NATO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NATO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences B Physics C Mathematical and Physical Sciences D Behavioural and Social Sciences E Applied Sciences F Computer and Systems Sciences G Ecological Sciences H Cell Biology I Global Environmental Change PARTNERSHIP SUB-SERIES 1. Disarmament Technologies 2. Environment 3. High Technology 4. Science and Technology Policy 5. Computer Networking Plenum Publishing Corporation London and New York Dordrecht, Boston and London Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Springer-Verlag The Partnership Sub-Series incorporates activities undertaken in collaboration with NATO's Cooperation Partners, the countries of the CIS and Central and Eastern Europe, in Priority Areas of concern to those countries. NATO-PCO DATABASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to about 50000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO DATABASE compiled by the NATO Publication Coordination Office is possible in two ways: - via online FILE 128 (NATO-PCO DATABASE) hosted by ESRIN, Via Galileo Galilei, I-00044 Frascati, Italy. - via CD-ROM "NATO Science & Technology Disk" with user-friendly retrieval software in English, French and German ( WTV GmbH and DATAWARE Technologies Inc. 1992). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. Series F: Computer and Systems Sciences, Vol. 146
The ASI Series F Books Published as a Result of Activities of the Special Programme on ADVANCED EDUCATIONAL TECHNOLOGY This book contains the proceedings of a NATO Advanced Research Workshop held within the NATO Special Programme on Advanced Educational Technology, running under the auspices of the NATO Science Committee.The volumes published so far in the Special Programme are as follows (further details are given at the end of this volume): 67: Designing Hypermedia for Learning. 1990 76: Multimedia Interface Design in Education. 1992, 2nd corr. print 1994 78: Integrating Advanced Technology into Technology Education. 1991 80: Intelligent Tutoring Systems for Foreign Language Learning. 1992 81: Cognitive Tools for Learning. 1992 84: Computer-Based Learning Environments and Problem Solving. 1992 85: Adaptive Learning Environments: Foundations and Frontiers. 1992 86: Intelligent Learning Environments and Knowledge Acquisition in Physics. 1992 87: Cognitive Modelling and Interactive Environments in Language Learning. 1992 89: Mathematical Problem Solving and New Information Technologies. 1992 90: Collaborative Learning Through Computer Conferencing. 1992 91: New Directions for Intelligent Tutoring Systems. 1992 92: Hypermedia Courseware: Structures of Communication and Intelligent Help. 1992 93: Interactive Multimedia Learning Environments. 1992 95: Comprehensive System Design: A New Educational Technology. 1993 96: New Directions in Educational Technology. 1992 97: Advanced Models of Cognition for Medical Training and Practice. 1992 104: Instructional Models in Computer-Based Learning Environments. 1992 105: Designing Environments for Constructive Learning. 1993 107: Advanced Educational Technology for Mathematics and Science. 1993 109: Advanced Educational Technology in Technology Education. 1993 111: Cognitive Models and Intelligent Environments for Learning Programming. 1993 112: Item Banking: Interactive Testing and Self-Assessment. 1993 113: Interactive Learning Technology for the Deaf. 1993 115: Learning Electricity and Electronics with Advanced Educational Technology. 1993 116: Control Technology in Elementary Education. 1993 119: Automating Instructional Design, Development, and Delivery. 1993 121: Learning from Computers: Mathematics Education and Technology. 1993 122: Simulation-Based Experiential Learning. 1993 125: Student Modelling: The Key to Individualized Knowledge-Based Instruction. 1994 128: Computer Supported Collaborative Learning. 1995 129: Human-Machine Communication for Educational Systems Design. 1994 132: Design of Mathematical Modelling Courses for Engineering Education. 1994 133: Collaborative Dialogue Technologies in Distance Learning. 1994 135: Technology Education in School and Industry. 1994 137: Technology-Based Learning Environments. 1994 138: Exploiting Mental Imagery with Computers in Mathematics Education. 1995 140: Automating Instructional Design. 1995 141: Organizational Learning and Technological Change. 1995 142: Dialogue and Instruction. 1995 146: Computers and Exploratory Learning. 1995
