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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 Plenum Publishing Corporation B Physics London and New York C Mathematical and Physical Sciences Kluwer Academic Publishers D Behavioural and Social Sciences Dordrecht, Boston and London E Applied Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin Heidelberg New York H Cell Biology London Paris Tokyo Hong Kong I Global Environmental Change Barcelona Budapest PARTNERSHIP SUB-SERIES 1. Disarmament Technologies Kluwer Academic Publishers 2. Environment Springer-Verlag 3. High Technology Kluwer Academic Publishers 4. Science and Technology Policy Kluwer Academic Publishers 5. Computer Networking Kluwer Academic Publishers 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 ISBN 978-3-642-57799-4 (eBook) DOI 10.1007/978-3-642-57799-4 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, broadcast ing, 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 De sign 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 Andrea A. diSessa February, 1995 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 1. Computers and Exploratory Learning: Setting the Scene Andrea A. diSessa Celia Hoyles Richard Noss Laurie Edwards Love is a better teacher than duty. -Albert Einstein Exploratory learning names a family of approaches to education that share principles like the following: • Learners can take substantial control of their own learning. We should cultivate them as responsible intellectual agents. • Knowledge is rich and multidimensional. There is no need to follow narrow, prescribed paths to enlightenment. • Ina similar way, learners are diverse. There is no need to christen anyone intellectual style or short list of achievements as preferred. • In an appropriately designed physical and cultural context, learning can often, if not always, feel easy and natural. These general directions are scarcely modern inventions. The most casual reader of Dewey, for example, will find a strong family resemblance to these principles in his philosophical writings. However, there are two more distinctly modern trends that have brought exploratory learning from a visionary's chimera (which it surely has been regarded by many) closer to the mainstream. First, constructivism has emerged as a strong scientific orientation and political force. As a scientific orien tation, the gradual construction of new knowledge out of old on the basis of the learner's own interpretive powers now has endless support in research studies. Po litically, constructivism has clearly spilled over into, for example, the current math ematics reform movement. Problem solving and even a move toward projects-based learning are sanctioned at the highest levels not only in academia but in "real-world" professional circles such as framework documents that guide development of text u.s. books and curricula for many states. The second modern impetus toward exploratory learning is the emergence of computers as a genuinely practical basis for revised instructional forms. Advocates of exploratory learning seem finally to have a medium adaptable enough to alter the balance of power between, on the one side, blind conservatism and the tyranny of "covering the established curriculum" and, on the other side, enticing new ex ploratory learning modes. The seminal image is, perhaps, Papert's mathland wherein children learn mathematics gradually and naturally as the computer-implemented principles of manipulation for achieving effects they value and understand. 2 diSessa et al. But computer-based exploratory learning is not yet the steamroller it might be. Scientifically, there are still knotty problems that need attention. Foremost, perhaps, we still don't adequately understand the relationships among material environments (like computermicroworlds), the activities they support and the knowl edge represented in the environments or emergent from the activities. Technically, there are still emotional internescine wars between advocates of open, general systems (computational media) and systems that are open in a narrower sense, tools focused on topics like, for example, geometric constructions. Politically, educa tional reform and computer-based learning are still a somewhat divided coalition. For example, computers continue to be all too frequently marginalized into voca tional ("learning programming") or enrichment slots and kept out of significant roles in core educational curricula. Computers are addenda in reform documents, and, worse, many of the best constructivist reformers and teachers view them as "something else" rather than key instruments to their ends. This volume has been brought together to display the state of the art in computers and exploratory learning. We want to portray progress and limitations: a) in current technology: systems like Boxer, Cabri, Logo, and StarLogo b) in the scientific understanding of the principles oflearning and knowl edge development in exploratory systems c) in principles of systems and learning activity design d) in understanding the social, cultural and institutional processes related to widespread use (or non-use) of computers in exploratory modes. The Plan for the Book Our strategy for introducing and synthesizing these issues is a little unusual. First, in this Introduction, we try to present a view of the issues as they emerged in dis cussions at the workshop that led to this volume. We are attempting to capture a bit of the spontaneity and spirit of a lively community, represented in microcosm by the participants in the conference, not just an erudite list of ideas and accomplish ments. We do this, in part, by quoting participants' contributions extensively to carry the burden of a tour of issues. Second, we "commissioned" three thematic chapters with a slightly broader charge than the rest of the contributions. Each of the thematic chapters concentrates on one layer of issues: Theme I, epistemology (theories of knowledge) and systems de sign; Theme II, psychological, pedagogical and educational issues; Theme III, broader social and cultural issues, especially those that affect how designed arti facts are reconstructed in broad appropriation. The trick for these chapters is to achieve some breadth and "coverage" without sacrificing the coherence of a story line and the sparkle of detail. The other contributions of workshop participants were divided, admittedly somewhat arbitrarily, among these thematic divisions.
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