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These proceedings are a written record of the research presented at the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Nashville, Tennessee, and virtually. This year's conference theme is "Critical Dissonance and Resonant Harmony." The aim of this theme is to reflect not only the time and place that of gathering, but also the time and place in which to conduct academic work. Dissonance can be jarring to experience, whereas harmony can be pleasing. Nashville -- Music City -- which is no stranger to both dissonance and harmony. The papers accepted comprised 101 research reports, 140 brief research reports, 84 Posters, and 16 Working Groups or Research Colloquia. [Individual papers are indexed in ERIC.]

For the thirty-third year, the Research and Theory Division of the Association for Educational Communications and Technology (AECT) is sponsoring the publication of these Proceedings. Papers published in this volume were presented at the national AECT Convention in Anaheim, California. The Proceedings of AECT's Convention are published in two volumes. The papers contained in this volume deal primarily with research and development topics, and represent some of the most current thinking in educational communications and technology. Papers dealing with the practice of instructional technology, including instruction and training issues, are contained in the companion volume (Volume 2). (Individual papers contain references, figures, and tables.) [For Volume 2, see ED514647.]

The theme of the 39th proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) conference was "Synergy at the Crossroads: Future Directions for Theory, Research, and Practice." The metaphor of crossroads was inspired by the conference venue--the historic Indianapolis Union Station, as well as by the state motto, a reference to how Indiana is connected to the rest of the United States. PME-NA 39 includes research presentations, discussion, and reflection focusing on four driving questions connecting to the metaphor of crossroads: (1) What have we learned from the routes we have traversed; what are potential routes for mathematics education research in the future; and what considerations are relevant as we make choices about future directions in mathematics education?; (2) How do we address issues of access and equity within mathematics education today?; (3) How can we lay the groundwork for future crossroads or intersections between theory, research, and practice?; and (4) What barriers within research traditions, educational policy, and teaching practice impede researchers', students', and teachers' success, and how can we work to overcome these barriers? The accepted proposals included 75 research reports, 142 brief research reports, 167 posters, and 13 working groups. Chapters include: (1) Plenary Papers; (2) Curriculum and Related Factors; (3) Early Algebra, Algebra, and Number Concepts; (4) Geometry and Measurement; (5) Inservice Teacher Education/Professional Development; (6) Mathematical Knowledge for Teaching; (7) Mathematical Processes; (8) Preservice Teacher Education; (9) Statistics and Probability; (10) Student Learning and Related Factors; (11) Teaching and Classroom Practice; (12) Technology; (13) Theory and Research Methods; and (14) Working Groups. Individual papers include references. [Individual plenary and research papers are available in ERIC. Some papers are written in both Spanish and English.]

The ND Annual Conference--Teaching of Psychology: Ideas and Innovations was held on March 7-8, 2008 at the Crowne Plaza in White Plains, New York. The conference was sponsored by the Psychology Department of Farmingdale State College. The conference featured Dr. Douglas Bernstein from the University of South Florida, Tampa as the keynote speaker. Participants also had a number of presentations from which to choose, publishers' displays to visit, and many colleagues with whom to network. Thirty abstracts and nine complete papers are included in these proceedings. Presenters covered topics such as teaching psychology through storytelling, using visual displays of data, the benefits of using Excel-based homework assignments, and incorporating multiculturalism in the psychology curriculum. The following complete papers are included in the proceedings: (1) Use of Electronic Discussion Boards to Enhance Classroom Learning (Richard J. DioGuardi); (2) Innovations in Mentoring: Interdisciplinary Perspectives (Joseph Maiorca, Daniel Benkendorf, Praveen Chaudhry, Ernest Poole, and Christine Pomeranz); (3) Child's Play: Creating Observational Research Experiences for 21st Century Undergraduates (Joan F. Kuchner); (4) A Student Perspective on Traditional, Hybrid, and Distance Learning Courses (Patricia A. Oswald and Katherine Zaromatidis); (5) Teach Them What They Need to Know for Life (Gretchen Wehrle); (6) The Perils of PowerPoint: Students' Perceptions of Classroom Technology (Judith Krauss, Lori Murphy, and Marybeth Ruscica); (7) The Values and Habits of the 21st Century College Student (Mary Streit); (8) Technology in the Classroom: Three Useful Interventions (James Regan and Daniel Lackaye); and (9) A 21st Century Statistics Course for the 21st Century Student (Karen Y. Holmes and Darlene G. Colson). (Individual papers contain references.) [Abstract modified to meet ERIC Guidelines. For the 2007 proceedings, see ED499916.]

