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CANADIAN MATHEMATICS EDUCATION

STUDY GROUP

GROUPE CANADIEN D'ÉTUDE EN DIDACTIQUE

DES MATH

ÉMATIQUES

PROCEEDINGS / ACTES

2010

ANNUAL MEETING /

RENCONTRE ANNUELLE 2010

Simon Fraser University

May 21

- May 25, 2010

EDITED BY:

Peter Liljedahl, Simon Fraser University

Susan Oesterle, Simon Fraser University

Darien Allan, Simon Fraser University

Proceedings of the 2010

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 2011 in Burnaby, BC.

iii

PROCEEDINGS OF THE 2010 ANNUAL MEETING OF THE

CANADIAN MATHEMATICS

EDUCATION STUDY GROUP / ACTES

DE LA RENCONTRE ANNUELLE 2010 DU GROUPE CANADIEN

D'ÉTUDE EN DIDACTIQUE DES MATHÉMATIQUES

34
th

Annual Meeting

Simon Fraser

University

May 21

- May 25, 2010

CONTENTS / TABLES DE

S MATIÈRES

vii Acknowledgements / Remerciements ix Schedule / Horaire

ELAINE SIMMT xi Introduction

PLENARY LECTURES / CONFÉRENCES

PLÉNIÈRES

WILLIAM BYERS

3 Ambiguity and Mathematical Thinking

MARTA CIVIL 13 Learning From and With Parents: Resources for Equity in

Mathematics Education

BERNARD R. HODGSON 31 Collaboration et échanges internationaux en éducation mathématique dans le cadre de la CIEM : regards selon une perspective canadienne

ICMI as a Space for International

Collaboration and Exchange in Mathematics Education: Some

Views From a Canadian Perspective

WORKING GROUPS / GRO

UPES DE TRAVAIL

CATHY BRUCE,

GENEVIÈVE LESSARD, &

LAURENT THEIS

53 A Teaching Mathematics to Special Needs Students: Who Is At-

Risk?

VEDA ABU-BAKARE,

LINDA GATTUSO, &

GEORGES MONETTE

63 B Attending to Data Analysis and Visualizing Data

iv

MIROSLAV LOVRIC,

OLIVIER TURCOTTE, &

WALTER WHITELY

73 C Recruitment, Attrition, and Retention in Post-Secondary

Mathematics

EDWARD DOOLITTLE,

LISA LUNNEY BORDEN,

& DAWN WISEMAN

81 D Can We Be Thankful for Mathematics? Mathematical

Thinking and Aboriginal Peoples

FRANCE CARON &

LEO JONKER

95 E Beauty in Applied Mathematics

EGAN J. CHERNOFF,

EVA KNOLL, &

AMI MAMALO 107 F Noticing and Engaging the Mathematicians in Our

Classrooms

TOPIC SESSIONS / SÉANCES THÉMATIQUES

FRÉDÉRIC GOURDEAU 123 Émotion, réflexion et action: mathématiques et enseignement / Doing, Feeling, Thinking Mathematics...in Teacher Preparation

NICHOLAS JACKIW &

NATHALIE SINCLAIR 137 On the Origins of Dynamic Number in the Breakdown of Structural, Metaphoric, and Historic Conceptions of Human Mathematics

NEW PHD REPORTS / PRÉSENTATIONS DE

THÈSES DE DOCTORAT

SOULEYMANE BARRY

149 Analysis of Resources Mobilized by a Teacher and Researcher in

Designing/Experimenting/Reflecting Upon Modelling Sequences Based on Elementary Combinatorics and Aimed at Introducing 7 th

Graders to Modelling

MARY BEISIEGEL

157
Being (Almost) a Mathematician: Teacher Identity Formation in

Post-Secondary Mathematics

EGAN J. CHERNOFF

165 Subjective Probabilities Derived from the Perceived Randomness of

Sequences of Outcomes

KRISTA FRANCIS-

POSCENTE

171 Learning to Play with Mathematics Online

NADIA HARDY 181 Students" Models of the Knowledge to Be Learned About Limits in College-Level Calculus Courses: The Influence of Routine Tasks and the

