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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 document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr and Dri: (1) The Odds of Understanding the Law of Large Numbers: A Design for Grounding Intuitive Probability in Combinatorial Analysis (Dor Abrahamson and Rose M. Cendak); (2) Imaginary-Symbolic Relations, Pedagogic Resources and the Constitution of Mathematics for Teaching in In-Service Mathematics Teacher Education (Jill Adler and Zain Davis); (3) Relationship between Pre-Service Mathematics Teachers' Teaching and Learning Beliefs and Their Practices (Hatice Akkoc and Feral Ogan-Bekiroglu); (4) Teachers' Awareness of Dimensions of Variation: A Mathematics Intervention Project (Thabit Al-Murani); (5) The Student Teacher and the Others: Multimembership on the Process of Introducing Technology in the Classroom (Nelia Amado and Susana Carreira); (6) Improving Student Teachers' Understanding of Fractions (Solange Amorim Amato); (7) Autodidactic Learning of Probabilistic Concepts through Games (Miriam Amit and Irma Jan); (8) Graduate Students' Processes in Generating Examples of Mathematical Objects (Samuele Antonini); (9) Reasoning in an Absurd World: Difficulties with Proof by Contradiction (Samuele Antonini and Maria Alessandra Mariotti); (10) Will Penelope Choose Another Bridegroom? Looking for an Answer through Signs (Ferdinando Arzarello, Luciana Bazzini, Francesca Ferrara, Ornella Robutti, Cristina Sabena, and Bruna Villa); (11) Motivation and Perceptions of Classroom Culture in Mathematics of Students across Grades 5 to 7 (Chryso Athanasiou and George N. Philippou); (12) Deductive Reasoning: Different Conceptions and Approaches (Michal Ayalon and Ruhama Even); (13) The Tendency to Use Intuitive Rules among Students with Different Piagetian Cognitive Levels (Reuven Babai); (14) Coming to Appreciate the Pedagogical Uses of CAS (Lynda Ball and Kaye Stacey); (15) Students' Conceptions of "m" and "c": How to Tune a Linear Function (Caroline Bardini and Kaye Stacey); (16) A Contradiction between Pedagogical Content Knowledge and Teaching Indications (Ibrahim Bayazit and Eddie Gray); (17) Identifying and Supporting Mathematical Conjectures through the Use of Dynamic Software (David Benitez Mojica and Manuel Santos Trigo); (18) Students Constructing Representations for Outcomes of Experiments (Palma Benko and Carolyn A. Maher); (19) Logarithms: Snapshots from Two Tasks (Tanya Berezovski and Rina Zazkis); (20) Trying to Reach the Limit--The Role of Algebra in Mathematical Reasoning (Christer Bergsten); (21) Semiotic Sequence Analysis--Constructing Epistemic Types Empirically (Angelika Bikner-Ahsbahs); (22) Service Teaching: Mathematical Education of Students of Client Departments (Erhan Bingolbali, John Monaghan, and Tom Roper); (23) Students' Thinking about the Tangent Line (Irene Biza, Constantinos Christou, and Theodossios Zachariades); (24) Habermas' Theory of Rationality as a Comprehensive Frame for Conjecturing and Proving in School (Paulo Boero); (25) Extending Students' Understanding of Decimal Numbers via Realistic Mathematical Modeling and Problem Posing (Cinzia Bonotto); (26) Different Media, Different Types of Collective Work in Online Continuing Teacher Education: Would You Pass the Pen, Please? (Marcelo C. Borba and Rubia B. A. Zulatto); (27) Reformulating "Mathematical Modelling" in the Framework of the Anthropological Theory of Didactics (Marianna Bosch, Fco. Javier Garcia, Josep Gascon, and Luisa Ruiz Higueras); (28) Students' Impressions of the Value of Games for the Learning of Mathematics (Leicha A. Bragg); (29) The Transition from Arithmetic to Algebra: To Reason, Explain, Argue, Generalize and Justify (Trygve Breiteig and Barbro Grevholm); (30) Resisting Reform Pedagogy: Teacher and Learner Contributions (Karin Brodie); (31) Manifestations of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (32) Types