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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.)

The aim of the study (Johnsen Hoines 2002) reported here was to shed light on the process through which student teachers express and interpret their understandings about mathematical notions and thereby gain insight into them. This paper focuses on how students cooperate and move between different ways of understandings. It emphases in particular on how differences in the ways of explaining a mathematical content make different conditions for the dialogue and learning processes that develop. [For complete proceedings, see ED 489538].

This document contains the third volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics. Conference presentations are centered around the theme "Inclusion and Diversity". A total of 65 research reports are presented here: (1) A Teacher's Model of Students Algebraic Thinking About Equivalent Expressions (Jean E. Hallagan); (2) On Motivational Aspects of Instructor-Learner Interactions in Extra-Curriculum Activities (Stefan Halverscheid); (3) Development of Understanding and Self-Confidence in Mathematics, Grades 5-8 (Markku S. Hannula, Hanna Maijala, and Erkki Pehkonen); (4) Mathematics Teachers' Knowledge Base: Preliminary Results (Guershon Harel and Kien H. Lim); (5) The Role of Tool and Teacher Mediations in the Construction of Meanings for Reflection (Lulu Healy); (6) The Proving Process in Mathematics Classroom--Method and Results of a Video Study (Aiso Heinze); (7) Structure Sense in High School Algebra: The Effect of Brackets (Maureen Hoch and Tommy Dreyfus); (8) Explaining Variability in Retrieval Times for Addition Produced by Students with Mathematical Learning Difficulties (Sarah L. Hopkins and Michael J. Lawson); (9) Early Gender Differences (Marj Horne); (10) Perceptual and Symbolic Representations as a Starting Point of the Acquisition of the Derivative (Markus Hahkioniemi); (11) Implementation of a Model Using Authentic Investigative Activities for Teaching Ratio & Proportion in Pre-Service Teacher Education (Bat-Sheva Ilany, Yaffa Keret, and David Ben-Chaim); (12) Mathematicians and the Selection Task (Matthew Inglis and Adrian Simpson); (13) Insight into Pupils' Understanding of Infinity in a Geometrical Context (Darina Jirotkova and Graham Littler); (14) Textual Differences as Conditions for Learning Processes (Marit Johnsen Hoines); (15) Students' Gender Attitudes Towards the Use of Calculators in Mathematics Instruction (L. M. Kaino and E. B. Salani); (16) Teaching Arithmetic and Algebraic Expressions (K. Subramakhi Banerjee); (17) An Introduction to the Profound Potential of Connected Algebra Activities: Issues of Representation, Engagement and Pedagogy (James J. Kaput and Stephen J. Hegedus); (18) The Tension between Teacher Beliefs and Teacher Practice: The Impact of the Work Setting (M. Kerem Karaagac and John Threlfall); (19) What a Simple Task Can Show: Teachers Explore the Complexity of Children's Thinking (Heather Kelleher, Cynthia Nicol, and Carole Saundry); (20) Constructing Knowledge about the Bifurcation Diagram: Epistemic Actions and Parallel Constructions (Ivy Kidron and Tommy Dreyfus); (21) Experiencing Research Practice in Pure Mathematics in a Teacher Training Context (Eva Knoll, Paul Ernest, and Simon Morgan); (22) Enhancing Mathematical Literacy with the Use of Metacognitive Guidance in Forum Discussion (Bracha Kramarski); (23) The Impact of Developing Teacher Conceptual Knowledge on Students' Knowledge of Division (Janeen Lamb and George Booker); (24) Kinds of Arguments Emerging While Exploring in a Computerized Environment (Ilana Lavy); (25) Using Solo to Analyse Group Responses (Christine Lawrie and Chris Reading); (26) Connections between Qualitative and Quantitative Thinking about Proportion: The Case of Paulina (Elena Fabiola Ruiz Ledesma and Marta Elena Valdemoros Alvarez); (27) Towards High Quality Geometrical Tasks: Reformulation of a Proof Problem (Roza Leikin); (28) Mathematical Thinking & Human Nature: Consonance & Conflict (Uri Leron); (29) The Mathematics Pedagogical Values Delivered by an Elementary Teacher in Her Mathematics Instruction: Attainment of Higher Education and Achievement (Yuh-Chyn Leu and Chao-Jung Wu); (30) Visual Reasoning in Computational Environment: A Case of Graph Sketching (Allen Leung and King Wah Chan); (31) Elementary School Students' Use of Mathematically-Based and Practically-Based Explanations: The Case of Multiplication (Esther Levenson, Dina Tirosh, and Pessia Tsamir); (32) Mathematical Discovery: Hadamard Resurrected (Peter Liljedahl); (33)Supporting Teachers on Designing Problem-Posing Tasks as a Tool of Assessment to Understand Students' Mathematical Learning (Pi-Jen Lin); (34) Prospective Elementary School Teachers' Solution Strategies and Reasoning for a Missing Value Proportion Task (Jane Lo); (35) Introduction of Calculus in 12th Grade: The Role of Artefacts (Michela Maschietto); (36) The Critical Role of Institutional Context in Teacher Development (Kay McClain and Paul Cobb); (37) Students' Perceptions of Factors Contributing to Successful Participation in Mathematics (Andrea McDonough, Peter Sullivan, and Robyn Turner Harrison); (38) The Cognitive--Motivational Profiles of Students Dealing with Decimal Numbers and Fractions (Kaarina Merenluoto); (39) The Number Line as a Representation of Decimal Numbers: A Research with Sixth Grade Students (Niki Michaelidou, Athanasios Gagatsis, and Demetra Pitta-Pantazi); (40) Preservice Teachers Conceptions of Mathematics-Based Software (James Middleton, Terri Kurz, and H. Bahadir Yanik); (41) Helping Children to Model Proportionally in Group Argumentation: Overcoming the "Constant Sum" Error (Christina Misailidou and Julian Williams); (42) Abstraction in Mathematics and Mathematics Learning (Michael Mitchelmore and Paul White); (43) Reflective Symmetry in Construction and Proving (Takeshi Miyakawa); (44) Students' Improper Proportional Reasoning: The Case of Area and Volume of Rectangular Figures (Modestina Modestou, Athanasios Gagatsis, and Demetra Pitta-Pantazi); (45) Abstraction and Consolidation (John Monaghan and Mehmet Fatih Ozmantar); (46) Critical Sense in Interpretations of Media Graphs (Carlos Monteiro and Janet Ainley); (47) Between Affect and Cognition: Proving at University Level (Francesca Morselli and Fulvia Furinghetti); (48) An Aspect of Mathematical Understanding: The Notion of "Connected Knowing" (Judith Mousley); (49) Algebraic and Geometric Approach in Function Problem Solving (Nikos Mousoulides and Athanasios Gagatsis); (50) Children's Development of Structure in Early Mathematics (Joanne Mulligam, Anne Prescott, and Michael Mitchelmore); (51) On the Fragile, Yet Crucial, Relationship between Mathematicians and Researchers in Mathematics Education (Elena Nardi and Paola Iannone); (52) Students' Preference of Non-Algebraic Representations in Mathematical Communication (Dorit Neria and Miriam Amit); (53) Learning to See in Mathematics Classrooms (Cynthia Nicol and Sandra Crespo); (54) Students' Ways of Interpreting Aspects of Chance Embedded in a Dice Game (Per Nilsson); (55) The Impact of State-Wide Numeracy Testing on the Teaching of Mathematics in Primary Schools (Steven Nisbet); (56) "The Poetry of the Universe": New Mathematics Teachers' Metaphoric Meaning-Making (Andrew Noyes); (57) What Students Do When Hearing Others Explaining (Kazuhiko Nunokawa and Satoshi Ohzeki); (58) Changes in Teachers' Practices While Assuming New Leadership Roles (Jo Clay Olson); (59) Students' Structuring of Rectangular Arrays (Lynne Outhred and Michael Mitchelmore); (60) Construction of Mathematical Definitions: An Epistemological and Didactical Study (Cecile Ouvrier-Buffet); (61) Mathematical Abstraction through Scaffolding (Mehmet Fatih Ozmantar and Tom Roper); (62) The Use of Diagrams in Solving Non Routine Problems (Marilena Pantziara, Athanasios Gagatsis, and Demetra Pitta-Pantazi); (63) Designing for Local and Global Meanings of Randomness (Efi Paparistodemou and Richard Noss); (64) Integrating the History of Mathematics in Educational Praxis: An Euclidean Geometry Approach to the Solution of Motion Problems (Theodorus Paschos, Vassilike Farmaki, and Nikos Klaudatos); and (65) The Magic Circle of the Textbook--An Option or an Obstacle for Teacher Change (Leila Pehkonen). (Individual papers contain references.)

