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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).

We are delighted to welcome you to the International Conference on Education and New Developments 2015-END 2015, taking place in Porto, Portugal, from 27 to 29 of June. Education, in our contemporary world, is a right since we are born. Every experience has a formative effect on the constitution of the human being, in the way one thinks, feels and acts. One of the most important contributions resides in what and how we learn through the improvement of educational processes, both in formal and informal settings. Our International Conference seeks to provide some answers and explore the processes, actions, challenges and outcomes of learning, teaching and human development. Our goal is to offer a worldwide connection between teachers, students, researchers and lecturers, from a wide range of academic fields, interested in exploring and giving their contribution in educational issues. We take pride in having been able to connect and bring together academics, scholars, practitioners and others interested in a field that is fertile in new perspectives, ideas and knowledge. We counted on an extensive variety of contributors and presenters, which can supplement our view of the human essence and behavior, showing the impact of their different personal, academic and cultural experiences. This is, certainly, one of the reasons we have many nationalities and cultures represented, inspiring multi-disciplinary collaborative links, fomenting intellectual encounter and development. END 2015 received 528 submissions, from 63 different countries, reviewed by a double-blind process. Submissions were prepared to take form as Oral Presentations, Posters, Virtual Presentations and Workshops. It was accepted for presentation in the conference, 176 submissions (33% acceptance rate). The conference also includes a keynote presentation from an internationally distinguished researcher, Professor Dr. Martin Braund, Adjunct Professor at Cape Peninsula University of Technology in Cape Town, South Africa and Honorary Fellow in the Department of Education at the University of York, UK, to whom we express our most gratitude. This volume is composed by the proceedings of the International Conference on Education and New Developments (END 2015), organized by the World Institute for Advanced Research and Science (W.I.A.R.S.) and had the help of our respected media partners that we reference in the dedicated page. This conference addressed different categories inside the Education area and papers are expected to fit broadly into one of the named themes and sub-themes. To develop the conference program we have chosen four main broad-ranging categories, which also cover different interest areas: (1) In TEACHERS AND STUDENTS: Teachers and Staff training and education; Educational quality and standards; Curriculum and Pedagogy; Vocational education and Counseling; Ubiquitous and lifelong learning; Training programs and professional guidance; Teaching and learning relationship; Student affairs (learning, experiences and diversity); Extra-curricular activities; Assessment and measurements in Education. (2) In PROJECTS AND TRENDS: Pedagogic innovations; Challenges and transformations in Education; Technology in teaching and learning; Distance Education and eLearning; Global and sustainable developments for Education; New learning and teaching models; Multicultural and (inter)cultural communications; Inclusive and Special Education; Rural and indigenous Education; Educational projects. (3) In TEACHING AND LEARNING: Educational foundations; Research and development methodologies; Early childhood and Primary Education; Secondary Education; Higher Education; Science and technology Education; Literacy, languages and Linguistics (TESL/TEFL); Health Education; Religious Education; Sports Education. (4) In ORGANIZATIONAL ISSUES: Educational policy and leadership; Human Resources development; Educational environment; Business, Administration, and Management in Education; Economics in Education; Institutional accreditations and rankings; International Education and Exchange programs; Equity, social justice and social change; Ethics and values; Organizational learning and change. The proceedings contain the results of the research and developments conducted by authors who focused on what they are passionate about: to promote growth in research methods intimately related to teaching, learning and applications in Education nowadays. It includes an extensive variety of contributors and presenters, who will extend our view in exploring and giving their contribution in educational issues, by sharing with us their different personal, academic and cultural experiences. (Individual papers contain references.)

Though there has been limited empirical research on the cost component from the expectancy-value model, a recent interest in the construct has spurred advances in theory and measurement. We present a longitudinal analysis of four types of cost: effort, loss of valued alternatives, emotional, and outside cost. We focus on how cost changes over time in a critical short-term setting: gatekeeper courses. These courses are introductory university courses with high drop, withdrawal, and fail rates. We present data from calculus and statistics. In both samples we found that cost was strongly, negatively related to expectancy, and moderately, negatively related to value. Cost was also a significant predictor of course performance, with emotional cost having the largest effect.

