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.]