of Representations of the Number Line in Textbooks (Alicia Bruno and Noemi Cabrera); (33) Educational Neuroscience: New Horizons for Research in Mathematics Education (Stephen R. Campbell); (34) Variability in a Probability Context: Developing Pre-Service Teachers' Understanding (Daniel L. Canada); (35) Implementing a Reform-Oriented Mathematics Syllabus: A Survey of Secondary Teachers (Michael Cavanagh); (36) Student's Modelling with a Lattice of Conceptions in the Domain of Linear Equations and Inequations (Hamid Chaachoua, Marilena Bittar, and Jean-Francois Nicaud); (37) Using Reading and Coloring to Enhance Incomplete Prover's Performance in Geometry Proof (Ying-Hao Cheng and Fou-Lai Lin); (38) Aspects of Teachers' Pedagogical Content Knowledge for Decimals (Helen Chick, Monica Baker, Thuy Pham, and Hui Cheng); (39) Collaborative Action Research on Implementing Inquiry-Based Instruction in an Eighth Grade Mathematics Class: An Alternative Mode for Mathematics Teacher Professional Development (Erh-Tsung Chin, Yung-Chi Lin, Yann-Tyng Ko, Chi-Tung Chien, and Hsiao-Lin Tuan); (40) Routine and Novel Mathematical Solutions: Central-Cognitive or Peripheral-Affective Participation in Mathematics Learning (Mei-Shiu Chiu); (41) The Role of Self-Generated Problem Posing in Mathematics Exploration (Victor V. Cifarelli and Jinfa Cai); (42) A Longitudinal Study of Children's Mental Computation Strategies (Barbara Clarke, Doug M. Clarke, and Marj Horne); (43) Assessing Fraction Understanding Using Task-Based Interviews (Doug M. Clarke, Michal Sukenik, Anne Roche, and Annie Mitchell); (44) Evaluation of a Teaching Concept for the Development of Problem Solving Competences in Connection with Self-Regulation (Christina Collet and Regina Bruder); (45) Developing Probability Thinking in Primary School: A Case Study on the Constructive Role of Natural Language in Classroom Discussions (Valeria Consogno, Teresa Gazzolo, and Paulo Boero); (46) Collaboration with Teachers to Improve Mathematics Learning: Pedagogy at Three Levels (Tom J. Cooper, Annette R. Baturo, and Edlyn J. Grant); (47) "Aim High--Beat Yourself": Effective Mathematics Teaching in a Remote Indigenous Community (Tom J. Cooper, Annette R. Baturo, Elizabeth Warren, and Edlyn J. Grant); (48) Development of Children's Understanding of Length, Area, and Volume Measurement Principles (Margaret Curry, Michael Mitchelmore, and Lynne Outhred; (49) Mathematics-for-Teaching: The Cases of Multiplication and Division (Brent Davis, Elaine Simmt, and Dennis Sumara); (50) Generative Concept Images (Gary E. Davis and Catherine A. Pearn); (51) Developmental Assessment of Data Handling Performance Age 7-14 (Pauline Davis, Maria Pampaka, Julian Williams, and Lawrence Wo); (52) The Effect of Different Teaching Tools in Overcoming the Impact of the Intuitive Rules (Eleni Deliyianni, Eleni Michael, and Demetra Pitta-Pantazi); (53) Investigating Social and Individual Aspects in Teacher's Approaches to Problem Solving (Fien Depaepe, Erik De Corte, and Lieven Verschaffel); (54) Maths Avoidance and the Choice of University (Pietro Di Martino and Francesca Morselli); (55) Primary Students' Reasoning about Diagrams: The Building Blocks of Matrix Knowledge (Carmel M. Diezmann); (56) Integrating Errors into Developmental Assessment: "Time" for Ages 8-13 (Brian Doig, Julian Williams, Lawrence Wo, and Maria Pampaka); (57) Vygotsky's Everyday Concepts/Scientific Concepts Dialectics in School Context: A Case Study (Nadia Douek); (58) Creating Mathematical Models with Structures (Katherine Doyle); (59) Mechanisms for Consolidating Knowledge Constructs (Tommy Dreyfus, Nurit Hadas, Rina Hershkowitz, and Baruch Schwarz); and (60) Reconciling Factorizations Made with CAS and with Paper-and-Pencil: The Power of Confronting Two Media (Paul Drijvers, Carolyn Kieran, Andre Boileau, Fernando Hitt, Denis Tanguay, Luis Saldanha, and Jose Guzman). (Individual papers contain references.)

