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CANADIAN MATHEMATICS EDUCATION

STUDY GROUP

GROUPE CANADIEN D'ÉTUDE EN DIDACTIQUE

DES MATHÉMATIQUES

PROCEEDINGS / ACTES

2012 ANNUAL MEETING /

RENCONTRE ANNUELLE 2012

Université Laval

May 25 May 29, 2012

EDITED BY:

Susan Oesterle, Douglas College

Darien Allan, Simon Fraser University

Peter Liljedahl, Simon Fraser University

Proceedings of the 2012 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 May 2013 in Burnaby, BC.

ISBN: 978-0-86491-343-2

iii

PROCEEDINGS OF THE 2012 ANNUAL MEETING OF THE

CANADIAN MATHEMATICS EDUCATION STUDY GROUP / ACTES

DE LA RENCONTRE ANNUELLE 2012 DU GROUPE CANADIEN

D'ÉTUDE EN DIDACTIQUE DES MATHÉMATIQUES

36th Annual Meeting

Université Laval

May 25 May 29, 2012

CONTENTS / TABLES DES MATIÈRES

ELAINE SIMMT ix Introduction

xi Schedule / Horaire

PLENARY LECTURES / CONFÉRENCES

PLÉNIÈRES

MARGARET WALSHAW 3 Towards an Understanding of Ethical Practical Action in Mathematics Education: Insights from Contemporary Inquiries PAULUS GERDES 13 Old and New Mathematical Ideas from Africa: Challenges for

Reflection

ELDER TALK / LA PAROLE AUX ANCIENS

WILLIAM HIGGINSON 37 Cooda, Wooda, Didda, Shooda: Time Series Reflections on

CMESG/GCEDM

PANEL ELAINE SIMMT 47 Panel Introduction: What is Fundamental Mathematics for

Learners?

DARIEN ALLAN 49 What is Fundamental in Mathematics? RALPH MASON 53 What is Fundamental Mathematics for Learners? RUTH BEATTY 55 What is Fundamental Mathematics for Primary/Junior Learners? iv PETER TAYLOR 59 What it is Important for the Students to LearnAt the Post-

Secondary Level (and Arguably at Any Level)

HÉLÈNE PARADIS

61
/ What Mathematics are Considered to be Essential to Students Throughout Their

Learning Process?

WORKING GROUPS / GROUPES DE TRAVAIL

FRANCE CARON &

PETER LILJEDAHL

71 A y Numeracy: Goals, Affordances, and Challenges

BEVERLY CASWELL &

DAVID WAGNER

81 B y Diversities in Mathematics and their Relation to Equity

CHANTAL BUTEAU &

NATHALIE SINCLAIR

95 C y Technology and Mathematics Teachers (K-16) / La

(K-16)

DAVID REID &

DENIS TANGUAY

101 D y La preuve en mathématiques et en classe / Proof in

Mathematics and in Schools

PETER APPELBAUM &

SUSAN GEROFSKY

115 E y The Role of Text/books in the Mathematics Classroom / Le

rôle des manuels scolaires dans la classe de mathématiques

HASSANE SQUALLI,

CHRIS SUURTAMM, &

VIKTOR FREIMAN

125 F y Preparing Teachers to Develop Algebraic Thinking in Primary

and Secondary School / Préparer les enseignants au développement de la pensée algébrique au primaire et au secondaire

TOPIC SESSIONS / SÉANCES THÉMATIQUES

MIROSLAV LOVRIC 139 Collaboration Between Research in Mathematics Education and Teaching Mathematics: Case Study of Teaching Infinity in

Calculus

LOUIS CHARBONNEAU &

DAVID GUILLEMETTE

147 Dialogue sur la lecture de textes historiques dans la classe de

mathématiques / Dialogue on Reading Original Texts in the

Mathematics Classroom

v

NEW PHD REPORTS / PRÉSENTATIONS DE

THÈSES DE DOCTORAT

BEVERLY CASWELL 161 Teaching Toward Equity in Mathematics ELENA HALMAGHI 171 Inequalities in the History of Mathematics: From Peculiarities to a

