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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.

Didactics of mathematics --- Mathematics --- -Constructive mathematics --- 51:37 --- 51 --- 51 Mathematics --- 51:37 Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Mathematics, Constructive --- Logic, Symbolic and mathematical --- Math --- Science --- Study and teaching --- Constructive mathematics. --- Education. --- Philosophy and social sciences. --- Mathematics Education. --- Philosophy of Education. --- Study and teaching. --- Constructive mathematics --- Mathematics. --- Education --- Philosophy. --- Mathematics—Study and teaching . --- 51 Wiskunde. Mathematiek --- Wiskunde. Mathematiek --- Social sciences and philosophy --- Social sciences

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Constructivism (Education) --- Education --- Teachers --- Education. --- Aims and objectives. --- Curricula. --- Training of. --- Children --- Education, Primitive --- Education of children --- Human resource development --- Instruction --- Pedagogy --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Training --- Teacher education --- Teacher training --- Teachers, Training of --- Core curriculum --- Courses of study --- Curricula (Courses of study) --- Curriculums (Courses of study) --- Study, Courses of --- Instructional systems --- Aims and objectives of education --- Educational aims and objectives --- Educational goals --- Educational objectives --- Educational purposes --- Goals, Educational --- Instructional objectives --- Objectives, Educational --- Purposes, Educational --- Educational sociology --- Cognitive-developmental theory --- Constructionism (Education) --- Constructivist education --- Piagetian theory of cognitive development --- Learning, Psychology of --- Curricula --- Education - Aims and objectives. --- Education - Curricula. --- Teachers - Training of.

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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. Ernst von Glasersfeld’s work opens a window on how we know what we know. The present work grew out of a desire to make more accessible this line of thought, to highlight its originality and consistency, and to illustrate its fecundity in the domains of cognition and learning. The first three parts of this book contain texts by Glasersfeld that outline the constructivist approach and explicate the frequently drastic reconceptualizations he has suggested. Both the last part and the postscript consist of commentaries by Edith Ackermann, Jacques Désautels, Gérard Fourez, Leslie P. Steffe and Kenneth Tobin, scholars in the fields that Glasersfeld has been concerned with. They examine a number of critical aspects pertaining to (radical) constructivism’s current and future development, often tracing out paths that warrant further exploration and reflection, in particular concerning the sociopolitical dimension of knowledge. Key Works on Radical Constructivism is intended as a reference book for researchers, educators, and students of education—and for anyone interested in grasping, or deepening their grasp of, radical constructivism’s tenets, ambitions and concerns. Readers will discover in this collection of firsthand contributions the contours of a bold, contemporary debate about a most compelling current of thought.

Constructivism (Education) --- Education --- Research.