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary lectures include: (1) Modelling Students' Learning in Argumentation and Mathematics Proof (Fou-Lai Lin); (2) Travelling the Road to Expertise (Stacey); (3) Telling Identities (Sfar and Prusak); and (4) Co-Constructing Artefacts and Knowledge in Net-Based Teams (Reimann). The plenary panel section includes: (1) What Do Studies Like PISA Mean to the Mathematics Education Community? (Jones); (2) From a Profile to the Scrutiny of Student Performance (Yoshinori); (3) The PISA-Study (Neubrand); (4) Some Results from the PISA 2003 International Assessment of Mathematics Learning (Kieran); and (5) The Foundation and Spectacle of [the Leaning Tower of] PISA (Williams). The first research forum (RF01) includes: (1) Not Everything Is Proportional (De Brock, Van Dooren, and Verschaffel); (2) Designing Instruction on Proportional Reasoning with Average Speed (Gravemeijer, van Galen, and Keijzer); (3) Folding Perimeters (Friedlander and Arcavi); and (4) The Dolls' House Classroom (Ainley and Pratt). The second research forum (RF02) includes: (1) Shaping a Multi-Dimensional Analysis of Signs (Arzarello, Ferrara, Robutti, Paola, and Sabena); (2) Working with Artefacts (Bussi and Maschietto); (3) The Role of Gestures in Mathematical Discourse (Edwards); (4) Connecting Talk, Gesture, and Eye Motion for the Microanalysis of Mathematics Learning (Ferrara and Nemirovsky); (5) Why Do Gestures Matter? Gestures as Semiotic Means of Objectification (Radford); (6) Gestures, Signs and Mathematisation (Williams); and (7) Building Intellectual Infrastructure to Expose and Understand Ever-Increasing Complexity (Kaput). The third research forum (RF03) includes: (1) Using Growth Points to Describe Pathways for Young Children's Number Learning (Gervasoni); (2) Number Attainment in Sri Lankan Primary Schools (Hart); and (3) Mathematics Recovery (Pearn). The fourth research forum (RF04) includes: (1) The Place of Theory in Mathematics Education Research (Lester, Jr.); (2) Theories of Mathematics Education (Lerman); (3) The Articulation of Symbol and Mediation in Mathematics Education (Armella); (4) Using Theory to Advance Our Understandings of Student Cognitive Development (Pegg and Tall); (5) Trends in the Evolution of Models and Modeling Perspectives on Mathematical Learning and Problem Solving (Lesh and English); and (6) Issues and Tendencies in German Mathematics-Didactics (Torner and Sriraman). (Individual papers contain references.)

This document contains the second volume of the proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". This volume features 65 research report papers: (1) Constructing Meanings and Utilities within Algebraic Tasks (Janet Ainley, Liz Bills, and Kirsty Wilson); (2) Proportional Reasoning of Quasi-Illiterate Adults (Silvia Alatorre and Olimpia Figueras); (3) Uses of Example Objects in Proving (Lara Alcock); (4) Improving Student Teachers' Attitudes to Mathematics (Solange Amorim Amato); (5) Time and Flow as Parameters in International Comparisons: A View from an Eighth Grade Algebra Lesson (Miriam Amit and Michael N. Fried); (6) Disciplined Calculators or Flexible Problem Solvers? (Julia Anghileri); (7) A Statement, the Contrapositive and the Inverse: Intuition and Argumentation (Samuele Antonini); (8) Solution--What Does It Mean? Helping Linear Algebra Students Develop the Concept While Improving Research Tools (Ilana Arnon and David DeVries); (9) Organizing with a Focus on Defining a Phenomenographic Approach (Amir H. Asghari); (10) Mediation and Interpretation: Exploring the Interpersonal and the Intrapersonal in Primary Mathematics Lessons (Mike Askew); (11) Being Sensitive to Students' Mathematical Needs: What Does It Take? (Cettina Axiak); (12) A New Practice Evolving in Learning Mathematics: Differences in Students' Written Records with CAS (Lynda Ball and Kaye Stacey); (13) Empowering Andrea to Help Year 5 Students Construct Fraction Understanding (Annette R. Baturo); (14) Understanding Inverse Functions: The Relationship between Teaching Practice and Student Learning (Ibrahim Bayazit and Eddie Gray); (15) The Impact of Teachers' Perceptions of Student