These proceedings contain the papers and posters of the 11th International Conference on Mobile Learning 2015, which was organised by the International Association for Development of the Information Society, in Madeira, Portugal, March 14-16, 2015. The Mobile Learning 2015 Conference seeks to provide a forum for the presentation and discussion of mobile learning research which illustrate developments in the field. The following are included in these proceedings: (1) Evolution or Revolution? Diffusion and Adaptation of (Smart) Mobile Phones among Children and Adolescents (Gitte Bang Stald); (2) Wearables and the "Anatomy" of Information: Biodata, Privacy, and Ethics (Amber Hutchins and Jake McNeill); (3) Scaffolding Java Programming on a Mobile Phone for Novice Learners (Chao Mbogo, Edwin Blake and Hussein Suleman); (4) Implementation of an Intelligent Tutorial System for Socioenvironmental Management Projects (Gil Vera, Víctor Daniel and Gabriel Awad); (5) Patterns of Mobile Technology Use in Teaching: A Pilot Study (Tami Seifert); (6) Developing Students' Professional Digital Identity (Thomas Cochrane and Laurent Antonczak); (7) Impact of Contextuality on Mobile Learning Acceptance: An Empirical Study Based on Language Learning App (Stephan Böhm and Georges Philip Constantine); (8) Do Mobile Learning Devices Enhance Learning in Higher Education Anatomy Classrooms? (Kate Wilkinson and Phil Barter); (9) It's Not Just the Pedagogy: Challenges in Scaling Mobile Learning Applications into Institution-Wide Learning Technologies (Peter Bird and Mark Stubbs); (10) Mobile Learning and Teacher Education: Researching MLEARN Pilot Development (Don Passey and Joana Zozimo); (11) Mobile-Assisted Language Learning: Student Attitudes to Using Smartphones to Learn English Vocabulary (Neil Davie and Tobias Hilber); (12) Active Students in Webinars (Line Kolås, Hugo Nordseth and Jørgen Sørlie Yri); (13) Expanding the Media Mix in Statistics Education through Platform-Independent and Interactive Learning Objects (Hans-Joachim Mittag); (14) Research on Mobile Learning Activities Applying Tablets (Eugenijus Kurilovas, Anita Juskeviciene and Virginija Bireniene); (15) Learner Centered Experiences with Flipped Classroom and Mobile Online Webinars in Distance Education Program (Lisbeth Amhag); (16) Walk Like an Egyptian: A Serious, Pervasive Mobile Game for Tourism (Fatema Mohsen Gabr and Slim Abdennadher); (17) Educational Materials for Mobile Learning (Kosuke Kaneko, Yoshihiro Okada, Motofumi Yoshida, Hitoshi Inoue and Naomi Fujimura); (18) Boosting up JSL Learners' Outside-Class Learning Time with Learning Log System (Noriko Uosaki, Hiroaki Ogata and Kousuke Mouri); (19) An Integrated Learning Management System for Location-Based Mobile Learning (Christian Sailer, Peter Kiefer and Martin Raubal); (20) The Influence of Affordances on Learner Preferences in Mobile Language Learning (Maria Uther and Adrian Banks); (21) Microlearning as Innovative Pedagogy for Mobile Learning in MOOC (Despina Kamilali and Chryssa Sofianopoulou); (22) Cross-Platform User Interface of e-Learning Applications (Michal Stoces, Jan Masner, Jan Jarolímek, Pavel Šimek, Jirí Vanek and Miloš Ulman); (23) Technology Trends in Mobile Computer Supported Collaborative Learning in Elementary Education from 2009 to 2014 (Mia Carapina and Ivica Boticki); (24) Challenges of Using Learning Analytics Techniques to Support Mobile Learning (Marco Arrigo, Giovanni Fulantelli and Davide Taibi); (25) Effectiveness and Utility of Terminal Tablet as Electric Textbooks for Nursing Practicum (Yumiko Nakamura, Kaori Fukayama and Yukie Majima); (26) A Study on the Process of Development of Collective Intelligence for Utilization of Unused Space of Abandoned Schools (Uk Kim and Junyoung Yang); (27) Implementation of an Adaptive Learning System Using a Bayesian Network (Keiji Yasuda, Hiroyuki Kawashima, Yoko Hata and Hiroaki Kimura); (28) Mathematics and Mobile Learning (Fayez Sayed); and (29) A Framework to Support Global Corporate M-Learning: Learner Initiative and Technology Acceptance across Cultures (Wendy Farrell). An author index is provided. (Individual papers contain references.)

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place October 14-18, 2020; it was postponed, due to the COVID pandemic. In accordance with the major goals of PME-NA that include promoting international contacts and stimulating interdisciplinary research, the theme was proposed as "Entre Culturas/Across Cultures". The goal of the theme was an academic exchange that would reflect the ample diversity of ways of teaching and learning of mathematics, and of the tools and communities involved in mathematics education; as well as an exploration of how the differences in cultures imply a need to consider how research results can be taken into account in varying contexts. The papers comprise 80 Research Reports, 190 Brief Reports, 147 Poster Presentations, 10 Working Groups, 2 Research Colloquia, and Plenary and special lectures. The program also includes a special tribute to Eugenio Filloy and a tribute to the PME-NA members who were affected by the COVID-19 pandemic. [These proceedings were produced with Cinvestav (Centro de Investigación y de Estudios Avanzados del IPN), México and AMIUTEM (Asociación Mexicana de Investigadores del Uso de Tecnología en Educación Matemática, A.C.), México. Individual papers are indexed in ERIC.]

