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Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21St, Lahti, Finland, July 14-19, 1997)

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Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21St, Lahti, Finland, July 14-19, 1997) DOCUMENT RESUME ED 416 082 SE 061 119 AUTHOR Pehkonen, Erkki, Ed. TITLE Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21st, Lahti, Finland, July 14-19, 1997). Volume 1. INSTITUTION International Group for the Psychology of Mathematics Education. ISSN ISSN-0771-100X PUB DATE 1997-00-00 NOTE 335p.; For Volumes 2-4, see SE 061 120-122. PUB TYPE Collected Works Proceedings (021) EDRS PRICE MF01/PC14 Plus Postage. DESCRIPTORS Communications; *Educational Change; *Educational Technology; Elementary Secondary Education; Foreign Countries; Higher Education; *Mathematical Concepts; Mathematics Achievement; *Mathematics Education; Mathematics Skills; Number Concepts IDENTIFIERS *Psychology of Mathematics Education ABSTRACT The first volume of the proceedings of the 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following 13 full papers: (1) "Some Psychological Issues in the Assessment of Mathematical Performance"(0. Bjorkqvist); (2) "Neurcmagnetic Approach in Cognitive Neuroscience" (S. Levanen); (3) "Dilemmas in the Professional Education of Mathematics Teachers"(J. Mousley and P. Sullivan); (4) "Open Toolsets: New Ends and New Means in Learning Mathematics and Science with Computers"(A. A. diSessa); (5) "From Intuition to Inhibition--Mathematics, Education and Other Endangered Species" (S. Vinner); (6) "Distributed Cognition, Technology and Change: Themes for the Plenary Panel"(K. Crawford); (7) "Roles for Teachers, and Computers" (J. Ainley); (8) "Some Questions on Mathematical Learning Environments" (N. Balacheff); (9) "Deepening the Impact of Technology Beyond Assistance with Traditional Formalisms in Order To Democratize Access To Ideas Underlying Calculus"(J. J. Kaput and J. Roschelle); (10) "The Nature of the Object as an Integral Component of Numerical Processes"(E. Gray, D. Pitta, and D. Tall);(11) "Unifying Cognitive and Sociocultural Aspects in Research on Learning the Function Concept"(R. Hershkowitz and B. B. Schwarz); (12) "Emergence of New Schemes for Solving Algebra Word Problems: The Impact of Technology and the Function Approach" (M. Yerushalmy);(13) "Approaching Geometry Theorems in Contexts: From History and EpistemologyTo Cognition" (M. A. Mariotti, M. G. Bartolini Bussi, P. Boero, F. Ferri, and R. Garuti). In addition, volume 1 contains three brief reaction papers (two reacting to Gray and one to Mariotti), and 92 one-page abstracts of working group sessions, discussion group sessions, short oral communication sessions, and poster sessions. (ASK) ******************************************************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * ******************************************************************************** Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education DERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL edited by HAS BE GRANTED :Y Erkki Pehkonen TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as E from the person or organization originating it. Minor changes have been made to gro improve reproduction quality. Points of view or opinions stated in this July 14-19,1997 document do not necessarily represent Lahti, Finland official OERI position or policy. ii University of Helsinki Volume 1 Lahti Research and Training Centre 1997 ZEST COPY AVM LE 2 Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education edited by Erkki Pehkonen University of Helsinki Volume 1 Lahti Research and Training Centre 1997 BEST COPY AVAILABLE, Proceedings of the 21St Conference of the International Group for the Psychology of Mathematics Education Volume 1 Editor: Erkki Pehkonen Department of Teacher Education University of Helsinki P.O. Box 38 (Ratakatu 6A) FIN-00014 Helsinki Finland Fax: 358-9-191-8073 Email: [email protected] Copyright © 1997 left to the Authors All rights reserved ISSN 0771-100X Logo: The logo of the PME 21 Conference has been designed by Paivi Susiluoto. Printed by Gummerus Jyvaskyla, Finland Preface The PME group has now its 21st conference, and nowadays 20 years is an honour- able long time without bigger changes. But during the recent conferences, there has been a vivid discussion on the role of P in the acronym PME. Therefore, I have purposefully selected for the proceedings the cover picture of three circles. During the conference, everybody may ponder what is actually our field of research as the PME group. Is it per definition the intersection PnMnE of the sets P, M and E? Or is it their union PuMuE? Or