Characteristics on the Enactment of Their Beliefs (Kim Beswick); (16) Towards the Emergence of Constructing Mathematical Meanings (Angelika Bikner-Ahsbahs); (17) Identity, Knowledge and Departmental Practices: Mathematics of Engineers and Mathematicians (Erhan Bingolbali and John Monaghan); (18) Elementary Grades Students' Capacity for Functional Thinking (Maria L. Blanton and James J. Kaput); (19) For the Sake of the Children: Maintaining the Momentum of Professional Development (Janette Bobis); (20) From Formal to Semi-Informal Algorithms: The Passage of a Classroom into a New Mathematical Reality (Ada Boufi and Frosso Skaftourou); (21) A Measure of Rulers--The Importance of Units in a Measure (Philippa Bragg and Lynne Outhred); (22) In the Serpent's Den: Contrasting Scripts Relating to Fear of Mathematics (Chris Breen); (23) Formal Inclusion and Real Diversity in an Engineering Program of a New Public University (Tania Cristina Baptista Cabral and Roberto Ribeiro Baldino); (24) Primary Students' Understanding of Tessellation: An Initial Exploration (Rosemary Callingham); (25) Facilitating Peer Interactions in Learning Mathematics: Teachers' Practical Knowledge (Olive Chapman); (26) Towards a Unified Model on Teachers' Concerns and Efficacy Beliefs Related to a Mathematics Reform (Charalambos Charambous, George Philippou, and Leonidas Kyriakides); (27) What Is Unusual? The Case of a Media Graph (Helen L. Chick and Jane M. Watson); (28) Proofs through Exploration in Dynamic Geometry Environments (C. Christou, N. Mousoulides, M. Pittalis, and D. Pitta-Pantazi); (29) Establishing a Professional Learning Community among Middle School Mathematics Teachers (Karen Koellner Clark and Hilda Borko); (30) Patterns of Participation in the Mathematics Classroom (David Clarke); (31) Young "White" Teachers' Perceptions of Mathematics Learning of Aboriginal and Non-Aboriginal Students in Remote Communities (Tom J. Cooper, Annette R. Baturo, Elizabeth Warren, and Shani M. Doig); (32) Two Important Invariant Tasks in Solving Equations: Analyzing the Equation and Checking the Validity of Transformations (Anibal Cortes and Nelly Kavafian); (33) Certainty during the Early Stages of Problem Solving (Maria de Hoyos, Eddie Gray, and Adrian Simpson); (34) Studying the Mathematical Concept of Implication through a Problem on Written Proofs (Virginie Deloustal-Jorrand); (35) From Single Beliefs to Belief Systems: A New Observational Tool (Pietro Di Martino); (36) Assessment as a Strategic Tool for Enhancing Learning in Teacher Education: A Case Study (Brian Doig and Susie Groves); (37) Patterns of Reasoning in Classroom (Paola Domingo, Marco Cartiglia, Fulvia Furinghetti); (38) Generalized Diagrams as a Tool for Young Children's Problem Solving (Barbara J. Dougherty and Hannah Slovin); (39) Correspondences, Functions and Assignation Rules (M. Downs and J. Mamona-Downs); (40) Unjustified Assumptions Based on Diagrams in Geometry (Tali Dvora and Tommy Dreyfus); (41) The Impact of Individual Curricula on Teaching Stochastics (Andreas Eichler); (42) The Functions of Pictures in Problem Solving (Iliada Elia and George Philippou); (43) Mathematical Modelling with Young Children (Lyn D. English and James J. Watters); (44) Extending Linear Models to Non-Linear Contexts: An In-Depth Study about Two University Students' Mathematical Productions (Cristina Esteleyi, Monica Villarreal, and Humberto Alagia); (45) University Students' Conceptions of Function (Anastasia Evangelidou, Panayiotis Spyrou, Iliada Elia, and Athanasios Gagatsis); (46) Practical Constraints upon Teacher Development in Pakistani Schools (Razia Fakir-Mohammad); (47) Towards a Definition of Function (Rossana Falcade, Maria Alessandra Mariotti, and Colette Laborde); (48) "Why Doesn't It Start From the Origin?": Hearing the Cognitive Voice of Signs (Francesca Ferrara); (49) Mathematical Language and Advanced Mathematics Learning (Pier Luigi Ferrari); (50) Arithmetic/Algebraic Problem-Solving and the Representation of Two Unknown Quantities (Eugenio Filloy, Teresa Rojano, and Armando Solares); (51) Equity and Computers for Mathematics Learning: Access and Attitudes (Helen J. Forgasz); (52) The