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01 Front Matter CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D’ÉTUDE EN DIDACTIQUE DES MATHÉMATIQUES PROCEEDINGS / ACTES 2004 ANNUAL MEETING Université Laval May 28 – June 1, 2004 EDITED BY: Elaine Simmt, University of Alberta Brent Davis, University of Alberta CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D’ÉTUDE EN DIDACTIQUE DES MATHÉMATIQUES PROCEEDINGS / ACTES 2004 ANNUAL MEETING Université Laval May 28 – June 1, 2004 EDITED BY: Elaine Simmt, University of Alberta Brent Davis, University of Alberta Proceedings of the 2004 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 2005 in Edmonton, AB. Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group / Groupe Canadien d’Étude en Didactique des Mathématiques 28th Annual Meeting Université Laval May 28 – June 1, 2004 Contents / Table des matières v Remerciements vii Schedule FRÉDÉRIC GOURDEAU ix Introduction Plenary Lectures / Conférences plénières CLAIRE MARGOLINAS 3 La situation du professeur et les connaissances en jeu au cours de l’activité mathématique en classe NICOLAS BOULEAU 23 La personnalité d’Evariste Galois : le contexte psychologique d’un goût prononcé pour les mathématiques abstraites Working Groups / Groupes de travail NATHALIE SINCLAIR, ANNE 45 A • Learner-Generated Examples WATSON, & RINA ZAZKIS TOM O’SHEA & PETER TAYLOR 55 B • Transition to University Mathematics FRANCE CARON & 63 C • L’intégration de l’application et de la modélisation dans les mathé- ERIC MULLER matiques au secondaire et au collégial / Integrating Applications and Modelling in Secondary and Postsecondary Mathematics ANN KAJANDER & 81 D • Elementary Teacher Education: Defining the Crucial JEAN DIONNE Experiences GEOFF ROULET & 87 E • La technologie dans l’enseignement des mathématiques : ANDRÉ BOILEAU regard critique sur le discours et la pratique / A Critical Look at the Language and Practice of Mathematics Education Topic Sessions / Sessions thématiques RENÉE CARON 99 L’enseignement des probabilités dans les écoles primaires du Québec DAVE HEWITT 105 Feedback LUIS RADFORD 111 Body, Tool, and Symbol: Semiotic Reflections on Cognition STEVE THORNTON 119 Standards for Excellence in Teaching Mathematics iii New PhD Reports / Présentations de thèses de doctorat PETER LILJEDAHL 129 The AHA! Experience: Mathematical Contexts, Pedagogical Implications LAURENT THEIS 135 The Issues of Learning the Equals Sign for Grade 1 Students Ad Hoc Sessions / Séances ad hoc A. J. (SANDY) DAWSON 145 Measuring the Impact of a Mentor Program DOUGLAS MCDOUGALL 147 Ten Dimensions of Mathematics Education—A Framework for Improving Mathematics TOM STEINKE & 149 To JUMP or not to JUMP STEWART CRAVEN KALIFA TRAORÉ, CAROLINE 151 Undergraduate Students’ Errors That May Be Related to LAJOIE, & ROBERTA MURA Confusing a Set with Its Elements DAVID WAGNER 153 Expressing Mathematical Fluency Panel Discussion / Table Rond DAVID A. REID 157 What is Canadian about Canadian Mathematics Education? / La didactique des mathématiques au Canada se distingue-t-elle de ce qui se fait ailleurs dans le monde ? ERIC MULLER 165 What are the Issues and Problems Facing Mathematical Education in Canada? THOMAS E. KIEREN 169 Unique Features of the Body of Mathematics Education in Canada: A Brief Sketch Appendices 173 A • Working Groups at Each Annual Meeting 177 B • Plenary Lectures at Each Annual Meeting 181 C • Proceedings of Annual Meetings 183 D • List of Participants iv Remerciements Le travail d’organisation de la rencontre annuelle de 2004 à l’Université Laval a été couronné d’un grand succès. Caroline Lajoie, coordonnatrice des rencontres annuelles au sein de l’exécutif du groupe, y est pour beaucoup. Sur le plan local, nous remercions Bernard R. Hodgson et Frédéric Gourdeau, qui ont su organiser la rencontre annuelle avec efficacité et entrain, Sylvie Drolet, qui a fourni un appui technique impeccable, ainsi que Jean-Lou De Carufel, Jean-François Maheux et Luc Tremblay, les trois étudiants qui ont aidé à ce que tout se déroule sans mauvaise surprise. Les éditeurs voudraient remercier (en français !) Jérôme Proulx pour l’aide fournie à la vérification des documents écrits en français. v Schedule Vendredi/ Samedi/ Dimanche/ Lundi/ Mardi/ Friday Saturday Sunday Monday Tuesday May 28 mai May 29 mai May 30 mai May 31 mai June 01 juin 1234567890123 1234567890123 1234567890123 9h00–9h30 1234567890123 