A rising epistemological paradigm in the cognitive sciences – embodied cognition – has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students’ physical movements, eye-gaze paths, and verbal–gestural utterance so as to track and evaluate emerging conceptual capacity. We – a cohort of cognitive scientists and design-based researchers of embodied mathematics – survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.

“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.

Open peer commentary on the article “Foresight Rather than Hindsight? Future State Maximization As a Computational Interpretation of Heinz von Foerster’s Ethical Imperative” by Hannes Hornischer, Simon Plakolb, Georg Jäger & Manfred Füllsack. Abstract: As artificial intelligence (AI) continues to have a fundamental impact in our world and lives, a crucial need arises for integrating ethical and constructivist principles in the design of AI systems, and related computational thinking. We discuss aspects and examples of ethical and constructivist design of AI in the context of the target article, and especially in the domains of future-oriented ethical design and computing education.

Open peer commentary on the article “Constructivism, Fast Thinking, Heuristics and Sustainable Development” by Hugh Gash. Abstract: Understanding how best to educate for sustainability must be a priority in this time of environmental uncertainty. This commentary examines the role of inquiry-based learning in education for sustainability, and the importance of learning in relationship with a world that is lively and sentient.

Villalobos and Razeto-Barry propose a theory of living individuals that includes both considerations about autopoietic systems and about material individuals. However, I think that their characterisation of individuality is problematic and would not be useful to account for living individuals.

Key words: individual bodies, autopoiesis.

Context: For Graham Barnes, the starting point of his research was the observation that most psychotherapists are trained in a theory-centered style of practice, neglecting epistemological and hermeneutical aspects. The consequence is an absence of critical self-reflection about some basic assumptions of psychotherapy theories and clinical practices in the psychotherapy community. When using a particular theory, therapists forget that the theory is “using” them, as well, i.e., they are unaware of the effects the theory has on them and on their relationships with clients. As an alternative to this ignorance, Barnes developed the concept, research project and clinical application of what he called “second-order psychotherapy.” Problem: How can we encourage therapists to engage in systematic self-reflection on the influence of theory on the content and structure of their therapeutic conversations? Following Bateson’s epistemological guidelines, we give an example of how our conversation about understanding his ideas includes conversation about our understanding of the conversation about an understanding of his ideas. Method: Bateson created a new didactic form of dialogical presentation to facilitate the understanding of knowing, called a metalogue, in which the content and the structure of the conversation are intertwined in such a way that it becomes more transparent how the metalevel of relationships between the speakers influences the content and vice versa. Results: By presenting our dialogues as an exemplary metalogue, we propose that metalogues could be a valuable didactic way for promoting epistemological and constructivist teaching and learning, not only for psychotherapists, but for all professionals who need better understanding of their understanding. This second-order understanding opens the space for the inclusion of self-reflection on our relationship (and its evolution) and how our relationship has shaped our understanding. Implications: Our proposal is also meant as an encouragement for contemporary constructivist thinkers to continue to reflect on Bateson’s contribution to the foundation and evolution of constructivism.

Key words: Cybernetic epistemology, second-order psychotherapy, dialogotherapy, self-referential awareness, understanding, difference, schizophrenia, double bind, innocence

Open peer commentary on the article “I Can’t Yet and Growth Mindset” by Fiona Murphy & Hugh Gash. Abstract: Childhood is a sensitive developmental stage with lasting impacts into adulthood. Successful interventions that tackle poor learning strategies provide the child with a stronger foundation for dealing with adversity. Roleplays and immediacy are proposed as two methods of improving learning strategies.

Open peer commentary on the article “Précis of The Philosophy of Affordances” by Manuel Heras-Escribano. Abstract: I question the notion that we need to understand affordances in terms of Rylean non-factualist dispositions. This is not because I disagree with Herlas-Escribano’s analysis; on the contrary, I consider it illuminating and essential. Rather, his analysis shows that affordances can be understood as originally defined by Gibson and elaborated by Stoffregen (i.e., as a particular kind of non-reductionist, non-physicalist relation between organism and environment. Translation into Rylean dispositions is therefore unnecessary.

I agree with Villalobos and Razeto-Barry’s main argument that living beings are autopoietic bodies. I suggest, however, that if we apply this definition of life to a consideration of living beings as dissipative systems, we find opportunities for further refinement. I propose that living bodies are autopoietic bodies that maintain themselves by using their boundaries to control their constituent processes of dissipative adaptation.

Key words: dissipative systems, autopoiesis, living bodies.

The notion of structural coupling plays a central role in Maturana and Varela’s biology of cognition framework and strongly influenced Varela’s subsequent enactive elaboration of this framework. Building upon previous work using a glider in the Game of Life (GoL) cellular automaton as a toy model of a minimal autopoietic system with which to concretely explore these theoretical frameworks, this article presents an analysis of structural coupling between a glider and its environment. Specifically, for sufficiently small GoL universes, we completely characterize the nonautonomous dynamics of both a glider and its environment in terms of interaction graphs, derive the set of possible glider lives determined by the mutual constraints between these interaction graphs, and show how such lives are embedded in the state transition graph of the entire GoL universe.

Key words: autopoiesis, enaction, structural coupling, cellular automata, enactivism