Proceedings of the International Conference on the Psychology of Mathematics Education (PME) (11th, Montreal, Canada, July 19-25, 1987), Volumen1

The first volume of this proceedings contains three plenary addresses: (1) "Visualization in 3-dimensional geometry: In search of a framework" (A. Gutierrez); (2) "The ongoing value of proof" (G. Hanna); and (3) "Modern times: The symbolic surfaces of language, mathematics and art" (D. Pimm). Plenary panels include: (1) "Contribution to the panel 'Putting mathematics into language and language into mathematics'" (C. Laborde); (2) "Language and the socialization of thinking" (T. Nunes); and (3) "Pupils' prompted production of a medieval mathematical sign system" (L. Puig). Research forums include: (1) "The role of representation systems in the learning of numerical structures" (L. Rico, E. Castro, and I. Romero); (2) "Mathematics teacher development: Connections to change in teachers' beliefs and practices" (J.R. Becker and B.J. Pence); and (3) "Teacher subject matter knowledge and pedagogical content knowledge: Research and development" (R. Even, D. Tirosh, and Z. Markovits). Short oral communications include: (1) "Understanding decimal numbers: From measurement towards the number line" (M. Basso, C. Bonotto, and P. Sorzio); (2) "The role of the graphic calculator as a mediating sign in the zones of proximal development of university students" (M. Berger); (3) "Professional development in performance assessment for Queensland years 1-10 mathematics teachers" (R. Bleicher, T.J. Cooper, S. Dole, S. Nisbet, and E. Warren); (4) "A student teacher's attempts to analyze a student's learning" (A. Boufi and S. Kafoussi); (5) "Teachers' and students' images about learning mathematics" (I. Branco and I. Oliveira); (6) "Prioritising mathematics teacher education choices at pre- and inservice levels" (C. Breen), (7) "Graphic calculators and precalculus: Effects on curriculum design" (C. Carulla and P. Gomez); (8) "The use of two different types of graphs in a statistical task (7th Grade)" (C. Carvalho); (9) "The influence of integrating an innovating project in pupils' ideas about mathematics" (M. Cesar); (10) "Using teaching cases: A portrait of teachers' thinking about reform" (M. Civil); (11) "Euclidean geometry: Cognitive gender differences" (L.S. Cronje); (12) "'The middle of what?': Students' images of mean, median, and mode" (D. Cudmore); (13) "Generalization in algebra problem solving and attitudes toward mathematics" (M.R.F. de Brito); (14)"Point configurations as representation system for the study of natural sequences" (M. de la Fuente and E. Castro); (15) "Learning and teaching percent problem solving" (S. Dole, A.R. Batturo, and T.J. Cooper); (16) "Cartesian graphs and students conceptions: Looking for relationships between interpretation and construction" (M. Fabra and J. Deulofeu); (17) "Logo: Big step and small step" (E.K. Fainguelernt, F.C. Gottlieb, and J.B. Frant); (18) "Students' mathematical activity and cooperative work in the classroom" (E. Fernandes); (19) "Thinking processes used by two preservice teachers facing problem solving" (L. Fonseca); (20) "Personal strategies of generalization in linear generalizing problems" (J.A. Garcia-Cruz and A. Martinon); (21) "Conceptualizing non-unit fractions: An historical approach" (A. Goldblatt and C.L. Raymond); (22) "Transition between institutions: The case of algebra in the transition from vocational high schools to general high schools" (B. Grugeon and M. Artigue); (23) "The effects of a graphing-approach college algebra curriculum on students' understanding of function" (J.C. Hollar and K.S. Norwood); (24) "Assessment in geometry from two points of view: Levels of reasoning and SOLO levels" (M.P. Huerta); (25) "Researching computers and collaborative learning in pre-service mathematics teacher education" (A.J. Jones); (26) "An experiment on computer-assisted problem posing in undergraduate mathematics" (P. Kent); (27) "Student teachers' understanding of mathematics education" (S.H. Knudtzon); (28) "Knowledge of transformations of functions: Point-plotting as opposed to use of the graphics calculator" (P.E. Laridon); (29) "Learning from students' out-of-school mathematics practice" (J.O. Masingila); (30) "Assessing pre-service teachers' conceptual understanding of perimeter and area" (R. Menon); (31) "A framework for the quality of explanation in relation to the distributive law" (I.A. Mok); (32) "Division word problems: The construction of representation and procedures in young children" (L. Morgado and C. Abreu); (33) "The quality of students' reflection in problem solution" (M.D. Mosimege); (34) "An expert system to guide the geometry teacher" (L. Nasser, G.O.G. Zapata, and I.C.M. Bernardo); (35) "Going deeper into mathematical activity" (I. Plasencia, R.M. Guemes, and