E-Book Overview
Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.
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DIDACTICS OF MATHEMATICS AS A SCIENTIFIC DISCIPLINE
Mathematics Education Library VOLUME 13
Managing Editor A.J. Bishop, Monash University, Melbourne, Australia
Editorial Board H. Bauersfeld, Bielefeld, Germany J. Kilpatrick, Athens, U.S.A. G. Leder, Melbourne, Australia S. Turnau, Krakow, Poland G. Vergnaud, Paris, France
The titles published in this series are listed at the end of this volume.
DIDACTICS OF MATHEMATICS AS A SCIENTIFIC DISCIPLINE
Edited by ROLF BIEHLER ROLAND W. SCHOLZ RUDOLF STRÄSSER BERNARD WINKELMANN Institute for Didactics of Mathematics, University of Bielefeld, Germany
KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: Print ISBN:
0-306-47204-X 0-7923-2613-X
©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©1994 Kluwer Academic Publishers Dordrecht All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
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Dedicated to Hans-Georg Steiner. R. B., R. W. S., R. S., B. W.
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TABLE OF CONTENTS Preface 1
1. PREPARING MATHEMATICS FOR STUDENTS Introduction Bernard Winkelmann
9
Eclectic approaches to elementarization: Cases of curriculum construction in the United States James T. Fey
15
Didactical engineering as a framework for the conception of teaching products Michèle Artigue
27
Mathematical curricula and the underlying goals Uwe-Peter Tietze
41
2. TEACHER EDUCATION AND RESEARCH ON TEACHING Introduction Rolf Biehler
55
Reflections on mathematical concepts as starting points for didactical thinking Hans-Joachim Vollrath
61
Beyond subject matter: A psychological topology of teachers' professional knowledge Rainer Bromme
73
Dialogue between theory and practice in mathematics education Heinz Steinbring
89
On the application of science to teaching and teacher education Thomas J. Cooney
103
3. INTERACTIO