Evolución conceptual del pensamiento algebraico en educación media: estudio de caso

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Fecha de publicación:: 2024

Institución:: Universidad de Caldas

Repositorio:: Repositorio Institucional U. Caldas

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network_acronym_str	REPOUCALDA
network_name_str	Repositorio Institucional U. Caldas
repository_id_str
dc.title.none.fl_str_mv	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
title	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
spellingShingle	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso 370 - Educación 6. Humanidades Pensamiento algebraico Modelos explicativos Evolución conceptual Registros de representaciones semióticas Aprendizaje de las matemáticas Algebraic thinking Explanatory models Conceptual evolution Registers of semiotic representations Learning of mathematics Educación
title_short	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
title_full	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
title_fullStr	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
title_full_unstemmed	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
title_sort	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso
dc.contributor.none.fl_str_mv	Tamayo Alzate, Óscar Eugenio Universidad de Caldas CASTRO GORDILLO, WALTER FERNANDO Blanco-Álvarez, Hilbert
dc.subject.none.fl_str_mv	370 - Educación 6. Humanidades Pensamiento algebraico Modelos explicativos Evolución conceptual Registros de representaciones semióticas Aprendizaje de las matemáticas Algebraic thinking Explanatory models Conceptual evolution Registers of semiotic representations Learning of mathematics Educación
topic	370 - Educación 6. Humanidades Pensamiento algebraico Modelos explicativos Evolución conceptual Registros de representaciones semióticas Aprendizaje de las matemáticas Algebraic thinking Explanatory models Conceptual evolution Registers of semiotic representations Learning of mathematics Educación
description	Tablas, figuras
publishDate	2024
dc.date.none.fl_str_mv	2024-09-17T16:21:07Z 2024-09-17T16:21:07Z 2024-09-16 2026-09-16
dc.type.none.fl_str_mv	Trabajo de grado - Doctorado http://purl.org/coar/resource_type/c_db06 Text info:eu-repo/semantics/doctoralThesis
dc.identifier.none.fl_str_mv	https://repositorio.ucaldas.edu.co/handle/ucaldas/20193 Universidad de Caldas Repositorio Institucional Universidad de Caldas repositorio.ucaldas.edu.co
url	https://repositorio.ucaldas.edu.co/handle/ucaldas/20193
identifier_str_mv	Universidad de Caldas Repositorio Institucional Universidad de Caldas repositorio.ucaldas.edu.co
dc.language.none.fl_str_mv	spa
language	spa
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dc.publisher.none.fl_str_mv	Universidad de Caldas Facultad de Artes y Humanidades Manizales Doctorado en Educación
publisher.none.fl_str_mv	Universidad de Caldas Facultad de Artes y Humanidades Manizales Doctorado en Educación
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spelling	Evolución conceptual del pensamiento algebraico en educación media: estudio de caso370 - Educación6. HumanidadesPensamiento algebraicoModelos explicativosEvolución conceptualRegistros de representaciones semióticasAprendizaje de las matemáticasAlgebraic thinkingExplanatory modelsConceptual evolutionRegisters of semiotic representationsLearning of mathematicsEducaciónTablas, figurasA partir de una revisión sistemática de las tendencias conceptuales sobre el aprendizaje del pensamiento algebraico, se destaca la falta de consenso sobre el concepto de variable y su papel en dicho aprendizaje. Este estudio se centra en la identificación de modelos explicativos de variables, constantes y parámetros en un estudiante de grado undécimo de una institución educativa pública en Manizales, Caldas, basándose en los lineamientos curriculares colombianos. El objetivo principal es comprender la evolución del pensamiento algebraico y la influencia de las variables, las constantes y los parámetros en el aprendizaje algebraico-variacional en un problema socio-científico. La metodología empleada consistió en un estudio de caso en profundidad, utilizando la teoría de la evolución conceptual, una intervención en el aula para recopilar datos y su procesamiento mediante el software ATLAS.ti.23. Se desarrolló un modelo de pensamiento algebraico estructurado en un circuito semiótico que permitió analizar las transiciones semióticas entre diferentes registros de representaciones. Se concluyó que las variables son unidades que permiten el flujo de significados y están asociadas a las estructuras algebraicas por medio de las propiedades cuantitativas del fenómeno a analizar; mientras que, el significado de los parámetros ajusta la estructura algebraica de las variables, modificando su comportamiento dentro del modelo explicativo y adicionando más significados, lo que posibilita generar modelos más abstractos y realizar pronósticos más precisos.From a systematic review of conceptual trends in learning algebraic thinking, the need for more consensus on the concept of variables and their role in such learning is highlighted. Based on the Colombian