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Geeslin, William, Ed.; Graham, Karen, Ed. Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (PME) (16th, Durham, NH, August 6-11, 1992). Volumes I-III.
International Group for the Psychology of Mathematics
Education.
Aug 92
95Ap.
Collected Works - Conference Proceedings (021) MF06/PC39 Plus Postage.
Action Research; Affective Behavior; Algebra; Arithmetic; Cognitive Development; College Mathematics; Constructivism (Learning); Content Area Writing; Context Effect; Cooperative Learning; "Cultural Influences; Discussion (Teaching Technique); Elementary Secondary Education; Equations (Mathematics); ^Geometry; Imagery; Language; Mathematics Achievement; Mathematics Education; Mathematics Instruction; Metacogni t i on ; Misconceptions; Number Systems; Problem Solving; Proof (Mathematics); Ratios (Mathematics); Sex Differences; Social Psychology; Spatial Ability; Student Attitudes; *Teacher Education; Thinking Skills; Visualization; Writing Across the Curriculum
Advanced Mathematics; LOGO Programming Language; Mathematical Communications; Mathematical Thinking; "Mathematics Education Research; '^Psychology of Mathematics Education; Representations (Mathematics); Teacher Candidates; Teacher Change; Teacher Researchers
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ABSTRACT
The Proceedings of PME-XVI has been published in three volumes because of the large number of papers presented at the conference. Volume 1 contains: (1) brief reports from each of the 11 standing Working Groups on their respective roles in organizing PME-XVI; (2) brief reports from 6 Discussion Groups; and (3) 35 research reports covering authors with last names beginning A~K. Volume II contains 42 research reports covering authors with last names beginning K~S. Volume III contains (1) 15 research reports (authors S~W) ; (2) 31 short oral presentations; (3) AO poster presentations; (4) 9 Featured Discussion Groups reports; (5) 1 brief Plenary Panel report and 4 Plenary Address reports. In summary, the three volumes contain 95 full-scale research reports, 4 full-scale plenary reports, and 96 briefer reports. Conference subject content can be conveyed through a listing of Work Group topics, Discussion Group topics, and Plenary Panels/Addresses, as follows. Working Groups: Advanced Mathematical Thinking; Algebraic Processes and Structure; Classroom Research; Cultural Aspects in Mathematics Learning; Geometry; Psychology of Inservice Education of Mathematics Teachers; Ratio and Proportion; Representations; Research on the Psychology of Mathematics Teacher Development; Social Psychology of Mathematics Education; Teachers as Researchers in Mathematics Education. Discussion Groups: Dilemmas of Constructivist Mathematics Teaching; Meaningful Contexts for School Mathematics; Paradigms Lost - What Can Mathematics Education Learn From Research in Othe- Disciplines?; Philosophy of Mathematics Education; Research in the Teaching and Learning of Undergraduate Mathematics; Visualization in Problem Solving and Learning. Plenary Panels/Addresses: Visualization and Imagistic Thinking; "The Importance and Limits of Epistemological Work in Didactics" (M. Artigue) ; "Mathematics as a Foreign Language" (G. Ervynck) ; "On Developing a Unified Model for the Psychology of Mathematical Learning and Problem Solving" (G. Goldin) ; "Illuminations and Reflections — Teachers, Methodologies, and Mathematics" (C. Hovles). (MKR)
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• Points ol view or opinions Hated in this docu ment do not necesMrily represent ottiCial of Ri position or policy
"PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY
TO THE ECU'" ATIONAL RESOURCES INFORMATION CENTER lEf"' "
INTERNATIONAL GROUP FOR
THE PSYCHOLOGY OF MATHEMATICS EDUCATION
University of New Hampshire Durham, NH (USA) August 6- 11, 1992
Volume I
Published by the Program Committee of the 16th PME Conference, USA.
All rights reserved. Editors:
William Geeslin and Karen Graham Department of Mathematics University of New Hampshire Durham, NH 03824 USA
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PME XVI PROCEEDINGS Edited by WiUiam Geeslin and Karen Graham Mathematics Department University of New Hampshire Durham NH USA
PREFACE
The first meeting of PME took place in Karlsruhe, Germany in 1976. Thereafter different countries (Netherlands, Germany, U.K., U.S.A., France, Belgium, Israel, Australia, Canada, Hungary, Mexico, Italy) hosted the conference. In 1992, the U.S.A. will again pjay host to PME. The conference will take place at the University of New Hampshire in Durham, NH. The University was founded in 1866 as the New Hampshire College of Agriculture and the Mechanic Arts. The state legislature granted it a new charter as the University of New Hampshire in 1923. The University now has about 800 faculty members and more than 10,000 students enrolled in 100 undergraduate and 75 graduate programs. The University's Mathematics Department has a strong history of commitment to research and service in mathematics education. We are pleased to be the host site for PME XVI.
The academic program of PME XVI includes:
• 92 research reports
• 4 plenary addresses
• 1 plenary panel
• 11 working groups
• 6 discussion groups
• 2 featured discussion groups
• 31 short oral presentations
• 40 poster presentations.
The short oral presentations represent a new format for sessions at PME.
The review process
The Program Committee received a total of 181 research proposals that encompassed a wide variety of themes and approaches. Each proposal was submitted to three outside reviewers who were knowledgeable in the specific research area. In addition, one or more program committee members read each paper. Based on these reviews each paper was accepted, rejected, or accepted as a short oral presentation or poster. If a reviewer submitted written comments, they were forwarded to the authors) along with trie Program Committee's decision.
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List of PME XVI Reviewers
The Program Committee wishes to thank the following people for their help during the review process.
