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

In philosophy, there is an as yet unresolved discussion on whether there are different kinds of kinds and what those kinds are. In particular, there is a distinction between indifferent kinds, which are unaffected by observation and representation, and interactive kinds, which respond to being studied in ways that alter the very kinds under study. This is in essence a discussion on ontologies and, I argue, more precisely about ontological levels. The discussion of kinds of kinds can be resolved by using a semiotic approach to ontological levels, building on the key semiotic concept of representation. There are three, and only three, levels of semiosis: nonor protosemiotic processes without representation, such as physical or causal processes, semiotic processes with representation, such as the processes of life and cognition, and second-order semiotic processes with representation of representation, such as self-awareness and self-reflexive communication. This leads to the distinction between not two, but three kinds of kinds: indifferent, adaptive and reflexive kinds, of which the last two hitherto have not been clearly distinguished.

Key words: Peirce, biosemiotics, constructivist, natural kinds, ontological levels, representation, second-order cybernetics, semiotic levels, semiotic thresholds

Recognising and representing one’s self as distinct from others is a fundamental component of self-awareness. However, current theories of self-recognition are not embedded within global theories of cortical function and therefore fail to provide a compelling explanation of how the self is processed. We present a theoretical account of the neural and computational basis of self-recognition that is embedded within the free-energy account of cortical function. In this account one’s body is processed in a Bayesian manner as the most likely to be “me”. Such probabilistic representation arises through the integration of information from hierarchically organised unimodal systems in higher-level multimodal areas. This information takes the form of bottom-up “surprise” signals from unimodal sensory systems that are explained away by top-down processes that minimise the level of surprise across the brain. We present evidence that this theoretical perspective may account for the findings of psychological and neuroimaging investigations into self-recognition and particularly evidence that representations of the self are malleable, rather than fixed as previous accounts of self-recognition might suggest.

Key words: self-recognition, self-awareness, voice recognition, face recognition, body ownership, bayesian, free energy, predictive coding, prediction error, rubber hand illusion, enfacement

The classical formulation of the object of ethics refers to a knowledge of the rules of the adaptation of the human species to their natural environments, to normative expectations supposed in the others and to the biographical evolution of the self. Accordingly, a doctrine of the duties was edified on three pillars, embracing a reference to the duties towards nature, towards the others and towards oneself. Notwithstanding the fact that human action obeys to a variety of factors including bio-physiological conditions and the dimensions of the social environment, ancient and modern metaphysical models of ethics favored the commendatory discourse about the predicates “right” and “wrong,” concurring to ultimate goals. The ethical discussions consisted chiefly in the investigation of the adequacy of the subordinate goals to the final ends of the human action or in the treatment of the metaphysical questions related to free will or determinism, the opposition of the intentionality of the voluntary conduct of man to the mechanical or quasi-mechanical responses of the inferior organisms or machines. From a “second order” approach to the ethical action and imperatives, I propose with this book a critical analysis of the metaphysical and the Kantian ethics. Relevance: In “Ethics and Second-Order Cybernetics” (1992) Heinz von Foerster referred the importance of the application of his notion of “second-order cybernetics” to ethics and moral reasoning. Initially, second-order cybernetics intended an epistemological discussion of recursive operations in non-trivial machines, which were able to include in their evolving states their own self-awareness in observations. The application of his views to ethics entails new challenges. After H. von Foerster essay, what I mean with “second-order ethics is an attempt to identify the advantages of the adoption of his proposal, some consequences in the therapeutically field and lines for new developments.

Key words: Ethics, moral discourse, commendations, second-order cybernetics, observer, objectivity

Context: South African public universities are currently undergoing a transitional period as they traverse the sensitive road of curriculum redesign that achieves an inclusive approach to education for the goal of the decolonisation of knowledge. Problem: Many classrooms have students from several cultural backgrounds yet in these spaces there is often a single dominant discourse on offer. An ethical question is raised in terms of what content should be addressed in the classroom. Method: An approach to curricula design as a conversation is presented. The philosophical aspects underlying shifts in epistemology are presented following an eclectic approach to curricula design that embraces second-order science in achieving the ongoing goal of decolonisation. The method used to achieve this goal is conversational heterarchical curriculum design assuming non quidem tabula rasa. Students can act as reference points (Nunataks) for curricula design, thus reducing the abstraction in the syllabus. Results: A heterarchical conversational approach offers a platform whereby social justice may be addressed in the classroom by providing a means by which the students’ own epistemology is embraced within the curriculum as the students provide the trajectory for the course content based on their own epistemology. A dynamic curriculum is then available that has immediate use in the communities that the students reside in. Students demonstrate understanding of the content as it is tied to their own way of knowing. Implications: The benefits of this approach include moving away from defining science according to a realist view. Educators may accept the idea that knowledge is not impartial and that method is tied to epistemology. When the observer is included in science, an awareness arises that theories (at least in the social sciences) affect what is studied, which in turn affects society. Constructivist content: The approach builds on von Foerster’s ideas on reflexivity. Pask’s conversation theory is a vehicle for the attainment of reflexive conversational teaching and learning.

Key words: Adaptation, curriculum design, conversation theory, cybernetics, decolonisation, ethics, heterarchy, nunatak, reflexivity, second-order science, ubuntuism.

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The evaluation of what (we think) we knew is an urgent and evolving issue. The issues discussed by Umpleby have been raised earlier, particularly in the social sciences. Arguably, in some quarters they are exaggerated. But an awareness of observer effects is of great importance and is greatly enhanced by second-order cybernetics applied more widely as second-order science.

