This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during Practicum (George Philippou, Charalambos Charalambous and Leonidas Kyriakides); (3) Recognising Equivalent Algebraic Expressions: An Important Component of Algebraic Expectation for Working with Cas (Robyn Pierce, Lynda Ball and Kaye Stacey); (4) Heuristics of Twelfth-Graders Building Isomorphisms (Arthur B. Powell and Carolyn A. Maher); (5) Interactive Whiteboards and the Construction of Definitions for the Kite (Dave Pratt and Ian Davison); (6) Development of Personal Constructs about Mathematical Tasks--A Qualitative Study using Repertory Grid Methodology (Susanne Prediger and Katja Lengnink); (7) Lesson Study Characterized as a Multi-Tiered Teaching Experiment (Norma Presmeg and Jeff Barrett); (8) Calculators, Graphs, Gestures and the Production of Meaning (Luis Radford, Serge Demers, Jose Guzman and Michele Cerulli); (9) The Effects of Numerical and Figural Cues on the Induction Processes of Preservice Elementary Teachers (Ferdinand D. Rivera and Joanne Rossi Becker); (10) Five Key Considerations for Networking in a Handheld-Based Mathematics (Jeremy Roschelle, Phillip Vahey, Deborah Tatar, Stephen Hegedus and Jim Kaput); (11) An Interpreting Game in a Third Grade Classroom (Adalira Saenz-Ludlow); (12) Thinking in Images and its Role in Learning Mathematics (Ildar S. Safuanov and Valery A. Gusev); (13) Primary Teachers' Conceptions about the Concept of Volume: The Case of Volume--Measurable Objects (Mariana Saiz); (14) Assessment Practices in School Mathematics: Acting and Debating (Haralambos Sakonidis and Anna Klothou); (15) Influential Aspects of Dynamic Geometry Activities in the Construction of Proofs (Ernesto Sanchez and Ana Isabel Sacristan); (16) Students' Use of Technology in Mathematical Problem Solving: Transforming Technological Artifacts into Mathematical Tools (Manuel Santos, Evelyn Aguero, Alexander Borbon and Cristhian Paez); (17) Algebra in Elementary School (Analucia Schliemann, David Carraher, Barbara Brizuela, Darrell Earnest, Anne Goodrow, Susanna Lara-Roth and Irit Peled); (18) The Impact of Preparing for the Test on Classroom Practice (Roberta Y. Schorr and Sylvia Bulgar); (19) An Analysis of Mental Space Construction in Teaching Linear Equation Word Problems (Yasuhiro Sekiguchi); (20) Language Use in a Multilingual Mathematics Classroom In South Africa: A Different Perspective (Mamokgethi Setati); (21) Middle School Students' Thinking about Variability in Repeated Trials: A Cross-Task Comparison (J. Michael Shaughnessy, Dan Canada and Matt Ciancetta); (22) Students' Understanding Of Z(Subscript)n (Daniel Siebert and Steven R. Williams); (23) Teachers' Mathematics: Curious Obligations (Elaine Simmt, Brent Davis, Lynn Gordon and Jo Towers); (24) Logico-Mathematical Activity versus Empirical Activity: Examining a Pedagogical Distinction (Martin A. Simon); (25) The Provision of Accurate Images with Dynamic Geometry (Margaret P. Sinclair,); (26) Aesthetic Values in Mathematics: A Value-Oriented Epistemology (Nathalie Sinclair); (27) From Cognitive Science to School Practice: Building the Bridge (Florence Mihaela Singer); (28) Connecting Theory and Reflective Practice through the Use of Personal Theories (Tracey Smith); (29) Two Meanings of the 'Equal' Sign and Senses of Comparison and Substitution Methods (Armando Solares, Eugenio Filloy and Teresa Rojano); (30) Goal Sketches in Fraction Learning (Catherine Sophian and Samara Madrid); (31) Using an Empowerment Professional Development Model to Support Beginning Primary Mathematics Teachers (Len Sparrow and Sandra Frid); (32) Getting at the Mathematics: Sara's Journal (Bob Speiser and Chuck Walter); (33) Emergence ofMath Knowledge Structures. Introspection (Nad'a Stehlikova); (34) Grade-Related Trends in the Prevalence and Persistence of Decimal Misconceptions (Vicki Steinle and Kaye Stacey); (35) Being Explicit about Aspects of Mathematics Pedagogy (Peter Sullivan, Robyn Turner Harrison, Judy Mousley and Robyn Zevenbergen); (36) Self-Efficacy in Mathematics and Students' Use of Self-Regulated Learning Strategies during Assessment Events (Howard Tanner and Sonia Jones); (37) The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts (Anne R. Teppo, Warren W. Esty and Kay Kirkpatrick); (38) The Role of Representation in Teacher Understanding of Function (Mike Thomas); (39) Effective Teaching with Virtual Material: Years Six and Seven Case Studies (Kylie Thompson, Annette Baturo and Tom Cooper); (40) Obstacles for Mental Representations of Real Numbers: Observations from a Case Study (Gunter Torner); (41) Teacher and Students' Joint Production of a Reversible Fraction Conception (Ron Tzur); (42) On the Search for Gender-Related Differences in Dutch Primary Mathematics Classrooms (Marja Van Den Heuvel-Panhuizen); (43) Remedying Secondary School Students' Illusion of Linearity: A Teaching Experiment (Wim Van Dooren, Dirk De Bock, An Hessels, Dirk Janssens and Lieven Verschaffel); (44) The Value of Wenger's Concepts of Modes of Participation and Regimes of Accountability in Understanding Teacher Learning (Laura R. Van Zoest and Jeffrey V. Bohl); (45) Computers in the Primary Classroom: Barriers to Effective Use (Carolyn Vela, presented by Michael O.J. Thomas); (46) Students and Teachers Listening to Themselves: Language Awareness in the Mathematics Classroom (David Wagner); (47) The Context Sensitivity of Mathematical Generalizations (Joseph F. Wagner); (48) How Does Flexible Mathematical Thinking Contribute to the Growth of Understanding? (Lisa Warner, Lara J. Alcock, Joseph Coppolo, Jr. and Gary E. Davis); (49) Young Children's Understanding of Equals: A LongalStudy (Elizabeth Warren); (50) Statistical Variation in a Chance Setting (Jane M. Watson, and Ben A. Kelly); (51) A Procedural Route toward Understanding the Concept of Proof (Keith Weber); (52) Teaching Angles by Abstraction from Physical Activities with Concrete Materials (Paul White and Michael Mitchelmore); (53) Undergraduate Students' Mental Operations in Systems of Differential Equations (Karen Whitehead and Chris Rasmussen); (54) Empirical Generalisation as an Inadequate Cognitive Scaffold to Theoretical Generalisation of a More Complex Concept (Gaye Williams); (55) Comparing Competence in Transformational and Generational Algebraic Activities (Kirsty Wilson, Janet Ainley and Liz Bills); (56) Complexity in Teaching and Children's Mathematical Thinking (Terry Wood and Betsy Mcneal); (57) Students' Understanding of Proof by Contradiction (Jya-Yi Wu Yu, Fou-Lai Lin and Yuan-Shun Lee); (58) What Does 'Positive' Attitude Really Mean? (Rosetta Zan and Pietro Di Martino); and (59) Translation of a Function: Coping with Perceived Inconsistency (Rina Zazkis, Peter Liljedahl and Karen Gadowsky). An author index is included. (Individual papers contain references.) [For Volume 3 of the 2003 Proceedings, see ED500858.]