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This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl and Fre: (1) Working with Learners' Mathematics: Exploring a Key Element of Mathematical Knowledge for Teaching (Jill Adler, Zain Davis, Mercy Kazima, Diane Parker, and Lyn Webb); (2) A Comparison between Teachers' and Pupils' Tendency to Use a Representativeness Heuristic (Thekla Afantiti-Lamprianou, Julian S. Williams, and Iasonas Lamprianou); (3) Purposeful Task Design and the Emergence of Transparency (Janet G. Ainley, Liz Bills, and Kirsty Wilson); (4) A Developmental Model for Proportional Reasoning in Ratio Comparison Tasks (Silvia Alatorre and Olimpia Figueras); (5) Referential and Syntactic Approaches to Proof: Case Studies from a Transition Course (Lara Alcock and Keith Weber); (6) Teachers' Beliefs about Students' Development of the Pre-Algebraic Concept of Equation (Vassiliki Alexandrou-Leonidou and George N. Philippou); (7) Developing Students' Understanding of the Concept of Fractions as Numbers (Solange Amorim Amato); (8) Multiple Representations in 8th Grade Algebra Lessons: Are Learners Really Getting It? (Miriam Amit and Michael N. Fried); (9) Reform-Oriented Teaching Practices: A Survey of Primary School Teachers (Judy Anderson and Janette Bobis); (10) The Genesis of Signs by Gestures: The Case of Gustavo (Ferdinando Arzarello, Francesca Ferrara, Ornella Robutti, and Domingo Paola); (11) Students' Experience of Equivalence Relations: A Phenomenological Approach (Amir H. Asghari and David Tall); (12) How Series Problems Integrating Geometric and Arithmetic Schemes Influence Prospective Secondary Teachers' Pedagogical Understanding (Leslie Aspinwall, Kenneth L. Shaw, and Hasan Unal); (13) Dealing with Learning in Practice: Tools for Managing the Complexity of Teaching and Learning (Sikunder Ali Baber and Bettina Dahl); (14) Situations of Psychological Cognitive No-Growth (Roberto R. Baldino and Tania C. B. Cabral); (15) Good CAS Written Records: Insight from Teachers (Lynda Ball and Kaye Stacey); (16) Developing Procedure and Structure Sense of Arithmetic Expressions (Rakhi Banerjee and K. Subramaniam); (17) Struggling with Variables, Parameters, and Indeterminate Objects, or How to Go Insane in Mathematics (Caroline Bardini, Luis Radford, and Cristina Sabena); (18) Exploring How Power is Enacted in Small Groups (Mary Barnes); (19) A Framework for the Comparison of PME Research into Multilingual Mathematics Education in Different Sociolinguistic Settings (Richard Barwell); (20) Vygotsky's Theory of Concept Formation and Mathematics Education (Margot Berger); (21) Preservice Teachers' Understandings of Relational and Instrumental Understanding (Kim Beswick); (22) The Transformation of Mathematics in On-Line Courses (Marcelo C. Borba); (23) Using Cognitive and Situated Perspectives to Understand Teacher Interactions with Learner Errors (Karin Brodie); (24) Identification of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (25) The "A4-Project": Statistical World Views Expressed through Pictures (Michael Bulmer and Katrin Rolka); (26) A Whole-School Approach to Developing Mental Computation Strategies (Rosemary Callingham); (27) A Comparison of Perceived Parental Influence on Mathematics Learning among Students in China and Australia (Zhongjun Cao, Helen Forgasz, and Alan Bishop); (28) Using Word Problems in Malaysian Mathematics Education: Looking beneath the Surface (Kah Yein Chan and Judith Mousley); (29) Constructing Pedagogical Knowledge of Problem Solving: Preservice Mathematics Teachers (Olive Chapman); (30) Revisiting a Theoretical Model on Fractions: Implications for Teaching and Research (Charalambos Y. Charalambous and Demetra Pitta-Pantazi); (31) Students' Reflection on Their Sociomathematical Small-Group Interaction: A Case Study (Petros Chaviaris and Sonia Kafoussi); (32) Investigating Teachers' Responses to Student Misconceptions (Helen L. Chick and Monica K. Baker); (33) Studying the Distribution of Responsibility for the Generation of Knowledge in Mathematics Classrooms in Hong Kong, Melbourne, San Diego and Shanghai (David Clarke and Lay Hoon Seah); (34) Indigenous and Non-Indigenous Teaching Relationships in Three Mathematics Classrooms in Remote Queensland (Tom J. Cooper, Annette R. Baturo, and Elizabeth Warren); (35) Exploring the Strategies Used by Grade 1 to 3 Children through Visual Prompts, Symbols and Worded Problems: A Case for a Learning Pathway for Number (Ty Corvell Cranfield, Cally Kuhne, and Gary Powell); (36) Primary Students' Knowledge of the Properties of Spatially-Oriented Diagrams (Carmel Diezmann); (37) A Conceptual Framework for Studying Teacher Preparation: The Pirie-Kieren Model, Collective Understanding, and Metaphor (Maria A. Droujkova, Sarah B. Berenson, Kelli Slaten, and Sue Tombes); (38) Mathematical Modelling with 9-Year-Olds (Lyn English and James Watters); (39) Exploring "Lesson Study" in Teacher Preparation (Maria L. Fernandez); (40) Child-Initiated Mathematical Patterning in the Pre-Compulsory Years (Jillian Fox); (41) The Tacit-Explicit Nature of Students' Knowledge: A Case Study on Area Measurement (Cristina Frade); (42) Teachers as Interns in Informal Mathematics Research (John M. Francisco and Carolyn A. Maher); and (43) Exploring Excellence and Equity within Canadian Mathematics Classrooms (George Frempong). (Individual papers contain references.)