Hard Discipline

MANON LEBLANC 179 The Study of On-line Situations of Validation Experienced by 13- and 14-year-old Students With and Without the Aid of an Electronic Forum GENEVIÈVE LESSARD 187 Institutional Acculturation of the Researcher, Teacher, and Secondary 1 Students with Learning Difficulties in Problem

Situations Involving Rational Numbers

action didactique conjointe de lenseignant,

JEAN-FRANÇOIS

MAHEUX

199 Mathematics Education: An Aporetic of Epistemology, Language

and Ethics SUSAN OESTERLE 209 Diverse Perspectives on Living the

Tensions

ARMANDO PAULINO

PRECIADO BABB

217 Conversations Held and Roles Played During Mathematics

OANA RADU 225 The Ordinary Yet Extraordinary Emotions and Motives of

Preservice Mathematics Teachers

MIREILLE SABOYA 233 -construite

Development and Analysis of a Didactic Intervention, Co- constructed Between Researcher and Teacher For the Development of a Control of the Mathematical Activity Among High School

Students

AD HOC SESSIONS / SÉANCES AD HOC

OLIVE CHAPMAN &

MARGARET WALSHAW

243 Publishing in the Journal of Mathematics Teacher Education

TARAS GULA 245 Is It Possible to Measure the Effectiveness of a Specific Approach to Teaching Foundations Mathematics in a Post-Secondary Setting? / Est- secondaire ? vi LIONEL LACROIX 247 Challenges in Supporting Mathematics Teachers to Develop Their

Teaching Practices

JEAN-FRANÇOIS

MAHEUX

249 Rapport sur le ad hoc éthique et éducation mathématique / Report

on the Ethics & Mathematics Education Ad Hoc VEDA ROODAL PERSAD 251 Reading Biographies and Autobiographies of Mathematicians: What Do They Tell Us About the Subject of Mathematics? GEOFFREY ROULET 253 Online Environments for Mathematics Sharing and Collaboration PETER TAYLOR 255 Ad Hoc Session on Planning for the Next Canadian Math Education

Forum (CMEF) to be Held in May 2014

MATHEMATICS GALLERY / GALLÉRIE

MATHÉMATIQUE

SEAN BEAUDETTE,

ALEXANDRA PENN, &

GEOFFREY ROULET

259 and

Mathematics Teaching

LAURA BROLEY 261 Gearing Up For Grade 9: A Learning Object

DALIA CHALLITA &

NADIA HARDY

263 of the Role of Theory and Examples in

College Level Mathematics

LUCIE DEBLOIS 265 Une expérimentation de pratiques gagnantes en enseignement des mathématiques / An Experiment with Successful Practices in

Mathematics Teaching

JILL LAZARUS &

GEOFFREY ROULET

267 Blended Mathematical Collaboration Using a Wiki, Geogebra and

Jing

JEAN-FRANÇOIS

MAHEUX &

FABIENNE VENANT

269 Some Things Technologies Can Tell Us About Technologies: An

Instrumented Analysis of Two Successive Mathematics Curricula

TOD L. SHOCKEY &

SIBYLLE WECK-

SCHWARZ

271 Investigating the Teaching Practices of a Group of Mathematics

Graduate Students

DIANE TEPYLO, JOAN

MOSS, CATHERINE

BRUCE, TARA FLYNN,

DIANA CHANG, &

ZACHARY HAWES

273 Mathematics For Young Children: Exploring What is Possible in

Early Mathematics Education?

