Pensamiento matemático, cálculo diferencial y computadoras
Tipo de documento
Autores
Lista de autores
Villarreal, Mónica
Resumen
Este trabajo tiene como objetivo caracterizar los procesos de pensamiento de estudiantes universitarios al abordar cuestiones matemáticas de cálculo diferencial en un ambiente computacional. Tal caracterización se realiza a partir del análisis de episodios extraídos de experimentos de enseñanza realizados con estudiantes que participaron voluntariamente en el estudio. En dichos episodios, la computadora se muestra como un dispositivo que está mediando el pensamiento humano, y así, se constituye en una herramienta que transforma y, al mismo tiempo, forma parte de dicho pensamiento, integrando un colectivo pensante hombre-cosas. Los estudiantes desarrollan tanto abordajes visuales como algebraicos en el ambiente computacional, lo que sugiere la necesidad de coordinarlos para superar la dicotomía visual/algebraico. Juegos de conjeturas y refutaciones caracterizan los procesos de pensamiento matemático de los estudiantes que no siguen caminos lineales sino en forma de red.
Fecha
2003
Tipo de fecha
Estado publicación
Términos clave
Cálculo | Computadores | Otro (métodos) | Otro (procesos cognitivos) | Pensamientos matemáticos
Enfoque
Idioma
Revisado por pares
Formato del archivo
Referencias
Borba, M. (1993), Students ́ understanding of transformations of functions using multirepresentational software, tesis de doctorado en Educación, Cornell Uni- versity, 377 pp. –––––– (1994), “A model for students ́ understanding in a multi representational environment”, en J. da Ponte y J. Matos (ed.), Proceedings of the 18th PME Conference, Lisboa 2, pp. 104-111. –––––– (1995a), “O uso de calculadoras gráficas no ensino de funções na sala de aula”, en Anais da Semana de Estudos em Psicologia da Educação Matemática, Recife, UFPE, pp. 67-72. –––––– (1995b), “Funções, representações múltiplas e visualização na Educação Matemática”, en Anais do I Seminário Internacional de Educação Matemática, Río de Janeiro, IM-UFRJ, pp. 71-90. –––––– (1995c), “Computadores, representações múltiplas e a construção de idéias matemáticas”, Bolema, Rio Claro, año 9, especial 3, pp. 83-101. –––––– (1997), “Graphing calculator, functions and reorganization of the classroom”, en M. Borba, T. Souza, B. Hudson, y J. Fey (ed.), Proceedings of Working Group 16 at ICME 8: the role of technology in the Mathematics classroom, Rio Claro, UNESP, pp. 53-62. Borba, M. y J. Confrey, (1996), “A student ́s construction of transformations of functions in a multiple representational environment”, Educational Studies in Mathematics, 31 (3), pp. 319-337. Borba, M. y M. Villarreal (1998), “Graphing calculators and reorganization of thinking: the transition from functions to derivative”, en A. Olivier, y K. Newstead (ed.), Proceedings of the 22nd PME Conference, Stellenbosch, 2, pp. 135-143. Capuzzo Dolcetta, I. et al. (1988), “The impact of new technologies on teaching calculus: a report of an experiment”, International Journal of Mathematical Education in Science and Technology, 19 (5), pp. 637-657. Cobb, P. y L. Steffe (1983), “The constructivist researcher as teacher and model builder”, Journal for Research in Mathematics Education, 14(2), pp. 83-94. Eisenberg, T. y T. Dreyfus (1991), “On the reluctance to visualize in mathematics”, en W. Zimmermann y S. Cunningham (eds.), Visualization in teaching and learning Mathematics, Washington, Mathematical Association of America, pp. 25-38. Freire, P. (1979), Educação e mudanza, trad. de M. Gadotti y L. L. Martin, Río de Janeiro, Paz e Terra. Hallet, D. (1991), “Visualization and calculus reform”, en W. Zimmermann y S. Cunningham (ed.), Visualization in teaching and learning mathematics, Washington, Mathematical Association of America, pp. 121-126. Heid, M.K. (1988), “Resequencing skills and concepts in applied calculus using the computer as a tool”, Journal for Research in Mathematics Education, 19 (1), pp. 3-25. Heid, M.K. y T. Baylor (1993), “Computing technology”, en P.S. Wilson (ed.), Research ideas for the classroom-High School Mathematics, Reston, VA, NCTM, Macmillam, pp. 198-214. Hillel, J. et al. (1992), “Basic functions through the lens of Computer Algebra System”, Journal of Mathematical Behavior, 11(2), pp. 119-158. Lautem, A., K. Graham y Ferrini-Mundy (1994), “Student understanding of basic calculus concepts: interaction with the graphics calculator”, Journal of Mathematical Behavior, 13, pp. 225-237. Lawson, D. (1995), “The effectiveness of a computer-assisted learning programme in engineering mathematics”, International Journal of Mathematical Education in Science and Technology, 26(4), pp. 567-574. Levy, P. (1993), As tecnologias da inteligência. O futuro do pensamento na era da informática, trad. C. I. da Costa, São Paulo, Editora 34, 203 p. Lincoln, Y. y E. Guba (1985), Naturalistic inquiry, California, SAGE, 416 p. Machado, N. (1995), Epistemologia e didática: as concepções de conhecimento e inteligência e a prática docente, São Paulo, Cortez Editora, 320 p. Palmiter, J. (1991), “Effects of computer algebra systems on concept and skill adquisition in calculus”, Journal for Research in Mathematics Education, Reston, 22(2), pp. 151-156. Schoenfeld, A. (1995): “A brief biography of Calculus Reform”, UME Trends, Lafayette, Purdue University, 6(6), pp. 3-5. Smith, D. (1995), “Computers in Calculus Reform”, UME Trends, Lafayette, Purdue University, 6(6), pp. 14-15, 31. Tall, D. (1993), “Real Mathematics, rational computers and complex people”, en Proceedings of the Fifth Annual International Conference on Technology in College Mathematics Teaching, Addison-Wesley, pp. 243-258. –––––– (1996), “Information Technology and Mathematics Education: Enthusiasms, Possibilities and Realities”, texto de la conferencia dictada en el 8th International Congress on Mathematical Education (ICME 8), 1996, Sevilla. Tall, D. y M. Thomas (1989), “Versatile learning and the computer”, Focus on learning problems in Mathematics, 11 (2), pp. 117-126. Tikhomirov, O.K. (1981), “The psychological consequences of computarization”, en J.V. Wertsch (ed.), The concept of activity in Soviet Psychology, Nueva York, M.E. Sharpe, pp. 256-278. Villarreal, M. (1999), O pensamento matemático de estudantes universitários de Cálculo e tecnologias informáticas, tesis de doctorado en Educación Matemática, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Rio Claro.