Alice Alston, USA
MicWle Arn'gue, France
Arthur Baroody, USA
MarioUna Bartollni Bussi, Italy
Thomas Bassarear, USA
Michael Battista, USA
Merlyn Behr, USA
Alan Bell, United Kingdom
Jacques Bergeron, Canada
Alan Bishop, United Kingdom
Cathy Brown, USA
Deborah Carey, USA
Thomas Carpenter, USA
Randall Charles, USA
Daniel Chazan, USA
Doug Clements, USA
Paul Cobb. USA
Jere Confrey, USA
Beatriz D'Ambrosio, USA
Linda Deguire, USA
Barbara Dougherty, USA
EdDubinsky, USA
Sharon Dugdale, USA
Laurie Edwards, USA
Theodore Eisenberg, Israel
Nerida Ellerton, Australia
Joan Ferrini-Mundy, USA
Olimpia Figueras, Mexico
Eugenio FUloy, Mexico
Joaquim Giminez, Spain
Gerry Goldin, USA
David Green, United Kingdom
Brian Greer, United Kingdom
Angel Gutierrez, Spain
Gila Hanna, Canada
Guershon Harel, USA
Lynn Hart, USA
Rina Hershkowitz, Israel
Jim Hiebert, USA
Celia Hoyles, United Kingdom
Robert Hunting, Australia
Claude Janvier, Canada
Barbara Jaworski, United Kingdom
James Kaput, USA
Carolyn Kieran, Canada.
David Kirshner, USA
Cliff Konold. USA
Colette Laborde, France,
Sue Lamon, USA
Marsha Landau, USA
Gilah Leder, Australia
Miriam Leiva, USA
Fou-Lai Lin, Taiwan
Wendy Mansfield, USA
Zvia Markovits, Israel
Doug McLeod, USA
Jamce Mokros, USA
Steve Monk, USA
Jim Moser, USA
Ricardo Nemkovsky, USA
Pearia Nesher, Israel
Nobujiko Nohda, Japan
Terezinha Nunes, United Kingdom
Tony Orton, United Kingdom
John Pace, USA
Jo3o Pedro Ponte, Portugal
David Pimm, Canada
Thomas Post, USA
Ferd Prevost, USA
Ian Putt, Australia
Sid Rachlin, USA
John Richards, USA
Andee Rubin, USA
Susan Jo Russell, USA
Deborah Schifter, USA
Thomas Schroeder, Canada
Karen Schultz, USA
Mike Shaughnessy, USA
Yoshinori Shimizu, Japan
Edward Silver, USA
Larry Sowder, USA
Judith Sowder, USA
Leslie Steffe, USA
Kevin Sullivan, USA
Lindsay Tartre, USA
Dina Tirosh, Israel
Shlomo Vinner, Israel
Terry Wood. USA
EmaYackel.USA
Michal Yerushalmy, Israel
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INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION
PRESENT OFFICERS OF PME:
- President KathHart (United Kingdom)
- Vice-President Gilah Leder (Australia)
- Secretary Martin Cooper (Australia)
- Treasurer Angel Gutierrez (Spain)
OTHER MEMBERS OF THE INTERNATIONAL COMMITTEE:
Mich61e Artigue (France) - Frank Lester (USA)
Mariolina Bartolini-Bussi (Italy) - - Fou-Lai Lin (Taiwan)
BernadetteDenys (France) - Carolyn Maher (USA)
Claude Gaulin (Canada) - Nobuhiko Nohda (Japan)
Gila Hanna (Canada) - Joao Ponte (Portugal)
Barbara Jaworski (U.K.) - Dina Tirosh (Israel) Chronis Kynigos (Greece)
PME XVI PROGRAM COMMITTEE:
- Paul Cobb (USA) - Frank Lester (USA)
- Claude Gaulin (Canada) - Carolyn Maher (USA)
- William EGeeslin (USA) - Nobuhiko Nohda (Japan)
- Karen Graham (USA) - Barbara Pence (USA)
- Kathleen Hart (UK) - David Pimm (UK)
PME XVI LOCAL ORGANIZING COMMITTEE:
- Joan Ferrini-Mundy - Karen Graham
- William E. Geeslin - Lizabeth Yost
CONFERENCE PROGRAM SECRETARY -William EGeeslin
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HISTORY AND AIMS OF THE P.M.E. GROUP
At the Third International Congress on Mathematical Education (ICME 3, Karlsruhe, 1976) Professor E. Fischbein of the Tel Aviv University, Israel, instituted a study group bringing together people working in the area of the psychology of mathematics education. PME is affiliated with the International Commission for Mathematical Instruction (ICMI). Its past presidents have been Prof. Efraim Fischbein, Prof. Richard R. Skemp of the University of Warwick, Dr. Gerard Vergnaud of the Centre National de la Recherche Scientifique (C.N.R.S.) in Paris, Prof. Kevin F. Collis of the University of Tasmania, Prof. Pear la Nesher of the University of Haifa, Dr. Nicolas Balacheff, C.N.R.S. - Lyon.
The major goals of the Group are:
• To promote international contacts and the exchange of scientific information in the psychology of mathematics education;
• To promote and stimulate interdisciplinary research in the aforesaid area with the cooperation of psychologists, mathematicians and mathematics teachers;
• To further a deeper and better understanding of the psychological aspects of teaching and learning mathematics and the implications thereof.
Membership
Membership is open to people involved in active research consistent with the Group's aims, or professionally interested in the results of such research.
Membership is open on an annual basis and depends on payment of the subscription for the current year (January to December).
The subscription can be paid together with the conference fee.
