The fourth volume of the proceedings of 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following papers: (1) "A Model for Discriminating amongst Student Teachers of Mathematics" (P. Perks); (2) "A Study of Teachers' Conceptions about Mathematics" (G.N. Philippou and C. Christou); (3) "Emily and the Supercalculator" (D. Pitta and E. Gray); (4) "Knowing v. Knowledge-in-Action" (S. Prestage); (5) "Readability of Verbal Problems in Mathematics: Some Evidence from Secondary Schools in South Africa" (E.D. Prins); (6) "Images and Definitions for the Concept of Even/Odd Function" (S. Rasslan and S. Vinner); (7) "Constraints and Opportunities in Teaching Proving" (D.A. Reid); (8) "Assessment of Teacher-Student Interpersonal Behavior in Secondary Mathematics Classrooms: A Seed for Change" (T. Rickards and D. Fisher); (9) "Beliefs and Their Warrants in Mathematics Learning" (M.M. Rodd); (10) "Pupils' Strategies and the Cartesian Method for Solving Problems: The Role of Spreadsheets" (T. Rojano and R. Sutherland); (11) "Fallibilism and the Zone of Conjectural Neutrality" (T. Rowland); (12) "The Experience of Mathematics Teaching" (U. Runesson); (13) "Calculator Use by Upper Primary Pupils Tackling a Realistic Number Problem" (K. Ruthven); (14) "Spatial Abilities, van Hiele Levels and Language Use in Three Dimensional Geometry" (S. Saads and G. Davis); (15) "Algebraic Expressions and Equations: An Example of the Evolution of the Notions" (C. Sackur and J.P. Drouhard); (16) "Inferential Processes in Michael's Mathematical Thinking" (A. Saenz-Ludlow); (17) "Students Appropriation of Mathematical Artifacts during Their Participation in a Practice: 2 propos de A. Sfard..." (M. Pinto dos Santos and J.F. Matos); (18) "Does Teaching Mathematics as a Thoughtful Subject Influence the Problem-Solving Behaviors of Urban Students?" (R.Y. Schorr, C.A. Maher and R.B. Davis); (19) "Framing in Mathematical Discourse" (A. Sfard); (20) "Theory of Global and Local Coherence and Applications To Geometry" (A. Shriki and E. Bar-on); (21) "Generating Theoretical Accounts of Mathematics Teachers' Practices" (M.A. Simon and R. Tzur); (22) "Towards a New Theory of Understanding" (J. Duffin and A. Simpson); (23) "How Far Can You Go with Block Towers?" (C.A. Maher and R. Speiser); (24) "Chance Estimates by Young Children: Strategies Used in an Ordering Chance Task" (A.G. Spinillo); (25) "Multiple Referents and Shifting Meanings of Unknowns in Students' Use of Algebra" (K. Stacey and M. MacGregor); (26) "Elementary Components of Problem Solving Behaviour" (M. Stein); (27) "Changing Teaching and Teachers Change" (P. Sztajn); (28) "Is the Length of the Sum of Three Sides of a Pentagon Longer than the Sum of the Other Two Sides?" (P. Tsamir, D. Tirosh and R. Stavy); (29) "Investigating Change in a Primary Mathematics Classroom: Valuing the Students' Perspective" (D. Tomazos); (30) "Studying Children's Argumentation by Incorporating Different Representational Media" (D. Potari and T.A. Triadafillidis); (31) "Perceptions of Unfamiliar Random Generators--Links between Research and Teaching" (K. Truran and R. Ritson); (32)"Representations of Points" (P. Tsamir); (33) "Understanding of Different Uses of Variable: A Study with Starting College Students" (S. Ursini and M. Trigueros); (34) "Gender Differences in Cognitive and Affective Variables during Two Types of Mathematics Tasks" (H. Vermeer, M. Boekaerts, and G. Seegers); (35) "Coming To Know Pupils: A Study of Informal Teacher Assessment of Mathematics" (A. Watson); (36) "Supporting Elementary Teachers' Exploration of Children's Arithmetical Understanding: A Case for CD-ROM Technology" (J.W. Whitenack, N. Knipping, L. Coutts, and S. Standifer); (37) "Numbers versus Letters in Algebraic Manipulation: Which is More Difficult?" (M.P.H. Wong); (38) "'You Have To Prove as Wrong': Proof at the Elementary School Level" (V. Zack); (39) "Constructing Knowledge by Constructing Examples for Mathematical Concepts" (O. Hazzan and R. Zazkis); and (40) "Changes that Computer Algebra Systems Bring To Teacher Professional Development" (N. Zehavi). (ASK)