DOCUMENT RESUME ED 476 613 SE 065 231 AUTHOR Speiser, Robert, Ed.; Maher, Carolyn A., Ed.; Walter, Charles N., Ed Proceedings of the Annual Meeting of the North American. TITLE Chapter of the International Group for the Psychology of Mathematics Education (Snowbird, Utah, October 18-21, 2001). Volume 1 [and] Volume 2. INSTITUTION International Group for the Psychology of Mathematics Educition. North American Chapter. ISBN ISBN-0-88119-001-2 PUB DATE 2001-00-00 NOTE 1008p.; For selected individual papers, see SE 067 893-909, SE 067 913-914, and SE 067 924. AVAILABLE FROM ERIC/CSMEE Publications, 1929 Kenny Road, Columbus, OH 43210- 1080. Tel: 800-276-0462; Tel: 614-292-5680. PUB TYPE Collected Works Proceedings (021) Reports Descriptive (141) EDRS PRICE EDRS Price MF07/PC41 Plus Postage. DESCRIPTORS *Algebra; Educational Assessment; *Educational Research; Elementary Secondary Education; Graphs; Higher Education; *Mathematics Curriculum; *Mathematics Instruction; *Thinking Skills; Visualization IDENTIFIERS *Representations (Mathematics) ABSTRACT This book contains volume 1 of the proceedings of the 23rd annual meeting of the International Group for the Psychology of Mathematics Education (PME) held October, 2001 in Snowbird, Utah. Papers include: (1) "Opening the Dimensions of Mathematical Capability: The Development of Knowledge, Practice and Identity in Mathematics Classrooms" (Jo Boaler); (2) "Learning Mathematics as Developing a Discourse" (Anna Sfard); (3) "Gender and Mathematics: Themes Within Reflective Voices" (Diana B. Erchick and Linda Condron); .(4) "Representations and Mathematics Visualization" (Fernando Hitt); "Models and Modeling" (Richard Lesh, Helen Doerr, Thomas Post, (5) Judith S. Zawojewski, and Guadalupe Carmona); (6) "Geometry and Technology" (Douglas McDougall and Jean J. McGehee); "The Complexity of (7) Learning to Reason Probabilistically" (Carolyn A. Maher and Robert Speiser); and (8) "Problem Posing Research: Answered and Unanswered Questions" (Lyn D. English). Volume 2 of the proceedings of the 23rd annual meeting of the International Group for the Psychology of Mathematics Education (PME) held October, 2001 in Snowbird, Utah is also included. Papers include: "Growth (1) in Student Mathematical Understanding Through Precalculus Student and Teacher Interactions" (Daniel R. Ilaria and Carolyn A. Maher); "Investigating the (2) Teaching and Learning of Proof: First Year Results" (Tami S. Martin and Sharon Soucy McCrone); (3) "Beliefs About Proof in Collegiate Calculus" (Manya Raman); (4) "Metaphors of the Novice: Emergent Aspects of Calculus Students' Reasoning" (Mike Oehrtman); (5) "An Examination of the Interaction Patterns of a Single- Gender Mathematics Class" (Amy Burns Ellis); "The Role of Intellectual Culture of Mathematics in Doctoral (6) Student Attrition" (Abbe H. Herzig); (7) "Group Tests as a Context for / Learning How to Better Facilitate Small Group Discussion" (Judith Kysh); and (0 "Learning Paths to 5- and 10-Structured Understanding of Quantity: Addition and Subtraction Solution Strategies of Japanese Children" (Aki aLen uLaLa eproductions supplied by EDRS are the best that can be made from the original document Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Snowbird, UT, October 18 -21, 2001.) Volume 1 [and] Volume 2. U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement PERMISSION TO REPRODUCE AND EDUCATIONAL RESOURCES INFORMATION DISSEMINATE THIS MATERIAL HAS CENTER (ERIC) BEEN GRANTED BY o This document has been reproduced as received from the person or organization wei), originating it. Minor changes have been made to improve O reproduction quality TO THE EDUCATIONAL RESOURCES Points of view or opinions stated in this INFORMATION CENTER (ERIC) document do not necessarily represent 1 official OERI position or policy. 