Tacit-Explicit Dynamic in Learning Processes (Cristina Frade); (53) Tracking Primary Students' Understanding of the Equality Sign (Viktor Freiman and Lesley Lee); (54) Levels of Student Responses in a Spreadsheet-Based Environment (Alex Friedlander and Michal Tabach); (55) Sensitivity for the Complexity of Problem Oriented Mathematics Instruction--A Challenge to Teacher Education (Torsten Fritzlar); (56) ICT Tools and Students' Competence Development (Anne Berit Fuglestad); (57) The Effects of Different Modes of Representation on Mathematical Problem Solving (Athanasios Gagatsis and Iliada Elia); (58) Descriptions and Conflicts in Dynamic Geometry (Victor Giraldo, Elizabeth Belfort, and Luiz Mariano Carvalho); (59) Students Problem Solving and Justification (Barbara Glass and Carolyn A. Maher); (60) Didactical Knowledge Development of Pre-Service Secondary Mathematics Teachers (Pedro Gomez and Luis Rico); (61) Legitimization of the Graphic Register in Problem Solving at the Undergraduate Level: The Case of the Improper Integral (Alejandro S. Gonzalez-Martin and Matias Camacho); (62) Will "The Way They Teach" Be "The Way They Have Learned"? Pre-Service Teachers' Beliefs Concerning Computer Embedding in Math Teaching (D. Gorev, I. Gurevich, and M. Barabash); (63) Progressive Discourse in Mathematics Classes--The Task of the Teacher (Susie Groves and Brian Doig); (64) Teachers' Practices and Dynamic Geometry (Luiz Carlos Guimaraes and Elizabeth Belfort); and (65) Characterization of Students' Reasoning and Proof Abilities in 3-Dimensional Geometry (Angel Gutierrez, John Pegg, and Christine Lawrie). (Individual papers contain references.)

This document contains the fourth volume of the proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Inclusion and Diversity". This volume features 64 research report papers: (1) Situated or Abstract: The Effect of Combining Context and Structure on Constructing an Additive (Part-Part-Whole) Schema (Irit Peled and Ruth Meron); (2) Using Graphical Profiles to Study the Learning and Teaching of Mathematics (Dvora Peretz); (3) The Role of Number in Proportional Reasoning: A Prospective Teacher's Understanding (Axelle C. Person, Sarah B. Berenson, and Paula J. Greenspon); (4) Learning to Use CAS: Voices from a Classroom (Robyn Pierce and Kaye Stacey); (5) Technical School Students' Conceptions of Tangent Lines (Marcia Maria Fusaro Pinto and Valeria Guimaraes Moreira); (6) Elementary School Students' Mental Representations of Fractions (Demetra Pitta-Pantazi, Eddie M. Gray, and Constantinos Christou); (7) A Structural Model for Problem Posing (M. Pittalis, C. Christou, N. Mousoulides, and D. Pitta-Pantazi); (8) Some Undergraduates' Experiences of Learning Mathematics (Hilary Povey and Corinne Angier); (9) Normalising Geometrical Constructions: A Context for the Generation of Meanings for Ratio and Proportion (Georgos Psycharis and Chronis Kynigos); (10) The Sensual and the Conceptual: Artefact-Mediated Kinesthetic Actions and Semiotic Activity (Luis Radford, Serge Demers, Jose Guzman, and Michele Cerulli); (11) A Sociocultural Account of Students' Collective Mathematical Understanding of Polynomial Inequalities in Instrumented Activity (Ferdinand Rivera and Joanne Rossi Becker); (12) Infinity as a Multi-Faceted Concept in History and in the Mathematics Classroom (Ornella Robutti, Ferdinando Arzarello, and Maria G. Bartolini Bussi); (13) Successful Undergraduate Mathematicians: A Study of Students in Two Universities (Melissa Rodd and Margaret Brown); (14) Bilingual Lessons and Mathematical World Views--A German Perspective (Katrin Rolka); (15) The Use of Models in Teaching Proof by Mathematical Induction (Gila Ron and Tommy Dreyfus); (16) Reflecting on Prospective Elementary Teachers' Mathematics Content Knowledge: The Case of Laura (Tim Rowland, Peter Huckstep, and Anne Thwaites); (17) The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems. A Didactical Model Based on a Numerical Approach with Junior High Students (Guillermo Rubio and Rafael Del Valle); (18) Language and Concept Development in Geometry (Frode Ronning); (19) The Role of Gestures in Conceptualisation: An Exploratory