curricular guidelines, this study focuses on identifying explanatory models of variables, constants, and parameters in eleventh-grade students of a public educational institution in Manizales, Caldas. The main objective is to understand the evolution of algebraic thinking and the influence of variables, constants, and parameters in algebraic-variational learning in a socio-scientific problem. The methodology employed consisted of an in-depth case study using the theory of conceptual evolution, a classroom intervention to collect data, and its processing using ATLAS.ti.23 software. A model of algebraic thinking structured in a semantic circuit was developed that allowed the analysis of semiotic transitions between different representation registers. It was concluded that the variables are units that allow the flow of meanings and are associated with the algebraic structures using the quantitative properties of the phenomenon to be analyzed. In contrast, the meaning of the parameters adjusts the algebraic structure of the variables, modifying their behavior within the explanatory model and adding more meanings, which makes it possible to generate more abstract models and make more accurate forecasts.Introducción / Capítulo I: Antecedentes y problema de investigación /Antecedentes / Lenguaje Algebraico / Álgebra Escolar / Estructuras Aritméticas y Estructuras Algebraicas / Variables y la Dualidad Proceso-Objeto/ Cognición y Pensamiento Algebraico / Problema de Investigación / Capítulo II: Pregunta de Investigación / Capítulo III: Justificación /Capítulo IV: Objetivos de Investigación / Objetivo General / Objetivos Específicos / Capítulo V: Referentes Teóricos / Evolución Conceptual /Modelos Mentales / Modelo Conceptual de Pensamiento Algebraico /Variables: Unidades de Significado/ Modelos y Evolución Conceptual /Relaciones Semióticas / Espacio Semántico en el Álgebra Escolar / Modelos Epistemológicos de Variables /Flujo de Significados en el Espacio Semántico /Condensación Semiótica /Capítulo VI: Metodología / Diseño Metodológico / Unidades de Trabajo /Selección del Caso Único/ Diseño de la Investigación /Fases de la Investigación /Primera Fase /Segunda Fase /Tercera Fase /Cuarta Fase / Quinta Fase /Sexta Fase / Séptima Fase / Instrumento para la Recolección de Datos /Prueba de Diagnósticos Iniciales /Operacionalización de Variables /Capítulo VII: Análisis de los Resultados / Estudio de Caso: Estudiante Ezequiel / Análisis Evolución Conceptual /Análisis de la Evolución Conceptual en el Primer Momento/ Modelo SIR / Análisis de los Componentes del Modelo SIR / Concepciones sobre Contagio / Proceso de contagio / Tasas de Contagio /Crecimiento de los Casos de Contagio/ Concepciones sobre las Medidas de Bioseguridad / Concepciones sobre los Infectados / Concepciones sobre los Recuperados / Concepciones sobre los Fallecidos / Análisis de las Relaciones Internas del Modelo SIR / Modelo SIR: Red de Relaciones y Componentes del Primer Momento /Análisis de la Evolución Conceptual en el Segundo Momento / Análisis de los Componentes del Modelo SIR / Cantidad de Infectados y sus Relaciones / Relaciones de Crecimiento Exponencial /Relaciones de Decrecimiento Exponencial / Análisis de la Evolución Conceptual en el Tercer Momento / Tasas de Recuperación y Mortalidad / Ecuaciones del Modelo SIR /Estructura Compartimental del Modelo SIR /Tasa de Crecimiento Exponencial (B ) e Índice de Reproducción (R0) / Comportamiento Gráfico de las Variables del Modelo SIR / Análisis de los Registros de Representaciones / Análisis del Lenguaje Natural / Análisis del Lenguaje Natural en el Primer Momento / Análisis del Lenguaje Natural en el Segundo Momento /Análisis del Lenguaje Natural en el Tercer Momento/ Análisis del Lenguaje Icónico /Análisis del Lenguaje Icónico en el Primer Momento/ Análisis del Lenguaje Diagramático /Análisis del Lenguaje Gráfico/ Análisis del Lenguaje Icónico en el Segundo Momento / Análisis del Leguaje Icónico en el Tercer Momento /Análisis de las Representaciones en Lenguaje Simbólico / Análisis de los Modelos de Variable /Modelos de Variable en el Primer Momento/ Modelos de Variable en el Segundo Momento/ Modelos de Variable en el Tercer Momento/ Análisis de las Relaciones Semióticas/Capítulo VIII: Discusión /Capítulo IX: Conclusiones /Capítulo X: Recomendaciones/Apéndice: Modelización del Pensamiento Algebraico / Referencias Bibliográficas /Anexos.DoctoradoDoctor(a) en EducaciónEnseñanza de las ciencias y las matemáticasUniversidad de CaldasFacultad de Artes y HumanidadesManizalesDoctorado en EducaciónTamayo Alzate, Óscar EugenioUniversidad de CaldasCASTRO GORDILLO, WALTER FERNANDOBlanco-Álvarez, HilbertLara-Escobar, Rubén Darío2024-09-17T16:21:07Z2026-09-162024-09-17T16:21:07Z2024-09-16Trabajo de grado - Doctoradohttp://purl.org/coar/resource_type/c_db06Textinfo:eu-repo/semantics/doctoralThesis465 páginasapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttps://repositorio.ucaldas.edu.co/handle/ucaldas/20193Universidad de CaldasRepositorio Institucional Universidad de Caldasrepositorio.ucaldas.edu.cospaAbdullatif Khafaie, M., & Rahim, F. 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