2 PME-NA XXIII Snowbird, Utah October, 2001 CClearinghouse for Science, Mathematics, and Environmental Education Educational Resources Information Center r) i Proceedings of the Twenty-Third Annual Meeting North American Chapter of the International Group for the Psychology of Mathematics Education Volume 1: Plenaries, Working Groups, Discussion Groups, Research Reports, Short Oral Reports, Poster Presentations PME-NA XXIII October 18-21, 2001 Snowbird, Utah Editors: Robert Speiser Carolyn A. Maher Charles N Walter E CClearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH Educational Resources Information Center 3 Cite as: Speiser, R., Maher, C. A., & Walter, C. N. (Eds.). (2001). Proceedings of the twenty- third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vols. 1-2). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. ERIC Clearinghouse accession number: SE 065 164 International Standard Book Number 0-88119-001-2 Clearinghouse Production Team: Executive Editor: David L. Haury Copyeditor: Linda A. Milbourne Cover Design: Two Samurai Graphics Printed in the United States of America Order from: ERIC/CSMEE Publications, 1929 Kenny Road, Columbus, OH 43210-1080. Price per two-volume set is $45.00 plus shipping, handling, and relevant tax. All orders must be prepaid with delivery to a single address. Prices are subject to change without notice. To order by credit card, call 1-800-276-0462 or 614-292-5680. Note. The Proceedings were produced with financial support provided by the U. S. Department of Education under contract no. ED -99 -CO -0024. Opinions expressed in this document do not necessarily reflect the positions or policies of the U. S. Department of Education. 4 ii History and Aims of the PME Group PME came into existence at the Third International Congress on Mathematical Education (ICME 3) held in Karlsruhe, Germany in 1976. It is affiliated with the International Commission for Mathematical Instruction. The major goals of the International Group and the North American Chapter are: 1. To promote international contacts and the exchange of scientific information in the psychology of mathematics education. 2. To promote and stimulate interdisciplinary research in the aforesaid area with the cooperation of psychologists, mathematicians and mathematics educators. 3. To further a deeper and better understanding of the psychological aspects of teaching and learning mathematics and the implementation thereof. iii Reviewers PME-NA XXIII Proceedings, 2001 Silvia Alatorre Elizabeth Jakubowski Arthur Powell Alice Alston Amanda Jansen Norma Presmeg Dawn Leigh Anderson Debra Johanning David Pugalee Bridget Arvold Pat Lamphere Jordan Manya Raman Leslie Aspinwall C0115;',ance Kamii Christopher Rasrrn;seti Patricia Balderas-Canas Rochelle Goldberg Kay Reinke Jeffrey Barrett Kaplan Ron Ritchhart Joanne Rossi Becker Elhan Kazemi Manuel Santos Babette Benken Paul Kehle Roberta Schorr Sally Berenson Regina Kiczek John Selden Joyce Bishop Margaret Kinzel Annie Selden Linda Bolte Anita Kitchens Betty Senger Daniel Brahier Hari P. Koirala Ken Shaw Terri Bucci Judith