The momentum of the constructivist movement has had a profound effect on how prospective teachers are educated and on how they perceive the duties of a teacher, according to Mr. Baines and Mr. Stanley, who argue that students deserve a chance to learn at the elbow of an expert

Brier S. (1992) Information and consciousness: A critique of the mechanistic foundation for the concept of information. Cybernetics and Human Knowing 1(2/3): 71–94.

The paper presents a discussion of the epistemological and ontological problems of attempts to found information concepts on the often implicit mechanistic idea that the physical sciences hold the key to the nature of reality and information. It is furthermore shown through an analysis of the ethological and the Batesonian understanding of cognition and behavior that it is impossible to remove the fundamental epistemological position of the observer through a definition of information as neg-entropy. Instead Maturana and Varela’s concepts of autopoiesis and multiverse are invoked. But where the idea to derive information from the concept of negentropy is too physicalistic Maturana’s idea of a multiverse seems to be too close to a constructivistic idealism. To develop a more fruitful non-reductionistic world view it is shown that the more pragmatic understanding of physics, where thermodynamics is understood as the basic discipline and mechanics as an idealization, opens for a non-reductionistic con-ceptualization of chaos. Attention is drawn to C. S. Peirce’s conception of pure chance as living spontaneity which is to some degree regular as a realistic but non-reductionistic theory, which comprises a solution to the different world view problems of Bateson and Maturana. A fruitful connection between second order cybernetics and semiotics will then be possible and a bridge between the technical-scientific and the humanistic-social parts of cybernetics can be developed.

Dagienė V. & Futschek G. (2019) On the Way to Constructionist Learning of Computational Thinking in Regular School Settings. Constructivist Foundations 14(3): 231–233. Fulltext at https://cepa.info/6023

Context: Computational thinking denotes the thinking processes needed to solve problems in the way computer scientists would. It is seen as an ability that is important for everybody in a society that is rapidly changing due to applications of computational technologies. More and more countries are integrating computational thinking into their school curricula. Problem: There is a need for more effective learning environments and learning methods to teach computational thinking principles to children of all ages. The constructionist approach seems to be promising since it focuses on developing thinking skills. Method: We extract and discuss insights from the target articles. Results: There are several learning initiatives and curricula that successfully apply constructionist learning to acquiring computational thinking skills. Implications: Computational thinking as a subject at school presents a chance to bring more constructionist learning to schools.

Glasersfeld E. von (1996) Aspects of radical constructivism and its educational recommendations. In: Steffe L. P., Nesher P., Cobb P., Goldin G. A. & Greer B. (eds.) Theories of mathematical learning. Lawrence Erlbaum, Hillsdale: 307–314. Fulltext at https://cepa.info/1473

In the context of theories of knowledge, the name “radical constructivism” refers to an orientation that breaks with the Western epistemological tradition. It is an unconventional way of looking and therefore requires conceptual change. In particular, radical constructivism requires the change of several deeply rooted notions, such as knowledge, truth, representation, and reality. Because the dismantling of traditional ideas is never popular, proponents of radical constructivism are sometimes considered to be dangerous heretics. Some of the critics persist in disregarding conceptual differences that have been explicitly stated and point to contradictions that arise from their attempt to assimilate the constructivist view to traditional epistemological assumptions. This is analogous to interpreting a quantum-theoretical physics text with the concepts of a 19th-century corpuscular theory. It may be useful, therefore, to reiterate some points of our “post-epistemological” approach,1 so that our discussion might have a better chance to start without misinterpretations.

Goldenberg E. P. (2019) Problem Posing and Creativity in Elementary-School Mathematics. Constructivist Foundations 14(3): 319–331. Fulltext at https://cepa.info/6045

