Comprensión de la noción función cuadrática por medio del tránsito de registros de representación semiótica en estudiantes de quinto año de secundaria
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2016-04-20
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Pontificia Universidad Católica del Perú
Abstract
La presente investigación tiene como objetivo analizar cómo el tránsito por distintos registros
de representación semiótica favorece la comprensión de la noción de función cuadrática en
estudiantes de quinto año de educación secundaria. Utilizamos como marco teórico la Teoría
de Registros de Representación Semiótica propuesta por Duval. En cuanto a la metodología,
hemos tomado algunos aspectos de la ingeniería didáctica de Artigue. Con respecto a la
experimentación y análisis, elaboramos y aplicamos una secuencia de dos actividades: la
primera consta de cinco partes y la segunda, de dos partes. Estas fueron elaboradas con el
propósito de que los estudiantes transiten por los diversos registros de la representación
semiótica movilizando la noción de función cuadrática. Por esto, nos focalizamos en el
análisis de los aciertos y las dificultades que los estudiantes mostraron al realizar las
actividades cognitivas de tratamiento y conversión en los diferentes registros de dicha
representación. Los resultados obtenidos muestran que la mayoría de estudiantes lograron
transitar por los siguientes registros de representación semiótica: lengua natural, tabular,
algebraico y gráfico, lo cual permitió movilizar sus conocimientos previos referidos a
elementos y propiedades de la función cuadrática en sus diferentes representaciones. Sin
embargo, presentaron dificultades para explicar y justificar los elementos y propiedades de la
función cuadrática en lenguaje natural.
This research has as aim analyze how the transit through different registers of semiotic representation favors the understanding of the concept of quadratic function in fifth year of secondary education students. We use as a theoretical framework Records Theory of Semiotics Representation proposed by Duval. In terms of methodology, we have taken some aspects of Artigue didactic engineering. With respect to experimentation and analysis, we elaborate and apply a sequence of two activities: the first consists of five parts and the second of two parts. These were elaborated by the intention of which the students pass along the diverse records of the representation semiotics mobilizing the notion of quadratic function. For this, we focus ourselves in the analysis of the successes and the difficulties that the students showed on having realized the cognitive activities of treatment and conversion in the different records of the above mentioned representation. The obtained results show that the majority of students managed to pass along the following records of representation semiotics: natural language, tabulates, algebraic and graphically, which allowed mobilize their previous knowledge referred to elements and properties of the quadratic function in their different representations. Nevertheless, they presented difficulties to explain and to justify the elements and properties of the quadratic function in natural language.
This research has as aim analyze how the transit through different registers of semiotic representation favors the understanding of the concept of quadratic function in fifth year of secondary education students. We use as a theoretical framework Records Theory of Semiotics Representation proposed by Duval. In terms of methodology, we have taken some aspects of Artigue didactic engineering. With respect to experimentation and analysis, we elaborate and apply a sequence of two activities: the first consists of five parts and the second of two parts. These were elaborated by the intention of which the students pass along the diverse records of the representation semiotics mobilizing the notion of quadratic function. For this, we focus ourselves in the analysis of the successes and the difficulties that the students showed on having realized the cognitive activities of treatment and conversion in the different records of the above mentioned representation. The obtained results show that the majority of students managed to pass along the following records of representation semiotics: natural language, tabulates, algebraic and graphically, which allowed mobilize their previous knowledge referred to elements and properties of the quadratic function in their different representations. Nevertheless, they presented difficulties to explain and to justify the elements and properties of the quadratic function in natural language.
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Matemáticas--Estudio y enseñanza (Secundaria)., Algebra--Estudio y enseñanza., Educación secundaria--Investigaciones.
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