Diseño y valoración de la idoneidad cognitiva de una secuencia didáctica remota para la enseñanza del concepto de derivada
Fecha
2024-09-30
Tipo
tesis de maestría
Autores
Prendas Rojas, Juan Pablo
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Editor
Resumen
Las problemáticas referidas al concepto de derivada de una función se han reportado en muchas investigaciones y han sido punto de partida para numerosas propuestas sobre abordaje de este tema con la intención de solventarlas. Sin embargo, no siempre está claro de donde surgen las propuestas y si, al final de la puesta en escena, estas resultan idóneas para los objetivos que se persiguen.
En este proyecto de investigación se propone el uso de la teoría de Ingeniería Didáctica como guía para el proceso de diseño de una secuencia didáctica para la enseñanza del concepto de derivada de una función. Además, se muestra como los indicadores de Idoneidad Didáctica de la teoría del Enfoque Ontosemiótico de la Instrucción y el Conocimiento Matemáticos (EOS), en la faceta cognitiva, se complementan con la etapa de evaluación y reflexión docente. Se trabajó durante tres sesiones remotas con un grupo de Cálculo Diferencial e Integral del Instituto Tecnológico de Costa Rica. El proceso inició con análisis preliminares, luego análisis a priori, experimentación y finalmente reflexión sobre la labor docente desde la faceta cognitiva.
Como resultado se tiene un documento con al menos tres aristas: se constituye como una guía para el diseño de secuencias didácticas con sustento en indagaciones
preliminares generales en principio y locales posteriormente sobre aspectos afectivos, epistémicos y cognitivos, es una muestra sobre actividades y evaluaciones en una clase remota real y contiene una serie de indicadores para estructurar la reflexión de la labor docente.
Se destaca que, desde el punto de vista teórico, se fomenta la ubicación de la Evaluación como un componente por si mismo y para éste se proponen tres indicadores de los cuales la Evaluación temporal es novedoso.
Issues related to the concept of the derivative of a function have been extensively documented in research and have served as the basis for numerous proposals aimed at addressing these challenges with the intention of resolving them. Nonetheless, it is not always clear from where these proposals originate and whether, ultimately, they prove suitable for the objectives being pursued. This research project proposes utilizing Didactic Engineering theory as a guide for designing a didactic sequence for teaching the concept of the derivate of a function. Additionally, it demonstrates how the Didactic Suitability indicators of the Onto-Semiotic Approach to Instruction and Mathematical Knowledge (OSA), in the cognitive dimension, are complemented by the stage of teacher evaluation and reflection. The study was conducted over three sessions with a Differential and Integral Calculus group at the Instituto Tecnol´ogico de Costa Rica (Costa Rica Institute of Technology). The process commenced with preliminary analyses, followed by a priori analyses, experimentation, and finally, reflection on teaching practice from the cognitive perspective. The outcome is a document with at least three facets: it serves as a guide for designing didactic sequences based on initial general preliminary inquiries and later local inquiries on affective, epistemic, and cognitive aspects; it provides an example of activities and assessments in a real remote class; and it contains a series of indicators to structure the reflection on teaching practice. It is noteworthy that, from a theoretical perspective, the Evaluation is promoted as a standalone component, and three indicators are proposed for it, among which temporary Evaluation is novel.
Issues related to the concept of the derivative of a function have been extensively documented in research and have served as the basis for numerous proposals aimed at addressing these challenges with the intention of resolving them. Nonetheless, it is not always clear from where these proposals originate and whether, ultimately, they prove suitable for the objectives being pursued. This research project proposes utilizing Didactic Engineering theory as a guide for designing a didactic sequence for teaching the concept of the derivate of a function. Additionally, it demonstrates how the Didactic Suitability indicators of the Onto-Semiotic Approach to Instruction and Mathematical Knowledge (OSA), in the cognitive dimension, are complemented by the stage of teacher evaluation and reflection. The study was conducted over three sessions with a Differential and Integral Calculus group at the Instituto Tecnol´ogico de Costa Rica (Costa Rica Institute of Technology). The process commenced with preliminary analyses, followed by a priori analyses, experimentation, and finally, reflection on teaching practice from the cognitive perspective. The outcome is a document with at least three facets: it serves as a guide for designing didactic sequences based on initial general preliminary inquiries and later local inquiries on affective, epistemic, and cognitive aspects; it provides an example of activities and assessments in a real remote class; and it contains a series of indicators to structure the reflection on teaching practice. It is noteworthy that, from a theoretical perspective, the Evaluation is promoted as a standalone component, and three indicators are proposed for it, among which temporary Evaluation is novel.
Descripción
Palabras clave
Educación, Matemática, Derivada, Secuencia didáctica, Idoneidad cognitiva