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Item type:Publication, Argument schemes of high school students when using GeoGebra in the context of tessellations(Universidad Nacional, 2021-07-01)En esta investigación, se identifican y describen los argumentos expuestos por un grupo de estudiantes de bachillerato, cuando justifican sus respuestas a situaciones geométricas e incorporan el uso del software de geometría dinámica GeoGebra. El trabajo muestra que el proceso de argumentación es deficiente en un grupo de estudiantes entre 15 y 18 años de la escuela de bachilleres de la Universidad Autónoma de Querétaro. A esta agrupación de educandos se le propuso una secuencia de actividades que involucraron situaciones referentes a transformaciones isométricas, en las cuales ellos realizaron manipulación de applets y construcciones de teselados semirregulares, mediante el uso del software GeoGebra. Se trata de un estudio de casos de carácter descriptivo. Para el análisis de los argumentos de los estudiantes, se utilizan las configuraciones epistémicas del marco teórico del enfoque ontosemiótico del conocimiento y la instrucción matemáticos (EOS) y para el análisis de los resultados, los esquemas de argumentación. Estos resultados sugieren que en el proceso de argumentación de los alumnos recurren a los esquemas argumentativos empírico y fáctico, evidenciados a través del lenguaje informal y escaso lenguaje matemático. Además, la percepción visual, favorecida por el software GeoGebra fue esencial en el desarrollo del proceso de argumentación, aunque esta jugó el papel de argumento más que de apoyo a dicho procedimiento. - 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, High School Students' Mathematical Work on Rate of Change Tasks by Using GeoGebra(Universidad de Granada, Grupo de Investigacion Didactica de la Matematica, 2023-01-01)From the Mathematical Didactics’ viewpoint about teaching Calculus, this paper aims to characterize the knowledge and mathematical work that emerges when high school students solve tasks about the rate of change mediated by GeoGebra. Based on the theory of Mathematical Working Spaces, we analyze the mathematical production of Chilean students (1617 years old) and conclude that making sense of the change rate starts from a work based on algorithmic processes and an interpretation/experimentation approach to the idea of variation and change emphasizing the role of the artefact, being particular to establish proof and demonstration processes. - 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