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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.)

This document is the fourth 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 42 research reports by presenters with last names beginning between Mul and Wu: (1) Case Studies of Children's Development of Structure in Early Mathematics: A Two-Year Longitudinal Study (Joanne Mulligan, Michael Mitchelmore, and Anne Prescott); (2) A Case Study of How Kinesthetic Experiences Can Participate in and Transfer to Work with Equations (Ricardo Nemirovsky and Chris Rasmussen); (3) The Construction of Proportional Reasoning (Stephen Norton); (4) The Transition of a Secondary Mathematics Teacher: From a Reform Listener into a Believer (Jo Clay Olson and Karmen Kirtley); (5) Substantive Communication of Space Mathematics in Upper Primary School (Kay Owens); (6) Transforming Korean Elementary Mathematics Classrooms to Student-Centered Instruction (JeongSuk Pang); (7) The Effect of Improved Automaticity and Retrieval of Basic Number Skills on Persistently Low-Achieving Students (John Pegg, Lorraine Graham, and Anne Bellert); (8) Degrees of Freedom in Modeling: Taking Certainty out of Proportion (Irit Peled and Ronit Bassan-Cincinatus); (9) "I Know That You Don't Have to Work Hard": Mathematics Learning in the First Year of Primary School (Bob Perry and Sue Dockett); (10) Disentangling Mentors' Role in the Development of Prospective Teachers' Efficacy Beliefs in Teaching Mathematics (George Philippou and Charalambos Y. Charalambous); (11) Linear Functions and a Triple Influence of Teaching on the Development of Students' Algebraic Expectation (Robyn Pierce); (12) Engaging the Learner's Voice? Catechetics and Oral Involvement in Reform Strategy Lessons (Adrian J. Pinel); (13) Teaching Projectile Motion to Eliminate Misconceptions (Anne Prescott and Michael Mitchelmore); (14) An Investigation of a Preservice Teacher's Use of Representations in Solving Algebraic Problems Involving Exponential Relationships (Norma Presmeg and Rajeev Nenduradu); (15) On Embodiment, Artifacts, and Signs: A Semiotic-Cultural Perspective on Mathematical Thinking (Luis Radford, Caroline Bardini, Cristina Sabena, Pounthioun Diallo, and Athanase Simbagoye); (16) Generalization Strategies of Beginning High School Algebra Students (Joanne Rossi Becker and Ferdinand Rivera); (17) Synchronizing Gestures, Words and Actions in Pattern Generalizations (Cristina Sabena, Luis Radford, and Caroline Bardini); (18) Analyzing Student Modeling Cycles in the Context of a "Real World" Problem (Roberta Y. Schorr and Miriam Amit); (19) Negotiating about Perceived Value Differences in Mathematics Teaching: The Case of Immigrant Teachers in Australia (Wee Tiong Seah); (20) Development of Mathematical Norms in an Eighth-Grade Japanese Classroom (Yasuhiro Sekiguchi); (21) Solving Additive Problems at Pre-Elementary School Level with the Support of Graphical Representation (Ana Coelho Vieira Selva, Jorge Tarcisio da Rocha Falcao, and Terezinha Nunes); (22) From the Everyday, through the Authentic, to Mathematics: Reflecting on the Process of Teaching Mathematics through the Everyday (Godfrey Sethole); (23) Personal Experiences and Beliefs in Early Probabilistic Reasoning: Implications for Research (Sashi Sharma); (24) Assimilating Innovative Learning/Teaching Approaches into Teacher Education: Why Is It so Difficult? (Atara Shriki and Ilana Lavy); (25) Student Thinking Strategies in Reconstructing Theorems (Tatag Yuli Eko Siswono); (26) A Comparison of How Textbooks Teach Multiplication of Fractions and