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Addresses of Authors Presenting Research Reports at PME XVI
Vcma Adams
Dept. of Elementary/Secondary Education Washington State University Pullman. WA 99164-2122 USA
MAdler
Department of Education University of Witwatersrand PO Wits 2050, Johannesburg SOUTH AFRICA
M.C. Batanero
Escuela Universitaria del Profesorado Campus de Cartuja 18071, Granada SPAIN
Michael Battista 404 White Hall Kent State University Kent. OH 44242 USA
Nadine Bednarz
CP. 8888 - Sue a - Montreal
P.Quebec H3C3P8
CANADA
David Ben-Chaim Weizmann Institute of Science Rehovot, 76100 ISRAEL
Janette Bobis
University of New South Wales POBoxl
Kensington, NSW, 2033 AUSTRALIA
PaolaBoero
Dipartimento Matematica Umversita
VULB.Alberti4
16132, Genova
ITALY
Card Brekke Telemark Laercrhugskole N-3670Notodden NORWAY
Lynne Cannon
Faculty of Education
Memorial University of Newfoundland
St John's, Newfoundland A1B 3X8
CANADA
Olive Chapman
Dept of Curr. & Instruction, U. Calgary 2500 University Drive, NW Calgary, AB CANADA
Giampaolo Chiappini ViaL. B. Alberti, 4 16132 Genova ITALY
David Clarke
Australian Catholic University 17CastlebarRoad Oakleigh, Victoria, 3166 AUSTRALIA
M.A. (Ken) Clements Faculty of Education Deakin University Geelong, Victoria 3217 AUSTRALIA
JereConfrey
Dept of Education, Kennedy Hall Cornell University Ithaca, NY 14853 USA
Kathryn Crawford Faculty of Education The University of Sydney NSW 2006 AUSTRALIA
Linda Davenport P.O. Box 751 Portland, OR 97207 USA
Gary Davis
Institute of Mathematics Education La Trobe University Bundoora, Victoria 3083 AUSTRALIA
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Guida de Abreu
Dept. of Education, Trumpington St. Cambridge University Cambridge, CB2 1QA UNITED KINGDOM
Linda DeGuire Mathematics Department California State Univerisity Long Beach, CA 90840 USA
M. Ann Dirkes
School of Education
Purdue University at Fort Wayne
Fort Wayne, IN 46805-1499
USA
Barbara Dougherty University of Hawaii 1776 University Avenue Honolulu, HI 96822 USA
Laurie Edwards Crown College University of California Santa Cruz, CA 95064 USA
Pier Luigi Ferrari Dipattimento di Matematica via L.B. Alberti 4-16132 Genova ITALY
Rossella Garuti
Dipattimento Matematica University via L.B. Alberti, 4 16132, Genova ITALY
Linda Gattuso
College du Vieux Montreal
3417 Ave. de Vendome
Montreal, Quebec H4A 3M6
CANADA
J.D. Godino Escuela Universitaria del Profesorado Campus de Cartuja 18071, Granada SPAIN
Susie Groves
Deakin University • Burwood Campus 221 Burwood Highway Burwood, Victoria, 3125 AUSTRALIA
Elfriede Guttenberger Avenida Universidad 3000 Maestria en Education Matematica Mexico, D.F., Of Adm. 2, 1 piso MEXICO
Lynn Hart
Atlanta Math Project
Georgia State University
Atlanta, GA 30303
USA
James Hiebert College of Education University of Delaware Newark, DE 19716 USA
Robert Hunting La Trobe University Bundoora, Victoria, 3083 AUSTRALIA
Barbara Jaworski University of Birmingham Edgbaston Birmingham B15 2TT UNITED KINGDOM
Clivc Kanes Division of Education Griffith University Nathan, 4111 AUSTRALIA
TE. Kieran
Dept. of Secondary Education University of Alberta Edmonton T6G2G5 CANADA
Cliff Konold
Hasbrouck Laboratory
University of Massachusetts - Amherst
Amherst, MA 01003
USA
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Masataka Koyarna
Faculty of Education
Hiroshima University, 3-101
2-365 Kagamiyama Higashi-Hiroshima City
JAPAN
Konrad Krainer IFF/Universitat Klagenfurt Sterneckstrasse IS A-9010 AUSTRIA
Gilah Lcder Monash University Clayton, Victoria 3168 AUSTRALIA
Stephen Lerman 103 Borough Road London SE1 OAA UNITED KINGDOM
Liora Linchevski
School of Education
Hebrew University
Mount Scoups, Jerusalem 91-905
ISRAEL
R.C. Lins
Shell Centre for Math Education University Park Nottingham, NG7 2QR BRAZIL
Susan Magidson
EMST - 4533 Tolman Hall, School of Ed. University of California Berkeley, CA 94720 USA
Enrique Castro
Departamemo Didactica de la Matemaanca Campus de Cartuja s/n 18071 Granada SPAIN
Amy Martinet
Center for Math, Science, & Computer Ed.