Study on the Integral Function (Cristina Sabena); (20) Psychological Aspects of Genetic Approach to Teaching Mathematics (Ildar S. Safuanov); (21) Routines in Non-Routine Problem Solving Processes (Wolfgang Schloeglmann); (22) Teacher Guidance of Knowledge Construction (Baruch Schwarz, Tommy Dreyfus, Nurit Hadas, and Rina Hershkowitz); (23) Types of Student Reasoning on Sampling Tasks (J. Michael Shaughnessy, Matt Ciancetta, and Dan Canada); (24) Didactic Model--Bridging a Concept with Phenomena (Beba Shternberg and Michal Yerushalmy); (25) Elaborating the Teacher's Role--Towards a Professional Language (Dianne Siemon, Jo Virgona, Maria Lasso, Vanessa Parsons, and Juli Cathcart); (26) Making the Connection: Procedural and Conceptual Students' Use of Linking Words in Solving Problems (Adrian Simpson and Nora Zakaria); (27) Children's Conceptual Understanding of Counting (Hannah Slovin and Barbara J. Dougherty); (28) Adding Fractions Using "Half" as an Anchor for Reasoning (Alina Galvao Spinillo and Maria Soraia Silva Cruz); (29) Persistence of Decimal Misconceptions and Readiness to Move to Expertise (Vicki Steinle and Kaye Stacey); (30) Molly and Equations in A2: A Case Study of Apprehending Structure (Nada Stehlikova and Adrian Simpson); (31) Image--Metaphor--Diagram: Visualisation in Learning Mathematics (Rudolf Straber and Gert Kadunz); (32) Images of Fractions "as" Processes and Images of Fractions "in" Processes (Marek Sulista, Jan Herman, Lucia Ilucova, Veronika Kremsova, Jiri Pribyl, Janka Ruppeldtova, Adrian Simpson, Nada Stehlikova, and Michaela Ulrychova); (33) Describing Elements of Mathematics Lessons that Accommodate Diversity in Student Background (Peter Sullivan, Judy Mousley, and Robyn Zevenbergen); (34) Orchestrating Mathematical Proof through the Use of Digital Tools (Rosamund Sutherland, Federica Olivero, and Marnie Weeden); (35) School-Based Community of Teachers and Outcomes for Students (Paola Sztajn, Martha Alexsaht-Snider, Dorothy Y. White, and Amy Hackenberg); (36) Thinking through Three Worlds of Mathematics (David Tall); (37) The Effect of Students' Roles on the Establishment of Shared Meanings During Problem Solving (Konstantinos Tatsis and Eugenia Koleza); (38) Integrating CAS Calculators into Mathematics Learning: Partnership Issues (Michael O. J. Thomas and Ye Yoon Hong); (39) The Development of Structure in the Number System (Noel Thomas); (40) Orientations to Numeracy: Teachers' Confidence and Disposition to Use Mathematics Across the Curriculum (Steve Thornton and John Hogan); (41) Efficiency and Adaptiveness of Multiple School-Taught Strategies in the Domain of Simple Addition (Joke Torbeyns, Lieven Verschaffel, and Pol Ghesquiere); (42) Supporting Teachers on Developing Teaching Norms Based on Children's Learning Mathematics (Wen-Huan Tsai); (43) Prospective Teachers' Images and Definitions: The Case of Inflection Points (Pessia Tsamir and Regina Ovodenko); (44) Fostering Mathematical Meaning via Scientific Inquiry: A Case Study (Ron Tzur, Rita A. Hagevik, and Mary E. Watson); (45) Students Building Isomorphisms (Elizabeth B. Uptegrove and Carolyn A. Maher); (46) How Do High School Students Interpret Parameters in Algebra? (Sonia Ursini and Maria Trigueros); (47) Causes Underlying Pre-Service Teachers' Negative Beliefs and Anxieties about Mathematics (Liisa Uusimaki and Rod Nason); (48) Fractions in Adult's Elementary School: The Lucina (Marta Elena Valdemoros-Alvarez); (49) Students' Overreliance on Proportionality: Evidence from Primary School Pupils Solving Arithmetic Word Problems (Wim Van Dooren, Dirk De Bock, An Hessels; Dirk Janssens, and Lieven Verschaffel); (50) From Functions to Equations: Introduction of Algebraic Thinking to 13 Year-Old Students (Petros Verikios, Vasiliki Farmaki, and Nikos Nikoudatos); (51) Critical Awareness of Voice in Mathematics Classroom Discourse: Learning the Steps in the "Dance of Agency" (David Wagner); (52) Metaphors and Cultural Models Afford Communication Repairs of Breakdowns between Mathematical Discourses (G. D. Wake and J. S. Williams); (53) Generalising Arithmetic: Supporting the Process in the Early Years (Elizabeth Warren); (54) A