Role Played by Institutional Norms

ELIZABETH MOWAT 189 Making Connections: Network Theory, Embodied Mathematics, a nd Mathematical Understanding MARY STORDY 197 Recovering Mathematics: An Ontological Turn Toward Coming to Understand the Teaching of Mathematics with Children v

AD HOC SESSIONS / SÉANCES AD HOC

LORRAINE BARON 205 Who Teaches the Teachers? Challenging Our Practices RICHARD BARWELL 207 What Does Mathematics Education Have To Do With Climate

Change?

ANALIA BERGÉ

209 Construction du sens des objets mathématiques chez les élèves d"un

cours de mise à niveau PAVNEET BRAICH 211 The Study of Resilience in Mathematics Education ELIAS BRETTLER 213 What My Students Taught Me About Jim Totten"s Geometry

Problem in FLM

STEPHEN R. CAMPBELL 215 Social Interaction in a Virtual Environment: Fostering Online Communication and Collaboration in Mathematics Education

Research

SEAN CHORNEY,

EGAN J. CHERNOFF, &

PETER LILJEDAHL

217 Editing Mathematics Teachers" Journals in Canada: Bridging the

Gap Between Researchers

a nd Teachers SIMON KARUKU 219 Reasoning Demands in Mathematics Textbooks STEPHEN KHAN 221 Laughing @ Mathematics Education: Exploring Potentials of

Online Mathematics Comics (OMC)

f or Socially Just Pedagogies

KIM LEDGER-LANGEN 223 The Relocation Property

WES MACIEJEWSKI &

AMI MAMALO 225 Beyond the Superficial: Procedural Knowledge in University

Mathematics

JANELLE MCFEETORS,

RALPH MASON, &

ELAINE SIMMT

227 Inquiry Activities in High School Mathematics: Issues in Authoring

Curricular Products

AYOPO ODUNUGA

229 “I Don"t Understand What You Don"t Understand!": A Look at the

Phenomenon of “Not Understanding" in Mathematics Pedagogic

Situations

LYDIA OLADOSU &

OLIVE CHAPMAN

231 Geometric Reasoning: Developing Habits of Mind

TONY PASCUZZO

233 A Performance Assessment Approach to the Evaluation of

Mathematics Knowledge

f or Teaching ARMANDO P. PRECIADO 235 Teachers' Professional Development by Collaborative Design: Why

Does It Work?

vi KRISHNA SUBEDI 237 Reducing Abstraction: The Case of Logarithms AMANJOT TOOR 239 Identity of a Learner in an Undergraduate Mathematics

Programme

OLIVIER TURCOTTE 241 Rapport au savoir et service A.M.I. JOHN WIEST 243 Using Mathematical Proof to Enrich Conceptual Knowledge

APPENDICES /

ANNEXES

247 A Working Groups at Each Annual Meeting

253 B Plenary Lectures at Each Annual Meeting

257 C Proceedings of Annual Meetings

vii

ACKNOWLEDGEMENTS

/ REMERCIEMENTS The organisational work for our 2010 annual meeting at Simon Fraser University enabled us to have another memorab le meeting. Our local organisers, Peter Liljedahl, Rina Zazkis, Nathalie Sinclair, Sen Campbell, and Malgorzata Dubiel with exceptional help from Shiva Gol Tabaghi, Simin Chavoshi Jolfaee, Paulino Preciado, and Christian Bernèche, along with the rest of the SFU doctoral students, managed to do everything with utmost efficiency and pleasantness, and we thank them. We would also like to thank the Faculty of Education at SFU, the Vice President's office at SFU, PIMS, and MITACS for financial support for this conference. Finally, we extend our thanks to the guest speakers, working group leaders, topic session and ad hoc presenters, and all the participants for making the 2010 meeting a stimulating and worthwhile experience. L'organisation locale de notre rencontre annuelle de 2010 à l'Université Simon Fraser nous a permis d'avoir une autre rencontre mémorable. Nos organisateurs locaux,

