El Concepto de Función: Ideas pedagógicas a partir de su historia e investigaciones
Barra lateral del artículo
Contenido principal del artículo
Resumen
En esta artículo se hace un breve recorrido por la historia del concepto de función que nos muestra las distintas etapas y obstáculos por las que tuvo que pasar el concepto antes de arribar al concepto moderno de función, este análisis permite obtener algunas ideas pedagógicas para la enseñanza del mismo concepto. Mencionaremos también algunos resultados de las investigaciones en educación matemática referentes al concepto de función, que han permitido identificar las dificultades por las que pasa el estudiante y los errores conceptuales que adquiere al estudiar este concepto. Así, como los distintos aspectos y componentes que se requieren para comprenderlo.
Detalles del artículo
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.
Citas
Bell, A.& Janvier, C. (1981). The interpretation of graphics representing situations. For the learning of Mathematics. 2(1), 33-42.
Boyer, C. B. (1946). Proportion, equation, function. Three steps in the development of a concept. Scripta Mathematica. 12, 5-13.
Breidenbach, D. Dubinsky, E. Hawks, H., Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics. 23,243-239
Clement, J. (1985) Misconceptions in graphing. Proceedings of the 9 Int. Conf. PME Vol. 1, 369-375. L. Streefland, Eds
Dreyfus, T. (1990). Advanced Mathematical Thinking. In P. Nesher, & J. Kilpatrick. (Eds.). Mathematics and cognition: A research synthesis by the International Group for Psychology of Mathematics Education, pág, 113-134. Cambridge, Great Britain: Cambridge University Press
Dreyfus, T., Eisenberg, T. (1981). Functions Concepts: Intuitive Baseline. Proceedings of the 5 Int. Conf. PME. 183-185.
Dreyfus, T., Eisenberg, T. (1983). The function concept in college students linearity smoothenes and periodicity. Focus on Learning Problems in Mathematics 5, 119-132.
Dreyfus, T., Vinner, S. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20. 356-366.
Dubinsky, E. y, Harel, G. (1992). The Nature of the Process Conception of Function. En G. Harel y E. Dubinsky (eds.). The Concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. Notes Series, Vol. 25, pág. 85-106.
Duval, R. (1988). Gráficas y ecuaciones: La articulación entre dos registros. Annals de Didactique et de Sciences Cognitives 235-253. (versión español CINVESTAV-IPN)
Even, R. (1988). Pre-service teachers conceptions of the relationship between functions and equations. Proceedings of the PME XII, 304-311. Vezprem, Hungry.
Even, R. (1990). Subject matter knowledge for teaching and the case functions. Educational Studies in Mathematics, 21, 521-544.
Even, R. G. Lappan and W. Fitzgerald (1988). Pre Service Teachers Conceptions of the Relationship Between Functions and Equtions. Proceedings of th Annual Meeting of PME-NA, pp. 283-289. DeKalb, II; Northen Ilinois University.
Ferrini-Mundy, Graham, K. (1991). Research in calculus learning: understanding of limits derivatives and integrals. Paper presented at the Joint Mathematics meeting, Special session on Research in Undergraduate Mathematics Education, 1991. S. Fco.
Hitt, F. (1987). Obstáculos en el aprendizaje de función. Memorias 1a. Reunión Centroamericana y del Caribe sobre formación de Profesores e Investigación en Matemática Educativa. 245-248.
Hitt, F. (1989). Construction of function contradiction and proof. Proceedings PME, Paris
Kaput, J. (1987). Representation Systems and mathematics. C. Janvier (Eds.). Problems of representations in the Teaching and learning of Math. Hillsdale, N.J. Erlbaum
Kleiner, I. (1989). Evolution of the function concept: A brief survey. The college Mathematics Journal.20(4), 282-300.
Lovell, K. (1971). Some aspects of the growt of the concept function. In M. F. Rosskopf, L. P. Steffe and S. Taback (Eds.) Piagetian cognitive developmente research and mathematical education, pp. 12-33. Washington, DC. National Council of mathematics.
Marnyanskii, I. A. (1975) Psychological characteristics of Pupils Assimilation of the Concept of Function. In J. Kilpatrick Y, Wirsoup, E, Begle, and J. Wilson (Eds.) Soviet studies in the psychology of learning and teaching mathematics, v. 13, pp. 163-172. Chicago. University of Chicago Press.
Markovits, Z., Eylon, B. S. & Bruckheimer, M. (1986). Functions today and yesterday. For the Learning of Mathematics. Vol. 6, No.2, pág. 18-24.
Markovits, Z., Eylon, B. S., & Bruckheimer, M.(1988). Difficulties students have with the function concept. In A. F. Coxford and A. P. Shulte (Eds.). The Ideas of Algebra. 1988 Yearbook, pág. 43-60. Reston, VA: NCTM.
Orton, A. (1970). A Cross sectional study of the development of the Mathematical Concept of Function in Secondary School of Average and Above Average Ability. Master thesis Univ. Leeds.
Pedersen, O. Logistics and the Theory of Functions. Arch. Intern & Hist. d. Sciences. 24. N.94. 29-50(1974).
Ruiz, H. (1993). Concepciones de los alumnos de secundaria sobre la noción de función: Análisis epistemológico y didáctico. Borrador de Tesis Doctoral. Departamento de Didáctica de la Matemática Universidad de Granada, España.
Rüting, Dieter. (1984). Some definitions of the Concept of Function from John. Bernoulli to N. Bourbaki. The Mathematical Intelligencer. Vol. 6, No. 4.
Sfard, A. (1989). Transition from operational to structural conception: the notion of function revisited. Proceedings of the Psychology of Mathematics Education. Vol. 3 (pág. 151-158). Paris, France.
Sierpinska, Anna, (1992). On understanding the notion of function. The Concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. Notes Series, Vol. 25, págs. 23-58.
Schoenfeld, A.; Smith, J.; Arcavi, A. (1990). Learning- the microgenetic analysis of one student’s understanding of a complex subject matter domain; in R. Glaser (ed.) Advanced in Inst. Psychology. Erlbaum, Hillsdale.
Sfard, A. (1987). Two conceptions of mathematical notions: Operational and structural. In Bergeron, Herscovics, Kieran (Eds.) Proceedings of the 11 Inter. Conf. of PME. Université Montreal.
Sierpinska, A. (1988). Epistemological remarks on functions. Proceedings of 12 Inter. Conf. of PME. Thomas, H. L. (1971). The concepto of function. Paper presented at anual meeting of The american Educational association, february 4-7, New York. (Eric Document Reproduction Services No. ED.049926).
Thomas, H. L. (1975). The concept of function. Children’s Mathematical Concepts. Six Piagetian Studies in Mathematics education New York: Teachers College Press. Vinner, S. (1983). Concept definition, concept image and the notion of function. The International Journal of Mathematical Education in science and technology, 14, 293-305.
Vinner, S. and T. Dreyfus (1989). Image and Definitions for the Concept of Function. Journal for Reaserch in mathematics Education., 20(4), 356-366
Youschkevitch, A. P. The Concept of Function up to the Middle of the 19 th Century. Arch. Hist. Ex. Sci. 16, (1976) 37-85.