Framework for Describing the Processes that Undergraduates Use to Construct Proofs (Keith Weber); (55) The Nature of Spontaneity in High Quality Mathematics Learning Experiences (Gaye Williams); (56) Spreadsheet Generalising and Paper and Pencil Generalising (Kirsty Wilson, Janet Ainley, and Liz Bills); (57) A Comparison of a Visual-Spatial Approach and a Verbal Approach to Teaching Mathematics (Pamela Woolner); (58) Differentiation of Students' Reasoning on Linear and Quadratic Geometric Number Patterns (Kai-Lin Yang and Fou-Lai Lin); (59) Map Construction as a Context for Studying the Notion of Variable Scale (Nikoleta Yiannoutsou and Chronis Kynigos); (60) Understanding How the Concept of Fractions Develops: A Vygotskian Perspective (Kaori Yoshida); (61) Secondary Mathematics Teachers' Knowledge Concerning the Concept of Limit and Continuity (T. Zachariades and E. Mastorides); (62) Characteristics of Mathematical Problem Solving Tutoring in an Informal Setting (Orit Zaslavsky and Iris Zodik); (63) Making Sense of Irrational Numbers: Focusing on Representation (Rina Zazkis and Natasa Sirotic); and (64) Numeracy Practices of Young Workers (Robyn Zevenbergen and Kelly Zevenbergen). (Individual papers contain references.)

This submission contains the Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Queen's University in Kingston, Ontario. 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 and special anniversary sessions. Papers include: (1) Toward a Practice-Based Theory of Mathematical Knowledge for Teaching (Deborah Ball and Hyman Bass); (2) The Experimental Mathematician: The Pleasure of Discovery and the Role of Proof (Jon Borwein); (3) Mathematics and the Arts (Susan Gerofsky, Nathalie Sinclair, and Brent Davis); (4) Philosophy for Children and Mathematics (Richard Pallascio and Elaine Simmt); (5) The Arithmetic/Algebra Interface: Implications for Primary and Secondary Mathematics / Articulation arithmetique/algebre: Implications pour l'enseignement des mathematiques au primaire et au secondaire (Nadine Bednarz and Lesley Lee); (6) Mathematics, the Written and the Drawn (David Pimm and Nick Jackiw); (7) Des cours de mathematiques pour les futurs (et actuels) maitres au secondaire / Types and Characteristics Desired of Courses in Mathematics Programs for Future (and In-Service) Teachers (Walter Whiteley, Peter Taylor, and Harry White) [Presented in both French and English]; (8) High School Mathematics Teachers' Perspectives of Mathematical Word Problems (Olive Chapman); (9) What are Critical Online Experiences for Mathematics Teachers and Students? (George Gadanidis); (10) Socioeconomic Gradients in Mathematics Achievement: Findings for Canada from the Third International Mathematics and Science Study (George Frempong); (11) Light and Shadows (in) Knowing Mathematics and Science (Kathleen Nolan); (12) Supporting Student Efforts to Learn with Understanding: An Investigation of the Use of "JavaSketchpad" Sketches in the Secondary Geometry Classroom (Margaret P. Sinclair); (13) Conceptualizing Limit in Calculus (Why is It Still a Problem?) (Allan Brown); (14) Amplifying Mathematical Intelligence Using Web-Based Interactive Activities (George Gadanidis); (15) Grades 5-6 Teachers' Algebra Teaching Beliefs and Practices (George Gadanidis); (16) Researching the Effect of Interactive Applets in Mathematics Teaching (George Gadanidis); (17) Creativity and the Psychology of Mathematical Invention (Peter Liljedahl); (18) Logical Reasoning and Mathematical Games (Ralph Mason and Janelle McFeetors); (19) Collective Mathematical Thinking (Immaculate Namukasa); (20) Proofs and Refutations on the Web: Mathematics Environments for Grades 7 & 8 (Geoffrey Roulet); (21) Being in a Mathematical Place: Immersion in Mathematical Investigation (David Wagner); (22) Reflections on 25 Years with CMESG (Eric Muller); (23) Reflexions d'un mathematicien sur le GCEDM (Frederic Gourdeau) [Written in French]; (24) A Historical Perspective on Mathematics Education Research in Canada: The Emergence of a Community (Carolyn Kieran); (25) Lessons from the Past, Questions for the Future (Brent Davis); and (26) Lessons from the Past, Questions for the Future: meditation sur theme impose (Roberta Mura) [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, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2001 proceedings, see ED472094.]