Computers and Exploratory Learning Edited by Andrea A. disessa University of California at Berkeley Graduate School of Education 4533 Tolman Hall, Berkeley, CA 94720-1670, USA Celia Hoyles University of London, Institute of Education Department of Mathematics, Statistics and Computing 20 Bedford Way, London WC1H OAL, UK Richard Noss University of London, Institute of Education Department of Mathematics, Statistics and Computing 20 Bedford Way, London WC1H OAL, UK with Laurie D. Edwards University of California at Santa Cruz Crown College, Santa Cruz, CA 95064, USA jfin Springer Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Research Workshop on the Design of Computational Media to Support Exploratory Learning, held at the Asilomar Conference Center, Pacific Grove, California, October 3-7, 1993 CR Subject Classification (1991): K.3, K.8, J.2 ISBN 978-3-642-63359-1 DOI 10.1007/978-3-642-57799-4 ISBN 978-3-642-57799-4 (ebook) CIP data applied for This work is subject to copyright. Ail rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1995 Softcover reprint of the hardcover 1 st edition 1995 Typesetting: Camera-ready by editors Printed on acid-free paper SPIN: 10486119 45/3142-54321 0
Foreword From October 3 to 7, 1993 the NATO Advanced Research Workshop on "The Design of Computational Media to Support Exploratory Learning" was convened at the exquisite Asilomar Conference Center in Pacific Grove, California, U.S.A. The attending participants were as follows: Mariola Alberti, Dipartimento di Scienze dell'informazione, Universita di Milano, Italy Augusto Chioccariello, Instituto per la Technologie Didattiche, C.N.R., Genova, Italy Kathryn Crawford, Department of Education, University of Sydney, New South Wales, Australia Al Cuoco, Education Development Center, Newton, MA, U.S.A. Andrea A. disessa, Graduate School of Education, University of California, Berkeley, CA, U.S.A. Laurie Edwards, Crown College, University of California, Santa Cruz, CA, U.S.A. Michael Eisenberg, Department of Computer Science, University of Colorado, Boulder, CO, U.S.A. Gerhard Fischer, Department of Computer Science, University of Colorado, Boulder, CO, U.S.A. Chris Hancock, TERC, Cambridge, MA, U.S.A. William Higginson, Queen's University, Kingston, Ontario, Canada Celia Hoyles, Department of Mathematics, Statistics and Computing, Institute of Education, University of London, U.K. Chronis Kynigos, Faculty of Education, University of Athens, Greece Colette Laborde, DidaTech, LSD2, IMAG, Grenoble Cedex, France Jean-Marie Laborde, DidaTech, LSD2, IMAG, Grenoble Cedex, France John Mason, The Open University, Milton Keynes, U.K. Erich Neuwirth, Institute of Statistics and Computer Science, University of Vienna, Austria Liddy Nevile, Sunrise Research Laboratory, Royal Melbourne Institute of Technology, Melbourne, Victoria, Australia
VI Foreword Richard Noss, Department of Mathematics, Statistics and Computing, Institute of Education, University of London, London, u.k. Mitchel Resnick, Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. Jeremy Roschelle, University of Massachusetts, Dartmouth, MA, U.S.A. Bojidar Sendov, Educational Computer Systems Laboratory, Department of Mathematics and Informatics, Sofia, Bulgaria Bruno Vitale, University of Geneva, Switzerland Stella Vosniadou, University of Athens, Greece In addition, a number of guests were in attendance for part or all of the workshop. Julie DiBiase, Department of Computer Science, University of