192 College Avenue
New Brunswick, NJ 08903-5062
USA
Joanna Masingila Education 309 Indiana University Bloomington, IN 47405 USA
S.Maury
University Montpellier U
Place Eugene Bataillon
34095 MONTPELLIER CEDEX 5
FRANCE
Luciano Meira
Mestrado em Psicologia Cognitiva CFCH - 8" andar, Recife 50739 PE BRAZIL
A.L Mesquita R. Marie Brown, 7/8c 1500 Lisbon PORTUGAL
Saburo Minato College of Education Akita University Gakuencho, Tegata, Akita City JAPAN
Michael Mitchelmore School of Education Macquarie University NSW 2109 AUSTRALIA
Judit Moschkovich 4533 Tolman Hall University of California Berkeley, CA 94720 USA
Judith Mousley Faculty of Education Deakin University * Geelong, Victoria, 3217 AUSTRALIA
Joanne Mulligan
27 King William Street
Greenwich 2065
Sydney
AUSTRALIA
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Hanlie Murray Faculty of Education University of Stellenbosch SOUTH AFRICA
Mitchell Nathan LRDC
University of Pittsburgh Pittsburgh, PA 15260 USA
Dagmar Neuman Box 1010
University of GSteburg S-43126 MOlndal SWEDEN
F.A. Norman Dept. of Mathematics University of North Carolina Charlotte, NC 28223 USA
Richard Noss
Institute of Education, U. of London 20 Bedford Way London WC1H0AL UNITED KINGDOM
LynneOuthred School of Education Macquarie University NSW 2109 AUSTRALIA
Kay Owens P.O. Box 555
University of Western Sydney, Macarthur Campbelltown, NSW 2560 AUSTRALIA
Marcela Perlwitz
EMAD414
Purdue University
West Lafayette, IN 47907-1442
USA
JoSo Pedro Ponte
Av. 2y de Julmo, 134-4"
1300 Lisboa, PORTUGAL
PORTUGAL
Matthias Reiss Stedingerstr. 40 7000 Stuttgart 31 GERMANY
Joe Relich PO Box 10
c/o Faculty of Education
Kingswood
AUSTRALIA
Anne Reynolds
Math Education, 219 Carothers, B-182 Florida State University Tallahassee, FL 32306 USA
Mary Rice Deakin University Geelong, Victoria 3217 AUSTRALIA
Naomi Robinson
Department of Science Teaching
Weizmann Institute
Rehovoth, 76100
ISRAEL
Adaiira Sienz-Ludlow
Dept of Mathematical Sciences
Northern Illinois University
DcKalb, IL 60115
USA
Victoria Sanchez Avdo. Ciudad Jardin, 22 41005 Sevilla SPAIN
Vinia Maria Santos
School of Education, Room 309
Indiana University
Bloomington, IN 47405
USA
Manvel Joaquim Saraiva Universidade da Beira Interior Rue Ferreira de Castro, 5-3 PORTUGAL
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Analucia Schliemann Mestrado em Psicologia 8" andar, CFCH-UFPE 50739 Recife BRAZIL
Thomas Schroeder
Faculty of Education, 212S Main Mall University of British Columbia Vancouver, BC, V6T 1Z4 CANADA
Yasuhiro Sekiguchi Institute of Education University of Tsukuba Tsukuba-shi, Ibaraki, 305 JAPAN
Keiichi Shigematsu Takabatake Nara University of Education Nara630 JAPAN
Yoshinori Shimizu 4- 1 - 1 , Nukuikita-Machi Koganei-shi Tokyo, 184 JAPAN
Dianne Seimon
School of Education
Phillip Institute of Technology
Alva Grove, Coburg 3058
AUSTRALIA
Martin Simon
176 Chambers Building
Department of Curriculum and Instruction
Univesity Park, PA 16802
USA
Jack Smith
ColL of Education, 436 Erickson Hall Michigan State University East Lansing, MI 48824 USA
Judith Sowder
Ctr. for Research in Math and Science Ed. 5475 Alvarado Road, Suite 206 San Diego, CA 92120 USA
Kaye Stacey
School of Science & Math Education University of Melbourne Parkville, Victoria 3 142 AUSTRALIA
Rudolf StrSsser
Institut fur Didaktik dcr Mathematik UniversitSt Bielefeld 4800 Bielefeld GERMANY
L. Streefland Tibcrdrcef4 3561 GG, Utrecht NETHERLANDS
Susan Taber 717 Harvard Lane Newark. DE 19711 USA
Cornelia Tierney TERC
2067 Massachusetts Avenue Cambridge, MA 02140 USA
DinaTirosh School of Education Tel Aviv University Tel Aviv, 69978 ISRAEL
Maria Trigueros Rio Hondo Num 1 ColoniaTizapan San Angel 03100, Mexico D.F. MEXICO
Pessia Tsamir School of Education Tel- Aviv University Tel Aviv, 69978 ISRAEL
Diana Underwood
Purdue University
ENAD414
West Lafayette, IN
USA
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Marjory Witte
OCT - University of Amsterdam Grote Bidiersstnut 72 1013 KS, Amsterdam NETHERLANDS
Addresses of Presenters of Plenary Sessions at PME XVI
Michele Artigue IREM, Universe Paris 7 2 Place Jussieu 75251 Paris Cedex 5 FRANCE
M.A. (Ken) Cleme-its Faculty of Education Deakin University Geelong, Victoria, 3166 AUSTRALIA
Tommy Dreyfus
Center for Technological Education PO Box 305 Holon 58102 ISRAEL
Gontran Ervynck Kath.Univ. Leuven Campus Kortrijk B-8500Konrijk BELGIUM