The first volume of the 31st annual proceedings of the International Group for the Psychology of Mathematics Education conference presents plenary lectures; research forums; discussion groups; working sessions; short oral communications; and posters from the meeting. Plenary lecture papers include: (1) On Humanistic Mathematics Education: A Personal Coming of Age? (Chris Breen); (2) Certainty, Explanation and Creativity in Mathematics (Michael Otte); (3) I Need the Teacher to Tell Me If I Am Right or Wrong (Anna Sierpinska); and (4) School Mathematics and Cultivation of Mind (Jeong-Ho Woo). Plenary panel papers include: (1) Introduction to the PME Plenary Panel, "School Mathematics for Humanity Education" (Koeno Gravemeijer); (2) Humanizing the Theoretical and the Practical for Mathematics Education (Cristina Frade); (3) Making Mathematics More Mundane--A Semiotic Approach (Willibald Dorfler); (4) Mathematics: A Human Potential (Martin A. Simon); and (4) Need for Humanising Mathematics Education (Masataka Koyama). The first research forum, Learning through Teaching: Development of Teachers' Knowledge in Practice (RF01) includes: (1) A View on the Teachers' Opportunities to Learn Mathematics through Teaching (Roza Leikin and Rina Zazkis); (2) Integrating Virtual and Face-to-Face Practice: A Model for Continuing Teacher Education (Marcelo C. Borba); (3) Teachers' Learning Reified: The Professional Growth of Inservice Teachers through Numeracy Task Design (Peter Liljedahl); (4) Constraints on What Teachers Can Learn from their Practice: Teachers' Assimilatory Schemes (Martin A. Simon); and (5) What and How Might Teachers Learn via Teaching: Contributions to Closing an Unspoken Gap (Ron Tzur). The second research forum, Researching Change in Early Career Teachers (RF02), includes: (1) Introduction (Peter Sullivan); (2) Researching Relief of Mathematics Anxiety among Pre-Service Elementary School Teachers (Markku S. Hannula, Peter Liljedahl, Raimo Kaasila, and Bettina Rosken);(3) Teachers' Learning from Learning Studies: An Example of Teaching and Learning Fractions in Primary Four (Lo Mun Ling and Ulla Runesson); (4) Tracking Teachers' Learning in Professional Development Centered on Classroom Artifacts (Lynn T. Goldsmith and Nanette Seago); (5) Teacher Change in the Context of Addressing Students' Special Needs in Mathematics (Orit Zaslavsky and Liora Linchevski); (6) Researching Change in Prospective and Beginning Teachers (Laurinda Brown and Alf Coles); and (7) Summary and Conclusions (Markku S. Hannula). Information relating to discussion groups, working sessions, short oral communications, and poster presentations conclude this volume of the 31st proceedings. (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.)

In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both confirm and extend the work of Hadamard on the inventive process. In addition, the results also speak to the larger context of "doing" and learning mathematics. [For complete proceedings, see ED489538.]

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.)