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.)