Gerald A. Goldin
Center for Math, Science, & Computer Ed. Rugers University Piscataway, NJ 08855-1179 USA
CeliaHoyles
Institute of Education, Math University of London 20 Bedford Way London WC1HOAL UNITED KINGDOM
John Mason Open University Walton Hall
Milton Keynes MK7 6AA UNITED KINGDOM
Bernard Parzysz
IUFMde Lorraine
Departement de mathematiques
University deMetz
lie du Suilcy
F 57000 Metz
FRANCE
Norma Presmeg
219 Corothers Hall, B-182
Florida State University
Tallahassee, FL 32306-3032
USA
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CONTENTS OF VOLUME I
Preface P- l-»
International Group for the Psychology of Mathematics Education p. 1-i"
History and Aims of the PME Group p. Mv
Addresses of Authors Presenting Research Reports at PME XVI p. 1-v
Addresses of Presenters of Plenary Sessions at PME XVI p. 1-x
Working Groups
Advanced mathematical thinking P- 1-3
Organizers: G. Ervynck & D. Tall
Algebraic processes and structure P- 1-4
Organizer R. Sutherland
Classroom Research P- 1-5
Organizer F.J. van den Brink
Cultural aspects in mathematics learning P- 1-7 Organizer B. Denys
Geometry P- 1-8 Organizer: H. Mansfield
Psychology of inservice education of mathematics teachers: A research perspective p. 1-9
Organizers: S. Dawson, T. Wood, B. Dougherty, & B. Jaworski
Ratio and proportion P- Organizers: F.L. Lin, K.M. Hart, & J.C. Bergeron
Representations P- 1-11 Organizer G. Goldin
Research on the psychology of mathematics teacher development P- 1-12 Organizer N.EUerton
Social psychology of mathematics education P- 1-13 Organizer: A.J. Bishop
Teachers as researchers in mathematics education p. 1-14 Organizers: S. Lerman & J. Mousley
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Discussion Groups
Dilemmas ofconstructivist mathematics teaching: Instances from classroom practice Organizers: R. Carter & J. Richards
Meaningful contexts for school mathematics Organizers: L. Bazzini & L. Grugnctti
Paradigms lost: What can mathematics education learn from research in other disciplii Organizer B A. Doig
Philosophy of mathematics education Organizer P.Ernest
Research in the teaching and learning of undergraduate mathematics: Where are we? Where do we go from here?
Organizers: J. Ferrini-Mundy, E. Dubinsky. & S. Monk
Visualization in problem solving and learning Organizers: M.A. Mariotti & A. Pesci
Research Reports de Abreu, Guida
Approaches to research into cultural conflicts in mathematics learning Adams, V.M.
Rhetorical problems and mathematical problem solving: An exploratory study
Action research and the theory-practice dialectic: Insights from a small post graduate project inspired by activity theory
Batanero, M.C., Vallecillos. M.A. & Godino, J.D.
Students' understanding of the significance level in statistical tests
Battista. M.T. & Clements. D.H.
Students' cognitive construction of squares and rectangles in Logo Geometry
Bcdnarz, N., Radford, L., Janvier, B. & Lepage, A. Arithmetical and algebraic thinking in problem-solving
Ben-Chaim, D., Carmeii, M. & Fresko, B.
Consultant as co-teacher: Perceptions of an intervention for improving mathematics instruction
Bobis, J., Cooper, M. & Sweller, J.
The redundancy effect in a simple elementary-school geometry task: An extension of cognitive-load theory and implications for teaching
p. 1-20 p. 1-21
p. 1-22
p. 1-25 p. 1-33 p. 1-41
p. 1-49 p. 1-57 p. 1-65 p. 1-73
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Boero, Shapiro, L. P> !'89
On some factors influencing student!' solutions in multiple operations problems: Results and interpretations
Brckke,G.&B*H,A. P- 1-97
Multiplicative structures at ages seven to eleven
Cannon, P.L. P- 1-105
Middle grade students' representations of linear units
Castro, E.M. LJ p. 1-113
Choice of structure and interpretation of relation in multiplicative compare problems
Chapman, O. p. 1-121
Personal experience in mathematics learning and problem solving
Chiappini, G. & Lemut, E. p. 1-129
Interpretation and construction of computer-mediated graphic representations for the development of spatial geometry skills
Clarke, D.J. & Sullivan, P.A. P- I-I37
Responses to open-ended tasks in mathematics: Characteristics and implications
Clements, M.A. & EUerton, N.F. P- 1-145
Over-emphasising process skills in school mathematics: Newman error . analysis data from five countries
Confrey, J. & Smith, E. , P- 1-153.