Colorado, Boulder, CO, U.S.A. Elizabeth McCullough, Crown College, University of California, Santa Cruz, CA, U.S.A. Henri Picciotto, The Urban School, San Francisco, CA, U.S.A. Bruce Sherin, SESAME Program, University of California, Berkeley, CA, U.S.A. Uri Wilensky, Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. This book comprises an outcome of this workshop augmented by several chapters from those invited to the workshop but unable to attend. The financial support of the NAill Scientific Affairs Division-both for organizing and conducting the workshop and for preparation of this volume-was indispensable. Celia Hoyles was principal investigator (co-principal investigator, Andy disessa) and administrator of the grant from NATO. Laurie Edwards handled the local organization for the workshop. Bruce Sherin and Elizabeth McCullough acted as local support staff, including transport and setup of demonstration equipment on loan from the University of California, Berkeley and Santa Cruz. Finally, Academic Arts of Berkeley, CA provided technical editorial assistance, formatted and prepared camera-ready copy for the book. To all of these, and especially to authors of chapters for their contributions and patience during the extended editorial process, our sincerest thanks. Berkeley, London February, 1995 Andrea A. disessa Celia Hoyles Richard Noss Laurie Edwards
Table of Contents 1. Computers and Exploratory Learning: Setting the Scene... 1 Andrea A. disessa, Celia Hoyles, Richard Noss, Laurie D. Edwards Section I: Computers and Knowledge 2. Thematic Chapter: Epistemology and Systems Design... 15 Andrea A. disessa 3. New Paradigms for Computing, New Paradigms for Thinking... 31 Mitchel Resnick 4. From Local to Global: Programming and the Unfolding of Local Models in the Exploratory Learning of Mathematics and Science... 45 Bruno Vitale 5. East or West-GEOMLAND is Best, or Does the Answer Depend on the Angle?... 59 Bojidar Sendov, Evgenia Sendova 6. Computational Media to Support the Learning and Use of Functions... 79 Al Cuoco 7. Knowledge Representation in a Learning Environment for Euclidean Geometry... 109 Maria Alberta Alberti, Daniele Marini 8. Microworlds as Representations... 127 Laurie D. Edwards 9. Visualizing Formal and Structural Relationships with Spreadsheets... 155 Erich Neuwirth 10. Creating Software Applications for Children: Some Thoughts About Design... 175 Michael Eisenberg Section II: Computers and Learning 11. Thematic Chapter: Exploratory Software, Exploratory Cultures?... 199 Celia Hoyles 12. The Medium and the Curriculum: Reflections on Transparent Tools and Tacit Mathematics... 221 Chris Hancock 13. What About a Learning Environment Where Euclidean Concepts are Manipulated with a Mouse?... 241 Colette and lean-marie Laborde
VIII Table of Contents 14. Four Steps to the Right... 263 Augusto Chioccariello, Nadia Culotta Leccioli, Chiara Oreste 15. Learning Dynamic Geometry: Implementing Rotations... 275 Angel Gutierrez 16. Sketching a Multidisciplinary Microworld: A Collaborative Exploration in Boxer... 289 Jeremy Roschelle, John Mason 17. Design of Computer-Based Cognitive Tools... 305 Emrah Orhun 18. The Spreadsheet as a Tool for Mathematical Modeling: A Case Study... 321 Jotio Filipe Matos 19. The Many Faces of a Computational Medium: Teaching the Mathematics of Motion... 337 Andrea A. disessa Section III: Computers and Cultures 20. Thematic Chapter: Computers as Commodities... 363 Richard Noss 21. Exploring the Sketch Metaphor for Presenting Mathematics Using Boxer... 383 John Mason 22. Programming as a Means of Expressing and Exploring Ideas: Three Case Studies Situated in a Directive Educational System... 399 Chronis Kynigos 23. Do Users Inhabit Or Build Their Boxer Environment?... 421 Liddy Nevile 24. Designing, Exploring and Interacting: Novice Activities in the Boxer Computational Medium... 443 Kathryn Crawford 25. Learning Opportunities Provided by Domain-Oriented Design Environments... 463 Gerhard Fischer Subject Index... 481