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

This paper is a report of a study conducted with preservice elementary teachers at the University of Wyoming during the summer of 1993. The study had two purposes: (1) to observe the effectiveness of using a constructivist approach in teaching mathematics to preservice elementary teachers, and (2) to focus on teaching probability using a constructivist approach. The study was conducted by one instructor in one class, The Theory of Arithmetic II, a required mathematics class for preservice elementary teachers.

Key words: educational methods, teacher education, concept formation, constructivist teaching, preservice teacher education, problem solving, classroom techniques, mathematical concepts, teacher education programs

Open peer commentary on the article “Creativity in Solving Short Tasks for Learning Computational Thinking” by Valentina Dagienė, Gerald Futschek & Gabrielė Stupurienė. Abstract: Computational thinking (CT) skills are nowadays strongly advocated for educational institutions at all levels. CT refers broadly to skills of thinking about the world from a computational perspective, however, not necessarily referring to programming skills in particular. There is still a lack of consensus about what CT means, and how CT should be taught. This open peer commentary briefly discusses some ongoing trends of CT in response to the target article, which reports development, field testing and piloting of an extensive set of new learning materials for teaching CT. Recent calls for interdisciplinary technology education, creativity and open-ended problem solving in CT are highlighted.

Open peer commentary on the article “From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research” by Jérôme Proulx & Jean-François Maheux. Upshot: The aim of this commentary is to extend the work of Proulx and Maheux to include consideration of the teacher-observer whose role (in part) in the mathematics classroom is to ensure that curriculum goals are being met.

This paper presents an architecture of autopoietic intelligent systems (AIS) as systems of automated “software production”-like processes based on meta-engineering (ME) theory. A self-producing AIS potentially displays the characteristics of artificial general intelligence (AGI). The architecture describes a meta-engineering system (MES) comprising many subsystems which serve to produce increasingly refined “software-production”-like processes rather than producing a solution for a specific domain. ME-theory involves a whole order of MES and the ME-paradox, expressing the fact that MES can potentially achieve a general problem-solving capability by means of maximal specialization. We argue that high-order MES are readily observable in software production systems (sophisticated software organizations) and that engineering practices conducted in such domains can provide a great deal of insight on how AIS can actually work.

Key words: autopoiesis, meta-engineering, meta-learning, software production system, artificial general intelligence.

Constructivist family therapy offers a model for the application of Maturana’s theories to practice. This paper describes key concepts of a constructivist approach and draws on family therapy to provide guidelines for applying them in an organizational setting. It offers a view of the organization as a network of conversations in which change occurs through the coconstruction of new conversations which widen or change the rational domain in which a problem occurs.

Key words: systemic therapy, family therapy, constructivism, autopoiesis, organization, problem solving, human service organizations, management, resistance to change, systems methodology.

Teaching information retrieval through the Internet provides many opportunities for using the constructivist approach to learning. This approach emphasizes knowledge construction through experiences that reinforce mental models which, in turn, facilitate the assimilation of new information into knowledge. The Internet provides these processes because a conceptual understanding of information retrieval, subject knowledge, problem-solving skills and hands-on experience are vital components of successful searches in this online resource.

Open peer commentary on the article “From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research” by Jérôme Proulx & Jean-François Maheux. Upshot: After a description of Varela’s four key points to a science of inter-being: embodiment, emergence, intersubjectivity and circulation, three questions are asked and briefly explored: Are these key points illustrated in the target article? What is a problem? And what could classrooms look like where knowing is doing?

Constructivism rejects the metaphysical position that “truth,” and thus knowledge in science, can represent an “objective” reality, independent of the knower. It modifies the role of knowledge from “true” representation to functional viability. In this interview, Ernst von Glasersfeld, the leading proponent of Radical Constructivism underlines the inaccessibility of reality, and proposes his view that the function of cognition is adaptive, in the biological sense: the adaptation is the result of the elimination of all that is not adapted. There is no rational way of knowing anything outside the domain of our experience and we construct our world of experiences. In addition to these philosophical claims, the interviewee provides some personal insights; he also gives some suggestions about better teaching and problem solving. These are the aspects of constructivism that have had a major impact on instruction and have modified the manner many of us teach. The process of teaching as linguistic communication, he says, needs to change in a way to involve actively the students in the construction of their knowledge. Because knowledge is not a transferable commodity, learning is mainly identified with the activity of the construction of personal meaning. This interview also provides glimpses on von Glasersfeld’s life.

Key words: radical constructivism, education

Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: Problem solving is an enormous field of study, where so-called “problems” can end up having very little in common. One of the least studied categories of problems is open-ended mathematical modeling research. Cifarelli and Sevim’s framework - although not developed for this purpose - may be a useful lens for studying the development of mathematical modelers and researchers in applied mathematics.