In der jüngeren Sozialisationstheorie wird vermehrt die Intention formuliert, die Eigenaktivität des Subjektes im Sozialisationsprozess stärker zu berücksichtigen. Zum einen wird dies mit der Formel des ‘produktiv realitätsverarbeitenden Subjektes’ auf den Begriff gebracht, zum anderen bemüht sich insbesondere die kompetenzorientierte ‘konstruktivistische Sozialisationsforschung’ dieses Programm zu verfolgen. Dabei wird jedoch ein handlungstheoretisches Subjektverständnis bemüht, das eine begriffliche Unschärfe produziert, die eine konsistente Subjekttheorie und damit eine trennscharfe Bestimmung der Eigenaktivität des Subjektes erschwert. Um dieses Problem zu lösen, wird in dem Beitrag der Vorschlag gemacht, das Subjekt erkennt-nistheoretisch bzw. -kritisch zu konzipieren. Dadurch wird ein Subjektverständnis instruiert, das die Subjekt-Objekt-Dichotomie überwindet und die Wirklichkeit als je subjektives Konstrukt begreift Der Vorteil dieses zunächst heuristischen Vorschlages liegt einerseits in der Möglichkeit einer konsistenten Subjektbestimmung und andererseits in einer forschungsanleitenden Programmatik, die einen breiteren Zugang zu individuellen Entwicklungsverläufen ermöglicht. – English: From the “individual as a productive processor of reality” to the “individual as a productive producer of reality”. A philosophical foundation of theory of socialization. In recent theory of socialisation there is an increasing awareness giving more attention to the agency of subjects itself in the process of socialization. Direct indications about that change into the focus of theory of socialization are the often used formula of the “ individual as a productive processor of reality” or the programme of the constructivist research of socialization. In both cases still many problems are produced first of all through the idea of an action-theory based subject. One of the main theses in this article is that this understanding aggravates a consistent theory of subject in theories of socialization and so an unequivocal definition of agency of subjects. To solve that problems 1 suggest to conceptualise the subject epistemologically. The consequence of this strategy will offer a comprehension of the subject that is able to overcome the subject-object-dichotomy and to recognize “reality” as a construct made by subjects in a strict sense. On the one hand the advantage of this firstly heuristic proposal is the possibility to ascertain consistently the subject. On the other hand further research may be fruitful instructed because of the broader understanding of individual development. ||

This paper challenges proceduralized, rule-bound approaches to ethics and considers how social workers and teams can develop an attitude of compassionate concern and become more effective in dealing with ethical problems in their day-to-day practice. It introduces the work of Humberto Maturana, a widely respected theorist, whose work has received little attention in social work. It stresses the importance of emotions, particularly love, and considers the way in which ethical action is shaped by culture. It emphasizes the importance of engaging in reflection on professional practices and team, professional and organizational culture in order for social workers to improve their awareness of ethical dilemmas and promote ethical practice. For those teaching ethics, this paper suggests an alternative to the rational consideration of moral dilemmas and proposes approaches to training that can help social workers become more attuned and responsive to ethical conflicts. Relevance: The paper argues that Maturana’s biology of cognition provides an approach to ethics that takes into account the spontaneous nature of everyday work in which social workers undertake their ethical actions.

Context: We are presently witnessing a revival of introspective methods, which implicitly challenges an impressive list of in-principle objections that were addressed to introspection by various philosophers and by behaviorists. Problem: How can one overcome those objections and provide introspection with a secure basis? Results: A renewed definition of introspection as “enlargement of the field of attention and contact with re-enacted experience,” rather than “looking-within,” is formulated. This entails (i) an alternative status of introspective phenomena, which are no longer taken as revelations of some an sich slice of experience, but as full-fledged experiences; and (ii) an alternative view of the validity of first-person reports as “performative coherence” rather than correspondence. A preliminary empirical study of the self-assessed reliability of introspective data using the elicitation interview method is then carried out. It turns out that subjects make use of reproducible processual criteria in order to probe into the authenticity and completeness of their own introspective reports. Implications: Introspective inquiry is likely to have enough resources to “take care of itself.” Constructivist content: It is argued that the failure of the introspectionist wave of the turn of the 19th/20th centuries is mostly due to its unconditional acceptance of the representationalist theory of knowledge, and that alternative non-representationalist criteria of validity give new credibility to introspective knowledge.

Key words: Introspection, first-person, phenomenology, consciousness, awareness, epistemology, non-representationalism, experience, subjectivity

We need to realize that a paradigm based on the view of the universe that makes irreversible time and evolution fundamental forces us to view man as a product of evolution and therefore an observer from inside the universe. The theories of the phenomenological life world and the hermeneutics of communication and understanding seem to defy classical scientific explanations. The humanities therefore send another insight the opposite way down the evolutionary ladder, with questions like: What is the role of consciousness, signs and meaning in evolution? These are matters that the exact sciences are not constructed to answer in their present state. Phenomenology and hermeneutics point out to the sciences that they have prerequisite conditions in embodied living as a conscious being imbued with meaningful language and a culture. One can see the world view that emerges from the work of the sciences as a reconstruction back into time of our present ecological and evolutionary self-understanding as semiotic intersubjective conscious cultural historical creatures, but unable to handle the aspects of meaning and conscious awareness. How can we integrate these two directions of explanatory efforts? The problem is that the scientific one is without concepts of qualia and meaning, and the phenomenological-hermeneutic “sciences of meaning” do not have a foundation in material evolution. Relevance: A modern interpretation of C.S. Peirce’s pragmaticistic evolutionary and phaneroscopic semiosis in the form of a biosemiotics is used and integrated with N. Luhmann’s evolutionary autopoietic system theory of social communication. This framework, which integrates cybernetics and semiotics, is called Cybersemiotics.