JOSIANNE TRUDEL 275 -apprentissage en lien

avec le métier du scénograp mathématique des élèves du 1er cycle du secondaire vii

APPENDICES / ANNEXES

279 A y Working Groups at Each Annual Meeting

285 B y Plenary Lectures at Each Annual Meeting

289 C y Proceedings of Annual Meetings

ix

INTRODUCTION

Elaine Simmt President, CMESG/GCEDM

University of Alberta

Each year our membership comes together to interact with each other around a variety of mathematics education interests, challenges and (of course) problems (math problems, that is). Thi important conversations. For me, highlights of the meeting emerged from the formal program, my time in a working group, dinner conversations and two excellent plenaries. It was with great pleasure that I sat with Paulus Gerdes (and my Canadian colleagues) at dinner, where we experienced stimulating conversation and absolutely wonderful wine and cheese. The evening with Gerdes left me inspired to think more about mathematics for the particular cohort of mathematics teachers after independence and how he and his colleagues began by asking those first candidates what mathematics was for them. Margaret Walshaw asked a similar question of the teacher candidates she worked with, trying to understand mathematics identity. Both of our keynotes then, one explicitly and the other implicitly, reminded all of us of the reciprocal relationship between personal identity and cultural mathematics and how each shapes the other. Although I attended the Proof in Mathematics and in Schools working group, and really appreciated the experience that our co-leaders facilitated, I know that there were a number of other working groups (Numeracy: Goals, Affordances, and Challenges; Diversities in Mathematics and their Relation to Equity; Technology and Mathematics Teachers (K-16); The Role of Text/books in the Mathematics Classroom; and Preparing Teachers to Develop Algebraic Thinking in Primary and Secondary School) that I would have enjoyed and from which I would have learned just as much. Topic group sessions by Lovric and Charbonneau & Guillemette provided members with an opportunity to think more about teaching infinity in calculus and reading original texts in mathematics. As well, the panel discussion offered us a diverse set of perspectives from which we could think more about the content that should be in our mathematics curriculum in Kindergarten through Baccalaureate programs. Finally, the program was kept fresh and relevant with the new PhD presentations, the ad hoc sessions and the presentations in the Math Gallery. Thanks to all of you who contributed to our program. The wine and cheese dinner was certainly a highlight for me, but I know that many of you enjoyed the other aspects of the local program as well. From the opening reception to our dinner out at Le Moulin de Saint-Laurent, our visit to Montmorency Falls and the night in Vieux-Québec, the local organizers knew just how to keep us fed and happy. On behalf of our executive and all of the conference participants, I would like to thank Frédéric Gourdeau and his incredibly helpful and pleasant math students, Marie-Pier Bédard, Simon B. Lavallé, and Sarah Mathieu-Soucy for their hospitality. Special thanks to Andréa Deschênes, Anick Lévesque-Gravel, Joannie Harvey, Malik Younsi, Jonathan Godin, Laurent Pelletier, and Emmanuelle Renauld for setting their mathematics aside long enough to serve at the opening reception and then again at the wine and cheese soirée. And, one last thank you to Lucie DeBlois who looked after the executive once the conference was over. xi

Horaire

Vendredi

25 mai

Samedi

26 mai

Dimanche

27 mai

Lundi

28 mai

Mardi

29 mai

8:45 10:15

Groupes de

travail

8:45 10:15

Groupes de

travail

8:45 10:15

Groupes de

travail

8:45 9:15

Nlles thèses (3)

9:20 9:50

Séances ad hoc

10:00 11:30

Panel

10:15 10:45

Pause café

10:30 11:00

Pause café

10:30 11:00

Pause café

10:45 12:15

Groupes de

travail

10:45 12:15

Groupes de

travail

10:45 12:15

Groupes de

travail

11:30 11:45

Pause café

11:45 12:30

Séance

de clôture

12:30 13:30

Dîner

12:30 13:30

Dîner

12:30 13:30

Dîner

13:30 14:45

Gallérie

mathématique

13:30 14:30

Plénière 2

13:30 14:00

Petits groupes

14:30 17:00

Inscription

Pavillon De

Koninck

15:00 16:30

Plénière GDM

15:30 16:20

Amis de FLM

14:00 15:00

Plénière 2 :

Séance questions

14:40 15:40

Séances

thématiques

15:00 15:30

Petits groupes

15:05 15:30

Séances ad hoc

15:30 16:00

Pause café

15:30 16:00

Pause café

16:00 16:50

Plénière 1 :

Séance questions

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