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Front Matter.1.1 CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D’ETUDE´ EN DIDACTIQUE DES MATHEMATIQUES´ PROCEEDINGS / ACTES 2003 ANNUAL MEETING Acadia University May 30 – June 3, 2003 EDITED BY: Elaine Simmt, University of Alberta Brent Davis, University of Alberta CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D’ETUDE´ EN DIDACTIQUE DES MATHEMATIQUES´ PROCEEDINGS / ACTES 2003 ANNUAL MEETING Acadia University May 30 – June 3, 2003 EDITED BY: Elaine Simmt, University of Alberta Brent Davis, University of Alberta Proceedings of the 2003 Annual Meeting of the Canadian Mathematics Education Study Group / Groupe Canadien d’Étude en Didactique des Mathématiques are published by CMESG/GCEDM. They were printed in April 2004 in Edmonton, AB. Proceedings of the 2003 Annual Meeting of the Canadian Mathematics Education Study Group / Groupe Canadien d’Etude´ en Didactique des Mathématiques 27th Annual Meeting Acadia University May 30 – June 3, 2003 Contents / Table des matières v Acknowledgements vii Schedule MALGORZATA DUBIEL ix Introduction xi Special Announcement: Zoltan Dienes, Extraordinary Member of CMESG/GCEDM Plenary Lectures / Conférences plénières TOM ARCHIBALD 3 Using History of Mathematics in the Classroom: Prospects and Problems ANNA SIERPINSKA 11 Research in Mathematics Education Through a Keyhole Working Groups / Groupes de travail LOUIS CHARBONNEAU 39 A •L’histoire des mathématiques en tant que levier pédagogique & IRENE PERCIVAL au primaire et au secondaire / The History of Mathematics as a Pedagogic Tool in Grades K–12 FLORENCE GLANFIELD, LOUISE 55 B • Teacher Research: An Empowering Practice? POIRIER, & VICKI ZACK MIROSLAV LOVRIC 69 C • Images of Undergraduate Mathematics & DAVID POOLE WALTER WHITELY 79 D • A Mathematics Curriculum Manifesto & BRENT DAVIS Topic Sessions / Sessions thématiques MALGORZATA DUBIEL 87 A Report on the Canadian School Mathematics Forum 2003 ZOLTAN DIENES 91 The Theory of Six Stages in Learning with Integers JO TOWERS 103 Exploring the Fragility and Robustness of Students’ Mathematical Understanding JOHN GRANT McLOUGHLIN 111 The Role of Mathematics Contests iii New PhD Reports / Présentations de thèses de doctorat FRANCE CARON 119 Effects of Secondary Education on Mathematical Competencies: An Exploratory Study ALEX LAWSON 125 Documenting the Nature and Degree of Reform Instruction in the Intermediate Classroom JOYCE MGOMBELO 131 Mathematics Content-Pedagogy Knowledge: A Psychoanalytic and Enactivist Approach EILEEN PHILLIPS 139 Classroom Explorations of Mathematical Writing with Nine- and Ten-Year-Olds Ad Hoc Sessions / Séances ad hoc RINA COHEN 147 Empowering Math-Anxious, Upper Elementary Teachers in Over- coming Their Anxiety and Improving Their Teaching: An Explor- atory Study GARY FLEWELLING 149 MOM, Sense Making and Rich Learning Tasks RICHARD HOSHINO 151 A “Proof” that all Triangles are Equilateral: Drawing out the Math- ematics from a Rich Investigative Problem IMMACULATE NAMUKASA 153 Multiple Meanings: Why Should We Encourage Their Use? Panel Discussion / Table Rond NADINE BEDNARZ 157 New Curriculum in Mathematics in Quebec: Continuities, Changes and Challenges / Nouveau curriculum d’études en mathématiques au Québec: Continuités et changements, questions qui se posent STEWART CRAVEN 165 Excerpts: The State of Mathematics Education in Ontario—Where We Came From and Where We Are in March, 2003 DONNA KARSTEN 171 Atlantic Canada Mathematics Curriculum and Nova Scotia Implementation TOM O’SHEA 175 Mathematics Curriculum in Canada Appendices 181 A • Working Groups at Each Annual Meeting 185 B • Plenary Lectures at Each Annual Meeting 189 C • Proceedings of Annual Meetings 191 D • List of Participants iv Acknowledgements On behalf of the members, the CMESG/GCEDM Executive would like to take this opportu- nity to thank our local hosts for their contributions to the 2003 Annual Meeting and Confer- ence. Specifically thank you to: David Reid, chair of the local organising committee; Jeff Hooper, treasurer; Debbie Boutilier, excursions; Sarah Perkins & Tony Wile, technical assis- tance, registrations, etc.; Richard Hoshino, transport; and Glen MacDuff, umbrellas. Supplementary materials to some of the contributions in these Proceedings are posted on the CMESG/GCEDM website (http://www.cmesg.math.ca), maintained by David Reid. The editors gratefully acknowledge the permission to reprint the following images and text: · The image of Napier’s Rods on page 45 is used by permission of the AIMS Education Foundation (Fresno, CA; http://www/aimseduorg; 1.888.733.2467). · The images in Appendices 1 & 2 of the Report of Working Group A (pp. 52–54) are re- printed with the permission of Dover, publishers of D.E. Smith’s The History of Mathemat- ics, Volume II. · The text on pages 76–77 is reprinted with the permission of Pbilosophy of Mathematics Edu- cation Journal (http://www.ex.ac.uk/~PErnest/pome11/art6htm). ·Simon’s Model of the Integrated Mathematics Teaching Cycle on page 126 is reprinted with the permission of Martin Simon. v Schedule Vendredi/ Samedi/ Dimanche/ Lundi/ Mardi/ Friday Saturday Sunday Monday Tuesday May 30 mai May 31 mai June 01 juin June 02 juin June 03 juin 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 1234567890123 9h00–11h00 1234567890123 1234567890123 Table rond/Panel 1234567890123 1234567890123 09h00–12h15 Discussion Matin/ 1234567890123 1234567890123 Groupes de travail / Working Groups 12345678901234 Morning1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 1234567890123 11h30–12h30 1234567890123 1234567890123 Séance de cloture/ 1234567890123 1234567890123 12345678901234Closing Session 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12h15–13h45 12345678901234 1234567890123 12345678901234 1234567890123 Dîner / Lunch 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 13h45–14h30 13h45–14h45 13h45–14h30 12345678901234 1234567890123 12345678901234 1234567890123 Petits groupes/ Conférence 2/ Petits groupes/ 12345678901234 1234567890123 12345678901234 1234567890123 Small Groups Plenary 2: Small Groups 12345678901234 1234567890123 12345678901234 1234567890123 Sierpinska 12345678901234 1234567890123 14h30–15h30 14h30–15h30 12345678901234 1234567890123 14h45–15h45 12345678901234 Aprés- 1234567890123 Discussion de/of Discussion de/of 12345678901234 1234567890123 Archibald Groupes thématiques/ Sierpinska 12345678901234 midi/ 1234567890123123456789012345 12345678901234512345678901234 12345678901234123456789012345 Topic Groups 12345678901234152345678901234 After- 15h30–16h30 1234567890123415234567890123142345678901234152345678901234 noon 12345678901234512345678901231234567890123454 12345678901234 Registration/ 12345678901234 12345678901234 12345678901234 12345678901234 Inscription 16h00–17h00 12345678901234 12345678901234 Groupes thématiques/ 16h00–17h30 12345678901234 16h15–17h15 12345678901234 16h30–17h30 Topic Groups AGA / AGM 12345678901234 Ouverture/ New PhDs/Thèses 12345678901234 12345678901234 Opening Session 17h00–18h30 12345678901234 12345678901234 Teacher Workshops 12345678901234 12345678901234 ou/or Grand Pré 17h30–18h30 12345678901234 17h30–19h00 12345678901234 Grand Pré Ad Hocs 12345678901234 Souper/Supper 12345678901234 12345678901234 12345678901234 12345678901234 12345678901234 18h30–20h00 12345678901234 19h00–20h00 12345678901234 Soir/ Conférence 1/ Souper/Supper 12345678901234 12345678901234 Evening Plenary 1: 12345678901234 12345678901234 Archibald 12345678901234567890123456789012123456789012345678901234 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 20h00 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 Dessert & Social 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789012345678901234 vii Introduction Malgorzata Dubiel - President, CMESG/GCEDM Simon Fraser University It is my great pleasure to write an introduction to the CMESG/GCEDM Proceedings from the 2003 meeting, held at Acadia University in Wolfville, Nova Scotia. Alas, this volume cannot possibly convey the spirit of the meeting it reports on. It can merely describe the content of activities without giving much of the flavour of the process. Therefore, this introduction will attempt to tell you a little about our organization, and about our meetings. CMESG/GCDEM is unlike other professional organizations: One belongs to it not because of who one is professionally, but because of one’s interests. And that is why our members come from mathematics departments and faculties of education, from universi- ties and colleges, and from schools and other educational institutions. What unites them is an interest in mathematics and how it is taught at every level, and a desire to make teaching more exciting, more relevant, and more meaningful. Our meetings are unique, too. One does not simply attend a CMESG meeting the way one attends other professional meetings, by coming to listen to a few chosen talks. You are immediately part of it; you live and breathe it. And, even though the format, embedded in tradition, does not change much from year to year, there are
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