First Published in 1995. In the past decade or two, the most important theoretical perspective to emerge in mathematics education has been that of constructivism. This burst onto the international scene at the controversial Eleventh International Conference on the Psychology of Mathematics Education in Montreal in the summer of 1987. No one there will forget von Glasersfeld's authoritative plenary presentation on radical con­structivism, and his replies to critics. Ironically, the conference, at which attacks on radical constructivism were perhaps intended to expose fatally its weaknesses, served as a platform from which the theory was launched to widespread international acceptance and approbation. Radical constructivism is a theory of knowing that provides a pragmatic approach to questions about reality, truth, language and human understanding. It breaks with the philosophical tradition and proposes a conception of knowledge that focuses on experiential fit rather than metaphysical truth. It claims to be a useful approach, not the revelation of a timeless world. The ten chapters of this book present different facets in an elegantly written and thoroughly argued account of this epistemological position, providing a profound analysis of its central concepts.

Mathematics is the science of acts without things - and through this, of things one can define by acts. 1 Paul Valéry The essays collected in this volume form a mosaik of theory, research, and practice directed at the task of spreading mathematical knowledge. They address questions raised by the recurrent observation that, all too frequently, the present ways and means of teaching mathematics generate in the student a lasting aversion against numbers, rather than an understanding of the useful and sometimes enchanting things one can do with them. Parents, teachers, and researchers in the field of education are well aware of this dismal situation, but their views about what causes the wide-spread failure and what steps should be taken to correct it have so far not come anywhere near a practicable consensus. The authors of the chapters in this book have all had extensive experience in teaching as well as in educational research. They approach the problems they have isolated from their own individual perspectives. Yet, they share both an overall goal and a specific fundamental conviction that characterized the efforts about which they write here. The common goal is to find a better way to teach mathematics. The common conviction is that knowledge cannot simply be transferred ready-made from parent to child or from teacher to student but has to be actively built up by each learner in his or her own mind.

Key Works on Radical Constructivism brings together a number of essays by Ernst von Glasersfeld that illustrate the application of a radical constructivist way of thinking in the areas of education, language, theory of knowledge, and the analysis of a few concepts that are indispensable in almost everything we think and do.

Over the last twenty-five years Ernst von Glasersfeld has had a tremendous impact on mathematics and science education through his fundamental insights into the nature of knowledge and knowing. Radical Constructivism in Action is a new volume of papers honouring his work by building on his model of knowing. The contributions by leading researchers present constructivism in action, tying the authors' actions regarding practical problems of mathematics and science education, philosophy, and sociology to their philosophical constraints, giving meaning to constructivism operationally. The book begins with a retrospective analogy between radical constructivism's emergence and changes in what is thought of as "certain" scientific knowledge. It aims to increase understanding of constructivism and Glasersfeld's achievement, and is vibrant evidence of the continued vitality of research in the constructivism tradition.

Explores the range of issues and perspectives about the nature of knowledge and reflexive knowing, this book shows how a concern with reflexivity can inform research methodologies and practice. The text is intended for academics and researchers in communication and the sociology of knowledge.

Nothing that can be said is independent of us. Whatever can be said is coloured by our dreams and aspirations, by the way our brain works, by human nature and human culture. Whoever claims to know or to observe is - according to the central constructivist assumption - inescapably biased. This book presents the views of the founders of constructivism and modern systems theory, who are still providing stimulating cues for international scientific debate. The conversations of Heinz von Foerster, Ernst von Glasersfeld, Humberto R. Maturana, Francisco J. Varela, Gerhard Roth, Siegfried J. Schmidt, Helm Stierlin, and Paul Watzlawick with Bernhard Poerksen, display a kind of thinking that steers clear of rigid fixation and reveals the ideal of objectivity to be a myth. The conversations turn on the results of brain research, the breaks through of cybernetics, the linguistic determination of thought, and the intrinsic connection between epistemology and ethical practice. Throughout, the central figure of the observer is examined with sophisticated wit and just enough irritating grit to create the pearl in the oyster. Constructivism thus emerges as a philosophy of possibilities that keeps generating new points of view, insists on fundamental scepticism with regard to certainties and dogmas, and provides the foundation for an ethics of perception: Each and every one of us is responsible for their view of things.

Niklas Luhmann (1927-1998) was a German sociologist and system theorist who wrote on law, economics, politics, art, religion, ecology, mass media, and love. Luhmann advocated a radical constructivism and antihumanism, or "grand theory," to explain society within a universal theoretical framework. Nevertheless, despite being an iconoclast, Luhmann is viewed as a political conservative. Hans-Georg Moeller challenges this legacy, repositioning Luhmann as an explosive thinker critical of Western humanism. Moeller focuses on Luhmann's shift from philosophy to theory, which introduced new perspectives on the contemporary world. For centuries, the task of philosophy meant transforming contingency into necessity, in the sense that philosophy enabled an understanding of the necessity of everything that appeared contingent. Luhmann pursued the opposite—the transformation of necessity into contingency. Boldly breaking with the heritage of Western thought, Luhmann denied the central role of humans in social theory, particularly the possibility of autonomous agency. In this way, after Copernicus's cosmological, Darwin's biological, and Freud's psychological deconstructions of anthropocentrism, he added a sociological "fourth insult" to human vanity. A theoretical shift toward complex system-environment relations helped Luhmann "accidentally" solve one of Western philosophy's primary problems: mind-body dualism. By pulling communication into the mix, Luhmann rendered the Platonic dualist heritage obsolete. Moeller's clarity opens such formulations to general understanding and directly relates Luhmannian theory to contemporary social issues. He also captures for the first time a Luhmannian attitude toward society and life, defined through the cultivation of modesty, irony, and equanimity.