Revised accounts of the function concept using multi-representational software, contextual problems and student paths
Crawford, K. P- 1-161
Applying theory in teacher education: Changing practice in mathematics education
Davenport, L. & Narode, R. P- 1-169
School math to inquiry math: moving from here to there
Davis, G. p. 1-177
Cutting through Chaos: A case study in mathematical problem solving
DeGuire,L.J. p. 1-185
The development of problem-solving abilities: its influence on classroom teaching
Dirkes, M.A. P- M93
Self-directed problem solving: Idea production in mathematics
Dougherty, B.J. P- 1-201
Project DELTA: Teacher change in secondary classrooms
Edwards, L.D. P- 1'209
Reasoning and representation in first year high school students
Ferrari, P.L. L ^ J p. 1-217
Problem-solving in geometrical setting: Interactions between figure and strategy
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Garuti, R. & Boero, P. p. 1-225
A sequence cf proportionality problems: An exploratory study
Gattuso, L. p. 1-233
Discrepancies between conceptions and practice: A case study
Godino, J.D., Navarro-Pelayo, V. & Batanero, M.C p. 1-241
Analysis of students' errors and difficulties in solving combinatorial problems
Groves, S. p. 1-249
Processes and strategies of third and fourth graders tackling a real world problem amenable to division
Hart, L.C. & Najce-ullah, D.H. p. 1-257
Pictures in an exhibition: Snapshots of a teacher in the process of change
Heiscovics, N. & Linchevski, L. p. 1-265
"Cancellation within-the-equation" as a solution procedure
Hiebert, J. & Weame, D. p. 1-273 Emerging relationships between teaching and learning arithmetic during the primary grades
Hunting, R.P., Pepper, K.L. & Gibson, SJ. p. 1-281 Preschoolers' schemes for solving partitioning tasks
Jaworski, B. p. 1-289
The emancipatory nature of reflective mathematics teaching
Kanes, C. p. 1-297
Reference, structure and action: Eliminating paradoxes in learning and teaching mathematics
CONTENTS OF VOLUME II Research Reports (continued)
Kieren, T. & Pine, S. p. 2- 1
The answer determines the question. Interventions and the growth of mathematical understanding
Konold, C. & Falk, R. p. 2-9
Encoding difficulty: A psychological basis for 'misperceptions' of randomness
Koyama, M. p. 2-17
Exploring basic components of the process model of understanding mathematics for building a two axes process model
Krainer, K. p. 2-25
Powerful tasks: Constructive handling of a didactical dilemma
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Letter, G.C. P- 2-33
Measuring attitudes to mathematics
Lerman, S. P- 2-40
The Junction of language in radical constructivism: A Vygotskian perspective
Linchevsky, L., Vinner, S.. & Karscnty, R. P- 2-48
To be or not to be minimal? Student teachers' views about definitions in geometry
Lins, R. P- 2-56
Algebraic and non-algebraic algebra
Magidson. S. ^ P- 164
What's in a problem? Exploring slope using computer graphing software
Martino, A.M. & Maher, C.A. P- 2-72 Individual thinking and the integration of the ideas cf others in problem solving situations
Masingila.J. P- 2-80 Mathematics practice in carpet laying
Maury, S., Lerouge, A., & Bailie, J. P- 2-88
Solving procedures and type of rationality in problems involving Cartesian graphics, at the high school level (9th grade)
Meira,L. P- *96
The microevolution of mathematical representations in children s activity
Mesquita, AJL. P- 2-104
Les types d'apprehension en geometrie spatiale: une etude clinique sur le developpement-plan du cube
Minato,S.AKamada,T. J . J p. 2-112
Results of researches on causal predominance between achievement and attitude in junior high school mathematics of Japan
Mitchelmore, M. P- 2"120
Children's concepts of perpendiculars
Moschkovich, J. P- 2-128
Students' use of the x-intercept: An instance of a transitional conception
Mousley, J. ^ P- 2-136
Teachers as researchers: Dialectics cf action and reflection
Mulligan, J. „ P- 2-144
Children's solutions to multiplication and division word problems: A longitudinal study
Murray, H., Olivier, A., & Human, P. P- 2-152
The development of young students' division strategies
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Nathan, M.J. p. "160
Interactive depictions of mathematical constraints can increase students' levels cf competence for word algebra problem solving
Neuman, D. p. 2- no
The influence cf numerical factors in solving simple subtraction problems
Norman, F.A. & Prichard, M.K. p. 2-178
AKrutetskiianframeworkfor the interpretation of cognitive obstacles: An example from the calculus
Noss, R. & Hoyles C. p. 2-186
Logo mathematics and boxer mathematics: Some preliminary comparisons
Outhred, L. & Mitchelmore, M. p. 2- 194
Representation of area: A pictorial perspective
Owens, K. p. 2-202
Spatial thinking takes shape through primary-school experiences
Perlwitz, MD. p. 2-2 10
The interactive constitution of an instructional activity: A case study
Ponte, J.P., Matos, J. F., Guimaries, H.M., Leal, L.C., & Canavarro, A.P. p. 2-218
Students' views and attitudes towards mathematics teaching and learning: A case study of a curriculum experience
Reiss, M. & Reiss, K. p. 2-226
Kasimir: A simulation of learning iterative structures
Relich, J. p. 2-234 Self-concept profiles and teachers of mathematics: Implications for teachers as role models
Reynolds, A. & Wheatley, G.H. p. 2-242 The elaboration of images n the process of mathematics meaning making
Rice, M. p. 2-250
Teacher change: A constructivist approach to professional development
Robinson, N., Even, R., & Tirosh, D. p. 2-258
Connectedness in teaching algebra: A novice-expert contrast
Saenz-Ludlow, A. p. 2-266
Ann's strategies to add fractions
Sanchez, V. & Llinares, S. p. 2-274 Prospective elementary teachers' pedagogical content knowledge about equivalent fractions
Santos, V. & Kroll, D.L. p. 2-282 Empowering prospective elementary teachers through social interaction, reflection, arid communication
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Saraiva, M J. P- 2-290 Students' understanding of proof in a computer environment
Schliemann, A., Avel«r, A.P., & Santiago, M. p. 2-298 Understanding equivalences through balance scales
