The fourth volume of this proceedings contains full research articles. Papers include: (1) "Conceptual and procedural approaches to problem-solving" (Y. Mohammad-Yusof and D. Tall); (2)"Teaching differential equations to chemistry and biology students: An overview on methodology of qualitative research. A case study" (M. Moreno and C. Azcarate); (3) "Language and assessment issues in mathematics education" (C. Morgan); (4) "Learning math in two languages" (J. Moschkovich); (5) "Hermeneutic experiences in constructing lessons and classroom research" (J.A. Mousley); (6) "Young students' informal knowledge of fractions" (H. Murray, A. Olivier, and P. Human); (7) "Tensions in the novice mathematician's induction to mathematical abstraction" (E. Nardi); (8) "Students assessment of an alternative approach to geometry" (L. Nasser, N. Sant'Anna, and A.P. Sant'Anna); (9) "Solving word problems with different mediators: How do deaf children perform?" (T. Nunes and C. Moreno); (10) "Telling definition and conditions: An ethnomethodological study of sociomathematical activity in classroom interaction" (M. Ohtani); (11) "Making sense of children's patterning" (J. Orton and A. Orton); (12) "Children's intuitive understanding of area measurement" (L. Outhred and M. Mitchelmore); (13) "Responsiveness: A key aspect of spatial problem solving" (K. Owens); (14) "The first algebraic learning. The failure of success" (M. Panizza, P. Sadowsky, and C. Sessa); (15) "Extending the educational conversation: Administrator's views of staff development" (T. Peluso, J.R. Becker, and B.J. Pence); (16) "The teaching of mathematics from within the school. Teachers and principals as researchers" (P. Perry, P. Gomezm, and P. Valero); (17) "Teachers' conceptions about mathematical assessment" (G. Philippou and C. Christou); (18) "Student teachers' conceptions of the rational number" (M. Pinto and D. Tall); (19) "Folding back to collect: Knowing you know what you need to know" (S. Pirie, L. Martin, and T. Kieren); (20) "Nouns, adjectives and images in elementary mathematics" (D. Pitta and E. Gray); (21) "Designing a domain for stochastic abstraction" (D. Pratt and R. Noss); (22) "Cord's story: An African American student points to the need for change in college mathematics pedagogy" (N.C. Presmeg); (23) "On dialectical relationships between signs and algebraic ideas" (L. Radford and M. Grenier); (24) "Exploiting understanding of data reduction" (C. Reading and J. Pegg); (25) "'Wouldn't it be good if we had a symbol to stand for any number': The relationship between natural language and symbolic notation in pattern description" (E. Redden); (26) "Enactivism as a methodology" (D.A. Reid); (27) "Teaching linear algebra: Role and nature of knowledges in logic and set theory which deal with some linear problems" (M. Rogalski); (28) "Ways of solving algebra problems: The influence of school culture" (T. Rojano, R. Sutherland, S. Ursini, S. Molyneux, and E. Jinich); (29) "On the introduction of real numbers in secondary school. An action-research experience" (I. Romero and L. Rico); (30) "Counting, estimation and the language of uncertainty" (T. Rowland); (31) "The transformation of mathematical objects in the didactic system: The case of the notion of function" (L. Ruiz Higueras and J.L. Rodriguez Fernandez); (32) "The use of illustrations in mathematics textbooks" (D. Santos-Bernard); (33) "Effects of computerized tools on prototypes of the function concept" (B.B. Schwarz and R. Hershkowitz); (34) "Affective constraints in mathematics education" (B. Southwell and M. Khamis); (35) "On the ability of high-school students to cope with a self-learning task in algebra" (J. Stupp and S. Vinner); (36) "Learning about teaching: The potential of specific mathematics teaching examples, presented on interactive multimedia" (P. Sullivan and J. Mousley); (37) "Mathematical modeling in the sciences through the eyes of Marina and Adam" (R. Sutherland, T. Rojano, S. Mochon, E. Jinch, and S. Molyneux); (38) "Pre-service teachers' problem solving strategies" (M. Taplin); (39) "Children's representation of the counting sequence 1-100: Cognitive structural development" (N. Thomas, J. Mulligan, and G.A. Goldin); (40) "College students' conceptions of variable" (M. Trigueros, S. Ursini, and A. Reyes); (41) "Seeing is reality: How graphic calculators may influence the conceptualization of limits" (L. Trouche and D. Guin); (42) "Children's misconceptions about the independence of random generators" (J.M. Truran); (43) "Children's use of a representativeness heuristic" (K.M. Truran); (44) "Two problems under one title: The case of division by zero" (P. Tsamir); (45) "Children's interaction and fraction learning in a computer microworld: Construction of the iterative fraction scheme" (R. Tzur); (46) "Precalculus and graphic calculators: The influence on teacher's beliefs" (P. Valero and C. Gomez); (47) "Conditional probability and the level of significance in the tests of hypotheses" (A. Vallecillos and C. Batanero); (48) "Students' awareness of the distributive property" (N. Vermeulen, A. Olivier and P. Human); (49) "Pre-service teachers' conceptions and beliefs about the role of real-world knowledge in arithmetic word problem solving" (L. Verschaffel, E. De Corte, and I. Borghart); (50) "Semiotics as a descriptive framework in mathematical domains" (A. Vile and S. Lerman); (51) "Some psychological aspects of professional lives of secondary mathematics teachers--The humiliation, the frustration, the hope" (S. Vinner); (52) "Teachers' knowledge of pupils' errors in algebra" (E.K. Wanjala and A. Orton); (53) "Children's strategies for comparing two types of random generators" (J. Way); and (54) "Teaching to create discussion as mathematical argumentation" (T. Wood). (ASK)