I have different approaches to this contribution. My concerns as a teacher and a teacher educator are to discuss how we manage to organise for inclusion of the variety of children's mathematics. How do we organise for the mathematics to be included into their mathematics? A message from children about what they expect mathematics to be has impact on this complexity. Their voice is a voice of the culture and affects the position of "we". What impact has the authoritarian nature of the mathematics for our discussions about diversity and inclusion? [For complete proceedings, see ED489178]

This document contains the first 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". In total, 147 presentations centered around the vision of mathematics for all. This volume features eight plenary and five research forum papers, and papers from four groups of discussions groups, working sessions, and short orals and poster presentations. Plenary Lectures; Plenary Panel compilations; and Research Forum compilations: (1) Classroom Business Same as Usual? (What) Do Researchers and Policy Makers Learn from Classroom Studies? (Kirsti Klette); (2) Grappling with Complexity: Co-Learning in Inquiry Communities in Mathematics Teaching Development (Barbara Jaworski); (3) Class, Diversity, and Race in Research on the Psychology of Mathematics Learning (Arthur B. Powell); (4) From Diversity to Inclusion and Back: A Lens on Learning (Rina Hershkowitz); (5) Lives, learning and Liberty: The Impact and Responsibilities of Mathematics Education (Peter Gates); (6) Do We Welcome Children's Mathematics? Who are We? (Marit Johnsen Hoines); (7) Learning (and Researching) as Participation in Communities of Practice (Madalena Pinto dos Santos); (8) Researching and Learning Mathematics at the Margin: From "Shelter" to School (Renuka Vithal); (9) Affect in Mathematics Education--Exploring Theoretical Frameworks (Markku Hannula, Jeff Evans, George Philippou, and Rosetta Zan); (10) Algebraic Equations and Inequalities: Issues for Research and Teaching (Luciana Bazzini and Pessia Tsamir); (11) International Perspectives on the Nature of Mathematical Knowledge for Secondary Teaching: Progress and Dilemmas (Helen Doerr and Terry Wood); (12) Contrasting Comparative Research on Teaching and Learning in Mathematics (Jonas Emanuelsson and David Clarke); and (13) Researching Mathematics Education in Multilingual Contexts: Theory, Methodology and Teaching Mathematics. (Individual papers contain references.)