Schroeder. T.L. P- 2-306 Knowing and using the Pythagorean theorem in grade 10
Sekiguchi, Y. P- 2-314 Social dimensions of proof in presentation: From an ethnographic inquiry in a high school geometry classroom
Shigcmatsu. K. P- 2-322 Metacognidon: The role of the "inner teacher"
Shimizu. Y. P- 2-330 Metacognition in cooperative mathematical problem solving: An analysis focusing on problem transformation
CONTENTS OF VOLUME III Research Reports (continued)
Seimon, D. P- 3-3
Children's approaches to mathematical problem solving
Simon. MA. & Blumc. G.W. P- 3-H
Understanding multiplicative structures: A study of prospective elementary teachers
Smith. J.P. P- 3-19
Misconceptions and the construction of mathematical knowledge
Sowder, J.. Philipp, R., & Flores, A. P- 3-27
The act of teaching mathematics: A case study
Stacey. K. & del Bcato. C P- 3"35
Sources ofcertainy and uncertainty in mathematical problem solving
SuHBer, R. & Bromine, R. P- S"43
The description of solids in technical drawing - Results from interviews of experienced draughtsmen
Streefland, L. & van den Heuvel-Panhuizen, M. P- 3-51
Evoking pupils' informal knowledge on percents
Taber S.B. P- 3"'^
The "multiplier effect" and sixth-grade students' performance on multiplication word problems with unit-fraction factors
Tiemey, C.C., Weinberg, A.S., & Nemirovsky, R. P- 3-66
Telling stories about plant growth: Fourth grade students interpret graphs
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Tirosh, D. & Sttvy, R. p. 3-74 Overgeneralization between science end mathematics: The case of successive division problems
Trigueros, M. & Cantoral, R. p. 3-82 Exploring understanding and its relationship with teaching: Variation and movement
Tsarnir, P. & Tiiosh, D. p. 3-90 Students' awareness of inconsistent ideas about actual infinity
Underwood, D.L. p. 3-98 Mathematics and gender: An interactional analysis
Wenzelburger, E. p. 3-106 The learning of trigonometric functions in a graphical computer environment
Witte.M. p. 3-114 Euclidian constraints in mathematics education
Short Oral Presentations
Abcle, A. . p. 3-125
The concept of speed: Two case studies in the primary school
Albert, J. & Friedlander, A. p. 3- 1 26
Achievement and thinking strategies on "reversed items"
Boulton-Lewis, G.M. p. 3-126
The processing loads and relations between counting and place value
Cantoral-Uriza, R. p. 3-127
From research to teaching: An analysis of students' performance on calculus
Ernest, P. p. 3-127
Metaphors for the mind and the world in the psychology of mathematics education
Oelfman, E., Demidovt, L., Kholodnaja, M., Lobanenko, N., & Wolfengaut, J. p. 3-128
The psychology of pupil's intellect development in the process of teaching mathematics
Kaplan, R.G., Jani, M, & Schmidt, A. p. 3-128
Implementing the NCTM Standards: Reconciling the planned impact with the experienced reality in an urban school district
Kynigos, C. p. 3-129
Children using the turtle metaphor to construct a computational tool in a geometrical Logo microworld
Lo, J. & Wheatley, G.H. p. 3-129
Understanding mathematics class discussions
MacGregor, M. & Sttcey, K. p. 3-130
Cognitive origins of students' errors in writing equations
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Malara, N.A., Pellegrino. C. & Iaderosa, R. P- 3-130
Towards applied problem solving
Markovits, Z. & Hershkowitz, R. P- 3-131 Visual estimation
Morgan. C. P- 3-131 Written mathematical communication: The child's perspective
Nantais, N., Francavilla, M., & Boulet, G. P- 3-132
Young pupils' logico-physical concept of multiplication: 15 case studies
Nevile. L. P- 3-132
Teaching recursion as shifts of attention
Nunes, T. & Bryant, P. P- 3-133
Rotating candy bars and rearranging oranges: A study of children's understanding of commutativity
Pegg., J. & Davey, G. p. 3-133
Interpreting children's understanding of geometric concepts: A comparison of the Van Hiele theory and the solo taxonomy
Pchkonen. E. & Tompa. K. . p. 3-134
Are there any differences in pupils' conceptions about mathematics teaching in different countries? The case of Finland and Hungary
Perks. P. P- 3-134
Introducing calculators to six-year olds: Views on support for teachers
Quintal, C. P- 3-135
Hierarchies of cognitive difficulty in early algebra
Rojano, T. & Sutherland, R. P- 3-135
Pupil strategies for solving algebra word problems with a spreadsheet
Rubin. A. & Russell. S.J. P- 3-136
Children's developing concepts of landmarks in the number system
Sfard. A. & Linchevsky. L. P- 3-136
Equations and inequalities • Processes without objects?
Shiu. C. p. 3-137
Assumptions and intentions in distance learning materials for mathematics
Swinson. K.V. & Partridge. B.D. P- 3-137
Writing in mathematics: Is it always beneficial?
Teppo.A.R. „ P-3'138
The impact of understanding and expectations of performance on college students' self-conjidence
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Experiences and effects of realistic mathematics education: The case of exponential growth
Watson, J.M., Collis, K.F., & Campbell, KJ.
Ikonic and early concrete symbolic responses to two fraction problems
Williams, S.R. & Walen. S.B.
Conceptual splatter and metaphorical noise: The case of graph continuity
Yoshida, M.
Trying the theory on the determination to study - Applying mathematical activities based on varied problem solving
Zazkis, R.
Inverse of a product - A theorem out of action
Poster Presentations
Barocio Quijano, R. & Brefia Sanchez, J.
Teaching mathematics in the first years of elementary education: Kama's proposal in action
Becker, G.
Analogical reasoning: Basic component in problem solving activities
Bell, A., Crust, R., Shannon, A. & Swan, M. Pupils' evaluations of learning activities
Berenson, S.B.
Race and gender interactions and constructivist teaching
Bergsten, C.
Schematic structures of mathematical form
Borba, M. & Confrcy, J.
Transformations of functions using multi-representational software: Visualization and discrete points
Carraher, D.W.
Relational thinking and rational numbers
Chazan, D.
F(x) = G(x)?: An approach to modeling with algebra
Clarke, D., Wallbridge, M., & Fraser, S.
The other consequences of a problem-based mathematics curriculum
Clements, D.H., Meredith, J.S., & Battista, M.T.
