PME-NA 36 (Vol

____________________________________________________________________ Cite as: Liljedahl, P., Nicol, C., Oesterle, S., & Allan, D. (Eds.). (2014). Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 1). Vancouver, Canada: PME. or Liljedahl, P., Nicol, C., Oesterle, S., & Allan, D. (Eds.). (2014). Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 1). Vancouver, Canada: PME. Website: http://www.pme38.com/ The proceedings are also available via http://www.igpme.org Copyrights © 2014 left to the authors All rights reserved ISSN 0771-100X Vol. 1 ISBN 978-0-86491-361-6 Set ISBN: 978-0-86491-360-9 Cover Design: Kirsty Robbins, University of British Columbia Salmon Design: Haida artist William (Billy) NC Yovanovich Jr. Ts’aahl Formatting Assistance: Robert Browne, Jacky McGuire Production: Lebonfon, Québec PREFACE We are pleased to welcome you to PME 2014. This year’s meeting is a joint conference of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36). PME is one of the most important international conferences in mathematics education and draws educators, researchers, and mathematicians from all over the world. PME 2014 convenes in Vancouver, Canada, located on the traditional and unceded territory of the Musqueam, Squamish, and Tsleil-Waututh First Nations. On behalf of the conference local organizing committee we are very excited to welcome you to Vancouver. This is a conference of firsts. This is the first time PME has returned to Canada since 1987 PME 11 in Montreal. This is also the largest PME conference to date. For the first time in PME history more than 800 people will attend the conference, representing almost 50 countries around the world. This is the first time that a session devoted to supporting new researchers in mathematics education will be included in the conference meeting and, for some of you, it will be your first time in Vancouver. We are honoured to host you at this prestigious conference. Mathematics Education at the Edge has been chosen as the theme of the conference. Academically, the theme provides opportunities to highlight and examine mathematics education research that is: 1) breaking new ground or on the cutting edge of innovative research and research methodologies; and 2) exploring issues with groups that are often positioned at the edge or periphery of educational research, such as social justice, peace education, equity, and Indigenous education. Geographically, the theme Mathematics Education at the Edge describes the very place of the conference setting, Vancouver, a city situated at the edge of Canada on the Pacific Ocean and Coast Mountain Range. The papers in the six volumes of these proceedings are organized according to the type of presentation. Volume 1 contains the presentations of our plenary speakers, Research Forum activities, Discussion Group activities, Working Session activities and the National Presentation of mathematics education in Canada. Volumes 2 – 5 contain the Research Reports of the conference, while Volume 6 consists of the Short Oral and Poster Presentations. The organization of PME 2014 is a collaborative effort involving teams of colleagues at the University of British Columbia and Simon Fraser University. We are grateful for the support received from each university. The conference is also organized with the support of three committees: the International Program Committee for PME 2014, the International Committee of PME, and the Local Organizing Committee, along with the PME Administrative Manager. We acknowledge the tremendous support and effort of these various committees. PME 2014 is possible only with the time and energy of the many volunteers who have dedicated hundreds of hours before, during and following the conference. Thank you to each of you. Finally, we thank each PME participant for PME 2014 1 - I making your journey to PME 2014 in Vancouver and for your contributions to this conference. Place has a powerful impact on what and how we learn. We hope Vancouver, as the place of PME 2014, will evoke and inspire exciting, critical, and difficult discussions that are on the edge of mathematics education research. Cynthia Nicol and Peter Liljedahl PME 2014 Conference co-Chairs SPONSORS We are grateful for the generous support received for this conference from the following sponsors: Faculty of Education, Simon Fraser University Vice President Academic, Simon Fraser University Faculty of Education, University of British Columbia Department of Curriculum and Pedagogy, University of British Columbia Pacific Institute for the Mathematical Sciences Actuarial Foundation of Canada The Fields Institute for Research