1234567890123 New PhDs/Thèses 1234567890123 1234567890123 1234567890123 1234567890123 9h30–11h00 1234567890123 1234567890123 Table ronde/Panel 1234567890123 1234567890123 09h00–12h15 Matin/ 1234567890123 Groupes de travail / Working Groups Morning1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 12345678901234 1234567890123 1234567890123 11h30–12h30 1234567890123 1234567890123 Séance de cloture/ 1234567890123 1234567890123 Closing Session 1234567890123 12345678901234 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 Bouleau 12345678901234 14h30–15h30 14h30–15h30 12345678901234 12345678901234 Discussion de/of 14h45–15h15 Discussion de/of 12345678901234 Après- 12345678901234 Ad Hocs midi/ 14h30–16h30 Margolinas 12345678901234 Bouleau 12345678901234 1234567890123451234567890123412345678901234512345678901234 After- Registration/ 1234567890123415234567890123142345678901234152345678901234 1234567890123415234567890123142345678901234152345678901234 noon Inscription 1234567890123451234567890123412345678901234512345678901234 12345678901234 16h00–16h30 12345678901234 12345678901234 1234567890123 Ad Hocs 12345678901234 1234567890123 12345678901234 16h00–18h00 12345678901234 12345678901234 16h45–17h45 Groupes thématiques/ 16h30–18h00 12345678901234 12345678901234 Cocktails Topic Groups AGA / AGM 12345678901234 GDM/CMESG 12345678901234 12345678901234 15h30– 12345678901234 Excursion 12345678901234 17h45–18h45 18h00–18h30 12345678901234 12345678901234 Souper/Supper New PhDs/Thèses 18h00– 12345678901234 12345678901234 Excursion 12345678901234 18h45–19h30 12345678901234 to/au 12345678901234 Opening 18h30–20h00 Manoir 12345678901234 12345678901234 Soir/ BBQ Montmorency 12345678901234 19h30–20h30 12345678901234 Evening 12345678901234 Conférence 1/ 12345678901234 12345678901234567890123456789012123456789012345678901234 Plenary 1: 12345678901234567890123456789012123456789102345678901234 Margolinas 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 20h30 12345678901234567890123456789012123456789102345678901234 12345678901234567890123456789012123456789102345678901234 Reception 12345678901234567890123456789012123456789012345678901234 vii Introduction Frédéric Gourdeau - Président, CMESG/GCEDM Université Laval La rencontre annuelle 2004 du GCEDM/CMESG a permis de poursuivre la tradition d’excellence établie au fil des ans. La richesse des échanges et le plaisir manifeste que nous avons eus à travailler ensemble ont fait de cette rencontre une grande réussite. Le contenu des Actes vous permettra d’en apprécier la valeur. La rencontre 2004 avait une saveur particulière : tenue dans la ville de Québec, la présence francophone y était plus marquée qu’à l’habitude. Ainsi, avant même le début de la rencontre annuelle, les membres étaient conviés à des échanges avec le GDM (Groupe de Didactique des Mathématiques du Québec). En effet, l’exécutif avait réussi à organiser la rencontre annuelle en collaboration avec le GDM, ce qui a permis une plus grande partici- pation des membres du GDM aux activités de GCEDM. La conférence de Jacques Bélair, donnée dans le cadre de la rencontre du GDM, ainsi que le conférence d’ouverture de la rencontre annuelle du GCEDM, donnée par Claire Margolinas, étaient ouvertes aux membres des deux groupes. Les échanges fructueux qui ont suivi, agrémentés d’un cocktail offert conjointement par la Faculté des Sciences de l’éducation et par la Faculté des sciences et de génie de l’Université Laval, sont un témoignage de l’intérêt d’une telle initiative. France Caron, pour le GDM, et Caroline Lajoie, pour le GCEDM, sont les principales responsables de cette belle réussite, et nous les en remercions. Of course, the cultural impact of a meeting in Québec was not only visible in the larger participation by francophones at our meeting: it also manifested itself in the importance given to the evening meals which occupied us for many hours each day, and to the singing which accompanied two of those meals. Thanks to everyone for so playfully taking part in those activities. En ce qui a trait au contenu des échanges que nous avons eus, je ne peux tous les commenter. Je peux certainement souligner les contributions de nos deux brillants conférenciers pléniers, Claire Margolinas et Nicolas Bouleau, ainsi que les réflexions de Claude Gaulin, Tom Kieren, Eric Muller et David Reid lors du panel du mardi matin. En ce qui a trait aux
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