La comprensión del concepto de función en estudiantes de educación básica regular del Perú
Date
2023-11-23
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Pontificia Universidad Católica del Perú
Abstract
Distintas investigaciones han analizado la relación entre la comprensión y el uso de
los diferentes registros de representación cuando se trata de representar un objeto
matemático, evidenciando que algunos de ellos son predominantes respecto a otros;
además, nos muestran también las conversiones que son más utilizadas y su relación
con las dificultades que presentan los estudiantes. Esto evidencia la importancia de
identificar los tipos de registros y conversiones predominantes en las prácticas
matemáticas de estudiantes de educación básica regular (EBR) del Perú. En esta
investigación analizaremos la comprensión del objeto función, tomando como
referencia las investigaciones realizadas en otros países con estudiantes de
educación secundaria y primeros ciclos de educación superior. Esta investigación
toma como base teórica la Teoría de Registros de Representación Semiótica y sigue
principios metodológicos de la ingeniera didáctica. En primer lugar, tomando en
cuenta el Currículo Nacional y los materiales de clase de la institución se eligieron los
registros de representación para la investigación y se elaboró un cuestionario.
Después, se llevó a cabo la experimentación, la cual tuvo una duración de dos horas
pedagógicas, se realizó con 16 alumnas de quinto de secundaria, cuyas edades
oscilan entre 15 y 17 años. Finalmente, se realizó el análisis a posteriori de las
respuestas de las estudiantes, realizando una comparación con las investigaciones
de referencia y encontrando nuevos resultados en base a los procesos de tratamiento
y conversión, como por ejemplo que algunas conversiones son realizadas de manera
natural, pero al realizar la conversión inversa se presenta gran dificultad, es el caso
de las conversiones entre los registros algebraico y gráfico.
Several researchs have analyzed the relationship between the understanding and the use of the different registers of representation when it comes to representing a mathematical object, being some of them predominant over others; in addition, they also show us the conversions that are most used and how they are related to the difficulties that students present. This proves the importance of identifying the types of records and the predominant conversions in the mathematical practices of peruvian students of regular basic education (EBR). In this research we will analyze the conceptual understanding of the function object, taking as a reference the research carried out in other countries with high school and first years of higher education students. We will take as a theoretical basis the Theory of Semiotic Representation Records and we will use methodological principles of didactic engineering. In the first place, the representation records were chosen for the research and a questionnaire was elaborated based on the National Curriculum and the class materials of the institution. Then, we started with the experimental phase, wich lasted two pedagogical hours. The questionnaire was solved by 16 fifth-year female high school students, whose ages range between 15 and 17 years old. Finally, we made a posteriori analysis of the student’s responses, making a comparison with the references research and finding new results based on the treatment and conversion processes, as for example, some conversions are carried out naturally, but when we carry out the inverse conversion, it presents a lot of difficulty, as is the case of the conversions between the algebraic and graphic records..
Several researchs have analyzed the relationship between the understanding and the use of the different registers of representation when it comes to representing a mathematical object, being some of them predominant over others; in addition, they also show us the conversions that are most used and how they are related to the difficulties that students present. This proves the importance of identifying the types of records and the predominant conversions in the mathematical practices of peruvian students of regular basic education (EBR). In this research we will analyze the conceptual understanding of the function object, taking as a reference the research carried out in other countries with high school and first years of higher education students. We will take as a theoretical basis the Theory of Semiotic Representation Records and we will use methodological principles of didactic engineering. In the first place, the representation records were chosen for the research and a questionnaire was elaborated based on the National Curriculum and the class materials of the institution. Then, we started with the experimental phase, wich lasted two pedagogical hours. The questionnaire was solved by 16 fifth-year female high school students, whose ages range between 15 and 17 years old. Finally, we made a posteriori analysis of the student’s responses, making a comparison with the references research and finding new results based on the treatment and conversion processes, as for example, some conversions are carried out naturally, but when we carry out the inverse conversion, it presents a lot of difficulty, as is the case of the conversions between the algebraic and graphic records..
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Keywords
Matemáticas--Estudio y enseñanza, Funciones (Matemáticas), Estudiantes (Educación secundaria), Educación secundaria--Investigaciones
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