Análisis de una organización matemática de la función y la proporcionalidad directa en un libro de texto de matemáticas de educación secundaria
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2016-04-20
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Pontificia Universidad Católica del Perú
Abstract
Esta investigación tiene como objetivo analizar la organización matemática de la unidad, que
contiene los temas de función y proporcionalidad directa, de un libro de texto de matemática
del primer grado de educación secundaria y, a partir de ello, establecer si existe articulación
entre la función lineal y la proporcionalidad directa. El problema abordado se resume en la
siguiente pregunta: ¿cuál es la organización matemática de la unidad, que contiene los temas
de función y proporcionalidad directa, del libro de texto de matemática del primer grado de
educación secundaria? Para responder a esta interrogante se utiliza la Teoría Antropológica de
lo Didáctico de Chevallard. La investigación es de corte cualitativo y de tipo bibliográfico.
Para la organización del estudio, se usa los componentes de la organización matemática y,
para el análisis, se emplea los indicadores de completitud de una organización matemática
local de Fonseca y los niveles de algebrización, de la proporcionalidad de magnitudes,
desarrollado por Bolea, Bosch y Gascón. Los resultados de la investigación evidencian 17
tipos de tareas, 42 tareas, 38 técnicas, 18 tecnologías y 2 teorías. Respecto al grado de
completitud de la organización matemática, concluimos que es menos completa, pues no se
verifica una clara presencia de los indicadores de completitud. Además, se ha verificado que
en la unidad analizada no existe articulación entre la función lineal y la proporcionalidad
directa.
This research aims to analyze the mathematical organization of a unit including function and direct proportionality in a textbook of mathematics for the first year of highschool, and to determine if there is an interaction between the linear function and the direct proportionality. The issue we address can be summed up in the following question: what is the mathematical organization of the unit including function and direct proportionality in a textbook of mathematics for the first year of highschool? To answer this question, we use Chevallard’s Anthropological Theory of the Didactic as a basis. The research is bibliographical with a qualitative approach. To organize the study, we use Fonseca’s components of mathematical organization, and for the analysis, we use his completeness indicators of a local mathematical organization, as well as the algebraization levels of the magnitude proportionality developed by Bolea, Bosch and Gascón. The results of the research show 17 types of tasks, 42 tasks, 38 techniques, 18 technologies and 2 theories. Regarding the level of completeness of the mathematical organization, we concluded that it is low, since a clear presence of the completeness indicators is not verified. In addition, it was verified that in the analyzed unit there is no interaction between the linear function and the direct proportionality.
This research aims to analyze the mathematical organization of a unit including function and direct proportionality in a textbook of mathematics for the first year of highschool, and to determine if there is an interaction between the linear function and the direct proportionality. The issue we address can be summed up in the following question: what is the mathematical organization of the unit including function and direct proportionality in a textbook of mathematics for the first year of highschool? To answer this question, we use Chevallard’s Anthropological Theory of the Didactic as a basis. The research is bibliographical with a qualitative approach. To organize the study, we use Fonseca’s components of mathematical organization, and for the analysis, we use his completeness indicators of a local mathematical organization, as well as the algebraization levels of the magnitude proportionality developed by Bolea, Bosch and Gascón. The results of the research show 17 types of tasks, 42 tasks, 38 techniques, 18 technologies and 2 theories. Regarding the level of completeness of the mathematical organization, we concluded that it is low, since a clear presence of the completeness indicators is not verified. In addition, it was verified that in the analyzed unit there is no interaction between the linear function and the direct proportionality.
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Keywords
Matemáticas--Estudio y enseñanza (Secundaria)., Funciones (Matemáticas)., Educación secundaria--Investigaciones.
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