This conference proceedings contains 135 research reports, 73 short oral reports, 30 poster session reports, 4 plenary addresses, 3 research forums, 6 project groups, and 5 discussion group reports. Only the research reports, research forums, and plenary addresses are full reports; the others are generally one-page abstracts. The first volume includes: (1) "Where in shared knowledge is the individual knowledge hidden?" (R. Hershkowitz); (2) "Professional development, classroom practices, and students' mathematics learning. A cultural perspective" (G. B. Saxe); (3) "One theoretical perspective in undergraduate mathematics education research" (B. Czarnocha, E. Dubinsky, V. Prabhu, and D. Vidakovic); (4) "Cultural aspects in the learning of mathematics" (N. Presmeg and P. Clarckson); (5) "Developing skills of advanced mathematical thinking" (P. E. Kahn). The second volume includes: (1) "Teacher profile in the geometry curriculum based on the Van Hiele theory" (M. D. Afonso, M. Camacho, and M. M. Socas); (2) "Pupils' images of teachers' representations" (C. Bills and E. Gray); (3) "What kind of mathematical knowledge supports teaching for 'conceptual understanding'? Preservice teachers and the solving of equations" (D. Chazan, C. Larriva, and D. Sandow); (4) "Argumentative aspects of proving: Analysis of some undergraduate mathematics students' performances" (N. Douek); (5) "A numeracy assessment framework for the international life skills survey" (I. Gal). The third volume includes: (1) "'What Can We All Say?' Dynamic geometry in a whole-class zone of proximal development" (J. Gardiner, B. Hudson, and H. Povey); (2) "Pedagogy and the role of context in the development of an instrumental disposition towards mathematics (S. Goodchild); (3) "Alternative assessment for student teachers in a geometry and teaching of geometry course" (B-S. Ilany and N. Shmueli); (4) "Learning pre-calculus with complex calculators: Mediation and instrumental genesis" (J. B. Lagrange); (5) "This patient should be dead! Or: How can the study of mathematics in work advance our understanding of mathematical meaning-making in general?" (R. Noss, C. Hoyles, and S. Pozzi). The fourth volume includes: (1) "The research of ideas of probability in the elementary level of education" (A.-M. Ojeda); (2) "Monitoring of dynamics of students' intellectual growth in MPI-Project" (S. Rososhek); (3) "Conceptual understanding of conventional signs: A study without manipulatives" (C. Silveira); (4) "Does the understanding of variable evolve through schooling?" (M. Trigueros and S. Ursini); (5) "Boys, mathematics and classroom interactions: The construction of masculinity in working-class mathematics classrooms" (R. Zevenbergen). (ASK)