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Item type:Publication, Uso de GeoGebra y el razonamiento inductivo en un acercamiento al teorema fundamental del cálculo(2022-12-08)El estudio tuvo como objetivo analizar cómo estudiantes universitarios generan nociones sobre el Teorema Fundamental del Cálculo (TFC) al utilizar un razonamiento inductivo mediante el uso de GeoGebra. Se considera la noción de esquema desde la perspectiva del enfoque instrumental, y cómo se movilizan estos esquemas en cada uno de los procesos que comprenden el razonamiento inductivo. Los resultados muestran que los estudiantes utilizaron fórmulas de geometría, para determinar el área de un conjunto de regiones limitadas por funciones polinómicas y, a partir de un proceso inductivo, obtuvieron antiderivadas de estas funciones y describieron un procedimiento semejante al que se utiliza con el TFC para resolver integrales definidas. Se concluye que el uso de GeoGebra asociado con un proceso inductivo posibilita la observación de regularidades y la formulación de generalizaciones relacionadas con el TFC. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Exploring problem-solving strategies in integral calculus with GeoGebra: A collaborative approach(Centro de Información Tecnológica, 2024-01-01)The present study aims to identify strategies that university students put into play when solving a problem involving notions of integral calculus and GeoGebra mediation. Problem solving is considered as a theoretical approach aimed at characterizing resolution processes through the use of digital technologies. A mathematical problem involving two cyclists is designed and presented to 20 calculus students enrolled at a university in Lima (Peru). The results show that tasks performed in pairs allow identifying the need to graphically represent the speeds of two cyclists in GeoGebra to compare them. Antiderivatives, areas, and a defined integral are also used to find and compared the distances traveled. Discussions between pairs allow comparing resolution strategies, recognizing errors, and rectifying them, while improving learning in a collaborative way. It is concluded that GeoGebra enables various forms of reasoning to occur, which are transformed into problemsolving strategies by students. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Reconfiguração de figuras para o cálculo de áreas com a ferramenta polígono rígido do GeoGebra(Federal University of Mato Grosso, 2023-12-18)Pesquisas relatam que, no estudo da área de figuras geométricas, os alunos orientam seus procedimentos para o uso de fórmulas, reduzindo, assim, procedimentos geométricos como a reconfiguração e o uso de ferramentas tecnológicas para realizá-los, que são aspectos associados ao trabalho do professor. Nessa linha, foi realizado um estudo com o objetivo de descrever como professores de matemática do ensino médio em formação continuada realizam a configuração de figuras para o cálculo de áreas por meio do uso da ferramenta polígono rígido do GeoGebra. A noção de reconfiguração associada à apreensão operatória foi considerada como aspectos teóricos que corresponde à teoria dos registros de representação semiótica. Os resultados mostram que os professores realizaram reconfigurações de figuras geométricas para encontrar áreas e que aprenderam a usar a ferramenta polígono rígido para criar atividades no GeoGebra para que seus alunos reconfigurem figuras geométricas. Conclui-se que o GeoGebra proporciona aos professores uma variedade de ferramentas para ensinar aos alunos sobre áreas de figuras geométricas de forma dinâmica, prevalecendo os procedimentos geométricos.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Covariational Reasoning and Instrumented Techniques in the Resolution of an Optimization Problem Mediated by GeoGebra(Hipatia Editorial, 2023-02-01)The aim of this study was to document how different instrumental techniques are related to different mental actions during the work of university students in an optimization activity mediated by GeoGebra. To minimize the length of the fence of a rectangular plot, the students put into play mental actions, which were visible in the manipulations with GeoGebra, associated with different levels of covariational reasoning, and which allowed us to identify different instrumented techniques. It is concluded that the use of instrumented techniques involving concepts related to the derivative, such as the slope of the tangent line or the derivative function, make visible behaviors associated with mental actions of a more sophisticated covariational reasoning. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, REASONING COVARIATIONALLY WITH GEOGEBRA: AN APPROACH TO THE OPTIMIZATION OF FUNCTIONS(Didáctica de la Matemática: Pensamiento Numérico, 2026-04-06)El estudio tuvo por objetivo analizar la relación entre las acciones mentales de razonamiento covariacional y los esquemas de uso que movilizaron dos estudiantes al resolver una tarea de optimización con GeoGebra. Se consideran aspectos teóricos del razonamiento covariacional y de la aproximación instrumental, y el estudio de caso como método de investigación. La construcción de un jardín rectangular con GeoGebra pone en evidencia el razonamiento covariacional de los estudiantes, cuando asocian o no herramientas como deslizadores y puntos para variar sus dimensiones dinámicamente. Abordar situaciones de cambio utilizando GeoGebra favorece el razonamiento covariacional de los estudiantes.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Mathematical modeling in calculus: two technological approaches to an optimization problem(National University, Costa Rica, 2025-01-01)[Objective] The study aimed to analyze the modeling process conducted by university students when solving a problem involving the notion of function optimization. [Methodology] Mathematical modeling is approached from the perspective known as models and modeling, utilizing the modeling cycles from Blum, Leiß, and Borromeo-Ferri, as well as the extended cycle for the use of digital technologies, to describe the processes students conduct during their resolution. The research design is an instrumental multiple case study. The paper reports the work of two second-semester students from the Business Administration program at a university in Lima, Peru, enrolled in the Calculus course during the first semester of 2022. Data was collected using worksheets, GeoGebra files, and semi-structured interviews. [Results] Results show that students developed skills in three areas: in the real world, by understanding that the cost of wiring varies according to the length and type of cable; in the mathematical world, by creating and using a mathematical model to optimize a function by applying prior knowledge on calculus; and in the computational world, by using GeoGebra to apply these concepts. [Conclusions] It is concluded that GeoGebra is a solid tool for developing modeling problems since its interface allows connecting the numerical, algebraic, geometric, and variational fields, providing a better interpretation of the phenomenon of change underlying an optimization problem.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Covariational reasoning and GeoGebra in the representation of functional relationships when simulating container filling(SciELO, 2025-01-01)Resumen: El presente estudio tiene por objetivo analizar el razonamiento covariacional de un estudiante al resolver tareas que involucran relaciones funcionales al simular con GeoGebra el llenado de recipientes. Se consideran las nociones de acción mental y de niveles de razonamiento covariacional como constructo teórico, y el estudio de caso como método de investigación. Como resultado, se identifican diferentes estrategias para representar gráficamente la relación entre la altura del agua dentro de un recipiente que cambia de forma, y el volumen de agua que ingresa de manera constante. Las estrategias guardan relación con el razonamiento covariacional del estudiante e incluyen utilizar áreas de figuras geométricas para relacionar ambas variables y construir un conjunto finito de puntos en el plano para representar gráficamente las relaciones funcionales. En conclusión, las simulaciones realizadas con GeoGebra posibilitan al estudiante una visualización de cómo se dan los cambios simultáneos entre dos variables, y con ello reconocer las relaciones funcionales como una covariación dinámica de variables.1