Perspectives on the Teaching of Geometry for the 21st Century An ICM
In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role i
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New ICMI Study Series VOLUME 5
Published under the auspices of The International Commission on Mathematical Instruction under the general editorship of Miguel de Guzman, President
Mogens Niss, Secretary
Perspectives on the Teaching of Geometry for the 21 8t Century An ICMI Study
Edited by
CARMELO MAMMANA Department of Mathematics, University ofCatania, ltaly and
VINICIO VILLANI Department of Mathematics, University of Pisa, ltaly
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-0-7923-4991-4 ISBN 978-94-011-5226-6 (eBook) DOI 10.1007/978-94-011-5226-6
Printed on acid-fru paper
AII Rights Reserved © 1998 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1998 Softcover reprint of the hardcover 1st edition 1998 No pari of the material protected by thls copynght nOllce may De reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner
TABLE OF CONTENTS
Introduction
1
I. Geometry and geometry-teaching through the ages C. Mammana fj V. Villani
1
II. About the present ICMI study V. Villani
4
III. Acknowledgements V. Villani
7 9
1. Geometry: Past and Future
I. Everlasting geometry V. Lundsgaard Hansen
9
II. Finding room in the curriculum for recent geometry J. Malkevitch
18
III. Space and plane A. Douady
25 29
2. Reasoning in Geometry I. About reasoning in geometry R. Hershkowitz
29
II. Geometry from a cognitive point of view R. Duval
37
III. Teaching and learning geometry in contexts M. Bartolini Bussi fj P. Boero
52
IV. Springboards to geometry R. Lehrer fj T. Romberg
62
V. The role of pupils' spatial knowledge in the elementary teaching of geometry R. Berthelot fj M. H. Salin
71
VI. Deductive and intuitive approaches to solving geometrical problems Kkn~
~
v
vi
3. Geometry in our World
85
I. Geometry and reality J. M alkevitch
85
II. Recent applications of geometry W. Meyer
100
III. Science and technology in geometry textbooks P. Legisa
106
4. Computer Technology and the Teaching of Geometry
109
Introduction I. Osta
109
I. Visual phenomena in the teaching/learning of geometry in a computer-based environment C. Laborde
113
II. Proof in dynamic geometry contexts C. Hoyles fj K. Jones
121
III. CAD tools and the teaching of geometry I. Osta
128
IV. The computer as a context for new possible geometrical activities K.-D. Graf fj B. Hodgson
144
5. Geometry in the Classroom R. Douady fj B. Parzysz
6. The Evolution of Geometry Education since 1900
159 193
I. The British experience H. B. Griffiths
194
II. The evolution of curricula as indicated by different kinds of change in geometry textbooks M. Galuzzi, M. Neubrand fj C. Laborde
204
III. General tendencies in the development of geometry teaching in the past two decades H. B. Griffiths fj M. Neubrand
223
vii
Appendix: Influe
