Una propuesta didáctica para la enseñanza del concepto de límite mediante fractales lineales
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Gómez Guevara, Jorge Leonardo
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El presente trabajo muestra una estrategia didáctica que permitió a los estudiantes de grado undécimo del Gimnasio los Andes (Bogotá) aproximarse al concepto de límite mediante la geometría de fractales lineales. La secuencia de actividades se enfoca en desarrollar por medio de las estructuras fractales el conjunto de obstáculos epistemológicos "horror al infinito", caracterizado por Ana Sierpinska, realizando un breve recorrido histórico- epistemológico del concepto en mención. La ingeniería didáctica se fundamentó en el contraste de una prueba de entrada y otra de salida, tomando como referencia dos grupos: experimental y de control. La investigación planteada concluye que los estudiantes confrontaron implícitamente las ideas de infinito actual y potencial; así se logró introducir de manera aproximada algunas nociones de convergencia y continuidad por medio de numerosas expresiones y modelos matemáticos como series, sucesiones y funciones, las cuales contribuyeron satisfactoriamente a la comprensión del concepto de límite.
Abstract: The present paper shows a didactic strategy that allows eleventh grade students of the Andes School (Bogot´a) to approach the concept of limit using the geometry of linear fractals. The sequence of activities focuses on developing, through fractal structures, the set of epistemological obstacles “horror to infinity”, characterized by Ana Sierpinska, making a brief historical-epistemological journey of the concept in question. The didactic engineering was based on the contrast of a pre-test and a post-test, taking as reference two groups: experimental and control. The proposed research concludes that the students implicitly confronted the ideas of current and potential infinity, and thus it was possible to introduce in an approximate way some notions of convergence and continuity through numerous expressions and mathematical models such as series, successions and functions, which contributed satisfactorily to the understanding of the concept of limit.
Abstract: The present paper shows a didactic strategy that allows eleventh grade students of the Andes School (Bogot´a) to approach the concept of limit using the geometry of linear fractals. The sequence of activities focuses on developing, through fractal structures, the set of epistemological obstacles “horror to infinity”, characterized by Ana Sierpinska, making a brief historical-epistemological journey of the concept in question. The didactic engineering was based on the contrast of a pre-test and a post-test, taking as reference two groups: experimental and control. The proposed research concludes that the students implicitly confronted the ideas of current and potential infinity, and thus it was possible to introduce in an approximate way some notions of convergence and continuity through numerous expressions and mathematical models such as series, successions and functions, which contributed satisfactorily to the understanding of the concept of limit.