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.]

This submission contains the Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of New Brunswick in Fredricton, New Brunswick. 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, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc sessions and a panel discussion. Papers include: (1) Understanding Abstraction in Mathematics Education: Meaning, Language, Gesture, and the Human Brain (Rafael Nunez); (2) Mathematics Departments, New Faculty, and the Future of Collegiate Mathematics (T. Christine Stevens); (3) Outreach in Mathematics--Activities, Engagement, & Reflection (Veronique Hussin and Eric Muller); (4) Geometry, Space, and Technology: Challenges for Teachers and Students (Shelley Hunter, Donna Kotsopoulos, and Walter Whiteley); (5) The Design and Implementation of Learning Situations (Anna McQuillan, Fernando Hitt, and Luis Radford); (6) The Multifaceted Role of Feedback in the Teaching and Learning of Mathematics (Jerome Proulx and Florence Glanfield); (7) Mathematics Educational Neuroscience: Origins, Activities, and New Opportunities (Stephen R. Campbell); (8) Communicating the Excitement and Beauty of Mathematics (Malgorzata Dubiel); (9) Conception et experimentation de situations didactiques au prescolaire/primaire / Design and Experimentation of Didactical Situations in Kindergarten and Elementary School (Jacinthe Giroux) [Written in French]; (10) Cabri 3D: An Environment for Purposeful Mathematical Activity? (Kate Mackrell); (11) Equity and Opportunities to Learn in Cooperative Mathematical Work (Indigo Esmond); (12) (Elargir les) Connaissances mathematiques des enseignants de mathematiques du secondaire: une etude sur la formation continue / (Enlarging) Secondary-Level Mathematics Teachers' Mathematical Knowledge: An Investigation of Professional Development (Jerome Proulx) [Presented in both French and English]; (13) Un paradigme d'experimentation au laboratoire de sciences pour l'identification et l'optimisation statistique d'un modele algebrique par interaction visuo-graphique (Georges Touma) [Written in French]; (14) What Factors Influence Understanding of Written Arithmetic Problems? (Dominic Voyer); (15) Probabilities / Probabilites (Egan Chernoff and Annie Savard); (16) First Steps toward an Archeology of Gesture in Graphing (Susan Gerofsky); (17) Function Modelling Using Secondary Data from Statistics Canada's E-STAT Database (Jennifer Hall); (18) Explanation and Proof in Mathematics and Mathematics Education (Gilla Hanna, Ella Kaye, and Riaz Saloojee); (19) Exploring Our Embodied Knowing of the Gauss-Bonnet Theorem: Barn-Raising and Endo-Pentakis-Icosi-Dodecahedron (Eva Knoll); (20) Mathematical Biography (John Grant McLoughlin); (21) This Is Mathematics; This Isn't Mathematics; But That... I'm Not So Certain About: The Possible "Emancipation" of Secondary School Mathematics from the Bonds of "Real" Mathematics (Craig Newell); and (22) What Courses Could or Should Mathematics Departments Offer to Graduate Programs in Mathematics Education? (France Caron, Morris Orzech, and Elaine Simmt). Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lecture at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2006 proceedings, see ED529562.]

