Learning by discovery in systems of special points and lines in a triangle
The article presents the results of a research about learning the special elements in a triangle in Euclidean geometry, carried out with tenth grade students of a school in Tunja, aged between 14 and 17. The conjecturing and the characterization of these elements were anal...
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2020
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| Online Access: | https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880 |
| _version_ | 1801706452506640384 |
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| author | Joya, Carlos Alberto Suárez, Publio |
| author_facet | Joya, Carlos Alberto Suárez, Publio |
| author_sort | Joya, Carlos Alberto |
| collection | OJS |
| description | The article presents the results of a research about learning the special elements in a triangle in Euclidean geometry, carried out with tenth grade students of a school in Tunja, aged between 14 and 17. The conjecturing and the characterization of these elements were analyzed based on the exploration of dynamic geometry environments designed in GeoGebra. The methodology was qualitative with descriptive-interpretative characteristics. The proposal is based on Bruner’s learning by discovery approach. The students progressed in their intuitive thinking by implementing activities focused on visualization, mediated by dynamic drawings. The results show that students learned about special lines and points in a triangle: they identified these in the graphic representation, prioritized the use of natural language, conjectured about their properties and discovered relations and properties in triangles; which caused significant learning. Thus, they advanced in the development of spatial thinking. An important element was the development of the students’ digital competence with the use of GeoGebra. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-9880 |
| institution | Revista Praxis & Saber |
| language | spa |
| publishDate | 2020 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-98802021-07-13T03:56:31Z Learning by discovery in systems of special points and lines in a triangle Aprendizaje por descubrimiento en sistemas de puntos y rectas notables del triángulo Aprendizagem por descobrimento em sistemas de pontos e retas notáveis do triangulo Joya, Carlos Alberto Suárez, Publio geometric objects conjecture formalization dynamic geometry objetivos geométricos conjeturación formalización geometría dinámica objetos geométricos conjecturas formalização geometria dinâmic The article presents the results of a research about learning the special elements in a triangle in Euclidean geometry, carried out with tenth grade students of a school in Tunja, aged between 14 and 17. The conjecturing and the characterization of these elements were analyzed based on the exploration of dynamic geometry environments designed in GeoGebra. The methodology was qualitative with descriptive-interpretative characteristics. The proposal is based on Bruner’s learning by discovery approach. The students progressed in their intuitive thinking by implementing activities focused on visualization, mediated by dynamic drawings. The results show that students learned about special lines and points in a triangle: they identified these in the graphic representation, prioritized the use of natural language, conjectured about their properties and discovered relations and properties in triangles; which caused significant learning. Thus, they advanced in the development of spatial thinking. An important element was the development of the students’ digital competence with the use of GeoGebra. Se presentan los resultados de una investigación acerca del aprendizaje de los elementos notables del triángulo en geometría euclidiana, realizada con estudiantes de grado décimo de un colegio de Tunja, con edades comprendidas entre 14 y 17 años. Se analizó la conjeturación y la caracterización de dichos elementos, a partir de la exploración de ambientes de geometría dinámica diseñados en GeoGebra. La metodología fue cualitativa de tipo descriptivo e interpretativo. La propuesta está basada en el aprendizaje por descubrimiento de Bruner. Hubo un progreso en el pensamiento intuitivo de los estudiantes al implementar las actividades centradas en la visualización, mediadas con dibujos dinámicos. Los resultados muestran que los estudiantes aprendieron sobre rectas y puntos notables del triángulo: los identificaron en la representación gráfica, priorizaron el uso del lenguaje natural, conjeturaron sobre sus propiedades y descubrieron relaciones y propiedades de los triángulos; lo cual generó un aprendizaje significativo. Así avanzaron en el desarrollo del pensamiento espacial. Un elemento importante fue el desarrollo de la competencia digital de los estudiantes con el uso de GeoGebra. O artigo apresenta os resultados de uma pesquisa sobre a aprendizagem dos elementosnotáveis do triângulo na geometria euclidiana, realizada com estudantes do décimo ano do ensino médio numa escola de Tunja, com idades entre 14 e 17 anos. Analisou-se a conjectura e a caracterização de ditos elementos, a partir da exploração de ambientes de geometria dinâmica projetada no GeoGebra. A metodologia foi qualitativa, descritiva e interpretativa. A proposta está baseada na aprendizagem por descobrimento de Bruner. Houve um progresso no pensamento intuitivo dos estudantes ao implementar as atividades focadas na visualização, mediadas com desenhos dinâmicos. Os resultados mostram que os estudantes aprenderam sobre retas e pontos notáveis do triângulo: eles os identificaram na representação gráfica, priorizaram o uso da linguagem natural, conjeturaram sobre suas propriedades e descobriram relações e propriedades dos triângulos; o que gerou uma aprendizagem significativa. Assim, os estudantes avançaram no desenvolvimento do pensamento espacial. Um item importante foi o desenvolvimento da competência digital dos estudantes com o uso do GeoGebra. Universidad Pedagógica y Tecnológica de Colombia 2020-06-19 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf text/html application/epub+zip application/xml https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880 10.19053/22160159.v11.n26.2020.9880 Praxis & Saber; Vol. 11 No. 26 (2020): Educación matemática; e9880 Praxis & Saber; Vol. 11 Núm. 26 (2020): Educación matemática; e9880 Praxis & Saber; Vol. 11 No 26 (2020): Educación matemática; e9880 Praxis & Saber; V. 11 N. 26 (2020): Educación matemática; e9880 Praxis & Saber; v. 11 n. 26 (2020): Educación matemática; e9880 2462-8603 2216-0159 spa https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880/9394 https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880/9395 https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880/9396 https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880/10364 Derechos de autor 2020 Carlos Alberto Joya, Publio Suárez |
| spellingShingle | geometric objects conjecture formalization dynamic geometry objetivos geométricos conjeturación formalización geometría dinámica objetos geométricos conjecturas formalização geometria dinâmic Joya, Carlos Alberto Suárez, Publio Learning by discovery in systems of special points and lines in a triangle |
| title | Learning by discovery in systems of special points and lines in a triangle |
| title_alt | Aprendizaje por descubrimiento en sistemas de puntos y rectas notables del triángulo Aprendizagem por descobrimento em sistemas de pontos e retas notáveis do triangulo |
| title_full | Learning by discovery in systems of special points and lines in a triangle |
| title_fullStr | Learning by discovery in systems of special points and lines in a triangle |
| title_full_unstemmed | Learning by discovery in systems of special points and lines in a triangle |
| title_short | Learning by discovery in systems of special points and lines in a triangle |
| title_sort | learning by discovery in systems of special points and lines in a triangle |
| topic | geometric objects conjecture formalization dynamic geometry objetivos geométricos conjeturación formalización geometría dinámica objetos geométricos conjecturas formalização geometria dinâmic |
| topic_facet | geometric objects conjecture formalization dynamic geometry objetivos geométricos conjeturación formalización geometría dinámica objetos geométricos conjecturas formalização geometria dinâmic |
| url | https://revistas.uptc.edu.co/index.php/praxis_saber/article/view/9880 |
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