Construcción de la función exponencial con estudiantes de quinto de secundaria por medio de situaciones didácticas
Date
2019-07-18
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Pontificia Universidad Católica del Perú
Abstract
La presente investigación se origina por la observación de diferentes dificultades y
vacíos que presentan distintos estudiantes de quinto de secundaria al estudiar el
concepto de función exponencial. Si bien, este objeto matemático está presente en el
Currículo Nacional del Perú, hemos observado que no existen muchas investigaciones
en nuestro país respecto a este tema; mucho menos las hay en el nivel secundario.
Por ello, consideramos importante su estudio en este nivel; ya que permitirá,
posteriormente, el desarrollo con mayor profundidad de este objeto matemático en el
nivel superior.
Frente a esta problemática, nuestro objetivo de investigación es analizar las
contribuciones de una secuencia didáctica para la construcción del concepto de
función exponencial en estudiantes de quinto de secundaria y, para ello, nos
apoyamos en el referente teórico de la Teoría de Situaciones Didácticas de
Brousseau. Asimismo, para darle una estructura a nuestra investigación, utilizamos
como metodología la Ingeniería Didáctica de Artigue.
La parte experimental de nuestra investigación se realizó con estudiantes de quinto
de secundaria, cuyas edades oscilan entre los 15 y 16 años. La secuencia de
actividades estuvo compuesta por tres situaciones problemas. Las acciones de los
estudiantes ante estas situaciones problema permitieron movilizar conocimientos
previos y construir otros nuevos, a partir de la formulación de hipótesis y
posteriormente la justificación de sus resultados. Por ello, concluimos que las
situaciones problemas contribuyen a la construcción del concepto de función
exponencial.
The present investigation originates from the observation of different difficulties and gaps that different fifth-grade high school students presented when studying the concept of the exponential function. Despite of the fact that this mathematical object is present in the National Curriculum of Peru, we have observed that there are not many investigations regarding this subject in our country. Therefore, we consider it is crucial to study it at this level because it will allow a deeper development of this mathematical object in high school in the future. Facing this challenge, our research aims to analyze the contributions of a didactic sequence for the construction of the concept of the exponential function in fifth-grade high school students. Therefore, we rely on the theorical reference of the Theory of Didactical Situations of Brousseau. Likewise, to provide structure to our research, we used Artigue’s Didactic Engineering as methodology basis. The experimental part of our research was carried out with fifthgrade high school students who are 15 or 16 years old. The sequence of activities consisted on three problem situations. The actions of the students in these situations allowed them to utilize previous knowledge and build some other new from the creation of hypotheses and the later justification of their results
The present investigation originates from the observation of different difficulties and gaps that different fifth-grade high school students presented when studying the concept of the exponential function. Despite of the fact that this mathematical object is present in the National Curriculum of Peru, we have observed that there are not many investigations regarding this subject in our country. Therefore, we consider it is crucial to study it at this level because it will allow a deeper development of this mathematical object in high school in the future. Facing this challenge, our research aims to analyze the contributions of a didactic sequence for the construction of the concept of the exponential function in fifth-grade high school students. Therefore, we rely on the theorical reference of the Theory of Didactical Situations of Brousseau. Likewise, to provide structure to our research, we used Artigue’s Didactic Engineering as methodology basis. The experimental part of our research was carried out with fifthgrade high school students who are 15 or 16 years old. The sequence of activities consisted on three problem situations. The actions of the students in these situations allowed them to utilize previous knowledge and build some other new from the creation of hypotheses and the later justification of their results
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Keywords
Matemáticas--Estudio y enseñanza (Secundaria), Funciones exponenciales
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