Design of a Logo environment for elementary geometry
p. 3-138
p. 3-139 p. 3-140 p. 3-141
p. 3-141
p. 3-145
p. 3-146 p. 3-147 p. 3-14S p. 3-149 p. 3-149
p. 3-150 p. 3-150 p. 3-151 p. 3-152
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Collis, K.F., Watson, J.M., & Campbell, KJ.
Multimodal functioning in mathematLal problem solving
Coidero-Osorio, F.
The idea of variation and the concept of the integral in engineering students: Situations and strategies
DeFranco, T.C.
The role ofmetacognition in mathematical problem solving among PhD. mathematicians
dc Villiers, M.
Childrens' acceptance of theorems in geometry
Doig, B.A.
Exploring mathematical beliefs
Ebert, C.L.
An assessment of students' graphing strategies in a technology-rich environment
Ellerton, N.F. & Clements, M.A.
Teaching mathematics education at a distance: The Dealdn University experience
Emori, H. & Nohda, N.
Communication process in learning mathematics
Farah-Sarkis, F.
Problem familiarity and experts: The case of transitivity
Gal, L. Mahoncy, P., & Moore, S. Children's usage of statistical terms
Gallaido, A. & Rojano, T.
The status of negative numbers in the solving process of algebraic equations
Gclfman, E., Demidova, L., Grinshpon, S., Kholodnaja, M., & Wolfengaut, J. Study of identities in the school course of algebra
Gimcnez, J.
Some wrong strategies to determine probabilities in 8th graders - Report of a preliminary study
Goldberg, M.D. Sc. Hershkowitz, R. From Concept to proof: A first step
vjuuya, *«.
Metacognitive strategies in the classroom: Possibilities and Imitations
Irwin, K. & Britt, M.
A two year project for improving the mathematics teaching for 11-13 year-olds
Ito-Hino, K.
An assessment of mathematics learning through students' intra- and inter- communication processes
p. 3-153 p. 3-153
p. 3-154
p. 3-155 p. 3-156 p. 3-157 p. 3-158 p. 3-159 p. 3-160 p. 3-160 p. 3-161 p. 3-162 p. 3-163
p. 3-163 p. 3-164 p. 3-165 p. 3-166
1 - xxii
Jones, G.A., Bidwell, J.K., & Ziukelis, R. p. 3-166
The effect of different school environ,,ients on mathematics learning across the elementary-secondary interface
Kaufman Fainguelemt, E. p. 3-167
The importance of teaching practice in mathematics teacher courses
Konold, C. p. 3-168
Prob Sim and Datascope: Interactive software tools for introductory courses in probability and data analysis
Krainer, K. p. 3-169
PFL-Mathematics: An in-service education university course for teachers
Lawson, M. & Chinnappan. M. p. 3-170
The effects of training in use of generation and management strategies on geometry problem solving
LeBlanc, M.D. p. 3-171
When more is less ■ Interactive tools for relational language
Long, E. p. 3-172
Teachers' questioning and students' responses in classroom mathematics
Ojeda,A.M. p. 3-173
Students' problems in understanding the idea of conditional probability
Putt, I., Annesley, F., & Clark, J. p. 3-174
Development of an instrument for teacher and student use in the measurement of affective development in school students
Rhodes, S. p. 3-175
Research and psychological factors influencing materials development in mathematics: Imagery
Schwarz, B. & Resnick, L. p. 3-175
Acquisition of meaning for pre-algebraic structures with "the Planner"
Shier, G.B. p. 3-176
Correlates of direct proportional reasoning among adolescents in the Philippines
Zellweger, S. p. 3-177
Cards, mirrors, and hand-held models that lead into elementary logic
Featured Discussion Group I Chair, Kath Hart (United Kingdom)
Fischbein, E. p. 3-181
The three facets of mathematics: The formal, the human, and the instrumental educational implications
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Martin, W.G. P- 3"182 Research-based curriculum development in high school geometry: A construcdvist model
Pace, J.P. . J p. 3-182
Needing conscious conceptions of human nature and values to inform and develop pedagogy
Featured Discussion Group II Chair, Eugenio RUoy (Mexico)
Bechara Sanchez, L. „ , ,. P- 3-185
An analysis of the development of the notion of similarity in confluence: Multiplying structures; spatial properties and mechanisms of logic and formal framework
Graciosa Velosa, M. P- 3-185
Appropriation and cognitive empowerment: Cultural artifacts and educational practices
Gutierrez, A. & Jaime, A. p. 3- 186
Exploring students' mental activity when solving 3 -dimensional tasks
Hitt, F. P- 3" 186
Visual images, availability and anchoring, related to the polynomial numbers and the use of microcomputers
Nasser, L. P- 3"187
A Van-Hlele-bascd experiment on the teaching of congruence
Orozco Hormaza, M. p. 3-187
Modes of use of the scalar and functional operators when solving multiplicative problems
Plenary Sessions Plenary Panel
Dreyfus, T. (organizer), Clements, K., Mason, J., Parzysz, B., & Presmeg, N. p. 3-191
Visualization and imagistic thinking
Plenary Addresses
Artique.M. ... . p. 3-195
The importance and limits of epistemological work in didactics
Ervynck, G. P- 3"217
Mathematics as a foreign language
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Goldin, G. p. 3-235 On developing a unified model for the psychology of mathematical learning and problem solving
Hoyles, C. p. 3-263 Illuminations and reflections - Teachers, methodologies and mathematics
23
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Working Groups
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WORKING GROUP ON ADVANCED MATHEMATICAL THINKING (A.M.T.)
Organisers: Gontran Ervynck, David Tall
• SESSION I: INTRODUCTION TO THE PROCESSES- OBJECTS THEME Four initiators will present different approaches to what seems to be basically the same theory.
- Michele Artigue (France): Tool