The second volume of the proceedings of 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following papers: (1) "The Dilemma of Transparency: Seeing and Seeing through Talk in the Mathematics Classroom" (J. Adler); (2) "Abstraction is Hard in Computer-Science Too" (D. Aharoni and U. Leron); (3) "Constructing Purpose in Mathematical Activity" (J. Ainley); (4) "Effective Teachers of Numeracy in UK Primary Schools: Teachers' Beliefs, Practices and Pupils' Learning" (M. Askew, M. Brown, V. Rhodes, D. Wiliam and D. Johnson); (5) "Can the Average Student Learn Analysis?" (R. R. Baldino, A. Buttner Ciani and A. Carolina Leal); (6) "Cognitive Units, Connections and Mathematical Proof" (T. Barnard and D. Tall); (7) "Subjective Elements in Children's Comparison of Probabilities" (M.J. Canizares, C. Batanero, L. Serrano and J.J. Ortiz); (8) "Reunitizing Hundredths: Prototypic and Nonprototypic Representations" (A.R. Baturo, and J. Cooper); (9) "Students' Perceptions of the Purposes of Mathematical Activities" (A. Bell, R. Phillips, A. Shannon, and M. Swan); (10) "Stereotypes of Literal Symbol Use in Senior School Algebra" (L. Bills); (11) "Approaching Theoretical Knowledge through Voices and Echoes: A Vygotskian Perspective" (P. Boero, B. Pedemonte, and E. Robotti); (12) "The Transition from Arithmetic To Algebra: Initial Understanding of Equals, Operations and Variable" (T.J. Cooper, G. M. Boulton-Lewis, B. Atweh, H. Pillay, L. Wilss & S. Y. Mutch); (13) "Exploring Imagery in P, M and E" (C. Breen); (14) "Teachers' Framework for Understanding Children's Mathematical Thinking" (G.W. Bright, A.H. Bowman and N.N. Vacc); (15) "The Story of Sarah: Seeing the General in the Particular?" (L. Brown, and A. Coles); (16) "Effective Teachers of Numeracy in UK Primary School: Teachers' Content Knowledge and Pupils' Learning" (M. Brown, M. Askew, V. Rhodes, D. Wiliam and D. Johnson); (17) "Metaphorical Thinking and Applied Problem Solving: Implications for Mathematics Learning" (S. Carreira); (18) "Algebra as Language in Use: A Study with 11-12 Year Olds using Graphic Calculators" (T.E.A. Cedillo); (19) "Emergence of Novel Problem Solving Activity" (V. Cifarelli); (20) "NESB Migrant Students Studying Mathematics: Vietnamese Students in Melbourne and Sydney" (P.C. Clarkson and L. Dawe); (21) "Young Children's Concepts of Shape" (D.H. Clements, J. Sarama and S. Swaminathan); (22) "Learning from Distributed Theories of Intelligence" (P. Cobb); (23) "Australian and Indonesian Student Teacher Beliefs about Mathematics and Performance on a Classic Ratio Task" (J. Conroy and B. Perry); (24) "The Transition from Arithmetic To Algebra: A Cognitive Perspective" (G.M. Boulton-Lewis, T.J. Cooper, B. Atweh, H. Pillay, L. Wilss and Mutch); (25) "A New Approach for Intelligent Tutoring Systems: An Example for Statistical Activities" (G. Bueno and C.A. Cuevas); (26) "Early Development of Algebraic Representation Among 6-13 year-old Children: The Importance of Didactic Contract" (L.A.P. Brito and F. Jorge-Tarcisio Da Rocha); (27) "The Affective Domain in Mathematical Problem-Solving" (V.A. DeBellis and G.A. Goldin); (28) "Creating a Shared Context: The Use of a Multimedia Case in a Teacher Development Course" (H.M. Doerr, K. McClain, and J. Bowers); (29) "Triple Approach: A Theoretical Frame To Interpret Students' Activity in Algebra" (T.-P Drouhard and C. Sackur); (30) "When Does a Way of Working Become a Methodology" (J. Duffin and A. Simpson); (31) "Development of Seventh-Grade Students' Problem Posing" (L.D. English); (32) "A Close Look at the Use of Mathematics-Classroom-Situation Cases in Teacher Education" (R. Even and Z. Markovits); (33) "Action-Based Strategies in Advanced Algebraic Problem Solving" (P.L. Ferrari); (34) "Tacit Mechanism of Combinatorial Intuitions" (E. Fischbein and A. Grossman); (35) "Shadows on Proof" (F. Furinghetti and D. Paola); (36) "Perpendicular Lines--What is the Problem? Pre-service Teachers' Lack of Knowledge on How To Cope with Students' Difficulties" (H. Gal & S. Vinner); (37) "Actions and Invariant Schemata in Linear Generalizing Problems" (J.A. Garcia-Cruz and A. Martinon); (38) "A Classroom Discussion and an Historical Dialogue: A Case Study" (R. Garuti); (39) "The Importance of Social Structure in Developing a Critical Social Psychology of Mathematics Education" (P. Gates); (40) "Meaning of Proofs in Mathematics Education" (J.D. Godino and A.M. Recio); and (41) "A Visual Presentation of a Longitudinal Study: Design and Analysis" (F.V. Gomes and C. Hoyles). (ASK)