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This submission contains the Proceedings of the 2012 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Laval University in Québec City, Québec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, a panel discussion, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc and poster sessions. Papers include: (1) Towards an Understanding of Ethical Practical Action in Mathematics Education: Insights from Contemporary Inquiries (Margaret Walshaw); (2) Old and New Mathematical Ideas from Africa: Challenges for Reflection (Paulus Gerdes); (3) Cooda, Wooda, Didda, Shooda: Time Series Reflections on CMESG/GCEDM (William Higginson); (4) Panel: What is Fundamental Mathematics for Learners? (Elaine Simmt, Darien Allan, Ralph Mason, Ruth Beatty, Peter Taylor, and Hélène Paradis); (5) Numeracy: Goals, Affordances, and Challenges (France Caron and Peter Liljedahl); (6) Diversities in Mathematics and their Relation to Equity (Beverly Caswell and David Wagner); (7) Technology and Mathematics Teachers (K-16) / La technologie et l'enseignant mathématique (K-16) (Chantal Buteau and Nathalie Sinclair); (8) La preuve en mathématiques et en classe / Proof in Mathematics and in Schools (David Reid and Denis Tanguay); (9) The Role of Text/books in the Mathematics Classroom / Le rôle des manuels scolaires dans la classe de mathématiques (Peter Appelbaum and Susan Gerofsky); (10) 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 (Hassane Squalli, Chris Suurtamm, and Viktor Freiman); (11) Collaboration Between Research in Mathematics Education and Teaching Mathematics: Case Study of Teaching Infinity in Calculus (Miroslav Lovric); (12) Dialogue sur la lecture de textes historiques dans la classe de mathématiques / Dialogue on Reading Original Texts in the Mathematics Classroom (Louis Charbonneau and David Guillemette) [Written in French]; (13) Teaching Toward Equity in Mathematics (Beverly Caswell); (14) Inequalities in the History of Mathematics: From Peculiarities to a Hard Discipline (Elena Halmaghi); (15) 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 (Manon Leblanc); (16) Institutional Acculturation of the Researcher, Teacher, and Secondary 1 Students with Learning Difficulties in Problem Situations Involving Rational Numbers / Les effets d'une démarche d'acculturation sur l'action didactique conjointe de l'enseignant, des élèves et du chercheur, dans l'enseignement/apprentissage des nombres rationnels auprès d'élèves en difficultés d'apprentissage (Geneviève Lessard) [Written in French]; (17) Mathematics Education: An Aporetic of Epistemology, Language and Ethics (Jean-François Maheux); (18) Diverse Perspectives on Teaching "Math for Teachers": Living the Tensions (Susan Oesterle); (19) Conversations Held and Roles Played During Mathematics Teachers' Collaborative Design: Two Dimensions of Interaction (Armando Paulino Preciado Babb); (20) The Ordinary Yet Extraordinary Emotions and Motives of Preservice Mathematics Teachers (Oana Radu); (21) Élaboration et analyse d'une intervention didactique, co-construite entre chercheur et enseignant, visant le développement d'un contrôle sur l'activité mathématique chez les élèves du secondaire / 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 (Mireille Saboya) [Written in French]; (22) Publishing in the Journal of Mathematics Teacher Education (Olive Chapman and Margaret Walshaw); (23) Is It Possible to Measure the Effectiveness of a Specific Approach to Teaching Foundations Mathematics in a Post-Secondary Setting? / Est-il possible de mesurer l'efficacité d'une approche spécifique à l'enseignement mathématiques fondations dans un cadre de