Informal inference is a critical practice for students to engage in if they are to understand formal statistical methods. However, during informal inference students often utilize complex ideas that many in-service teachers are not prepared for as they have not had the opportunity to think deeply about statistics and develop statistical knowledge for teaching (Groth, 2013). Research shows that engaging teachers in authentic inquiry of content supports the development of that content knowledge, and there is an urgent need to do so through professional developments (PDs). However, there is limited literature concerning PDs in statistics education, and a dearth of research focusing on teachers' engagement with informal inference tasks. This paper describes in detail how two teachers engaged with a seminal informal inference task during a PD, including their reasoning about variability and sample size when making inferences. [For the complete proceedings, see ED606556.]

The goal of the proposed working group is to create a space for those interested in researching issues around the teaching and learning of statistics to meet, discuss, synthesize past research, and begin to strategize ways of leveraging multiple perspectives and expertise to identify and address current challenges in statistics education. The nature of statistics being a methodological discipline make it such that statistics education is made up of a diverse array of people from various backgrounds, disciplines, fields, interests and expertise. We propose this working group to create a space for dialogue among people with diverse perspectives to tackle important issues in the teaching and learning of statistics. Diverse perspective help to look at problems in new ways and come up with new solutions. However, we also want to pragmatically make progress towards a goal, which requires some common direction as well. To balance these tensions we frame our work in the notion of learning environments as a way of organizing past work as well as ideas for future projects into a meaningful structure. Additionally we are layering on the consideration of teachers and teaching in the design and enactment of learning environments. [For the complete proceedings, see ED606556.]

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67 research reports, 184 brief research reports, 126 posters, and 13 working groups. Chapters include the following: (1) Plenaries; (2) Curriculum, Technology, and Assessment; (3) Early Algebra, Algebra, and Number Concepts; (4) Equity and Justice; (5) Geometry, Measurement, Statistics, and Probability; (6) In-Service Teacher Education and Professional Development; (7) Instructional Leadership, Policy, and Institutions/Systems; (8) Mathematical Knowledge for Teaching; (9) Mathematical Processes; (10) Precalculus, Calculus, and Higher Mathematics; (11) Pre-Service Teacher Education; (12) Student Learning and Related Factors; (13) Teaching and Classroom Practice; (14) Theory, Research Methods, and Miscellaneous Topics; and (15) Working Groups. [These proceedings were co-published by University of Missouri, St. Louis. Individual plenary and research papers are available in ERIC.]

It is acknowledged that there are connections between language use and mathematics in mathematics education, and the potential challenges this issue can pose have been investigated by researchers. Yet how the challenges can be overcome in statistics classrooms, where language is even more important as a medium of instruction, has received very little scrutiny. This article reports on research carried out in three New Zealand largely Pasifika dominated Year-12 classes. Findings from the teacher reflection aspect of the study indicate that teachers can struggle with how to use home language and real-life contexts to maximise learning in their classrooms. Some strategies to incorporate students' home language in their learning worked better than others. However, more research is needed to explore language issues and the barriers they might present in statistics education in greater depth.

The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum: Algebraic Reasoning, Geometrical and Spatial Reasoning, and Statistical Reasoning. [References after each paper.]

Data is everywhere. As a result the need for data scientists with the correct skill set to analyze and interpret the data has escalated. Not surprisingly, data scientists are currently one of the most wanted professions. Tertiary institutions are faced with the challenge of producing students with the correct blend of theoretical knowledge and practical skills. In an attempt to provide current post-graduate students with these skills, a flipped class room approach was adopted to teach students data warehousing as part of the data science curriculum. This paper used the four pillars of F-L-I-P (FLN 2014) to analyze data obtained from lecturer implementation experience and student course evaluation forms. It was shown that great strides have been made in this course in the adoption of the flipped class room although there is room for improvement in order to achieve flipped learning. The outcome of the study directly contributes to the improvement of subsequent implementations of the module. [For full proceedings, see ED571459.]

These Proceedings are a written record of the research presented at the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Greenville, South Carolina, November 15-18, 2018. The theme of the conference is "Looking Back, Looking Ahead: Celebrating 40 Years." The Proceedings include papers from 6 plenary papers, 69 research reports, 133 posters, and 17 working groups. Papers from the research reports, brief research reports, and posters are organized into chapters by topics. Chapters include the following: (1) Plenary Papers; (2) Curriculum and Related Factors; (3) Early Algebra, Algebra, and Number Concepts; (4) Geometry and Measurement; (5) Inservice Teacher Education/Professional Development; (6) Mathematical Knowledge for Teaching; (7) Mathematical Processes; (8) Preservice Teacher Education; (9) Statistics and Probability; (10) Student Learning and Related Factors; (11) Teaching and Classroom Practice; (12) Technology; (13) Theory and Research Methods; and (14) Working Groups. [Individual plenary and research papers are available in ERIC.]

With online learning becoming a more viable option for teachers to develop their expertise, our report shares one such effort focused on improving the teaching of statistics. We share design principles and learning opportunities, as well as discuss specific impacts evident in classroom teachers' course activity concerning changes to their beliefs and perspectives about statistics. Specific course experiences that served as triggers for critical reflection are discussed. [For complete proceedings, see ED581294.]

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school Mathematics teacher taught a lesson in Statistics where the students had the task create a pie graph representing the data. Results show us that their procedural vision of Statistics lead them to focus more on a graphical representation and thus led to avoid all statistical reasoning development (Garfield, 2002).

The article reviews features of teaching Medical Informatics and Statistics. The course is referred to the disciplines of Mathematical and Natural sciences. The course is provided in all the faculties of I. M. Sechenov First Moscow State Medical University. For students of Preventive Medicine Department the time frame allotted for studying the course is significantly larger than for similar course provided at other faculties. To improve the teaching methodology of the discipline an analysis of the curriculum has been carried out, attendance and students' performance statistics have been summarized. As a result, the main goals and objectives have been identified. Besides, general educational functions and the contribution to the solution of problems of education, students' upbringing and development have been revealed; two stages of teaching have been presented. Recommendations referred to the newest methodological development aimed at improving the quality of teaching the discipline are provided. The ways of improving the methods and organizational forms of education are outlined. [For the complete Volume 15 proceedings, see ED574185.]

The theme of this year's conference is "Sin Fronteras: Questioning Borders with(in) Mathematics Education." This theme is intended to encourage research presentations, discussion, and reflection on the variety of borders within mathematics education, as well as those that might be probed, challenged, explained, enhanced and/or potentially transformed by mathematics education. Sessions examine topics such as geographic, political, cultural and language borders with(in) mathematics education, as well as borders between mathematical content areas and grade levels, and how borders can limit access to mathematical content or impact mathematics teaching practices. To catalyze conversations about the conference theme, the organizers of this conference organized three plenary talks that each address different perspectives on borders with(in) mathematics education. The 2016 conference was attended by over 550 researchers, faculty, and graduate students from around the world including the US, Mexico, Canada, Sweden, Australia, Chile, Puerto Rico, Israel, Trinidad and Tobago, and Germany. Submissions received numbered 581. The acceptance rate was 92% for working groups, 48% for research reports, 36% for brief research reports, and 61% for posters. The conference program includes 104 Research Report sessions, 102 Brief Research Report sessions, 222 Posters, and 11 Working Groups. It is the hope of the organizers that this would be a model to follow in future Psychology of Mathematics Education-North American Chapter conferences. Chapters include: (1) Plenary Papers; (2) Curriculum and Related Factors; (3) Early Algebra, Algebra, and Number Concepts;(4) Geometry and Measurement; (5) Inservice Teacher Education/Professional Development; (6) Mathematical Knowledge for Teaching; (7) Mathematical Processes; (8) Preservice Teacher Education; (9) Statistics and Probability; (10) Student Learning and Related Factors; (11) Teaching and Classroom Practice; (12) Technology; (13) Theory and Research Methods; and (14) Working Groups. Individual papers include references. [Individual plenary and research papers are available in ERIC. Some papers are written in both Spanish and English.]

