Representations in matematics education: an onto-semiotic approach

Referencias

Bloor, D. (1983). Wittgenstein. A social theory of knowledge. London, UK: The Macmillan Press. Blumer, H. (1969). Symbolic interactionism: Perspective and method. Englewood Cliffs, NJ: Prentice-Hall Cobb, P., Yackel & McClain, K., (Eds.) (2000). Symbolizing and communicatins in mathematics classrooms. London, UK: Lawrence Erlbaum. Contreras, A., Font, V., Luque, L. & Ordóñez, L. (2005). Algunas aplicaciones de la teoría de las funciones semióticas a la didáctica del análisis infinitesimal. Recherches en Didactique des Mathématiques, 25 (2), 151-186. D’Amore, B. (2006). Didáctica de las Matemáticas. Bogotá, Colombia: Magisterio. D’Amore, B. (2005). Secondary school students’ mathematical argumentation and Indian logic (nyaya). For the Learning of Mathematics, 25 (2), 26-32. Duval, R. (2002). Representation, vision and visualization: cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt, (ed.), Representations and Mathematics Visualization (pp. 311-335). North American Chapter of PME: Cinvestav-IPN, México. Eco, U. (1979). Trattato di semiotica generale. Milano, Italy: Bompiani. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. New York, NY: SUNY. Font, V. (2001). Representation in Mathematics Education. Philosophy of Mathematics Education Journal, 14, 1-35. [http://www.ex.ac.uk/~PErnest/pome14/contents.htm] Font, V., Godino, J. D. & D'Amore, B. (2007). An onto-semiotic approach to representations in mathematics education. For the Learning of Mathematics, 27(2), 1-7. Font, V. & Peraire, R. (2001). Objetos, prácticas y ostensivos asociados. El caso de la cisoide. Educación Matemática, 13(2), 55-67. Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactique des Mathématiques, 22(2/3), 237-284. Godino, J. D. & Batanero, C. (1998). Clarifying the meaning of mathematical objects as a priority area of research in mathematics education. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics Education as a research domain: A search for identity (pp.177-195). Dordrecht: Kluwer, A. P. Godino, J. D., Batanero, C. & Roa, R. (2005). An onto-semiotic analysis of combinatorial problems and the solving processes by university students. Educational Studies in Mathematics, 60(1), 3-36. Goldin, G. (1998). Representations and the psychology of mathematics education: part II. Journal of Mathematical Behaviour, 17(2), 135-165. Goldin, G. (2002). Representation in mathematical learning and problem solving. In L. D. English (ed.), Handbook of International Research in Mathematics Education (pp. 197-218). London, UK: Lawrence Erlbaum. Goldin, G. & Janvier, C. (1998). Representation and the psychology of mathematics education. Journal of Mathematics Behaviour, 17 (1), 1-4. Goldin, G. & Stheingold, N. (2001). System of representations and the development of mathematical concepts. In A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics, 2001 yearbook (pp.1-23). Reston, VA: National Council of teachers of Mathematics. Hitt, F. (2002). Representations and mathematics visualization. North American Chapter of PME: Cinvestav-IPN, Mexico. Hjemslev, L. (1961). Prolegomena to a Theory of Language. Madison, Wisconsin: University of Wisconsin. Janvier, C. (ed.) (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum. Kaput, J. J. (1998). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows. Journal of Mathematical Behaviour, 17(2), 266-281. Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: towards a socio-cultural history of mathematics. For the Learning of Mathematics 17(1), 26-33. Radford, L. (2003). On the epistemological limits of language. Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123–150. Sfard, A. (2000). Symbolizing mathematical reality into being – or how mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and Communicating in Mathematics Classrooms (pp. 38-75). London, UK: Lawrence Erlbaum. Steinbrigng, H. (1997). Epistemological investigation of classroom interaction in elementary mathematics teaching. Educational Studies in Mathematics, 32, 49-92. Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactiques des Mathématiques, 10(2/3), 133-170. Wilhelmi, M. R., Godino, J. D. & Lacasta, E. (2005). Didactic effectiveness of equivalent definitions of a mathematical notion. The case of the absolute value. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4). Barcelona, Spain: Universitat Ramon Llull. Wittgenstein, L. (1953). Philosophical investigations. Basil Blackwell, Oxford [1958].