perhaps some other subset of the union than the intersection? Or is it a larger set which contains the union of P, M and E? The proceedings has been edited along the models of the earlier ones, especiallythe Valencia proceedings. All the presentations are in alphabetic order according tothe presenting author (underlined).In the introduction part, there is also an index of research reports and short oral communications ordered into the categories given by the authors as their first choice. During the editing process, I received help from many persons. Especially, my thanks are due to Ms. Marja-Liisa Neuvonen-Rauhala and Ms. Seija Lehtinen (both Lahti Research and Training Centre) for the huge amount of work they have donefor this conference and its proceedings. Erkki Pehkonen 5 !Y' Table of Contents VOLUME 1 Preface 1-iii Table of contents 1-v Introduction PME-description 1-xxi The review process of the PME-21 1-xxiii Proceedings of previous PME conferences 1-xxvi Index of research report categories 1-xxvii Plenary Addresses Ole Bjorkqvist 1-3 Some psychological issues in the assessment of mathematical performance Sari Levanen 1-19 Neuromagnetic approach in cognitive neuroscience Judith Mous ley & Peter Sullivan 1-31 Dilemmas in the professional education of mathematics teachers Andrea A. diSessa 1-47 Open toolsets: New ends and new means in learning mathematics and science with computers Shlomo Vinner 1-63 From intuition to inhibition - mathematics, education and other endangered species Plenary Panel COGNITION, TECHNOLOGY, AND CHANGE Kathryn Crawford (coordinator) 1-81 Distributed cognition, technology and change: Themes for the plenary panel Janet Ain ley 1-90 Roles for teachers, and computers Nicolas Balacheff 1-99 Some questions on mathematical learning environments James J. Kaput and Jeremy Roschelle 1-105 Deepening the impact of technology beyond assistance with traditional formalisms in order to democratize access to ideas underlying calculus Research Fora ELEMENTARY NUMERICAL THINKING Coordinator: Erna Yackel 1-v Eddie Gray, Demetra Pitta & David Tall 1-115 The nature of the object as an integral component of numerical processes Robert B. Davis (reactor) 1-131 Postulated cognitive processes in mathematics Dagmar Neuman (reactor) 1-139 Success or failure in elementary number development RESEARCH ON THE FUNCTION CONCEPT Coordinator: Gard Brekke Rina Hershkowitz & Baruch B. Schwarz 1-148 Unifying cognitive and sociocultural aspects in researchon learning the function concept Michal Yerushalmy 1-165 Emergence of new schemes for solving algebra word problems: The impact of technology and the function approach RESEARCH ON MATHEMATICAL PROOF Coordinator: Carolyn Maher Maria Alessandra Mariotti, Maria G. Bartolini Bussi, Paolo Boero, Franca 1-180 Ferri & Rossella Garuti Approaching geometry theorems in contexts: from history and epistemology to cognition Michael de Villiers (reactor) 1-196 Approaching geometry theorems in contexts: from history and epistemology to cognition Working Groups 1. Understanding of multiplicative concepts 1-200 Coordinator(s): Tom Cooper & Tad Watanabe 2. Geometry working group 1-201 Coordinators: M. A. Mariotti & A. Mesquita 3. A new research paradigm for social aspects of mathematics education: The evolutionary processin gender based research 1-202 Coordinator: Victor E. Parsons 4. Advanced mathematical thinking 1-203 Coordinator: David A. Reid 5. Algebraic processes and structure 1-204 Coordinators: Teresa Rojano & Luis Radford 6. Research on the psychology of mathematics teacher development 1-205 Coordinators: Andrea Peter & Vania Santos 7. Working group on the teaching and learning of stochastics 1-206 Coordinators: Carmen Batanero, John Truran & Kathleen Truran 8. Classroom research 1-207 Coordinators: Draga Vidakovic & Lyn D. English 1-vi 9. Cultural aspects in the learning of mathematics 1-208 Coordinators: Norma Presmeg, Marta Civil, Phil Clarkson & Judit Moschkovich Discussion Groups 1. Video tape interpretation 1-210 Coordinator(s): Laurinda Brown, David Reid & Vicki Zack 2. Number theory discussion group 1-211 Coordinator(s): Stephen Campbell & Rina Zazkis 3. Under-represented countries in PME: Towards the analysis of mathematics education research communities 1-212 Coordinator(s): Pedro Gomez, Paola Valero, Bernadette Denys & Susan Leung 4. Open-ended tasks and assessing mathematical thinking 1-213 Coordinator(s): Peter Sullivan 5. Semiotic theory and practice in mathematics education 1-214 Coordinator(s): Adam Vile & Luis Radford Short Oral Communications Afonso Martin M Candelaria, Camacho Machin Matias & Socas Robayna 1-216 Martin The implementation of a microcurriculum: angles,
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