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and ties in with the joint day of presentations with the 21st biennial conference of the Australian Association of Mathematics Teachers (AAMT). This special feature highlights the benefits of collaboration between researchers, practicing classroom teachers, and curriculum developers. Volume 1 contains the following papers: (1) The Beginnings of MERGA (Ken Clements); (2) Teaching and Learning by Example: The Annual Clements/Foyster Lecture (Helen L. Chick); (3) Introducing Students to Data Representation and Statistics (Richard Lehrer); (4) Studies in the Zone of Proximal Awareness (John Mason, Helen Drury and Liz Bills); (5) Empowered to Teach: A Practice-based Model of Teacher Education (Janette Bobi); (6) Communicating Students' Understanding of Undergraduate Mathematics using Concept Maps (Karoline Afamasaga-Fuata'i); (7) Primary Student Teachers' Diagnosed Mathematical Competence in Semester One of their Studies (Karoline Afamasaga-Fuata'i, Paul Meyer and Naomi Falo); (8) An Online Survey to Assess Student Anxiety and Attitude Response to Six Different Mathematical Problems (Vincent Anderson); (9) Mathematical Investigations: A Primary Teacher Educator's Narrative Journey of Professional Awareness (Judy Bailey); (10) Describing Mathematics Departments: The Strengths and Limitations of Complexity Theory and Activity Theory (Kim Beswick, Anne Watson and Els De Geest); (11) Three Student Tasks in a Study of Distribution in a "Best Practice" Statistics Classroom (Anthony Bill and Jane Watson); (12) Teacher Researchers Questioning their Practice (Linda Bonne & Ruth Pritchard); (13) Imagined Classrooms: Prospective Primary Teachers Visualise their Ideal Mathematics Classroom (Kathy Brady); (14) Early Notions of Functions in a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill Brown); (15) Collective Argumentation and Modelling Mathematics Practices Outside the Classroom (Raymond Brown and Trevor Redmond); (16) Visual Perturbances in Digital Pedagogical Media (Nigel Calder); (17) Professional Experience in Learning to Teach Secondary Mathematics: Incorporating Pre-service Teachers into a Community of Practice (Michael Cavanagh and Anne Prescott); (18) Young Children's Accounts of their Mathematical Thinking (Jill Cheeseman and Barbara Clarke); (19) Mathematical Reform: What Does the Journey Entail for Teachers? (Linda Cheeseman); (20) Year Six Fraction Understanding: A Part of the Whole Story (Doug M. Clarke, Anne Roche and Annie Mitchell); (21) Teaching as Listening: Another Aspect of Teachers' Content Knowledge in the Numeracy Classroom (Ngaire Davies and Karen Walker); (22) Essential Differences between High and Low Performers' Thinking about Graphically-Oriented Numeracy Items (Carmel M. Diezmann, Tom J. Lowrie and Nahum Kozak); (23) High School Students' Use of Patterns and Generalizations (Jaguthsing Dindyal); (24) The Teacher, The Tasks: Their Role in Students' Mathematical Literacy (Katherine Doyle); (25) Informal Knowledge and Prior Learning: Student Strategies for Identifying and Locating Numbers on Scales (Michael Drake); (26) Documenting the Knowledge of Low-Attaining Third- and Fourth-Graders: Robyn's and Bel's Sequential Structure and Multidigit Addition and Subtraction (David Ellemor-Collins, Robert Wright and Gerard Lewis); (27) Interdisciplinary Modelling in the Primary Mathematics Curriculum (Lyn English); (28) Students' Tendency to Conjoin Terms: An Inhibition to Their Development of Algebra (Judith Falle); (29) Towards "Breaking the Cycle of Tradition" in Primary Mathematics (Sandra Frid and Len Sparrow); (30) Exploring the Number Knowledge of Children to Inform the Development of a Professional Learning Plan for Teachers in the Ballarat Diocese as a Means of Building Community Capacity (Ann Gervasoni, Teresa Hadden and Kathie Turkenburg); (31) Technology-Enriched Teaching of Secondary Mathematics: Factors Influencing Innovative Practice (Merrilyn Goos and Anne Bennison); (32) Supporting an Investigative Approach to Teaching Secondary School Mathematics: A Professional Development Model (Merrilyn Goos, Shelley Dole, and Katie Makar); (33) Identity and Mathematics: Towards a Theory of Agency in Coming to Learn Mathematics (Peter Grootenboer and Robyn Zevenbergen); (34) Categorisation of Mental Computation Strategies to Support Teaching and to Encourage Classroom Dialogue (Judy Hartnett); (35) Student Experiences of VCE Further Mathematics (Sue Helme and Stephen Lamb); (36) Video Evidence: What Gestures Tell Us About Students' Understanding of Rate of Change (Sandra Herbert and Robyn Pierce); (37) The Role of Dynamic Interactive Technological Tools in Preschoolers' Mathematical Patterning (Kate Highfield and Joanne Mulligan); (38) Students Representing Mathematical Knowledge through Digital Filmmaking (Geoff Hilton); (39) What Does it Mean for an Instructional Task to be Effective? (Lynn Hodge, Jana Visnovska, Qing Zhao and Paul Cobb); (40) A School-Community Model for Enhancing Aboriginal Students' Mathematical Learning (Peter Howard and Bob Perry); (41) Benchmarking Preservice Teachers' Perceptions of their Mentoring for Developing Mathematics Teaching Practices (Peter Hudson); (42) Relational or Calculational Thinking: Students Solving Open Number Equivalence Problems (Jodie Hunter); (43) Scaffolding Small Group Interactions (Roberta Hunter); (44) Numeracy in Action: Students Connecting Mathematical Knowledge to a Range of Contexts (Chris Hurst); and (45) A Story of a Student Fulfilling a Role in the Mathematics Classroom (Naomi Ingram). Volume 2 contains the following papers: (1) Secondary-Tertiary Transition: What Mathematics Skills Can and Should We Expect This Decade? (Nicolas Jourdan, Patricia Cretchley and Tim Passmore); (2) The Power of Writing for all Pre-service Mathematics Teachers (Keith McNaught); (3) "Connection Levers:" Developing Teachers' Expertise with Mathematical Inquiry (Katie Makar); (4) Acquiring the Mathematics Register in te reo Maori (Tamsin Meaney, Uenuku Fairhall and Tony Trinick); (5) Teaching Ratio and Rates for Abstraction (Mike Mitchelmore, Paul White and Heather McMaster); (6) Setting a Good Example: Teachers' Choice of Examples and their Contribution to Effective Teaching of Numeracy (Tracey Muir); (7) Developing the Concept of Place Value (Mala Saraswathy Nataraj and Michael O. J. Thomas); (8) Interdisciplinary Learning: Development of Mathematical Confidence, Value, and the Interconnectedness of Mathematics Scales (Dawn Kit Ee Ng and Gloria Stillman); (9) Mathematical Methods and Mathematical Methods Computer Algebra System (CAS) 2006--Concurrent Implementation with a Common Technology Free Examination (Pam Norton, David Leigh-Lancaster, Peter Jones and Michael Evans); (10) A Concrete Approach to Teaching Symbolic Algebra (Stephen Norton and Jane Irvin); (11) Developing Positive Attitudes towards Algebra (Stephen Norton and Jane Irvin); (12) Changing Our Perspective on Measurement: A Cultural Case Study (Kay Owens and Wilfred Kaleva); (13) Enhancing Student Achievement in Mathematics: Identifying the Needs of Rural and Regional Teachers in Australia (Debra Panizzon and John Pegg); (14) The Growth of Early Mathematical Patterning: An Intervention Study (Marina Papic and Joanne Mulligan); (15) Whole Number Knowledge and Number Lines Help to Develop Fraction Concepts (Catherine Pearn and Max Stephens); (16) Identifying and Analysing Processes in NSW Public Schooling Producing Outstanding Educational Outcomes in Mathematics (John Pegg, Debra Panizzon and Trevor Lynch); (17) Teachers Research their Practice: Developing Methodologies that Reflect Teachers' Perspectives (Ruth Pritchard and Linda Bonne); (18) Teacher Professional Learning