Kysh Elaine Simmt Christianne Maria Butto Carol Larson Cynthia Smith Zarzar Keith Leatham John P. Smith III Marilyn Carlson Yeping Li Robert Speiser Jennifer Chauvot Lou Ann Lovin Elena Steencken Karen Koellner Clark Michael Lutz Kathryn Stewart Jose Contreras Carolyn A. Maher Hollylynne Drier Stohl Ann Crawford Lyndon Martin Walter Stone Christopher Danielson Armando Martinez-Cruz Susan Taber Roger Day Kay McClain Sylvia Taube Yolanda De La Cruz Doug McDougall Mourat Tchosanov Willi Doerfler Jean McGehee Pat Thompson Christopher Drumm Mercedes Mc Gowen Anthony Thompson Barbara Edwards David Meel Liz Uptegrove Rebekah Elliott Denise Mewborn Juliana Utley David Feikes James Middleton Jorge Villa Maria L. Fernandez Teri Jo Murphy Sharon Walen Jose Fonseca Janice Newton Janet G. Walter John Francisco Nancy O' Rode Charles Walter Isobel(Bobby) Gaensler Doug Owens John Weber Bradley Garner Stephen Pape Gideon Weinstein Florence Glanfield Erkki Pehkonen Dirk Wessels Karen Graham Barbara Pence Darlene Whitkenack Jose Guzman Fred Peskoff Dorthy Whitlow Karen Heinz Catherine Pomar Steve Williams Pao-Sheng Hsu Neil Portnoy Joseph Zilliox iv PME-NA Steering Committee (2000-2001) Robert Speiser Chair Denise Mewborn Chair-Elect Barbara Pence Treasurer Doug McDougall Secretary Maria Fernandez Past Chair Daniel Brahier Member-at-Large Karen Norwood Member-at-Large Patrick Thompson Member-at-Large PME-NA XXIII Program Committee Robert Speiser, Chair Fernando Hitt Sarah Berenson Douglas McDougall Maria Fernandez Denise Mewborn Carolyn A. Maher Karen Norwood Douglas T. Owens Barbara Pence Charles N. Walter Patrick Thompson Daniel J. Brahier Maria Trigueros V PME Proceedings in the ERIC Database ERIC Document Reproduction Service (800)443-ERIC ERIC Clearinghouse for Science, Mathematics, and Environmental Education (800)276-0462 North American Chapter Year Meeting Location ERIC Accession No. 1980 PME-NA 2/PME 4 California ED 250 186 PME-NA 3 1981 Minnesota ED 223 449 PME-NA 4 1982 Georgia ED 226 957 1983 PME-NA 5 Montreal ED 289 688 1984 PME-NA 6 Wisconsin ED 253 432 1985 PME-NA 7 Ohio SE 056 279 1986 PME-NA 8 Michigan ED 301 443 1987 PME-NA 9/PME 11 Montreal SE 055 633 1988 PME-NA 10 Illinois SE 056 278 1989 PME-NA 11 New Jersey SE 057 133 1990 PME-NA 12/PME 14 Mexico ED 411 137-139 1991 PME-NA 13 Virginia SE 352 274 1992 PME-NA 14/PME 16 New Hampshire SE 055 811 1993 PME-NA 15 California ED 372 917 1994 PME-NA 16 Louisiana SE 055 636 1995 PME-NA 17 Ohio SE 057 176 1996 PME-NA 18 Florida SE 059 001 1997 PME-NA 19 Illinois SE 060 729 1998 PME-NA 20 North Carolina SE 061 830 1999 PME-NA 21 Mexico SE 062 752 2000 PME-NA 22 Arizona SE 064 088 vi International Year Meeting Location ERIC Accession No. 1978 PME 2 W. Germany ED 226 945 PME 3 1981 England ED 226 956 1980 PME 4 California ED 250 186 PME 5 1981 France ED 225 809 1982 PME 6 Belgium ED 226 943 PME 7 1983 Israel ED 241 295 1984 PME 8 Australia ED 306 127 1985 PME 9 Netherlands ED 411 130-131 1986 PME 10 London ED 287 715 1987 PME 11 Montreal ED 383 532 1988 PME 12 Hungary ED 411 128-129 1989 PME 13 Paris ED 411 140-142 1990 PME 14 Mexico ED 411 137-139 PME 15 1991 Italy ED 413 162-164 1992 PME 16 New Hampshire ED 383 538 1993 PME 17 Japan ED 383 536 1994 PME 18 Portugal ED 383 537 PME 19 1995 Brazil ED 411 134-136 1996 PME 20 Spain SE 064 730-734 1997 PME 21 Finland ED 416 082-084 1998 PME 22 South Africa ED 427 969 PME 23 1999 Israel ED 436 403 2000 PME 24 Japan ED 452 031-034 9 vii