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CANADIAN MATHEMATICS EDUCATION GROUPE …

CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D TUDE EN DIDACTIQUE DES MATH MATIQUES PROCEEDINGS / ACTES 2015 ANNUAL MEETING / RENCONTRE ANNUELLE 2015 Universit de Moncton June 5 June 9, 2015 EDITED BY: Susan Oesterle, Douglas College Darien Allan, Simon Fraser University Proceedings of the 2015 Annual Meeting of the CANADIAN MATHEMATICS EDUCATION Study Group / GROUPE Canadien d tude en Didactique des Math matiques are published by CMESG/GCEDM. They were published online in May 2015. ISBN: 978-1-77287-003-9 iii PROCEEDINGS OF THE 2015 ANNUAL MEETING OF THE CANADIAN MATHEMATICS EDUCATION STUDY GROUP / ACTES DE LA RENCONTRE ANNUELLE 2015 DU GROUPE CANADIEN D TUDE EN DIDACTIQUE DES MATH MATIQUES 39th Annual Meeting Universit de Moncton June 5 June 9, 2015 CONTENTS / TABLES DES MATI RES OLIVE CHAPMAN vii Introduction ix Schedule / Horaire PLENARY LECTURES / CONF RENCES PL NI RES RIC RODITI 3 Diversit , variabilit et convergence des pratiques enseignantes / Diversity, Variabil

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1 CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D TUDE EN DIDACTIQUE DES MATH MATIQUES PROCEEDINGS / ACTES 2015 ANNUAL MEETING / RENCONTRE ANNUELLE 2015 Universit de Moncton June 5 June 9, 2015 EDITED BY: Susan Oesterle, Douglas College Darien Allan, Simon Fraser University Proceedings of the 2015 Annual Meeting of the CANADIAN MATHEMATICS EDUCATION Study Group / GROUPE Canadien d tude en Didactique des Math matiques are published by CMESG/GCEDM. They were published online in May 2015. ISBN: 978-1-77287-003-9 iii PROCEEDINGS OF THE 2015 ANNUAL MEETING OF THE CANADIAN MATHEMATICS EDUCATION STUDY GROUP / ACTES DE LA RENCONTRE ANNUELLE 2015 DU GROUPE CANADIEN D TUDE EN DIDACTIQUE DES MATH MATIQUES 39th Annual Meeting Universit de Moncton June 5 June 9, 2015 CONTENTS / TABLES DES MATI RES OLIVE CHAPMAN vii Introduction ix Schedule / Horaire PLENARY LECTURES / CONF RENCES PL NI RES RIC RODITI 3 Diversit , variabilit et convergence des pratiques enseignantes / Diversity, Variability, and Commonalities Among Teaching Practices DEBORAH HUGHES HALLET 17 Connections.

2 Mathematical, Interdisciplinary, Electronic, and Personal WORKING GROUPS / GROUPES DE TRAVAIL AMI MAMOLO & JOHN McLOUGHLIN 31 A Task Design and Problem Posing LISA LUNNEY BORDEN & FLORENCE GLANFIELD 37 B Indigenous Ways of Knowing in MATHEMATICS J R ME PROULX & ANNA SIERPINSKA 43 C Theoretical Frameworks in MATHEMATICS EDUCATION Research / Les cadres th oriques dans la recherche en didactique des math matiques ANN ANDERSON & HELENA P. OSANA 73 D Early Years Teaching, Learning and Research: Tensions in Adult-Child Interactions Around MATHEMATICS TARAS GULA & DENIS TANGUAY 87 E Innovations in Tertiary MATHEMATICS Teaching, Learning and Research / Innovations au post-secondaire pour l enseignement, l apprentissage et la recherche iv TOPIC SESSIONS / S ANCES TH MATIQUES RICHARD BARWELL 115 Some Thoughts on MATHEMATICS as the Alien Word PAUL DEGUIRE 123 Interaction Between a MATHEMATICS Department in a University and the School System / Interaction entre un d partement de math matiques universitaire et le syst me scolaire PETER LILJEDAHL 131 Building Thinking Classrooms.

3 Conditions for Problem Solving LYNDON MARTIN 139 Growing Mathematical Understanding and Folding Back: The Individual, the Collective, the Teacher SOPHIE REN DE COTRET 147 De la clochette de vigilance au changement de posture : Quelques questions issues de la didactique des math matiques et tudi es depuis la didactique du sens commun / From the Use of an Alert Bell to a Change of Posture: Some Questions Emerging from the Didactics of MATHEMATICS Being Studied by the Didactics of Common Sense NEW PHD REPORTS / PR SENTATIONS DE TH SES DE DOCTORAT ALEXANDER ANTROPOV 155 Secondary School MATHEMATICS Teacher Candidates Research, Pedagogical, and Content Knowledge RAQUEL ISABEL BARRERA CURIN 163 tude des significations de la multiplication pour diff rents ensembles de nombres dans un contexte de g om un aper u de quelques r flexions d ordre pist mologique LYS E-ROBERT CADET 173 The Role of Drawing in Arithmetic Word Problem Solving: Microanalysis of the Subject/Material Dialectic DAVID GUILLEMETTE 183 Histoire des math matiques dans la formation des enseignants du secondaire.

4 Une narration polyphonique sur la fragilit , l adversit et l empathie R sum de th se / History of MATHEMATICS in a Preservice Teacher s Training Context: A Polyphonic Narration on Fragility, Adversity and Empathy Thesis Summary JENNIFER HOLM 191 Improving MATHEMATICS Teaching Through Professional Learning Groups ASIA R. MATTHEWS 199 MATHEMATICS Problems and Thinking Mathematically in Undergraduate EDUCATION v P. JANELLE McFEETORS 207 Understanding Learning in MATHEMATICS Through the Metaphor of Authoring ELENA POLOTSKAIA 217 How Elementary Students Learn to Mathematically Analyze Word Problems: The Case of Addition and Subtraction SYLVAIN VERMETTE 227 Le concept de variabilit chez des enseignants de math matiques au secondaire AD HOC SESSIONS / S ANCES AD HOC DIANA ROYEA 237 Lesson and Learning Study: Collaborative Learning Structures for Preservice Teacher EDUCATION MATHEMATICS GALLERY / GALL RIE MATH MATIQUE ANN KAJANDER & JENNIFER HOLM 241 Hear My Voice.

5 Teachers Stories APPENDICES / ANNEXES 245 A Working Groups at Each Annual Meeting 253 B Plenary Lectures at Each Annual Meeting 257 C Proceedings of Annual Meetings vii INTRODUCTION Olive Chapman President, CMESG/GCEDM University of Calgary The 39th annual meeting of the CANADIAN MATHEMATICS EDUCATION Study Group/ GROUPE Canadien d tude en didactique des math matiques [CMESG/GCEDM-2015] was another highly memorable learning and social event! Our hosts at the Universit de Moncton made sure we were well fed, entertained, and accommodated. The excursion to the Bay of Fundy and the Hopewell Rocks allowed us to enjoy this natural wonder as we basked in the simple beauty of this land and seascape.

6 The conference dinner at the Plage Parlee Beach (which allowed some of us to also enjoy the ocean while getting our feet wet and sandy on the beach) was positively beyond expectation. Thanks to our colleagues Dr. Manon LeBlanc and Dr. Viktor Freiman for their time commitment and thoughtful planning and hosting of the conference. Manon s approach to encourage participants to engage with both languages throughout the conference was very successful in creating a welcomed bilingual atmosphere. Thanks to the other members of the organizing team and volunteers during the conference for their valuable contribution to the planning and smooth running of the conference: undergraduate and graduate students (who did a tremendous amount of work both before and during the meeting) Janelle Cormier, Mich le Cyr (better known as Mich le H bert during the she got married this summer!)

7 , Caitlin Furlong, Lise-Sara Rousselle Breau (better known as Lise-Sara Rousselle during the she also got married this summer!) and Myl ne Savoie. Graduate student Roman Chukalovskyy also helped with errands during the conference. In addition, thanks for the financial support (gifts for the participants) of the Faculty of EDUCATION , the Librairie acadienne, and the town of Moncton. In general, thanks to the Faculty of EDUCATION , the Faculty of Sciences, the associate vice-president of academics and faculty affairs (Jean-Fran ois Richard), the Dean of the Faculty of EDUCATION (Marianne Cormier) and the Universit de Moncton (Moncton campus) for their support.

8 Finally, from our hosts, Manon and Viktor: Thanks to the participants, who gave life to this meeting. Thanks for the energy, the positive comments, the smiles, and all that you did to make this meeting truly bilingual! I also acknowledge the CMESG/GCEDM-2015 executive for organizing another stimulating program with topics relevant to our membership of mathematicians, MATHEMATICS teacher educators and MATHEMATICS EDUCATION researchers. On behalf of the executive, thanks to the two plenary speakers Dr. ric Roditi for engaging us in his work on the diversity, variability and commonalities among teaching practices and Dr. Deborah Hughes Hallett for engaging us in the importance of enabling postsecondary students to see connections between different parts of MATHEMATICS and between MATHEMATICS and other fields.

9 Thanks also to the leaders of the five Working Groups; the presenters of the five Topic Sessions; the nine new-PhD presenters; the Ad Hoc and Math Gallery Walk presenters; the presenters of the Panel (Drs. Fr d ric Gourdeau, Peter Taylor, Ralph Mason, and Elaine Simmt) for an entertaining debate on Should we continue to teach fractions in school? ; and all of the participants for making the 2015 meeting a meaningful and worthwhile experience. viii This publication of the proceedings of the conference offers readers the opportunity to learn about some of the MATHEMATICS EDUCATION research and interests of our community. It is hoped that it also provides a means for participants to further reflect on and build on their experiences at the conference and for others to share in and be inspired by the work of the MATHEMATICS EDUCATION community in Canada.

10 Ix Horaire Vendredi 5 juin Samedi 6 juin Dimanche 7 juin Lundi 8 juin Mardi 9 juin 8:45 10:15 Groupes de travail 8:45 10:15 Groupes de travail 8:45 10:15 Groupes de travail 8:45 10:15 Panel 10:15 10:45 Pause caf 10:15 10:45 Pause caf 10:15 10:45 Pause caf 10:15 10:30 Pause caf 10:30 11:00 S ances ad hoc 10:45 12:15 Groupes de travail 10:45 12:15 Groupes de travail 10:45 12:15 Groupes de travail 11:10 11:40 Nlles th ses (4) 11:45 12:30 S ance de cl ture 12:30 13:30 D ner 12:30 13:30 D ner 12:30 13:30 D ner 13:30 14:30 Caf dessert et Gall rie math matique 13:30 14:20 S ances ad hoc 13:30 14:00 Petits groupes 14:10 15:10 Pl ni re 2 : S ance questions 14:30 15:30 Pl ni re 2 14:30 18:45 Inscription 15:30 16:20 Amis de FLM 14:40 15:10 Petits groupes 15:15 16:15 Pl ni re 1 : S ance questions 15:20 16:10 S ances Th matiques 16:00 22:00 Excursion Hopewell Rocks Magnetic Hill Winery Souper 16:15 16:35 Pause caf 16:10 16:30 Pause caf 16:40 17:10 Nlles th ses (1) 16:40 18:05 Assembl e g n rale annuelle 17:00 18:45 Souper 17:15 17:45 Nlles th ses (2) 17:50 18:20 Nlles th ses (3) 18:30 ?


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