post-secondaire? (Taras Gula); (24) Challenges in Supporting Mathematics Teachers to Develop Their Teaching Practices (Lionel Lacroix); (25) Rapport sur le ad hoc éthique et éducation mathématique / Report on the Ethics and Mathematics Education Ad Hoc (Jean-François Maheux); (26) Reading Biographies and Autobiographies of Mathematicians: What Do They Tell Us About the Subject of Mathematics? (Veda Roodal Persad); (27) Online Environments for Mathematics Sharing and Collaboration (Geoffrey Roulet); (28) Ad Hoc Session on Planning for the Next Canadian Math Education Forum (CMEF) to be Held in May 2014 (Peter Taylor); (29) Preservice Elementary Teachers' Beliefs Toward Mathematics and Mathematics Teaching (Sean Beaudette, Alexandra Penn, and Geoffrey Roulet); (30) Gearing Up For Grade 9: A Learning Object (Laura Broley); (31) Students' Perceptions of the Role of Theory and Examples in College Level Mathematics (Dalia Challita and Nadia Hardy); (32) Une expérimentation de pratiques gagnantes en enseignement des mathématiques / An Experiment with Successful Practices in Mathematics Teaching (Lucie Deblois); (33) Blended Mathematical Collaboration Using a Wiki, Geogebra and Jing (Jill Lazarus and Geoffrey Roulet); (34) Some Things Technologies Can Tell Us About Technologies: An Instrumented Analysis of Two Successive Mathematics Curricula (Jean-François Maheux and Fabienne Venant); (35) Investigating the Teaching Practices of a Group of Mathematics Graduate Students (Tod L. Shockey and Sibylle Weck-Schwarz); (36) Mathematics For Young Children: Exploring What is Possible in Early Mathematics Education? (Diane Tepylo, Joan Moss, Catherine Bruce, Tara Flynn, Diana Chang, and Zachary Hawes); and (37) Mise à l'essai d'une situation d'enseignement-apprentissage en lien avec le métier du scénographe pour favoriser l'engagement mathématique des élèves du 1er cycle du secondaire (Josianne Trudel) [Written in French]. Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, tables, and figures. [For the 2011 proceedings, see ED547245.]

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl and Fre: (1) Working with Learners' Mathematics: Exploring a Key Element of Mathematical Knowledge for Teaching (Jill Adler, Zain Davis, Mercy Kazima, Diane Parker, and Lyn Webb); (2) A Comparison between Teachers' and Pupils' Tendency to Use a Representativeness Heuristic (Thekla Afantiti-Lamprianou, Julian S. Williams, and Iasonas Lamprianou); (3) Purposeful Task Design and the Emergence of Transparency (Janet G. Ainley, Liz Bills, and Kirsty Wilson); (4) A Developmental Model for Proportional Reasoning in Ratio Comparison Tasks (Silvia Alatorre and Olimpia Figueras); (5) Referential and Syntactic Approaches to Proof: Case Studies from a Transition Course (Lara Alcock and Keith Weber); (6) Teachers' Beliefs about Students' Development of the Pre-Algebraic Concept of Equation (Vassiliki Alexandrou-Leonidou and George N. Philippou); (7) Developing Students' Understanding of the Concept of Fractions as Numbers (Solange Amorim Amato); (8) Multiple Representations in 8th Grade Algebra Lessons: Are Learners Really Getting It? (Miriam Amit and Michael N. Fried); (9) Reform-Oriented Teaching Practices: A Survey of Primary School Teachers (Judy Anderson and Janette Bobis); (10) The Genesis of Signs by Gestures: The Case of Gustavo (Ferdinando Arzarello, Francesca Ferrara, Ornella Robutti, and Domingo Paola); (11) Students' Experience of Equivalence Relations: A Phenomenological Approach (Amir H. Asghari and David Tall); (12) How Series Problems Integrating Geometric and Arithmetic Schemes Influence Prospective Secondary Teachers' Pedagogical Understanding (Leslie Aspinwall, Kenneth L. Shaw, and