The second volume of this proceedings contains full research articles. Papers include: (1) "Lave and Wenger's social practice theory and teaching and learning school mathematics" (J. Adler); (2) "Being a researcher and being a teacher" (J. Ainley); (3) "Procedural and conceptual aspects of standard algorithms in calculus" (M.B. Ali and D. Tall); (4) "Using small group discussions to gather evidence of mathematical power" (S.E. Anku); (5) "Seventh grade students' algorithmic, intuitive and formal knowledge of multiplication and division of non-negative rational numbers" (A. Barash and R. Klein); (6) "Theory and practice in undergraduate mathematics teaching: A case study" (T. Barnard and C. Morgan); (7) "Heuristics and biases in secondary school students' reasoning about probability" (C. Batanero, L. Serrano, and J.B. Garfield); (8) "Changes in student teacher views of the mathematics teaching/learning process at the secondary school level" (N. Bednarz, L. Gattuso, and C. Mary); (9) "A study of proportional reasoning among seventh grade students" (D. Ben-Chaim, J.T. Fey, and W.M. Fitzgerald); (10) "Children's word meanings and the development of division concepts" (S.B. Berenson and D. Vidakovic); (11) "The use of examples in the teaching and learning of mathematics" (L. Bills); (12) "The influences of significant others on student attitudes to mathematics learning" (A. Bishop, C. Brew, G. Leder, and C. Pearn); (13) "Student teachers' approaches to investigate mathematics: Iterative engagement or disjointed mechanisms?" (P. Blanc and R. Sutherland); (14)"The analgebraic mode of thinking and other errors in word problem solving" (H. Bloedy-Vinner); (15) "Challenging the traditional school approach to theorems: A hypothesis about the cognitive unity of theorems" (P. Boero, R. Garuti, E. Lemut, and M.A. Mariotti); (16) "Some dynamic mental processes underlying producing and providing conjectures" (P. Boero, R. Garuti, and M.A. Mariotti); (17) "Teachers' behaviours in teaching with computers" (R.M. Bottino and F. Furinghetti); (18) "A decimal number is a pair of whole numbers" (G. Brekke); (19) "The story of silence: Teacher as researcher--researcher as teacher" (L. Brown and A. Coles); (20) "The cultural evolution of mathematics" (T. Brown); (21) "Beginning learning negative numbers" (A. Bruno and A. Martinon); (22) "Concepts of multiplication of children and teachers in Mozambique" (F. Buikema Draisma); (23) "On preservice teachers' understanding of division with remainder" (S. Campbell); (24) "Referent transforming operations: Teachers' solutions" (T. Campos, S. Magina, M.C. Da Cunha, and S. Canoas); (25) "Reconstructing teachers' thinking in teaching problem solving" (O. Chapman); (26) "Bayesian implicative analysis: How to identify the concepts necessary to acquisition of a competence? One example of application to the conceptualization of fraction in teenagers" (C. Charron and J.M. Bernard); (27) "How does addition contribute to the construction of natural numbers in 4- to 13-year-old children?" (C. Charron and N. Ducloy); (28) "Overcoming isolation in teaching" (D. Chazan, D. Ben-Chaim, and J. Gormas); (29)"NESB migrant students studying mathematics: Vietnamese and Italian students in Melbourne" (P. Clarkson); (30) "Levels of formal reasoning in school algebra" (C. Coady and J. Pegg); (31) "Years 2 and 3 children's correct-response mental strategies for addition and subtraction word problems and algorithmic exercises" (T. Cooper, A.M. Heirdsfield, and C.J. Irons); (32) "Why the psychological must consider the social in promoting equity and social justice in mathematics education" (T. Cotton and P. Gates); (33) "Clinical analysis of difficulties in algebraic problem solving among Brazilian students: Principal aspects and didactic issues" (J.-T. Da Rocha Falcao); (34) "What is the difference between remembering someone posting a letter and remembering the square root of 2" (G.E. Davis); (35)"The illusion of linearity: A persistent obstacle in pupils' thinking about problems involving length and area of similar plane figures" (D. De Bock, L. Verschaffel, and D. Janssens); (36) "The development of whole-part relationship in situations of combine structure for a student with learning disabilities" (L. Deblois); (37) "Study of the evolution of graduate students' concept images while learning the notions of limit and continuity" (C. Delgado and C. Azcarate); (38) "Facets and layers of the function concept" (P. DeMarois and D. Tall); (39) "Evolution of conceptions in a mathematical modelling educational context" (G. Dettori, R. Garuti, E. Lemut, and M.A. Mariotti); (40) "The role of physical phenomena in students' investigations of the tangent function" (H.M. Doerr); (41) "Written subtraction in Mozambican schools" (J. Draisma); (42) "Children's reasoning in solving novel problems of deduction" (L. English); (43) "Association judgments in the comparison of two samples" (A. Estepa and F.T. Sanchez); (44) "On some factors affecting advanced algebraic problem solving" (P.L. Ferrari); (45) "Intuitions and schemata in probabilistic thinking" (E. Fischbein and D. Schnarch); (46) "The Fennema-Sherman 'mathematics as a male domain scale': A re-examination" (H.J. Forgasz, G.C. Leder, and P.L. Gardner); (47) "Students' misconceptions with decimal numbers. Preliminary results from a study of computer based teaching" (A.B. Fuglestad); (48) "Qualitative analysis in the study of negative numbers" (A. Gallardo); (49) "An analysis of some students' concept images related to the linear function when using a 'generic organizer'" (M.C. Garcia and C. Azcarate); (50) "Learning proportion using a computer environment in the classroom" (M. Garcia Mila, E. Marti, C. Gomez-Granell, and B. Steren); (51) "Development of concepts of the arithmetic average from high school to university" (L. Gattuso and C. Mary);(52) "Selling mathematics: The language of persuasion in an introductory calculus course" (S. Gerofsky); and (53) "Mathematical concepts, their meanings and understanding" (J.D. Godino). (ASK)