Peter Liljedahl,

Rina Zazkis, Nathalie Sinclair, Sen Campbell, et Malgorzata Dubiel, avec le support exceptionnel de Shiva Gol Tabaghi, Simin Chavoshi Jolfaee, Paulino Preciado, et Christian

Bernèche, ainsi que les autres étudiants de doctorat à SFU, ont réussi à organiser la rencontre

avec une grande efficacité et nous les en remercions. Nous aimerions aussi remercier la Faculté d'éducation à SFU, le bureau du vice-président à SFU, PIMS, et MITACS pour l'appui financier qu'ils ont fourni à la conférence. De plus, nous aimerions remercier les

conférenciers invités, les animateurs de groupes de travail, les présentateurs de séances

thématiques et d'ateliers ad hoc, ainsi que tous les participants pour avoir fait de la rencontre

2010 une expérience stimulante et mémorable.

ix

Horaire

Vendredi

21 mai Samedi

22 mai Dimanche

23 mai Lundi

24 mai Mardi

25 mai

Activité pré

colloque

8:30 - 4:00

Conférence

Changer la Culture

12:00 - 3:00

Un t our du laboratoire de Sen

Campbell

1:00 - 4:00

Inscription

8:00 - 9:00

Inscription

8:30 - 9:30

Séance thématique

9:00 - 10:30

Groupes de travail 9:00 - 10:30

Groupes de travail 9:00 - 10:30

Groupes de travail

9:45 - 10:45

Plénière 4

Dawson

10:30 - 11:00

Pause café

10:30 - 11:00

Pause café

10:30 - 11:00

Pause café

10:45 - 11:15

Pause café

11:00 - 12:30

Groupes de travail 11:00 - 12:30

Groupes de travail 11:00 - 12:30

Groupes de travail

11:15 - 12:30

Session de clôture

12:30 - 1:30

DÎNER

12:30 - 1:30

DÎNER

12:30 - 1:30

DÎNER

1:30 - 2:00

Discussion de la

plénière 1 en petit groupe

1:30 - 2:30

Plénière 2

Civil

1:30 - 2:00

Discussion de la

plénière 2 en petit groupe

2:00 - 3:00

Discussion de la

plénière 1 2:00 - 3:00

Discussion de la

plénière 2

2:45 - 3:15

Nouvelles thèses (3)

3:00 - 3:30

Pause café

3:00 - 3:30

Pause café

3:15 - 3:45

Pause café

3:30 - 4:00

Nouvelles thèses (1) 3:30 - 4:00

Séances ad hoc (2)

3:45 - 4:45

Plénière 3

Hodgson

4:00 - 5:00

Plénière 1

Byers

4:15 - 4:45

Nouvelles thèses (2) 4:15 - 4:45

Séances ad hoc (3)

5:00 - 6:00

Session d'ouverture

5:00 - 5:30

Séances ad hoc (1)