Division of Fractions in Korea and in U.S. (Ji-Won Son); (27) Mathematical Knowledge of Pre-Service Primary Teachers (Beth Southwell and Marina Penglase); (28) Analysing Longitudinal Data on Students' Decimal Understanding Using Relative Risk and Odds Ratios (Vicki Steinle and Kaye Stacey); (29) Girls Journey toward Proportional Reasoning (Olof Bjorg Steinthorsdottir); (30) University Student Perceptions of CAS Use in Mathematics Learning (Sepideh Stewart and Michael O. J. Thomas); (31) Prospective Teachers' Understanding of Proof: What if the Truth Set of an Open Sentence Is Broader than that Covered by the Proof? (Andreas J. Stylianides, Gabriel J. Stylianides, and George Philippou); (32) Planning and Teaching Mathematics Lessons as a Dynamic, Interactive Process (Peter Sullivan, Robyn Zevenbergen, and Judy Mousley); (33) Teacher Factors in Integration of Graphic Calculators into Mathematics Learning (Michael O. J. Thomas and Ye Yoon Hong); (34) Students' Overreliance on Linearity: An Effect of School-Like Word Problems (Wim Van Dooren, Dirk De Bock, Dirk Janssens, and Lieven Verschaffel); (35) A Process of Abstraction by Representations of Concepts (N. C. Verhoef and H. G. B. Broekman); (36) Argumentation Profile Charts as Tools for Analysing Students' Argumentations (Jill Vincent, Helen Chick, and Barry McCrae); (37) Characterizing Middle School Students' Thinking in Estimation (Tanya N. Volkova); (38) Reviewing and Thinking the Affect/Cognition Relation (Margaret Walshaw and Tania Cabral); (39) Young Children's Ability to Generalise the Pattern Rule for Growing Patterns (Elizabeth Warren); (40) Consolidating One Novel Structure whilst Constructing Two More (Gaye Williams); (41) Spreadsheets, Pedagogic Strategies and the Evolution of Meaning for Variable (Kirsty Wilson, Janet Ainley, and Liz Bills); and (42) A Study of the Geometric Concepts of the Elementary School Students Who Are Assigned to the van Hiele Level One (Der-bang Wu and Hsiu-Lan Ma). (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.)

The third volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains full research report papers. Papers include: (1) Students' Use of ICT Tools: Choices and Reasons (Anne Berit Fuglestad); (2) Interaction of Modalities in Cabri: A Case Study (Fulvia Furinghetti, Francesca Morselli, and Domingo Paola); (3) The Duality of Zero in the Transition from Arithmetic to Algebra (Aurora Gallardo and Abraham Hernandez); (4) Conflicts in Offshore Learning Environments of a University Preparatory Mathematics Course (Linda Galligan); (5) The Diverse Learning Needs of Young Children who were Selected for an Intervention Program (Ann Gervasoni); (6) Using Contradictions in a Teaching and Learning Development Project (Simon Goodchild and Barbara Jaworski); (7) A Sociocultural Analysis of Learning to Teach (Merrilyn Goos); (8) Three Case Studies on the Role of Memorizing in Learning and Teaching Mathematics (Sue Gordon and Jackie Nicholas); (9) Reconstructing Norms (Nuria Gorgorio and Nuria Planas); (10) Forming Teachers as Resonance Mediators (Paolo Guidoni, Donatella Iannece, and Roberto Tortora); (11) Investigating the Problem Solving Competency of Pre Service Teachers in Dynamic Geometry Environment (Shajahan Haja); (12) Structure and Typical Profiles of Elementary Teacher Students' View of Mathematics (Markku Hannula, Raimo Kaasila, Erkki Pehkonen, and Anu Laine); (13) Preservice Teachers' View on y= x+5 and y = [pi] x [superscript 2] Expressed through the Utilization of Concept Maps: A Study of the Concept of Function (Orjan Hansson); (14) Mistake-Handling