Algebraic, graphic and natural language registers to interrelate different worlds of Mathematics: the case of function
Palavras-chave:
Registers, Function, Concept Image, Embodiment, Symbolism, FormalismResumo
We designed a set of activities on one real variable functions, based on various semiotic registers of representation (Duval, 2000), expecting to answer the following research question: “Can the individual concept image (Tall & Vinner, 1981) of function be enriched by the use of various functions and their associate ones, using verbal texts, algebraic laws and graphs?”. Seven in-service Mathematics teachers from Brazil carried out these activities, during six two and a half hours sessions. In this paper, we ocused on protocols and observers’ written notes of one teacher from the group, which were analysed in the light of the theoretical framework of The Three Worlds of Mathematics (Tall, 2004a, 2004b). We found that this teacher had, in his concept image, notions related with only first and seconddegree polynomial functions, and used mostly the embodied world to justify his answers. The activities seemed useful for him to broaden his concept image.
Downloads
Referências
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, PontifÃcia Universidade Católica de São Paulo, São Paulo.
DE SOUZA, V. H., & Campos, T. M. (2005). Sobre a resolução da inequacao x2 < 25. Anais do Encontro Brasileiro de Estudantes de Pós-Graduação em Educação Matemática . 1, p. 40. São Paulo: FEUSP.
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. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Neuchâtel, Suisse: Peter Lang.
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. (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.
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.
Publicado
Como Citar
Edição
Seção
Este trabalho está licensiado sob uma licença Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