in Mathematical Studies Springer Publishing Company Sense Publishers Taylor & Francis Routledge Education 1 - II PME 2014 TABLE OF CONTENTS VOLUME 1 PREFACE ............................................................................................................................................. I SPONSORS ........................................................................................................................................ II TABLE OF CONTENTS VOLUME 1 .............................................................................................. III TABLE OF CONTENTS VOLUME 2 ....................................................................................... VII TABLE OF CONTENTS VOLUME 3 ........................................................................................... XIII TABLE OF CONTENTS VOLUME 4 ........................................................................................... XIX TABLE OF CONTENTS VOLUME 5 ......................................................................................... XXV TABLE OF CONTENTS VOLUME 6 ........................................................................................ XXXI THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION (PME) & THE NORTH AMERICAN CHAPTER (PME-NA) ............................ LXV THE PME 2014 CONFERENCE ................................................................................................ LXIX PROCEEDINGS OF PREVIOUS PME CONFERENCES ......................................................... LXXI REVIEW PROCESS OF PME 2014 .......................................................................................... LXXV LIST OF PME 2014 REVIEWERS ........................................................................................... LXXIX PLENARIES ON TEACHERS AND STUDENTS: AN ETHICAL CULTURAL-HISTORICAL PERSPECTIVE .................................................................................................................................... 1 Luis Radford THINKING WITH AND THROUGH EXAMPLES ........................................................................ 21 Orit Zaslavsky PROFESSIONAL KNOWLEDGE OF (PROSPECTIVE) MATHEMATICS TEACHERS – ITS STRUCTURE AND DEVELOPMENT ..................................................................................... 35 Gabriele Kaiser, Sigrid Blömeke, Andreas Busse, Martina Döhrmann, Johannes König PME 2014 1 - III Table of Contents – Volume 1 PLENARY PANEL THE CALCULUS OF SOCIAL CHANGE – MATHEMATICS AT THE CUTTING EDGE ........ 55 Mamokgethi Setati Phakeng (Chair) PRIVILEGING LOCAL CULTURES AND DEMOGRAPHICS IN THE MATHEMATICS CLASSROOM ................................................................................................................................... 61 David Wagner SOCIAL JUSTICE THROUGH MATHEMATICS EDUCATION: SKILLING YOUTH FOR SOCIETAL PARTICIPATION ......................................................................................................... 67 Anjum Halai CUTTING THE CALCULATIONS OF SOCIAL CHANGE WITH SCHOOL MATHEMATICS .............................................................................................................................. 73 Paola Valero RAISING POLITICAL, PSYCHOANALYTIC, AND CULTURAL QUESTIONS OF A PROPOSED EDUCATIONAL INTERVENTION ........................................................................... 79 Margaret Walshaw RESEARCH FORUMS THE CHALLENGES OF TEACHING MATHEMATICS WITH DIGITAL TECHNOLOGIES – THE EVOLVING ROLE OF THE TEACHER .............................................. 87 Alison Clark-Wilson, Gilles Aldon, Annalisa Cusi, Merrilyn Goos, Mariam Haspekian, Ornella Robutti, Mike Thomas MATHEMATICAL TASKS AND THE STUDENT ...................................................................... 117 David Clarke, Heidi Strømskag, Heather Lynn Johnson, Angelika Bikner-Ahsbahs, Kimberly Gardner MATHEMATICAL MODELING IN SCHOOL EDUCATION: MATHEMATICAL, COGNITIVE, CURRICULAR, INSTRUCTIONAL AND TEACHER EDUCATION PERSPECTIVES ............................................................................................................................. 145 Jinfa Cai, Michelle Cirillo, John A. Pelesko, Rita Borromeo Ferri, Marcelo Borba, Vincent Geiger, Gloria Stillman, Lyn D. English, Geoff Wake, Gabriele Kaiser, Oh Nam Kwon SPATIAL REASONING FOR YOUNG LEARNERS ................................................................... 173 Nathalie Sinclair, Catherine D. Bruce HABERMAS’ CONSTRUCT OF RATIONAL BEHAVIOR IN MATHEMATICS EDUCATION: NEW ADVANCES AND RESEARCH QUESTIONS .........................................

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