This publication responds to a paper by Judith Stecher which strongly urges that a law related/humanities curriculum be included at the elementary school level. Currently most elementary teachers are concentrating their efforts on just two skills--reading and computing. A recent study of elementary schools in the northern counties of California, for example, reveals that 70% of all class time now is devoted to reading and arithmetic. Very little, if any time, is alloted to social studies and the humanities. Research shows, however, that attempts to teach skills in isolation are doomed to failure. Skills are interrelated. To be taught successfully, they must be related to the process of problem solving, conflict resolution, and valuing. Reading, writing, and computing are not subjects which have content or concepts of their own. In order to teach these skills, teachers should use the ideas and concepts from the social sciences, law, music, art, and philosophy. These subjects are now being neglected in the elementary school. The inclusion of a law related/humanities curriculum in the primary school is critical because it serves children at their "prime time" of learning. Given the desirability of infusing law related, humanities centered content into grades K-6, there are several means of persuasion or courses of action open to concerned citizens: l) inform the public; 2) conduct more staff development and in-service training; and 3) make suitable materials available to teachers. (Author/RM)

This study sought to determine the effectiveness of self-instructional strategy training on the addition and subtraction problem-solving skills of four upper elementary-level learning-disabled students, and to evaluate maintenance and generalization of the trained skills. Each subject received individual criterion-based training in self-instructional strategies. Training emphasized the student's role as an active collaborator in the learning process, with responsibility for recruiting and applying strategies gradually placed upon the student. Strategies were explicitly and overtly modeled in context. Subjects' scores on one-step word problems in addition and subtraction significantly improved following training. All subjects showed that the skills were generalized across settings and were maintained 3-5 weeks after training. Subjects were more confident of their ability to complete the word problems following training, though they had overestimated their pre-training ability. The four students and their teacher evaluated the self-instructional strategy training positively. Inspection of students' papers collected when probes were administered provided concrete evidence of post-training use of the instructed problem-solving strategy. (JDD)

Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC, which consists of Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra. Next, data on LCC students' arithmetic test scores and MTH 012 success rates are examined, considering the relationships among test scores, success rates, previous high school algebra, and knowledge of specific items on the arithmetic placement test and MTH 012 success. The next section summarizes a number of other research studies that examined predictor variables for and influences on success in algebra. Next, a rationale is presented for awarding algebra prerequisite status to four arithmetic skills: understanding the meaning of symbols used in arithmetic; understanding basic properties of numbers, especially fractions; using the order of operations agreement; and understanding some of the structure behind solving applications. Concluding comments indicate that the best predictors of readiness for beginning algebra are having had prior algebra, grade received in last math class; and score on a test of arithmetic skills, while warning that completion of an arithmetic course appears to offer no advantage in the study of beginning algebra for a large body of students. (JMC)