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This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on A Number Line (Markku S. Hannula); (4) Preservice Teachers' Conceptions about Y=X+5: Do They See a Function? (Orjan Hansson and Barbro Grevholm); (5) Daring to Ask the Hard Questions: The Effect of Clinical Interview Training upon Teachers Classroom Questioning (Hanna Haydar); (6) Reducing Abstraction: The Case of Elementary Mathematics (Orit Hazzan and Rina Zazkis); (7) The Effect of a Simcalc Connected Classroom on Students' Algebraic Thinking (Stephen J. Hegedus and James J. Kaput); (8) "Spontaneous" Mental Computation Strategies (Ann Heirdsfield); (9) Notation Issues: Visual Effects and Ordering Operations (Dave Hewitt); (10) Attitudes of Mathematics and Language Teachers Towards New Educational Trends (Marie Hofmannova, Jarmila Novotna and Zuzana Hadj-Moussova); (11) Gender Differences in the Early Years in Addition and Subtraction ( Marj Horne); (12) High Achieving Girls in Mathematics: What's Wrong with Working Hard? (Ann C. Howe and Sarah B. Berenson); (13) Mental Functioning of Instruments in the Learning of Geometrical Transformations (Veronica Hoyos); (14) A Perspective for Examining the Link between Problem Solving and Problem Posing (Stephen Hwang and Jinfa Cai): (15) Multiplicative Strategies of New Zealand Secondary School Authors (Kathryn Irwin); (16) Effective Vs. Efficient: Teaching Methods of Solving Linear Equations (Kathy M. C. Ivey); (17) Student's Concept of Infinity in the Context if a Simple Geometrical Construct (Darina Jirotkova and Graham H. Littler); (18) Beyond Discourse: A Multimodal Perspective of Learning Mathematics in a Multilingual Context ( Lena Licon Khisty, Hector Morales and Kathryn Chval); (19) Spontaneous Emergence of Elementary Number-Theoretic Concepts and Techniques in Interaction with Computing Technology (Carolyn Kieran and Jose Guzman); (20) Secondary School Mathematics Preservice Teachers' Probabilistic Reasoning in Individual and Pair Settings (Hari P. Koirala); (21) Social Transformation of Students' Conceptual Model: Analysis of Students' Use of Metaphor for Differential Equations (Oh-Nam Kwon, Kyoung Hee Cho, Kyung Hee Shin and Jeong Sook Park); (22) 13 Year-Olds' Meanings around Intrinsic Curves with a Medium for Symbolic Expression and Dynamic Manipulation (Kynigos Chronis, and Georgos Psycharis); (23) The Probabilistic Thinking of Primary School Pupils in Cyprus: The Case of Tree Diagrams (Iasonas Lamprianou and Thekla Afantiti Lamprianou); (24) Pre-Service Teachers' Transition from "Knowing That" to "Knowing Why" via Computerized Project-Based-Learning (Ilana Lavy and Atara Shriki): (25) Mathematics Competitions, Gender, and Grade Level: Does Time Make a Difference (Gilah C. Leder and David G. Pederson, Graham H. Pollard); (26) Dynamic Geometry and the Theory of Variation (Allen Leung); (27) Enhancing Teachers' Understanding of Students' Learning by using Assessment Tasks (Pi-Jen Lin); (28) Early Mathematics Teaching: The Relationship between Teachers' Beliefs and Classroom Practices (Francis Lopez-Real and Nirmala Rao); (29) Factors Motivating Reform: Learning from Teachers' Stories (Azita Manouchehri); (30) Difficulties in Vector Space Theory: A Compared Analysis in Terms of Conceptions and Tacit Models (Mirko Maracci); (31) Function and Graph in Dgs Environment (Rossana Falcade, Maria Alessandra Mariotti and Colette Laborde); (32) Collective Mathematical Understanding as an Improvisational Process (Lyndon Martin and Jo Towers); (33) Supporting Teacher Change: A Case from Statistics (Kay McClain); (34) Describing the Practice of Effective Teachers of Mathematics in the Early Years (Andrea McDonough and Doug Clarke); (35) Mathematics Professional Development as the Development of Communities of Practice (Rebecca McGraw, Fran Arbaugh, Kathleen Lynch and Catherine A. Brown); (36) The Emergence of Mathematical Goals in a Recreational Practice (Luciano Meira and Monica Correira); (37) Abstracting the Density of Numbers on the Number Line--A Quasi-Experimental Study (Kaarina Merenluoto); (38) Measuring Children's Proportional Reasoning, The "Tendency" for an Additive Strategy and the Effect of Models (Christina Misailidou and Julian Williams); (39) Mathematicians' Writing (Morten Misfeldt); (40) A Co-Learning Partnership in Mathematics Lower Secondary Classroom in Pakistan: Theory into Practice (Razia Fakir Mohammad); (41) Prospective Elementary Teachers' Misunderstandings in Solving Ratio and Proportion Problems (Cecilia Monteiro); (42) What Counts as Mathematical Discourse? (Judit Moschkovich); (43) Mathematical and Pedagogical Understanding as Situated Cognition (Judith A. Mousley); (44) The Relative Influence of the Teacher in Third Grade Mathematics Classrooms (Hanlie Murray); (45) The Activity of Defining (Talli Nachlieli and Anna Sfard); (46) Collective Learning Structures: Complexity Science Metaphors for Teaching (Immaculate Namukasa); (47) Mathematicians on Concept Image Construction: "Single Landscape" vs "Your Own Tailor-Made Brain Version" (Elena Nardi and Paola Iannone); (48) Learning in and from Practice: Pre-Service Teachers Investigate their Mathematics Teaching (Cynthia Nicol and Sandra Crespo); (49) Mentoring Teaching of Mathematics in Teacher Education (Vivi Nilssen); (50) Getting Organised: The Role of Data Organisation in Students' Representation of Numerical Data (Steven Nisbet); (51) Strong and Weak Metaphors for Limits (Michael C. F. Oehrtman); (52) Applying Theory of Planned Behavior Model on Studying Teachers' Change in Mathematics Instruction (Youngyoul Oh); (53) Characteristics of 5th Graders' Logical Development through Learning Division with Decimals (Masakazu Okazaki); (54) Nathan's Strategies for Simplifying and Adding Fractions in Third Grade (John Olive); (55) Cabri as a Shared Workspace within the Proving Process (Federica Olivero); (56) The Construct Validity of an Inventory for the Measurement of Young Pupils' Metacognitive Abilities in Mathematics (Areti Panaoura and George Philippou); (57) Student-Centered Teaching Practices in Korean Elementary Mathematics Classrooms (Jeong Suk Pang); and (58) On Pupils' Self-Confidence in Mathematics: Gender Comparisons (Erkki Pehkonen, Anu Nurmi, Markku Hannula and Hanna Maijala). An author index is included. (Individual papers contain references.) [For Volume 2 of the 2003 Proceedings, see ED500859. For Volume 4, see ED500860.]