Activities in the Mathematics Classroom (Aiso Heinze); (15) One Teacher's Role in Promoting Understanding in Mental Computation (Ann Heirdsfield); (16) In the Middle of Nowhere: How a Textbook Can Position the Mathematics Learner (Beth Herbel-Eisenmann and David Wagner); (17) Chinese Whispers--Algebra Style: Grammatical, Notational, Mathematical and Activity Tensions (Dave Hewitt); (18) Pedagogy of Facilitation: How do we Best Help Teachers of Mathematics with New Practices? (Joanna Higgins); (19) Students' Difficulties with Applying a Familiar Formula in an Unfamiliar Context (Maureen Hoch and Tommy Dreyfus); (20) Learning Mathematics: Perspectives of Australian Aboriginal Children and Their Teachers (Peter Howard and Bob Perry); (21) Verification or Proof: Justification of Pythagoras' Theorem in Chinese Mathematics Classrooms (Rongjin Huang); (22) Mozambican Teachers' Professional Knowledge about Limits of Functions (Danielle Huillet); (23) Heuristic Biases in Mathematical Reasoning (Matthew Inglis and Adrian Simpson); (24) Three Utilities for the Equal Sign (Ian Jones and Dave Pratt); (25) Computer Algebra Systems (CAS) as a Tool for Coaxing the Emergence of Reasoning about Equivalence of Algebraic Expressions (Carolyn Kieran and Luis Saldanha); (26) Students' Colloquial and Mathematical Discourses on Infinity And Limit (Dong Joong Kim, Anna Sfard, and Joan Ferrini-Mundy); (27) The Effect of Mathmagic on the Algebraic Knowledge and Skills of Low-Performing High School Students (Hari P. Koirala); (28) Learning and Teaching Early Number: Teachers' Perceptions (Cally Kuhne, Marja Van Den Heuvel-Panhuizen, and Paula Ensor); (29) Situation-Specific and Generalized Components Of Professional Knowledge of Mathematics Teachers: Research on a Video-Based In-Service Teacher Learning Program (Sebastian Kuntze and Kristina Reiss); (30) Assessing Professional Growth of Pre-Service Teachers Using Comparison between Theoretical And Practical Image of the "Good Teacher" (Ilana Lavy and Atara Shriki); (31) Mathematically Gifted Students' Geometrical Reasoning and Informal Proof (Kyung Hwa Lee); (32) Investigation on an Elementary Teacher's Mathematics Pedagogical Values through Her Approach to Students' Errors (Yuh-Chyn Leu and Chao-Jung Wu); (33) How the Calculator-Assisted Instruction Enhances Two Fifth Grade Students' Learning Number Sense in Taiwan (Yung-Chi Lin and Erh-Tsung Chin); (34) Fourth-Grade Students' Performance on Graphical Languages in Mathematics (Tom Lowrie and Carmel Diezmann); (35) Preservice Teachers' Conceptions of Variation (Katie Makar and Dan Canada); (36) The Equivalence and Ordering of Fractions in Part-Whole and Quotient Situations (Ema Mamede, Terezinha Nunes, and Peter Bryant); (37) Growth of Mathematical Understanding in a Bilingual Context: Analysis and Implications (Sitaniselao Stan Manu); (38) Motivational Beliefs, Self-Regulated Learning and Mathematical Problem Solving (Andri Marcou and George Philippou); (39) Fractions in the Workplace: Folding Back and the Growth of Mathematical Understanding (Lyndon Martin, Lionel LaCroix, and Lynda Fownes); (40) Meaning Construction through Semiotic Means: The Case of the Visual Pyramid (Michela Maschietto and Maria G. Bartolini Bussi); (41) Students' Motivational Beliefs, Self-Regulation Strategies and Mathematics Achievement (Nikos Mousoulides and George Philippou); and (42) The Transition to Postgraduate Study in Mathematics: A Thinking Styles Perspective (Andreas Moutsios-Rentzos and Adrian Simpson). (Individual papers contain references.) [For Volume 2 of this Proceedings, see ED496859.]