Una experiencia de enseñanza dirigida al desarrollo del razonamiento proporcional
Palabras clave:
Enseñanza de las matemáticas, proporcionalidad directa, constante de proporcionalidad.Resumen
El objetivo de este artículo es comprender cómo se desarrolla el razonamiento proporcional de los alumnos del 6.° año de escolaridad, en especial en lo que se refiere a la distinción entre situaciones que involucran y que no involucran proporcionalidad directa. La experiencia de enseñanza está fundamentada en cinco tareas basadas en el cuento El conejo y la tortuga, realizadas en grupos dentro de la clase, y discutidas después colectivamente por todo el curso.
Descargas
Citas
Ben-Chaim, D. et ál., 1998, “Proportional reasoning among seventh grade students with different curricula experiences”, Educational Studies in Mathematics, vol. 36, pp. 247-273.
Boavida, A. M. y J. P. Ponte, 2002, “Investigação colaborativa: Potencialidades e problemas”, en: GTI, org., Reflectir e investigar sobre a prática profissional, Lisboa, APM, pp. 43-55.
Carpenter, T. P. et ál., 1999, Children’s Mathematics: Cognitively Guided Instruction, Portsmouth, NH, Heinemann.
Christiansen, B. y G., Walther, 1986, “Task and activity”, en: B. Christiansen, A. G. Howson y M. Otte, eds., Perspectives on Mathematics Education,Dordrecht, D. Reidel, pp. 243-307.
Cramer, K. y T. Post, 1993, “Connecting research to teaching proportional reasoning”, Mathematics Teacher, vol. 86, núm. 5, pp. 404-407.
Cramer, K., T. Post y S. Currier, 1993, “Learning and teaching ratio and proportion: Research implications”, Universidad de Minnesota, [en línea], disponible en: http://education.umn.edu/rationalnumberproject/93_4.html
Christou, C. y G. Philippou, 2002, “Mapping and development of intuitive proportional thinking”, Journal of Mathematical Behavior, vol. 20, pp. 321-336.
Denzin, N. K. y Y. S. Lincoln, 1994, “Introduction: Entering the field of qualitative research”, en: N. K. Denzin e Y. S. Lincoln, eds., Handbook of Qualitative Research, Londres, Sage, pp. 1-17.
Greer, B., 1997, “Modelling reality in the mathematics classroom: The case of word problems”, Learning and Instruction, vol. 7, pp. 293-307.
Heller, P. et ál., 1989, “Proportional reasoning: The effect of two context variables, rate type and problem setting2, Journal of Research in Science Teaching, vol. 26, núm. 3, pp. 205-220.
Kaput, J. y M. M. West, 1994, “Missing value proportional reasoning problems: Factors affecting informal reasoning patterns”, en: J. Confrey y G.Harel, eds., The Development of Multiplicative Reasoning in the Learning of Mathematics, Albany, NY, State University of New York Press, pp. 181-234.
Karplus, R., P. Steven y E. Stage, 1983, “Proportional reasoning of early adolescents”, en: R. Lesh y M. Landau, eds., Acquisition of Mathematical Concepts and Processes, Orlando, FL, Academic Press, pp. 45-90.
Lamon, S. J., 1993, “Ratio and proportion: Connecting and children’s thinking”, Journal for Research in Mathematics Education, vol. 24, pp. 41-61.
_, 1995, “Ratio and proportion: Elementary didactical phenomenology”, en: J. T. Sowder y B. P. Schappelle, eds., Providing a Foundation for Teaching Mathematics in the Middle Grades, Albany, NY, State University of New York Press, pp. 167-198.
Lesh, R., T. Post y M. Behr, 1988, “Proportional reasoning”, en: J. Hiebert y M. Behr, eds., Number Concepts and Operations in the Middle Grades, National Council of Teachers of Mathematics, Reston, VA, pp. 93-118.
Ministério da Educação (ME), 2007, Programa de Matemática do ensino básico, Lisboa, ME.
National Council of Teachers of Mathematics (NCTM), 1989, Curriculum and Evaluation Standards for School Mathematics, Reston, Virginia, NCTM.
Nesher, P., 1980, “The stereotyped nature of school word problems”, Learning of Mathematics, vol. 1,núm. 1, pp. 41-48.
Noelting, G., 1980, “The development of proportional reasoning and the ratio concept: Part 1, Differentiation of stages”, Educational Studies in Mathematics, vol. 11, pp. 217-253.
Ponte, J. P., 2005, “Gestão curricular em Matemática”, en: GTI, Ed., O professor e o desenvolvimento curricular, Lisboa, APM, pp. 11-34.
Post, T., M. Behr y R. Lesh, 1988, “Proportionality and the development of prealgebra understandings”, en: Algebraic Concepts in the Curriculum K-12, Yearbook, Reston, VA, National Council of Teachers of Mathematics, pp. 78-90.
Steffe, L. P. y P. W. Thompson, 2000, “Teaching experiment methodology: Underlying principles and essential elements”, en: R. Lesh y A. E. Kelly, eds., Research Design in Mathematics and science Education, Hillsdale, NJ, Erlbaum, pp. 267-307.
Steinthorsdottir, O. B., 2006, “Proportional reasoning: Variable influencing the problems difficulty level and one’s use of problem solving strategies Proceedings of the 30th PME International Conference, vol. 5, pp. 169-176.
Tourniaire, F. y S. Pulos, 1985, “Proportional reasoning: A review of the literature”, Educational Studies in Mathematics, vol. 16, pp. 181-204.
Tsuruda, G., 1994, Putting it together, Portsmouth, NH, Heinemann.
Vergnaud, G., 1983, “Multiplicative structures”, en: R. Lesh y M. Landau, eds., Acquisition of Mathematics Concepts and Processes, New York, Academic Press, pp. 127-174.
Van Dooren, W., D. de Bock, M. Evers y L. Verschaffel, 2006, “Pupils’ over-use of proportionality on missing-value problems: How numbers may change solutions”, Proceedings of the 30th PME International Conference, vol. 5, pp. 305-312.
Verschaffel, L., B. Greer y E. de Corte, 2000, Making sense of word problems, Lisse, The Netherlands, Swets y Zeitlinger.
Weidermann, W., 1995, “Problem solving in math class: Word problems were never like this”, Middle School Journal, vol. 27, núm. 1, pp. 11-17.
Wood, T., 1999, “Creating a context for argument in mathematics class”, Journal for Research in Mathematics Education, vol. 30, núm. 2, pp. 171-191.
Descargas
Publicado
Cómo citar
Número
Sección
Licencia
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional