CANADIAN MATHEMATICS EDUCATION STUDY GROUP GROUPE CANADIEN D'ÉTUDE EN DIDACTIQUE DES MATHÉMATIQUES PROCEEDINGS / ACTES 2007 ANNUAL MEETING / RENCONTRE ANNUELLE 2007 University of New Brunswick June 8 – June 12, 2007 EDITED BY: Peter Liljedahl, Simon Fraser University Proceedings of the 2007 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 2008 in Burnaby, BC. Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group / Actes de la rencontre annuelle 2007 du Groupe Canadien d'Étude en Didactique des Mathématiques 31st Annual Meeting University of New Brunswick June 8 – June 12, 2007 Contents / Tables des matières vii Acknowledgements / Remerciements ix Schedule / Horaire FRÉDÉRIC GOURDEAU xi Introduction Plenary Lectures / Conférences plénières RAFAEL NÚÑEZ 3 Understanding Abstraction in Mathematics Education: Meaning, Language, Gesture, and the Human Brain T. CHRISTINE STEVENS 5 Mathematics Departments, New Faculty, and the Future of Collegiate Mathematics Working Groups / Groupes de travail VÉRONIQUE HUSSIN & 17 A y Outreach in Mathematics – Activities, Engagement, & ERIC MULLER Reflection SHELLEY HUNTER, 37 B y Geometry, Space, and Technology: Challenges for Teachers DONNA KOTSOPOULOS, and Students & WALTER WHITELEY ANNA McQUILLAN, 43 C y The Design and Implementation of Learning Situations FERNANDO HITT, & LUIS RADFORD JÉRÔME PROULX & 53 D y The Multifaceted Role of Feedback in the Teaching and FLORENCE GLANFIELD Learning of Mathematics Topic Sessions / Séances thématiques STEPHEN R. CAMPBELL 71 Mathematics Educational Neuroscience: Origins, Activities, and New Opportunities iii MALGORZATA DUBIEL 79 Communicating the Excitement and Beauty of Mathematics JACINTHE GIROUX 83 Conception et expérimentation de situations didactiques au préscolaire/primaire / Design and Experimentation of Didactical Situations in Kindergarten and Elementary School KATE MACKRELL 91 Cabri 3d: An Environment for Purposeful Mathematical Activity? New PhD Reports / Présentations de thèses de doctorat INDIGO ESMOND 103 Equity and Opportunities to Learn in Cooperative Mathematical Work JÉRÔME PROULX 111 (Élargir les) Connaissances mathématiques des enseignants de mathématiques du secondaire : une étude sur la formation continue / (Enlarging) Secondary-level Mathematics Teachers' Mathematical Knowledge: An Investigation of Professional Development GEORGES TOUMA 127 Un paradigme d’expérimentation au laboratoire de sciences pour l’identification et l’optimisation statistique d’un modèle algébrique par interaction visuo-graphique DOMINIC VOYER 133 What Factors Influence Understanding of Written Arithmetic Problems? Ad Hoc Sessions / Séances ad hoc EGAN CHERNOFF & 141 Probabilities / Probabilités ANNIE SAVARD SUSAN GEROFSKY 143 First Steps Toward An Archaeology Of Gesture In Graphing JENNIFER HALL 145 Function Modelling using Secondary Data from Statistics Canada’s E-STAT Database GILLA HANNA, ELLA 147 Explanation and Proof in Mathematics and Mathematics Education KAYE, & RIAZ SALOOJEE EVA KNOLL 149 Exploring our Embodied Knowing of the Gauss-Bonnet Theorem: Barn-Raising and Endo-Pentakis-Icosi-Dodecahedron JOHN GRANT 151 Mathematical Biography McCLOUGHLIN CRAIG NEWELL 153 This Is Mathematics; This Isn’t Mathematics; But That…I’m Not So Certain About: The Possible “Emancipation” of Secondary School Mathematics From the Bonds of “Real” Mathematics iv Panel / Table ronde FRANCE CARON, 157 What Courses Could or Should Mathematics Departments Offer to MORRIS ORZECH, & Graduate Programs in Mathematics Education? ELAINE SIMMT Appendices / Annexes 167 A y Working Groups at Each annual Meeting 173 B y Plenary Lectures at Each Annual Meeting 177 C y Proceedings of Annual Meetings v Acknowledgements / Remerciements The organisational work for our 2007 annual meeting at the University of New Brunswick in Fredericton enabled us to have another memorable meeting. Our local organisers, Dave Wagner and John Grant McLoughlin, with the expert support of Sylvie Beaulieu, managed to do everything efficiently and with a smile, and we thank them. The university offered much support and we wish to thank the faculties of Science, of Education, of Graduate Studies as well as the Mathematics Department for it. Le travail d’organisation de la rencontre annuelle de 2007 à l’Université du Nouveau Brunswick à Fredericton a permis au groupe d’avoir une autre rencontre annuelle mémorable. Sur le plan local, Dave Wagner et John Grant McLoughlin qui, appuyé de Sylvie Beaulieu, ont su organiser la rencontre avec efficacité et bonne humeur, et nous les en remercions. L’appui de leur institution s’est manifesté de bien des manières et nous remercions les facultés