Hasan Unal); (13) Dealing with Learning in Practice: Tools for Managing the Complexity of Teaching and Learning (Sikunder Ali Baber and Bettina Dahl); (14) Situations of Psychological Cognitive No-Growth (Roberto R. Baldino and Tania C. B. Cabral); (15) Good CAS Written Records: Insight from Teachers (Lynda Ball and Kaye Stacey); (16) Developing Procedure and Structure Sense of Arithmetic Expressions (Rakhi Banerjee and K. Subramaniam); (17) Struggling with Variables, Parameters, and Indeterminate Objects, or How to Go Insane in Mathematics (Caroline Bardini, Luis Radford, and Cristina Sabena); (18) Exploring How Power is Enacted in Small Groups (Mary Barnes); (19) A Framework for the Comparison of PME Research into Multilingual Mathematics Education in Different Sociolinguistic Settings (Richard Barwell); (20) Vygotsky's Theory of Concept Formation and Mathematics Education (Margot Berger); (21) Preservice Teachers' Understandings of Relational and Instrumental Understanding (Kim Beswick); (22) The Transformation of Mathematics in On-Line Courses (Marcelo C. Borba); (23) Using Cognitive and Situated Perspectives to Understand Teacher Interactions with Learner Errors (Karin Brodie); (24) Identification of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (25) The "A4-Project": Statistical World Views Expressed through Pictures (Michael Bulmer and Katrin Rolka); (26) A Whole-School Approach to Developing Mental Computation Strategies (Rosemary Callingham); (27) A Comparison of Perceived Parental Influence on Mathematics Learning among Students in China and Australia (Zhongjun Cao, Helen Forgasz, and Alan Bishop); (28) Using Word Problems in Malaysian Mathematics Education: Looking beneath the Surface (Kah Yein Chan and Judith Mousley); (29) Constructing Pedagogical Knowledge of Problem Solving: Preservice Mathematics Teachers (Olive Chapman); (30) Revisiting a Theoretical Model on Fractions: Implications for Teaching and Research (Charalambos Y. Charalambous and Demetra Pitta-Pantazi); (31) Students' Reflection on Their Sociomathematical Small-Group Interaction: A Case Study (Petros Chaviaris and Sonia Kafoussi); (32) Investigating Teachers' Responses to Student Misconceptions (Helen L. Chick and Monica K. Baker); (33) Studying the Distribution of Responsibility for the Generation of Knowledge in Mathematics Classrooms in Hong Kong, Melbourne, San Diego and Shanghai (David Clarke and Lay Hoon Seah); (34) Indigenous and Non-Indigenous Teaching Relationships in Three Mathematics Classrooms in Remote Queensland (Tom J. Cooper, Annette R. Baturo, and Elizabeth Warren); (35) Exploring the Strategies Used by Grade 1 to 3 Children through Visual Prompts, Symbols and Worded Problems: A Case for a Learning Pathway for Number (Ty Corvell Cranfield, Cally Kuhne, and Gary Powell); (36) Primary Students' Knowledge of the Properties of Spatially-Oriented Diagrams (Carmel Diezmann); (37) A Conceptual Framework for Studying Teacher Preparation: The Pirie-Kieren Model, Collective Understanding, and Metaphor (Maria A. Droujkova, Sarah B. Berenson, Kelli Slaten, and Sue Tombes); (38) Mathematical Modelling with 9-Year-Olds (Lyn English and James Watters); (39) Exploring "Lesson Study" in Teacher Preparation (Maria L. Fernandez); (40) Child-Initiated Mathematical Patterning in the Pre-Compulsory Years (Jillian Fox); (41) The Tacit-Explicit Nature of Students' Knowledge: A Case Study on Area Measurement (Cristina Frade); (42) Teachers as Interns in Informal Mathematics Research (John M. Francisco and Carolyn A. Maher); and (43) Exploring Excellence and Equity within Canadian Mathematics Classrooms (George Frempong). (Individual papers contain references.)

