisciplinary research program has been designing and evaluating interactive tablet applications centered on motor-control tasks whose perceptual solutions then form the basis for understanding mathematical ideas (e.g., proportion). Analysis of multimodal data of students’ hand- and eye- movement as well as their linguistic and gestural expressions has pointed to the key role of emergent perceptual structures that form the developmental interface between motor coordination and conceptual articulation. Through timely tutorial intervention or peer interaction, these perceptual structures rise to the students’ discursive consciousness as “things” they can describe, measure, analyze, model, and symbolize with culturally accepted words, diagrams, and signs – they become mathematical entities with enactive meanings. We explain the theoretical background of enactivist mathematics pedagogy, demonstrate its technological implementation, list its principles, and then present a case study of a mathematics teacher who applied her graduate-school experiences in enactivist inquiry to create spontaneous classroom activities promoting student insight into challenging concepts. Students’ enactment of coordinated movement forms gave rise to new perceptual structures modeled as mathematical content.

Piaget defines intelligence as adaptation, or the ability to maintain a balance between stability and change, or, in his own words, between assimilation and accommodation. When people assimilate the world to their current knowledge, they impose their order upon things. This momentary closure is useful to build “invariants” that lend existence to the world, independent of immediate interaction. In accommodation, people become one with the object of attention. This may lead to momentary loss of control, since fusion loosens boundaries, but allows for change. I choose the domain of perspective-taking to illustrate how this alternation between assimilation and accommodation punctuate individuals’ interactions with the world. I show that the ability to move away from one’s own standpoint, and to take on another person’s view, requires the construction of cognitive invariants: a recasting of the world’s stabilities that transcends any given viewpoint. I conclude that separation is a necessary step toward the construction of a deeper understanding, and that adopting a “god’s eyes view” is by no means contrary to situating one’s one stance in the world.

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.

Consideration of a possible use of virtual reality technologies in school contexts requires gathering together the suggestions of many scientific domains aimed at understanding the features of these same tools that let them offer valid support to the teaching–learning processes in educational settings. Specifically, the present study is aimed at creating a theoretical framework for the didactic use of VR technologies in schools, highlighting the characteristics of these tools that are supported by a view of teaching that enhances sensorimotor activity in learning. The theoretical approach, through the study of the international scientific literature on this topic, offers interdisciplinary suggestions for realising teaching–learning practices that are supported by scientific principles and a concept of learning that is consistent with the processes that these tools may activate.

Experimental phenomenology is the study of appearances in subjective awareness. Its methods and results challenge quite a few aspects of the current debate on consciousness. A robust theoretical framework for understanding consciousness is pending: current empirical research waves on what a phenomenon of consciousness properly is, not least because the question is still open on the observables to be measured and how to measure them. I shall present the basics of experimental phenomenology and discuss the current development of experimental phenomenology, its main features, and the many misunderstandings that have obstructed a fair understanding and evaluation of its otherwise enlightening outcomes.

This paper is inspired by Edgar Morin’s paradigm of complexity and his constructivist and non-dualistic critique of scientific and philosophical forms of reductionism. It aims to challenge the fragmentation and the reduction framing the understanding of the notion of “critique” in educational sciences, and more broadly in the academia. Based on a review of the literature identified in French-speaking and English-speaking critical traditions in education, several factors determining the way the idea of critique is reduced are highlighted. Stressing the tacit character of those variables challenges the limits of traditional conceptions of critique in contemporary education. According to the constructivist, complex and non-dualistic position adopted, this paper illustrates the relevance of an epistemological framework integrating more systematically the conditions of emergence, the limitations, as well as the antagonistic, complementary and contradictory relationships, that connect educational theories of critique to one another. Based on this position, this paper finally suggests that a distinction be made between “hypocritique” and “hypercritique” as a semantic artifact, stressing the importance of challenging educational research and theories according to the level of complexity that one may attribute to them.

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 five questions that point to important common themes in the commentaries: why start in wicked problems, what kind of system is a scientific perspective, what is the nature of second-order research processes, what does this mean for understanding interdisciplinary work, and how may polyocular research help make real-world decisions.

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.