des sciences, d’éducation et des études graduées, en plus du département de mathématiques de l’université. vii Schedule Friday Saturday Sunday Monday Tuesday 8 June 9 June 10 June 11 June 12 June 9:00 – 10:00 Topic Sessions 9:30 – 11:00 9:30 – 11:00 9:30 – 11:00 C and D Working Groups Working Groups Working Groups 10:00 – 11:00 Panel 11:0 0 – 11:20 11:0 0 – 11:20 11:0 0 – 11:20 11:0 0 – 11:20 Coffee Break Coffee Break Coffee Break Coffee Break 11:20 – 12:30 11:20 – 12:30 11:20 – 12:30 11:30 – 12:30 Working Groups Working Groups Working Groups Closing Session 12:30 – 13:30 12:30 – 13:30 12:30 – 13:30 Lunch Lunch Lunch 13:45 – 14:15 13:45 – 14:15 Small Group Small Group Discussion of Discussion of Plenary 1 13:45 – 14:45 Plenary 2 Plenary 2 14:15 – 15:15 14:15 – 15:15 Discussion of Discussion of Plenary 1 Plenary 2 15:15 – 15:45 15:15 – 15:45 Ad Hoc Session (1) 15:00 – 16:00 Ad Hoc Session (3) Topic Sessions 15:00 – 18:00 15:45 – 16:15 A and B 15:45 – 16:15 Registration Coffee Break Coffee Break 16:15- 16:45 16:15- 16:45 New PhD's (1) New PhD's (2) 16:00 – 20:00 17:00 – 17:30 Free time to explore 17:00 – 18:15 17:30 – 18:45 Ad Hoc Session (2) Fredericton trailsand Annual General Dinner have dinner Meeting downtown 19:00 – 19:45 CMESG Opening 19:45 – 20:45 Plenary 1 19:00 Dinner 19:30 20:00 Dinner Dessets and 20:45 CELTIC MUSIC Reception ix Horaire Vendredi Samedi Dimance Lundi Mardi 8 Juin 9 Juin 10 Juin 11 Juin 12 Juin 9:00 – 10:00 Séances thématiques 9:30 – 11:00 9:30 – 11:00 9:30 – 11:00 C et D Groupes de travail Groupes de travail Groupes de travail 10:00 – 11:00 Table ronde 11:0 0 – 11:20 11:0 0 – 11:20 11:0 0 – 11:20 11:0 0 – 11:20 Pause-café Pause-café Pause-café Pause-café 11:20 – 12:30 11:20 – 12:30 11:20 – 12:30 11:30 – 12:30 Groupes de travail Groupes de travail Groupes de travail Séance de clôture 12:30 – 13:30 12:30 – 13:30 12:30 – 13:30 Dîner Dîner Dîner 13:45 – 14:15 13:45 – 14:15 Discussion en petits Discussion en petits groupes – groupes – Conférence 1 13:45 – 14:45 Conférence 2 Conférence 2 14:15 – 15:15 14:15 – 15:15 Discussion Discussion Conférence 1 Conférence 2 15:15 – 15:45 15:15 – 15:45 Séances ad hoc (1) 15:00 – 16:00 Séances ad hoc (3) Séances thématiques 15:00 – 18:00 15:45 – 16:15 A et B 15:45 – 16:15 Inscription Pause-café Pause-café 16:15- 16:45 16:15- 16:45 Thèses (1) Thèses (2) 16:00 – 20:00 Temps libre pour 17:00 – 17:30 17:00 – 18:15 17:30 – 18:45 explorer les rues de Séances ad hoc (2) Assemblée Générale Souper Fredericton et annuelle prendre un repas en ville 19:00 – 19:45 Ouverture GCEDM 19:45 – 20:45 19:00 Conférence 1 19:30 Souper 20:00 Souper Dessets et MUSIQUE 20:45 CELTIQUE Réception x Introduction Frédéric Gourdeau – Président, CMESG/GCEDM Université Laval As always, it is a pleasure to write the introduction to the proceedings. It forces me to think back to a wonderful meeting, to the planning and dedication that went into its organization, and to the meeting itself, the conversations, the sharing which occurred. First, I remember our initial planning, in 2006, when we had wisely (!) decided to plan four working groups, and not five as would have been needed in Calgary that same year. We figured that after record numbers in the West, we would be back to our usual smaller numbers in Fredericton. Well, once again, numbers were much higher than expected. Our local organizers Dave Wagner and John Grant Mc Loughlin contributed to this by ensuring good participation from their graduate students and from others in New Brunswick and Nova Scotia, helped in this by AARMS (Atlantic Association for Research in the Mathematical Science) which funded some graduate students attendance. The growth of the organization twinned with a great participation from Quebec did the rest. As a result, the organizers had to adjust, and so did the working group leaders. We all know how hard it can be to lead a group of fifteen intellectuals, not all pragmatic, towards some common goal… Well, imagine thirty or more! The meeting was superbly run, once Dave Wagner had ensured large enough supplies of coffee for all! The social program was great, but I won’t venture going into details as this may not look scholarly enough. La température était remarquable, et c’est presque une canicule qui nous a accompagnés dans nos travaux. La rencontre de 2008 nous a permis de rencontrer deux conférenciers pléniers aux profils très différents, alors que Christine Stevens (projet NExT) et Rafael Nunez étaient nos invités. Les groupes de travail étaient tout aussi variés, sinon davantage, et les impressions glanées ici et là quant aux travaux des uns et des autres nous donnaient le goût d’être partout à la fois.