in Mathematics: An Example of a Change Process (Pauline Rogers); (19) Seeking Evidence of Thinking and Mathematical Understandings in Students' Writing (Anne Scott); (20) Utilising the Rasch Model to Gain Insight into Students' Understandings of Class Inclusion Concepts in Geometry (Penelope Serow); (21) Exploring Teachers' Numeracy Pedagogies and Subsequent Student Learning across Five Dimensions of Numeracy (Jane Skalicky); (22) The Complexities for New Graduates Planning Mathematics Based on Student Need (Carole Steketee and Keith McNaught); (23) Students' Emerging Algebraic Thinking in the Middle School Years (Max Stephens); (24) A Framework for Success in Implementing Mathematical Modelling in the Secondary Classroom (Gloria Stillman, Peter Galbraith, Jill Brown and Ian Edwards); (25) Eliciting Positive Student Motivation for Learning Mathematics (Peter Sullivan and Andrea McDonough); (26) Learning from Children about their Learning with and without ICT using Video-Stimulated Reflective Dialogue (Howard Tanner and Sonia Jones); (27) Dependency and Objectification in a Year 7 Mathematics Classroom: Insights from Sociolinguistics (Steve Thornton); (28) Pedagogical Practices with Digital Technologies: Pre-service and Practicing Teachers (Colleen Vale); (29) Procedural Complexity and Mathematical Solving Processes in Year 8 Mathematics Textbook Questions (Jill Vincent and Kaye Stacey); (30) Designing Effective Professional Development: How do we Understand Teachers' Current Instructional Practices? (Jana Visnovska); (31) "Doing Maths:" Children Talk About Their Classroom Experiences (Fiona Walls); (32) The Role of Pedagogy in Classroom Discourse (Margaret Walshaw and Glenda Anthony); (33) Australian Indigenous Students: The Role of Oral Language and Representations in the Negotiation of Mathematical Understanding (Elizabeth Warren, Janelle Young and Eva deVries); (34) Student Change Associated with Teachers' Professional Learning (Jane Watson, Kim Beswick, Natalie Brown and Rosemary Callingham); (35) Choosing to Teach in the "STEM" Disciplines: Characteristics and Motivations of Science, ICT, and Mathematics Teachers (Helen M. G. Watt, Paul W. Richardson and James Pietsch); (36) Percentages as Part Whole Relationships (Paul White, Sue Wilson, Rhonda Faragher and Mike Mitchelmore); (37) My Struggle with Maths May Not Have Been a Lonely One: Bibliotherapy in a Teacher Education Number Theory Unit (Sue Wilson); (38) Students' Conceptual Understanding of Equivalent Fractions (Monica Wong and David Evans); (39) Statistics Teachers as Scientific Lawyers (Joanne Woodward and Maxine Pfannkuch); (40) Developing Pedagogical Tools for Intervention: Approach, Methodology, and an Experimental Framework (Robert Wright, David Ellemor-Collins and Gerard Lewis); (41) Pedagogy and Interactive Whiteboards: Using an Activity Theory Approach to Understand Tensions in Practice (Robyn Zevenbergen and Steve Lerman); (42) International Perspectives on Early Years Mathematics (Jillian Fox); (43) Early Childhood Mathematics Education Research: What is Needed Now? (Bob Perry and Sue Dockett); (44) Trimangles and Kittens: Mathematics Within Socio-dramatic Play in a New Zealand Early Childhood Setting (Shiree Lee); (45) Children's Number Knowledge in the Early Years of Schooling (Ann Gervasoni); (46) Listening to Students' Voices in Mathematics Education (Brian Doig, Susie Groves, Coral Campbell, Judith Mousley, and Gaye Williams); (47) Students' Pedagogical Knowledge: A Source of Pedagogical Content Knowledge (Brian Doig and Susie Groves); (48) Research Enriched by the Student Voice (Gaye Williams); (49) Listening to Student Opinions about Group Assessment (Judith Mousley and Coral Campbell); (50) Profiles of Thinking Skills and Levels of Motivation in a Problem-Solving Task (Sarah Buckley, Mary Ainley and Pip Pattison); (51) An Investigation of Mathematics Strategies in Traditional School Contexts and Real-World Contexts (Julie Clark and Kathy Brady); (52) Maori Student's Perspective on Their Mathematical Journey Through Maori Medium (Leeana Herewini); (53) Some Methodological Considerations in the Estonian Study about Students' Beliefs in Mathematics: Is Triangulation Necessary? (Kirsti Kislenko); (54) Progress in Mathematics--Learning through Home School Partnership (Denise Smith and Gaynor Terrill); (55) Exploring Data Representation and Statistical Reasoning through Integrated Investigations in a Grade 2 Classroom (Karen Ahearn); (56) Reform and Assessment Practice: The Need for an Investigation (Julie Anderson); (57) Autobiographical Research and Mathematics Curriculum (Andy Begg); (58) Mathematically Gifted Students Managing School Transfer (Brenda Bicknell); (59) Improving Procedures for Effective Teaching (Murray Black, Farida Kachapova and Ilias Kachapov); (60) Using Counter-Examples and Paradoxes in Teaching Probability: Students' Attitudes (Murray Black, Farida Kachapova, Sergiy Klymchuk and Ilias Kachapov); (61) Using Cabri Geometry to Explore the Geometric Properties of Parallelograms in Year 7 Mathematics Classrooms (Sahar Bokosmaty); (62) Defining Teacher Knowledge Needed in the Teaching of Statistics at Primary School Level (Tim Burgess); (63) Year 12 Students' Participation in Higher Mathematics Courses (Mohan Chinnappan, Stephen Dinham, Tony Herrington and Dale Scott); (64) Pre-service Primary Teachers Developing Positive Attitudes towards Teaching Mathematics (Julie Clark); (65) Measuring the Effectiveness and Efficiency of Language-In-Use for Algebra Learning: A Multi-Level Nested Modelling and DEA Approach (Robert de la Serna); (66) Te Poutama Tau (TPT): An Indigenous Response to the Numeracy Development Project 2002-2006 (Wini Emery and Leeana Herewini); (67) "I Have a Fear of Maths and it Does Worry Me a Bit as a Future Teacher:" The Cycle of Maths Anxiety (Gillian Frankcom); (68) Using Electronic Handwriting and Tablet PCs to Enhance Distance Students' Understanding of First Year Mathematics at University (Linda Galligan, Birgit Loch, Janet Taylor and Christine McDonald); (69) Mathematical Modelling in CAS Clothing (Vince Geiger, Rhonda Faragher and Trevor Redmond); (70) The Cognitive and Pedagogical Affordances of Digital Learning Tools on Early Mathematical Development (Kristy Goodwin, Joanne Mulligan and John Hedberg); (71) Revisions and Extensions of a Pirie-Kieren-Based Teaching Model (Peter Hughes); (72) An Insight into Norwegian Students' Thoughts about Mathematics (Kirsti Kislenko); (73) The Impact of Didactical Contract on Students' Perceptions of their Intentional Learning Acts (Troels Lange and Tamsin Meaney); (74) The Impact of an Intervention on the Development of Mathematical Pattern and Structure in the First Year of Schooling (Joanne Mulligan, Mike Mitchelmore, Coral Kemp, Jennie Marston and Kate Highfield); (75) Activity Theory as a Framework to Analyse the Positive Influence of Formative Assessment on Student Learning (Trish O'Toole); (76) Teaching Geometry with CAS in the Junior Secondary Classroom: A Case Study (Warren Palmer); (77) Wanted: One Great Maths Teacher! (Pamela Perger); (78) Building Early Childhood Educators' Knowledge, Skills and Confidence in the Facilitation and Assessment of Young Children's Mathematical Learning (Bob Perry, Elspeth Harley and Sue Dockett); (79) CAS in the Middle Secondary Years: Strengths, Weaknesses, Opportunities and Threats (Robyn Pierce); (80) Myths and Positioning: Insights from Hermeneutics (Steve Thornton); (81) Misconceptions in Locating Negative Decimals on the Number Line (Wanty Widjaja, Kaye Stacey and Vicki Steinle); and (82) Proportional Reasoning: A Global or Localised Development? (Vince Wright). [Individual papers contain references, figures, tables, and appendices.

