Glasersfeld von E. Radical Constructivism in Mathematics Education

Springer Netherlands, 1991. — 272 p. — (Mathematics Education Library ) — ISBN 9780306472015, 9780792312574, 0306472015, 0792312570.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.About the authors
Philip H. Steedman / There Is No More Safety in Numbers: A New Conception in Mathematic Teaching
John Richards / Mathematical Discussions
James J. Kaput / Notations and Representations as Mediators of Constructive Processes
Jack Lochhead / Making Math Mean 75
Nicolas Balacheff/ Treatment of Refutations: Aspects of the Complexity of a Constructivist Approach to Mathematics Learning
Jere Confrey / Learning to Listen: A Student’s Understanding of Powers of Ten
Clifford Konold / Understanding Students’ Beliefs about Probability
Paul Cobb, Terry Wood, and Erna Yackel / A Constructivist Approach to Second Grade Mathematics
Leslie P. Steffe / The Constructivist Teaching Experiment: Illustrations and Implications
Jan Van Den Brink / Didactic Constructivism
Robert G. Underhill / Two Layers of Constructivist Curricular Interacting