5:00 - 11:00

Souper croisière

5:00 - 6:00

Assemblée générale

annuelle

Souper libre

6:00 - 9:00

Réception

6:00 - 9:00

Repas x

Schedule

Friday

May 21 Saturday

May 22 Sunday

May 23 Monday

May 24 Tuesday

May 25

Pre-conference

Activities

8:30 - 4:00

Changing the

Culture Conference

12:00 - 3:00

Tour of Sen

Campbell's Lab

1:00 - 4:00

Registration

8:00 - 9:00

Registration

8:30 - 9:30

Topic Session

9:00 - 10:30

Working Groups 9:00 - 10:30

Working Groups 9:00 - 10:30

Working Groups

9:45 - 10:45

Plenary 4

Dawson

10:30 - 11:00

Coffee Break

10:30 - 11:00

Coffee Break

10:30 - 11:00

Coffee Break

10:45 - 11:15

Coffee Break

11:00 - 12:30

Working Groups 11:00 - 12:30

Working Groups 11:00 - 12:30

Working Groups

11:15 - 12:30

Closing Session

12:30 - 1:30

Lunch

12:30 - 1:30

Lunch

12:30 - 1:30

Lunch

1:30 - 2:00

Plenary 1

- Small

Group Discussion 1:30 - 2:30

Plenary 2

Civil

1:30 - 2:00

Plenary 2

- Small

Group Discussion

2:00 - 3:00

Plenary 1

- Q&A 2:00 - 3:00

Plenary 2

- Q&A

2:45 - 3:15

New PhD

s (3)

3:00 - 3:30

Coffee Break

3:00 - 3:30

Coffee Break

3:15 - 3:45

Coffee Break

3:30 - 4:00

New PhD

s (1) 3:30 - 4:00

Ad Hoc (2)

3:45 - 4:45

Plenary 3

Hodgson

4:00 - 5:00

Plenary 1

Byers

4:15 - 4:45

New PhD

s (2) 4:15 - 4:45

Ad Hoc (3)

5:00 - 6:00

Opening Session

5:00 - 5:30

Ad Hoc (1)

5:00 - 11:00

Dinner Cruise

5:00 - 6:00

AGM

Dinner on Own

6:00 - 9:00

Reception

6:00 - 9:00

Dinner

xi

INTRODUCTION

Elaine Simmt - President, CMESG/GCEDM

University of Alberta

For more than thirty years mathematics

educators (teachers, mathematicians, teacher educators, and educational researchers) have met annually in one of our Canadian public universities to engage in scholarly discussion and debates about mathematics education. Last year Simon Fraser University hosted the Canadian Mathematics Education Study Group. The vibrant group of SFU mathematics educators, Peter Liljedahl, Rina Zazkis, Nathalie Sinclair,

Sen Campbell, and

their SFU graduate students, Shiva Gol Tabaghi, Simin Chavoshi Jolfaee, Christian Bernèche, Paulino Preciado, Darien Allan, and Sean Chorney, hosted a wonderful meeting for some 120 delegates. Delegates had the privilege to learn about our history as an organisation from former SFU professor and CMESG Elder, Sandy Dawson. We also heard about the history of the International Congress on Mathematics Instruction from another of our CMESG Elders, Bernard Hodgson. As former Secretary General of ICMI he was able to call out the names of our community members who have provided service on our behalf to the international community of mathematics educators.

Our gratitude goes out to Bernard and

Sandy for their sharing.

Without the stories of our history we would have no memory from which to connect our past, present and future. The SFU conference is now another piece of our history and the document you are now reading serves as an important record of our work. In it is an account of the proceedings of our annual conference, as told by the people who took leadership roles in the scientific program. So, rather than try to provide a summary of the meeting, please indulge me as I share my recollections of the meeting with a top ten list. I know that I have been to a good conference when:

10) I am challenged to give up my certainty about mathematics and mathematics learning,

and embrace ambiguity, paradox and creativity;

9) I am challenged to give up my preconceived notions that as a teacher I am an exclusive

holder of mathematics knowledge, and to make space for parents and community to contribute to the mathematics education of their children and youth;

8) I see six interesting topics for working groups and I try to sneak into a different one

after each break;

7) I only have to choose between two topic groups and no matter which one I choose it

will be a great choice;

6) The new PhDs make the old PhDs look—well, old!

xii 5) At the breakfast table I make space for a newcomer only to learn that he is a football player and isn"t attending the conference—but he liked his math teacher;

4) The guitars and the accordion come out on the cruise ship;

3) There is no pizza place open on Burnaby Mountain late at night but there is someone

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