The research reported here uses a pre/post-test model and stimulated recall interviews to assess teachers' statistical reasoning about comparing distributions, when enrolled in a graduate-level statistics education course. We discuss key aspects of the course design aimed at improving teachers' learning and teaching of statistics, and the resulting different ways of reasoning about comparing distributions that teachers exhibited before and after the course.

The theme of this year's conference is "Critical Responses to Enduring Challenges in Mathematics Education." The theme of this year's conference invites mathematics education scholars to reflect upon and critically respond to enduring challenges in teaching and learning mathematics for all students. To ignite discussion within the field, the organizers of this conference organized the conference around four focal-enduring challenges, each of which is featured in one of four plenary talks: (1) teaching as responsive to various conceptions of mathematics; (2) addressing the needs of marginalized populations in school mathematics; (3) the impact of teacher evaluation and high-stakes assessment in teaching; and (4) the role of assessment in teaching and learning. It is the hope of the organizers that the conference will catalyze collective reflection, collaborative inquiry, and discussion about various means for responding to and addressing these, and other, challenges. Submissions received numbered 528. The overall acceptance rate was 64%. The conference program includes 92 Research Report sessions, 96 sessions, 136 Posters, and 12 Working Groups. Chapters include: (1) Plenary Papers; (2) Special Session; (3) Curriculum and Related Factors; (4) Early Algebra, Algebra, and Number Concepts; (5) Geometry and Measurement; (6) Mathematical Processes; (7) Statistics and Probability; (8) Student Learning and Related Factors; (9) Teacher Education and Knowledge; (10) Teaching and Classroom Practice; (11) Technology; (12) Theory and Research Methods; and (13) Working Groups. [Individual plenary and research papers are available in ERIC. Financial and personnel support was provided by the Michigan State University CREATE for STEM Institute.]

