Context: The idea for this article sprang from a desire to revive a conversation with the late Ernst von Glasersfeld on the heuristic function - and epistemological status - of forms of ideations that resist linguistic or empirical scrutiny. A close look into the uses of humor seemed a thread worth pursuing, albeit tenuous, to further explore some of the controversies surrounding the evocative power of the imaginal and other oblique forms of knowing characteristic of creative individuals. Problem: People generally respond to humor, i.e., they are inclined to smile at things they find funny. People like to crack jokes, make puns, and, starting at age two, human infants engage in pretense or fantasy play. Research on creativity, on the other hand, has mostly scorned the trickster within. Cognitivists in particular are quick to relegate wit, whimsy, and even playfulness to the ranks of artful or poetic frivolities. Method: We use the emblems of the craftsman, the trickster, and the poet to highlight some of the oblique ways of knowing by which creative thinkers bring forth new insights. Each epitomizes dimensions intrinsic to the art of “possibilizing.” Taken together, they help us better understand what it means to be playful beyond curious, rigorous beyond reasonable, and why this should matter, even to constructivists! Results: The musings characteristic of creative individuals (artists, scientists, children) speak to intelligent beings’ ability to use glitches intentionally or serendipitously as a means to open up possibilities; to hold on to a thought before spelling it out; and to resist treating words or images as conventional and arbitrary signs regardless of their evocative power. To fall into nominalism, Bachelard insisted, is a poet’s nightmare! Implications: Psyche is image, said Jung, and when we feel alive we rely on the imaginal to guide our reason. Note that image is not here to be understood as a picture in the head or a photographic snapshot of the world. The imaginal does not represent, it brings forth what we understand beyond words. It does not lock us into a single mode. Instead, it is a call to be mindful, in Ellen Langer’s sense: in the present, mentally alert, and on the outlook for our psyche’s own surprising wisdom (sagacity. Constructivist content: Debates on the heuristic function and epistemological status of oblique ways of knowing have long occupied constructivist scholars. I can only guess whether my uses of Jung’s imaginal or Bachelard’s anti-nominalism would have amused or exasperated Ernst! I do know that, on occasion, Ernst the connoisseur, bricoleur, and translator allowed the rationalist-within to include the poet’s power to evoke as a legitimate form of rationality. He himself has written about oblique knowing as legit!

Key words: Incongruity, playfulness, mindfulness, trickster, craftsman, poet, glitches.

Upshot: In view of Kenny’s clinical insights, Hug’s notes on the intricacies of rational vs. a-rational “knowing” in the design sciences, and Chronaki & Kynigos’s notice of mathematics teachers’ meta-communication on experiences of change, this response reframes the heuristic power of bisociation and suspension of disbelief in the light of Kelly’s notion of “as-if-ism” (constructive alternativism. Doing as-if and playing what-if, I reiterate, are critical to mitigating intra-and inter-personal relations, or meta-communicating. Their epistemic status within the radical constructivist framework is cast in the context of mutually enriching conversational techniques, or language-games, inspired by Maturana’s concepts of “objectivity in parenthesis” and the multiverse.

A series of articles has recently appeared in which implications of second-order cybernetics for the practice of family therapy have been discussed. In this article, we attempt to advance the discussion by addressing ideas that we think have not been adequately emphasized thus far. Specifically proposed are ideas about conditions that might facilitate the emergence of consciously pragmatic strategy informed by the kind of systemic wisdom that delicately balances natural systems without the benefit of human planning. It is argued that a shift in the personal habits of knowing and acting that typically organize individual human experience is required. After attempting to specify what this shift might involve, implications of these ideas for the practice of family therapy and for human action in general are discussed.

Upshot: Ranulph Glanville’s musings about cybernetics are statements of wonder as much as careful reconstructions of the core ideas of cybernetics. In Vol. III of his Black Boox all 39 of them are collected, which appeared between 1994 and 2009 in the Journal, Cybernetics and Human Knowing. If Heinz von Foerster said that the ideas of second-order cybernetics are nowadays to be found just about everywhere in everyday life, Glanville is not that sure about this.

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.

Radical constructivism grows out of the belief that knowledge is constructed and legitimated by individuals as they make sense of their experiences in particular contexts and drawing on their own histories. Extending this understanding of learning and ways of knowing to girls as they work in the terrain of science, we argue that honoring student experience as the starting place for science instruction fundamentally alters the nature of science, the purpose of teaching and learning science, and the focus of relationships in science class. The implications for this position are extensive: they suggest that the dynamic relationships between language and cultural background of students and teachers alter the ways in which science education historically has enacted discipline, curriculum and pedagogy. We argue that this is particularly important to understand, for science and science education have historically operated within the masculine domain and working with girls in science in ways that respect their (gendered and cultural) construction of knowledge and their experiences, fundamentally alters the enterprise of science – an idea contradictory to most visions of the purposes of education and current reform efforts in science education, even the most liberal.

Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing, understanding and learning. In this paper, using ideas from discursive psychology, I examine the discursive construction of mathematical thinking in the research process. I focus, in particular, on the role of researchers’ descriptions. Specifically, I examine discursive features of two well-known research papers on mathematical thinking. These features include the use of contrast structures, categorisation and the construction of facts. Based on this analysis, I argue that researchers’ descriptions of learners’ or researchers’ behaviour and interaction make possible subsequent accounts of mathematical thinking.

Key words: Mathematical thinking, research methodology, discursive psychology, contrast structures, descriptions, epistemology

Context: During the 1980s, Ernst von Glasersfeld’s reflections nourished various studies conducted by a community of mathematics education researchers at CIRADE, Quebec, Canada. Problem: What are his influence on and contributions to the center’s rich climate of development? We discuss the fecundity of von Glasersfeld’s ideas for the CIRADE researchers’ community, specifically in didactique des mathématiques. Furthermore, we take a prospective view and address some challenges that new, post-CIRADE mathematics education researchers are confronted with that are related to interpretations of and reactions to constructivism by the surrounding community. Results: Von Glasersfeld’s contribution still continues today, with a new generation of researchers in mathematics education that have inherited views and ideas related to constructivism. For the post-CIRADE research community, the concepts and epistemology that von Glasersfeld put forward still need to be developed further, in particular concepts such as subjectivity, viability, the circular interpretative effect, representations, the nature of knowing, errors, and reality. Implications: Radical constructivism’s offspring resides within the concepts and epistemology put forth, and that continue to be put forth, through a large number of new and different generations of theories, thereby perpetuating von Glasersfeld’s legacy.

Key words: radical constructivism, mathematics education, viability, reification, representation

Open peer commentary on the target article “Arguments Opposing the Radicalism of Radical Constructivism” by Gernot Saalmann. First paragraph: I appreciate Saalmann’s recognition that “there are considerable differences amongst the authors” and that these “have changed their opinions in the course of time” (§3); but given this, what are the consequences for an outline of the theses of radical constructivism (RC)? Which approach is best for outlining a theory of knowing under these hindering conditions? My suggestion would be to use a method specifically developed for this kind of situation and to present it explicitly, or, if it does not yet exist, to develop one.

Open peer commentary on the article “Applying Radical Constructivism to Machine Learning: A Pilot Study in Assistive Robotics” by Markus Nowak, Claudio Castellini & Carlo Massironi. Upshot: Applying radical constructivism to machine learning is a challenge that requires us to dive very deeply into its theory of knowing and learning. We need to clarify its fundamental concepts, if possible, in operational terms. This commentary aims at outlining how this kind of clarification could look in the case of 3 such concepts: (a) the construction of experiential reality; (b) learning as a constructive activity; (c) the viability of conceptual structures.