C. Espinel); (36) "Curriculum materials in mathematics education reform" (J.T. Remillard); (37) "Roots of teacher differences: Beliefs of preservice elementary vs secondary teachers" (B.F. Risacher); (38) "College students' knowledge and beliefs" (M. Risnes); (39) "The object and aim of teachers as regards pupils' learning in mathematics" (U. Runesson); (40) "Mathematics learning--Students' appropriation process of mathematical artifacts" (M. Santos); (41) "The initial growth of prospective mathematics teachers through participation in a teacher development project" (V.M.P. Santos); (42) "Mathematics, fractals and encoding images" (F. Sereno); (43) "Constructing knowledge together in the mathematics classroom: What do student teachers learn about teaching math from the practicum?" (R. Shane); (44) "The influence of 'supposed others' in the social process of making a mathematical definition" (Y. Shimizu); (45) "Developing new models of mathematics teaching: An imperative for research on mathematics teacher development" (M.A. Simon); (46) "Teacher beliefs and practices in primary mathematics" (S. Simon and M. Brown); (47) "Curriculum reform and teachers' conceptions of mathematics" (S.Z. Smith); (48) "Making connections: Representing understanding the number system" (N. Thomas); (49) "Deciding about studying mathematics at the senior secondary level of schooling in Australia" (R. Toomey, J. Deckers, B. Elliot, J. Malone, and R. O'Donovan); and (50) "Progress in mathematics education reform" (L.R. Van Zoest). Posters include: (1) "(divide) 2 litre" (J. Baena, M. Coriat, and P. Nieto); (2) "Evaluating an interactive CD-ROM designed for preservice teacher education" (L. Barron, J. Bowers, and K. McClain); (3) "The teacher as problem solver and his/her conception of problem solving in the mathematics classroom" (L.C. Contreras, J. Carrillo, and F. Guevara); (4) "The importance of relative code to young children's understanding of the division concept" (J. Correa and P.E. Bryant); (5) "Some adventures in Euclidian geometry" (M. de Villiers); (6) "Does language affect proportional reasoning?" (D. Desli); (7) "Making sense of science and mathematics through classroom dialogue" (B.A. Doig, S.C. Groves, and J.S. Williams); (8) "The assessment of algebraic partial knowledge: Model-eliciting activities for algebra" (F. Fernandez Garcia); (9) "Two case studies of future teachers' conceptions about mathematics, its teaching and learning" (P. Flores); (10) "Language and number notation: A study of deaf children" (M. Fuentes and L. Tolchinsky); (11) "An approach to analyzing the mathematics teacher's professional knowledge: The case of the concept of function" (M. Garcia, S. Llinares, and V. Sanchez); (12) "Mathematics teachers' beliefs concerning teaching and learning" (F. Gil and M.F. Moreno); (13) "The affective processes: A mathematical learning program in a socio-cultural context" (I.M. Gomez-Chacon); (14) "Algebraic thinking: Using magic squares with 5th grade students" (F.C. Gottlieb, J.B. Frant and R. Oliveira); (15) "Teachers responses to pupils' errors" (M.A. Inacio and G. Ramalho); (16) "A comparison of the geometric perceptions of Australian and American students" (C. Lawrie); (17) "A didactical engineering for a notion of limit of function" (A.L. Manrique and S.A. Almouloud); (18) "Supporting teachers of mathematics at a distance: Fifteen years of practice in the UK" (J. Mason, E. Love, C. Shiu, and D. Pimm); (19) "Arithmetic games with strategic components in the early primary mathematics classroom" (D. Mosel-Gobel, A. Peter, and P. Sorger); (20) "Number initiation--An African perspective" (R.K. Ngwa); (21) "Kites makes mathematics fly" (I. Oliveira, I. Branco, and J. Silva Pereira); (22) "Student decision making in a game of chance and misconceptions in probabilistic reasoning" (R. Peard); (23) "The use of cognitive maps for analyzing the understanding of transfinite numbers" (C. Penalva, C. Gaulin, and A. Gutierrez); (24) "Introduction of the concept of probability to teenagers (12/13 years old)" (C. Queiroz e Silva, I. Esteves, M. Henry, and T.M.M. Campos); (25) "Assessment of university students' mathematical generalization symbolization capacities" (A.M. Recio and J.D. Godino); (26) "Strategies used by mathematics university students in solving combinatorial problems" (R. Roa, C. Batanero, J.D. Godino, and M.J. Canizares); (27) "Additive operators in numerical tables" (F. Ruiz Lopez); (28) "Mathematics teachers' professional knowledge and their professional development" (M.J. Saraiva); (29) "Cognitive mapping: A study about the concepts of fractions in student teachers and elementary teachers (grades 1-4)" (V. Scomparim de Lima and M.R.F. de Brito); and (30) "Research of what-if-not strategy in problem posing" (H.S. Seo). (ASK)

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