In June 2018 the Canadian Mathematics Education Study Group/Groupe Canadien d'étude en didactique des mathématiques (CMESG/GCEDM) held its 42nd meeting in the idyllic setting of Squamish, British Columbia. This meeting marked the first time CMESG/GCEDM had been in British Columbia since 2010 and the first time it had been held at Quest University. Among the more than 150 attendees were 35 teachers, 17 of whom had been funded by the British Columbia Association of Mathematics Teachers (BCAMT) and the Pacific Institute for Mathematical Sciences (PIMS) to attend the meeting. The meeting featured a scientific program organized into five working groups, six topic sessions, eight new PhD presentations, 16 gallery walk presentations, and six Ad Hoc sessions. Thirty-four papers are included in these proceedings--two are written in French, four are provided in both French and English, and the remainder are written in English. [For the 2017 proceedings, see ED589990.]

In this study, we examined the ways in which teachers' statistical knowledge is enacted during instructional practice. Using classroom video recordings from three middle-grades' teachers, we qualitatively analyzed the conversations around a task designed to develop students' knowledge of statistical sampling. Our analyses showed how teachers' selection and use of contexts during instruction impacted students' opportunities for statistical reasoning. Our research extends other literature that has begun to identify the statistical knowledge needed for teaching. [For the complete proceedings, see ED584443.]

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning. The Proceedings include papers from 1 plenary talk, 2 panel presentations, 68 research reports, 121 brief research reports, 208 posters, and 14 working groups. Chapters include:(1) Plenary Papers; (2) Curriculum and Related Factors; (3) Early Algebra, Algebra, and Number Concepts; (4) Geometry and Measurement; (5) Math Processes; (6) Statistics and Probability; (7) Student Learning and Related Factors; (8) Teacher Education and Knowledge; (9) Teaching and Classroom Practice; (10) Technology; (11) Theory and Research Methods; and (12) Working Groups. Individual papers include references. [Individual plenary and research papers are available in ERIC.]