This submission contains the Proceedings of the 2006 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Calgary in Calgary, Alberta. 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, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc sessions and a joint session with the Canadian Mathematical Society. Papers include: (1) Developmental Research in Mathematics Teaching and Learning: Developing Learning Communities Based on Inquiry and Design (Barbara Jaworski); (2) Mathematics as Medicine (Edward Doolittle); (3) Secondary Mathematics Teacher Development / La formation des enseignants de mathematiques du secondaire (Joyce Mgombelo, Morris Orzech, David Poole, and Sophie Rene de Cotret); (4) Developing Links between Statistical and Probabilistic Thinking in School Mathematics Education / Le developpement de liens entre la pensee statistique et al pensee probabiliste dans l'apprentissage des mathematiques a l'ecole (Steward Craven, Linda Gattuso, and Cynthia Nicolson); (5) Developing Trust and Respect When Working with Teachers of Mathematics (Chris Breen, Julie Long, and Cynthia Nichol); (6) The Body, the Sense, and Mathematics Learning (Susan Gerofsky and Patricia Marchand); (7) Imagination and Digital Mathematical Performance (George Gadanidis); (8) Developing a Serious Enrichment Program (Keith F. Taylor); (9) Transforming Images of Mathematics/Teaching: A Study of Preservice Teachers/Teaching (Paul Betts); (10) Efficacy Shifts of Preservice Teachers Learning to Teach Mathematics (Cathy Bruce); (11) Composition of Functions and the Inverse Function of a Function: Main Ideas as Perceived by Teachers and Preservice Teachers (Calin Lucas); (12) Relations among "I," "Thou," and "It" in an Elementary Mathematics Professional Development Setting (Gladys Sterenberg); (13) Voices in the Silence: Narratives of Disadvantage, Social Context and School Mathematics in Post-Apartheid South Africa (Dalene M. Swanson); (14) Students, Teachers, Logarithms and I (Tetyana Berezovski); (15) Guitars & Mathematics -- Mathematiques et guitares (France Caron and David Lidstone); (16) Elluminating over Great Distance: Words and Images Cross the Waters (A. J. Dawson); (17) Mathematics Teaching and the Larger Purpose of Schooling: Developing "Moving Ideas" (Thomas Falkenberg); (18) A Framework for Reflecting on any "Learning Game" (Gary Flewelling); (19) Dialogical Relations in a Mathematics Classroom (Steven Khan); (20) Ethnomathematics and Audience (Lisa Lunney and David Wagner); (21) Team-Teaching Mathematics: Reflections on the Collaboration between a Mathematician and a Mathematics Educator (Ami Mamolo, Malgorzata Dubiel, and Peter Liljedahl); (22) What is Fundamental about the Fundamental Theorem of Calculus? (Bouchra Sabbagh and Olive Chapman); (23) "Why I'm Unhappy with Competition, Exams, Marks(!) and All that Stuff" (Peter Taylor); (24) E-STAT and Census at School as Resources for Inquiry-Based Mathematics Learning Using Authentic Data (Joel Yan); (25) A Teacher Education Success Story: A Collaborative Math and Health Assignment for Pre-Service Teachers Using the E-STAT Database (Joel Yan, Doug Franks, Barb Olmsted, and Mike McCabe); and (26) Does a Math Education PhD Program Belong in a Math Dept? (Peter Taylor, Pamela Hagen, Peter Liljedahl, and Lily Moshe). 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, figures, and tables. Individual papers contain references, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2005 proceedings, see ED529560.]

The theme 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) was "Mathematics Education at the Edge." 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 the 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.

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 proceedings report is divided into four sections that include: (1) two invited lectures by Colette Laborde and James Kaput on the topics of students' reading and writing of mathematics and an allegory in which writing is introduced into a technology-based mathematical society; (2) working group reports on the topics of fractal geometry in the curriculum, the socio-cultural aspects of mathematics, the role of technology in understanding mathematics as presented in nine appendices, and the implications constructivism has for the teacher; (3) topic group reports on the analysis of peer discussions in mathematics classes and their effects on pupil learning, children's behavior and thinking about partitioning, using software to develop pupil's probabilistic and statistical thinking, and discussion of the meaning of critical mathematics education; and (4) an ad hoc group report that discuss a constructivist approach to mathematics education. Appendices include lists of the conference participants and the ERIC document numbers for previous proceedings, and the paper "Our Theories, Ourselves" by Linda Brandau. (MDH)