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, panel discussions, working group reports, new PhD reports, and summaries of ad hoc and poster sessions. Papers include the following: (1) The Most Unglamorous Job of All: Writing Mathematics Exercises (Yvan Saint-Aubin); (2) 40+ Years of Teaching and Thinking about University Mathematics Students, Proofs, and Proving (Annie Selden); (3) 'Elder Talk'-A Revisionist Version (Joel Hillel); (4) Teaching First Year Mathematics Courses in Transition from Secondary to Tertiary (Ann Arden, Wesley Maciejewski, Nadia Hardy); (5) L'anxiété mathématique chez les futurs enseignants du primaire : à la recherche de nouvelles réponses à des enjeux qui perdurent / Elementary Preservice Teachers and Mathematics Anxiety: Searching for New Responses to Enduring Issues (Manion LeBlanc, Jamie Pyper, Jo Towers) [Written in French and English]; (6) Social Media and Mathematics Education (Judy Larsen, Egan Chernoff, Viktor Freiman); (7) Quantitative Reasoning in the Early Years / Le raisonnement quantitatif dans les premières années du parcours scolaire (Doris Jeannotte, Lynn McGarvey)[Written in English and French ]; (8) Social, Cultural, Historical and Philosophical Perspectives on Tools for Mathematics (Yasmine Abtahi, Susan Gerofsky, Jean Francois); (9) Compréhension approfondie des mathématiques scolaires / Deep Understanding of School Mathematics (Richelle Marynowski, Sarah Dufour, Peter Liljedhal); (10) Modelling Mathematical Modelling / Modéliser la modélisation mathématique (France Caron)[Written in French and English]; (11) Collective Learning: Re-thinking the Environment, Artifacts and Classroom Interactions (Joyce Mgombelo); (12) A Psychological View of Teaching Proof Construction (John Selden); (13) Things Kids Think With: The Role of the Physical Properties of Mathematical Tools in Children's Learning in the Context of Addition of Fractions (Yasmine Abtahi); (14) Examining Mathematics Anxiety Among Classroom Teachers (Atinuke Adeyemi); (15) Teaching Teachers: A Look Inside Professional Development (Melania Alvarez); (16) Be Innovative but Don't Be Wrong: Are 21st Century Students Experiencing 21st Century Mathematics? (Jennifer Godfrey Anderson); (17) College Foundational Mathematics: Can the Affordances of ICT Enhance Self-regulation Skill of Students? / Mathématiques fondamentales du collège : est-ce que les apports des « TIC » peuvent améliorer l'autorégulation des compétences des élèves? (Carol Carruthers)[Written in English and French]; (18) Influence of the Learning Environment on Student Test Performance in Undergraduate Mathematics Courses (Amenda Chow); (19) The Role of Oral Communication Strategies in Accessing and Assessing Mathematical Understanding: Case Studies of Primary School Teachers' Perceptions of Teaching Mathematics and Teaching Literacy (Celia Kutas Chisu); (20) Reciprocal Partnership: An Intervention to Enhance Mathematics Self-efficacy and Achievement of First- and Second-semester College Students (Kerry Kwan); (21) Understanding the Interactions within a New Teacher Learning Community Composed of First Time Participants and a Novice Facilitator (Terry Wan Jung Lin); (22) Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis (Gale L. Russell); (23) Opening Space: Complexity Thinking, Classroom Discourse, and Mathematics Learning in the Elementary Classroom / La technologie du forum ouvert: complexité, le discours de classe, et l'apprentissage de mathématiques en école élémentaire (Evan Throop-Robinson)[Written in English and French]; (24) Investigating Mathematics Teachers' Knowledge for Teaching and Their Learning Trajectories (Zhaoyun Wang]; (25) What/How Can We Learn from the Deaf Mathematics Classroom? (Christins M. Krause); (26) The Mathematical Association of Tanzania (MAT) Experience in CMESG Conference (Said A. Sima); (27) Toward a Hybrid Model to Describe Creative Acts in Mathematics Learning Environments (Ayman Aljarrah); (28) Problem Drift: Imaging Emerging Curricular Significance (Nat Banting); (29) Incorporating Writing into the Undergraduate Mathematics Curriculum (Lauren Dedieu); (30) Informing Local Materials Used for Concept-Rich Instruction Practice in Mathematics Class with Pre-service Teachers in Tanzanian Context (Emmanuel, Deogratias); (31) Les jeux technologiques dans les cours de mathématiques