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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.]

An intelligent textbook may be defined as an interaction layer between the text and the student, helping the student master the content in the text. The Mobile Fact and Concept Training System (MoFaCTS) is an adaptive instructional system for simple content that has been developed into an interaction layer to mediate textbook instruction and so is being transformed into the Mobile Fact and Concept Textbook System (MoFaCTS). In this paper, we document the several terms of the logistic regression model we use to track performance adaptively. We then examine the contribution of each component of our model when it is fit to 4 semesters of Anatomy and Physiology course practice data. Following this documentation of the model, we explain how it is applied in the MoFaCTS system to schedule performance by targeting practice for each item at an optimal efficiency threshold. [This paper was published in the CEUR workshop proceedings (Vol. 2895).]

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.)

Bayesian Knowledge Tracing, a model used for cognitive mastery estimation, has been a hallmark of adaptive learning research and an integral component of deployed intelligent tutoring systems (ITS). In this paper, we provide a brief history of knowledge tracing model research and introduce pyBKT, an accessible and computationally efficient library of model extensions from the literature. The library provides data generation, fitting, prediction, and cross-validation routines, as well as a simple to use data helper interface to ingest typical tutor log dataset formats. We evaluate the runtime with various dataset sizes and compare to past implementations. Additionally, we conduct sanity checks of the model using experiments with simulated data to evaluate the accuracy of its EM parameter learning and use real-world data to validate its predictions, comparing pyBKT's supported model variants with results from the papers in which they were originally introduced. The library is open source and open license for the purpose of making knowledge tracing more accessible to communities of research and practice and to facilitate progress in the field through easier replication of past approaches. [For the full proceedings, see ED615472.]

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher educators in a hybrid mathematics/mathematics education department. Valsiner's zone theory is used to analyse how their beliefs, institutional context and professional learning opportunities shape their identities as MTEs. Findings reveal that the MTEs had developed similar beliefs within supportive institutional context but drew on different sources of professional learning.

Many scholars have argued that mathematics classrooms often offer narrow conceptions of mathematical excellence, recognizing only some kinds of thinking and some kinds of people as valuable, and conflating mathematical aptitude with overall intelligence. Play offers the potential to disrupt such classroom mathematical practices, by offering new and broader ways to exercise agency, and, relatedly, more expansive visions of who is seen as mathematically capable. Offering an in-depth analysis of the participation of two students as they engage in mathematics in their Kindergarten class, whole group rug time and small group play centers, we investigate how different activity structures create space for students to exercise agency in ways that demonstrate multiple forms of competence, creating liberating mathematical spaces. [For the complete proceedings, see ED658295.]

Dramatic differences in children's math knowledge at school entry are thought to originate in the Home Math Environment (HME), where parents and caregivers are the primary provider of experiences that influence children's early math knowledge development. Little is known about what informs parent decision-making around "mathematical parenting" (i.e., parents' cognitions, motivations, and behaviors that impact and influence child math development in the HME). This study uses the RESET Framework and survey instrument to investigate parents' mathematical parenting perceptions (n = 847) across the domains of Role, Expectations, Skills, Efficacy, and Time. Parent self-reports of early childhood math knowledge and of shared math activity are also examined to shed light on the factors that influence mathematical parenting of 4-5-year-old children in the home. [For the complete proceedings, see ED658295.]

The Indian Institute of Science is proud to host the fully in-person sixteenth iteration of the International Conference on Educational Data Mining (EDM) during July 11-14, 2023. EDM is the annual flagship conference of the International Educational Data Mining Society. The theme of this year's conference is "Educational data mining for amplifying human potential." Not all students or seekers of knowledge receive the education necessary to help them realize their full potential, be it due to a lack of resources or lack of access to high quality teaching. The dearth in high-quality educational content, teaching aids, and methodologies, and non-availability of objective feedback on how they could become better teachers, deprive our teachers from achieving their full potential. The administrators and policy makers lack tools for making optimal decisions such as optimal class sizes, class composition, and course sequencing. All these handicap the nations, particularly the economically emergent ones, who recognize the centrality of education for their growth. EDM-2023 has striven to focus on concepts, principles, and techniques mined from educational data for amplifying the potential of all the stakeholders in the education system. The spotlights of EDM-2023 include: (1) Five keynote talks by outstanding researchers of eminence; (2) A plenary Test of Time award talk and a Banquet talk; (3) Five tutorials (foundational as well as advanced); (4) Four thought provoking panels on contemporary themes; (5) Peer reviewed technical paper and poster presentations; (6) Doctoral students consortium; and (7) An enchanting cultural programme. [Individual papers are indexed in ERIC.]

