Algebraic, graphic and natural language registers to interrelate different worlds of mathematics: the case of function

Referencias

AKKOÇ, H. (2006). The Concept of Function: what have students met before. In: A. Simpson (Ed.), Retirement as Process and Concept: A Festschrift for Eddie Gray and David Tall (pp. 1-8). Durham, Reino Unido: Durham University. ANGELINI, N. M. (2010). Funções: um estudo baseado nos Três Mundos da Matemática. Dissertação de Mestrado, Universidade Bandeirante de São Paulo, São Paulo. BAZZINI, L., & TSAMIR, P. (2003). Connections between theory and research findings: the case of inequalities. Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education (pp. 1-3). Bellaria: ERME. BONOMI, M. C. (1999). A construção/negociação de significados no curso universitário inicial de Cálculo Diferencial e Integral. Tese de Doutorado, Universidade de São Paulo, Faculdade de Educação, São Paulo. DE SOUZA, V. H. (2008). O uso de vários registros na resolução de inequações - uma abordagem funcional gráfica. Tese de Doutorado, Pontifícia Universidade Católica de São Paulo, São Paulo. DE SOUZA, V. H., & Campos, T. M. (2005). Sobre a resolução da inequacao x^2 < 25. Anais do Encontro Brasileiro de Estudantes de Pós-Graduação em Educação Matemática . 1, p. 40. São Paulo: FEUSP. DUVAL, R. (2000). Basic issues for research in Mathematics Education. In: M. J. Hoines, & A. B. Fuglestad (Ed.), Proceedings of the24th Conference fo the International Group for the Psychology of Mathematics Education. 1, pp. 55-69. Hiroshima: PME. DUVAL, R. (1993). Graphiques et équations: l'articulation de deux registres. In: Les science pour l'education pour l'ère nouvelle (pp. 57-72). França: Caen. DUVAL, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In: F. Hitt, & M. Santos (Ed.), Proceedings of the 21st North American Capter of the PME Conference, 1, pp. 3-26. DUVAL, R. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Neuchâtel, Suisse: Peter Lang. GRAY, E., & TALL, D. O. (1994). Duality, Ambiguity and Flexibility: a proceptual view of simple arithmetic. The Journal for Research in Mathematics Education , 26 (2), pp. 115-141. SIERPINSKA, A. (1992). On understanding the notion of function. In: E. Dubinsky, & G. H. (Eds.), The concept of function: Elements of Pedagogy and Epistemology ( Notes and Reports Series ed., Vol. 25, pp. 25-58). Mathematical Association of America. TALL, D. O. (2004). The Three Worlds of Mathematics. For the Learning of Mathematics , 23 (3), pp. 29-33. TALL, D. O. (2004). Thinking through three worlds of mathematics. Proceedings of the 28th Meeting of the International Conference for the Psychology of Mathematics Education. 4, pp. 281-288. Bergen, Norway: Bergen. TALL, D. O., & VINNER, S. (1981). Concept image and concept definition in mathematics, with special reference to limits and continuity. Educational Studies in Mathematics , 12, pp. 151-169. THOMAS, M. O., & TALL, D. O. (2001). The long-term cognitive development of symbolic algebra. International Congress of Mathematical Instruction Working Group Proceedings. 2, pp. 590-597. Melbourne: ICMI. WATSON, A., SPYROU, P., & TALL, D. (2003). The Relationship between Physical Embodiment and Mathematical Symbolism: The concept of vector. The Mediterranean Journal of Mathematics Education , 1 (2), pp. 73-97.