au secondaire (Caitlin, Furlong) [Written in French]; (32) De jeunes chercheurs à la rencontre de la philosophie des mathématiques (Sabrina Heroux, Sarah Mathieu-Soucy, Laura Broley) [Provided in French]; (33) Examining Parent Perspectives of Multiple Strategies (Jennifer Holm, Lynn McGarvey, Lixin Luo, Janelle McFeeters, and Iris Yin); (34) La dialectique perfection/imperfection : une nouvelle manière de penser l'activité mathématique (Marie-Line L. LaMarche, Jean-Francois Maheux) [Provided in French]; (35) Understanding School Leaders' Discourse in Regard to Mathematics Achievement (Jhonel Morvan); (36) I SEE What You're Saying: Visualization and the Growth of Mathematical Images (Jennifer Plosz); (37) Students' Relationships With Mathematics Revealed Through Drawings (Jennifer Plosz, Jo Towers, Kori Czuy, Ayman Aljarrah, Andrew Vorhies and Miwa Takeuchi); (38) Teacher Professional Learning in Tanzania: Experiences of Mathematics Teacher Leaders (Calvin Zakaria Swai); (39) "Perimeter is easier to work with than area": Students' Language Use in Group Work (Miwa Akoi Takeuchi); and (40) Toward an Understanding of Mathematics Teachers' Participation in Professional Learning Networks (Xiong Wang). Individual papers provide referenced. [For the 2016 proceedings, see ED581045.]

Mathematical reasoning features in curriculum documents around the world, but is understood and enacted poorly by teachers in classrooms. We explore teachers' noticing of reasoning during observed lessons. Two teams of primary teachers in Canada and Australia worked to plan, deliver, and observe lessons intended to include reasoning. They observed each other teaching a lesson that was planned with the assistance of a researcher, and later, a researcher observed each post-lesson discussion. Given the reported benefits of teachers' noticing of reasoning during peer-observed lessons, targeted professional learning support is required to further enact teachers' peer discourse to facilitate mathematical reasoning.

Using an innovative recruitment tool, the social network site Facebook, survey data were gathered from samples of the Australian general public and from around the world. Views on the gendering of mathematics, science, and ICT were gathered. In this paper we report the findings from six of the 15 questions on the survey, and only from respondents in predominantly English-speaking countries. The findings reveal that the majority was not gender-stereotyped about mathematics and related careers. However, if a gendered view was held, it was overwhelming to endorse the male stereotype. Male respondents' views were more strongly gendered than were females'. [For the complete proceedings, see ED585874.]

The papers in this document follow the order of the meeting and consist of two guest lecturers and reports from four working groups; two topic group presentations are noted but not included. One lecture, delivered by Peter Hilton, discusses the nature of mathematics today and implications for mathematics teaching, while, in the other paper, Stephen I. Brown explores the nature of problem generation in the mathematics curriculum. Working group reports concern statistical thinking, training in diagnosis and remediation for teachers, mathematics and language, and the influence of computer science on the undergraduate mathematics curriculum. Topic groups heard presentations by Daniel Kahneman on intuitions and fallacies in reasoning about probability and by Tom Kieren on mathematics curriculum development in Canada. A list of participants is given. (MNS)

The purpose of this study was to investigate whether gender accounts for student differences in performance and achievement in mathematics. Data for the study were drawn from the Second International Mathematics Study (SIMS) of seventh and eighth grade students from Japan, Belgium, Canada (British Columbia and Ontario), France, the United States, New Zealand, and Thailand. Students were tested on the same mathematical items and problems. Results indicated no substantial gender effects or differences in any of the mathematics content areas, problem types, or national origins. Other studies suggested that curricula, pedagogies, or cultural factors may interact with gender differences in impacting quantitative performance. Tables and 21 references are included. (JHP)