ChatGPT and Bard, two chatbots powered by Large Language Models (LLMs), are propelling the educational sector towards a new era of instructional innovation. Within this educational paradigm, the present investigation conducts a comparative analysis of these groundbreaking chatbots, scrutinizing their distinct operational characteristics and applications as depicted in current scholarly discourse. ChatGPT emerges as an exemplary tool in task-oriented textual interactions, while Bard brandishes unique features such as Text-To-Speech (TTS) functionality, which enhances accessibility and inclusive education, as well as integration with Google Workspace applications. This research critically examines their utilization in various spheres such as pedagogy, academic research, Massive Open Online Courses (MOOCs), mathematics, and software programming. Findings accentuate ChatGPT's superior efficacy in content drafting, code generation, language translation, and providing clinically precise responses, notwithstanding Bard's significant potential encapsulated in its exclusive features. Furthermore, the study traverses' crucial ethical aspects, including privacy concerns and inherent bias, underscoring the profound implications of these Artificial Intelligence (AI) technologies on literature and advocating against the indiscriminate reliance on such models. [For the full proceedings, see ED636095.]

In response to the challenge of geometry's abstract and less engaging nature for students, this study explored the potential of connecting geometry to cultural elements, specifically geometric ornaments found in various cultures worldwide. Geometric ornaments, laden with cultural and spiritual significance, serve as a bridge between mathematics education and cultural contexts. The current research focused on in-depth interviews with 10 school students chosen randomly from two ninth-grade classes from an Arab middle school who were engaged in activities involving analyzing of geometric properties of ornaments, constructing ornaments using a compass and straightedge, and problem-solving exercises related to these ornaments. The qualitative data were analyzed to answer how the students perceived the learning of geometry in the context of geometric ornaments. The findings revealed a significant positive view of the students towards geometry after engaging in these activities. [For the full proceedings, see ED656038.]

"Geometry--Do" is a textbook about plane geometry. It will be divided into two volumes, "Geometry without Multiplication: White through Red Belt," and "Geometry with Multiplication: Blue through Black Belt. "The white- and yellow-belt chapters are neutral geometry; the remainder of "Volume One" and all of "Volume Two" is Euclidean geometry. It is primarily intended to teach geometry from the ground up, starting with the postulates and citing only already-proven theorems. It trains mathletes for competition, but it is not the usual grab-bag of unproven theorems chosen haphazardly and solely because they appeared in past exams. The early chapters prepare students for jobs in construction, architecture, surveying, graphic arts, and military defense. The later chapters teach geometry needed by engineers and military officers. In this lecture, the White Belt chapter is presented. I will address these people: Pure Mathematicians: Moise derides the "lighthearted use of the word let." I prove the crossbar theorem and other foundations not usually taught in high school, and I discuss Hilbert's "Foundations of Geometry." High-School Teachers: Randomly assigning letters to points is what makes geometry confusing. I have special symbols for midpoints, perpendicular feet, and infeet (where the angle bisector cuts the opposite side of a triangle) and exfeet. Administrators: I present clear distinctions between "Geometry--Do" and "Common Core" with examples that concerned parents can understand. Construction Workers: I invent the Aguilar A-Frame, give detailed instructions on squaring abasement foundation wider than a tape measure without exiting the rectangle, and discuss how building with wood differs from steel construction. Military Officers: I discuss troop positioning along a frontier that is plagued with cross-border raids, which assumes that friendly and enemy troops move at the same speed, and a parabola is the set of points equidistant from the focus and the directrix. [For the complete proceedings, see ED655360.]