Context: In 1972, Papert emphasized that “[t]he important difference between the work of a child in an elementary mathematics class and […]a mathematician” is “not in the subject matter […]but in the fact that the mathematician is creatively engaged […]” Along with creative, Papert kept saying children should be engaged in projects rather than problems. A project is not just a large problem, but involves sustained, active engagement, like children’s play. For Papert, in 1972, computer programming suggested a flexible construction medium, ideal for a research-lab/playground tuned to mathematics for children. In 1964, without computers, Sawyer also articulated research-playgrounds for children, rooted in conventional content, in which children would learn to act and think like mathematicians. Problem: This target article addresses the issue of designing a formal curriculum that helps children develop the mathematical habits of mind of creative tinkering, puzzling through, and perseverance. I connect the two mathematicians/educators - Papert and Sawyer - tackling three questions: How do genuine puzzles differ from school problems? What is useful about children creating puzzles? How might puzzles, problem-posing and programming-centric playgrounds enhance mathematical learning? Method: This analysis is based on forty years of curriculum analysis, comparison and construction, and on research with children. Results: In physical playgrounds most children choose challenge. Papert’s ideas tapped that try-something-new and puzzle-it-out-for-yourself spirit, the drive for challenge. Children can learn a lot in such an environment, but what (and how much) they learn is left to chance. Formal educational systems set standards and structures to ensure some common learning and some equity across students. For a curriculum to tap curiosity and the drive for challenge, it needs both the playful looseness that invites exploration and the structure that organizes content. Implications: My aim is to provide support for mathematics teachers and curriculum designers to design or teach in accord with their constructivist thinking. Constructivist content: This article enriches Papert’s constructionism with curricular ideas from Sawyer and from the work that I and my colleagues have done. Key words: Problem posing, puzzles, mathematics, algebra, computer programming.

Hug T. (2007) Viability and Crusty Snow. Constructivist Foundations 2(2-3): 114–117. Fulltext at https://cepa.info/38

Excerpt: There is the difficulty in allowing for personal items when focussing on academic interests and in allowing for rational aspects when focussing on personal items for someone who has had the chance to get to know Ernst personally. At least for me the search for apposite words in English is not easy in view of the successful interplay between his philosophical ideas, his handling of everyday problems of life and his ability to cope with difficult situations. But let’s give it a try and look back at one of the most striking experiences we have had together.

Mathematical cognition is widely regarded as the epitome of the kind of cognition that systematically eludes enactivist treatment. It is the parade example of abstract, disembodied cognition if ever there was one. As it is such an important test case, this paper focuses squarely on what Gallagher has to say about mathematical cognition in Enactivist Interventions. Gallagher explores a number of possible theories that he holds could provide useful fodder for developing an adequate enactivist account of mathematical cognition. Yet if the analyses of this paper prove sound, then some of the central approaches he considers are simply not fit for such service. That said, in the final analysis, if crucial additions and subtractions are made, there is a real chance of fashioning a promising enactivist account of mathematical cognition.

Martin J. L. (2015) Peirce and Spencer-Brown on Probability, Chance, and Lawfulness. Cybernetics & Human Knowing 22(1): 9–33. Fulltext at https://cepa.info/3314

Before the pivotal work The Laws of Form, which made him influential among systems theorists, George Spencer-Brown had achieved wide publicity for work on statistics that seemed to explain away accumulated findings for extra-sensory perception. Interestingly, just as in his later work, there was a remarkable convergence here with the earlier writings of C. S. Peirce. Both emphasized the difference between the randomness of generating processes and the empirical distributions used for the production of generalizations. Both understood this as challenging theories of scientific inference. Yet Spencer-Brown’s conclusion – that science and magic were both eaten away by the tides of time through the accumulation of patterns through randomness – was not a necessary one for Peirce, for whom these patterns might have ontological significance, as they wore grooves of habit into the universe. Grappling with the puzzles at the heart of these questions may change how we incorporate the notion of information into our theories.

Moutoussis M., Fearon P., El-Deredy W., Dolan R. J. & Friston K. J. (2014) Bayesian inferences about the self (and others): A review. Consciousness and Cognition 25: 67–76. Fulltext at https://cepa.info/5542

Viewing the brain as an organ of approximate Bayesian inference can help us understand how it represents the self. We suggest that inferred representations of the self have a normative function: to predict and optimise the likely outcomes of social interactions. Technically, we cast this predict-and-optimise as maximising the chance of favourable outcomes through active inference. Here the utility of outcomes can be conceptualised as prior beliefs about final states. Actions based on interpersonal representations can therefore be understood as minimising surprise – under the prior belief that one will end up in states with high utility. Interpersonal representations thus serve to render interactions more predictable, while the affective valence of interpersonal inference renders self-perception evaluative. Distortions of self-representation contribute to major psychiatric disorders such as depression, personality disorder and paranoia. The approach we review may therefore operationalise the study of interpersonal representations in pathological states.

Ulanowicz R. E. (2000) Ontic closure and the hierarchy of scale. In: Chandler J. & Van de Vijver G. (eds.) Closure: Emergent organizations and their dynamics. New York Academy of Sciences, New York: 266–271.

The Newtonian, universalist world view is incompatible with the notion of ontological indeterminacy. A hierarchical, or granular perspective, however, reveals how the consequences of pure chance, at scales far removed from those at which the event occurs, can be mitigated.