Semejanza de triángulos: un concepto para promover niveles de razonamiento geométrico

Abstract

RESUMEN: En esta investigación se hace una reflexión sobre algunos factores que afectan la enseñanza y aprendizaje de los estudiantes para la comprensión de conceptos de geometría. Para ello, se utilizó en este estudio como referente el modelo educativo de van Hiele, porque ayuda a mejorar el razonamiento y a estructurar el aprendizaje de los estudiantes en conceptos geométricos; asimismo, ayudó en el análisis de cómo se promueven los niveles de razonamiento geométrico para la comprensión de conceptos enmarcados en la semejanza de triángulos en tres estudiantes de secundaria de la institución educativa Lusitania Paz de Colombia. La metodología utilizada tiene un enfoque cualitativo, pues es de corte cuasiexperimental-analítico y la recolección de los datos se hizo mediada por la observación, entrevistas, toma de notas y diarios de campo. Para dar cumplimiento a los objetivos propuestos se trazó una ruta metodológica que se desarrolló en tres etapas para guiar el trabajo de campo con la difusión e invitación a estudiantes, luego la preparación y aplicación de un experimento de enseñanza, el cual fue diseñado con descriptores para cada fase del modelo que proporcionaron el tránsito de manera secuencial al siguiente nivel, para este caso del nivel 2 al nivel 3 y la ejecución del análisis de los datos demostraron la validez y eficacia de este modelo al desarrollar en los estudiantes habilidades referentes a la visualización, el uso del lenguaje y la comprensión de conceptos de semejanza de triángulos. ABSTRACT: In this research a reflection is made on some factors that affect teaching and learning in students for the understanding of geometry concepts. For this purpose, van Hiele's educational model was used in this study as a reference because it helps to improve reasoning and to structure the learning of students in geometric concepts, likewise, it helped in the analysis of how the levels of geometric reasoning are promoted for the understanding of concepts framed in the similarity of triangles in three high school students of the Lusitania Paz de Colombia educational institution. The methodology used has a qualitative approach as it is quasi-experimental-analytical and the data collection was mediated by observation, interviews, note taking and field diaries. In order to comply with the proposed objectives, a methodological route was traced and developed in three stages to guide the field work with the dissemination and invitation to students, then the preparation and application of a teaching experiment which was designed with descriptors for each phase of the model that provided the sequential transition to the next level, in this case from level 2 to level 3, and the execution of the data analysis demonstrated the validity and effectiveness of this model in developing in students skills related to visualization, the use of language and the understanding of concepts of similarity of triangles.

ABSTRACT: In this research a reflection is made on some factors that affect teaching and learning in students for the understanding of geometry concepts. For this purpose, van Hiele's educational model was used in this study as a reference because it helps to improve reasoning and to structure the learning of students in geometric concepts, likewise, it helped in the analysis of how the levels of geometric reasoning are promoted for the understanding of concepts framed in the similarity of triangles in three high school students of the Lusitania Paz de Colombia educational institution. The methodology used has a qualitative approach as it is quasi-experimental-analytical and the data collection was mediated by observation, interviews, note taking and field diaries. In order to comply with the proposed objectives, a methodological route was traced and developed in three stages to guide the field work with the dissemination and invitation to students, then the preparation and application of a teaching experiment which was designed with descriptors for each phase of the model that provided the sequential transition to the next level, in this case from level 2 to level 3, and the execution of the data analysis demonstrated the validity and effectiveness of this model in developing in students skills related to visualization, the use of language and the understanding of concepts of similarity of triangles.