La demostración en geometría: procesos cognitivos y metacognitivos favorecidos por la inclusión de ambientes dinámicos
Autores
Lista de autores
Sua, Camilo
Resumen
Se presenta una propuesta de investigación cuyo objetivo es indagar por los procesos cognitivos y metacognitivos que tienen lugar en el marco de la resolución de problemas, cuando esta corresponde a la demostración de enunciados geométricos, que involucra ambientes virtuales que integran representaciones geométricas. Se presenta la pregunta de investigación que orientará en desarrollo de la investigación, algunos aportes desde la literatura que soportan la misma y una conceptualización frente a los elementos involucrados
Fecha
2015
Tipo de fecha
Estado publicación
Términos clave
Geometría | Informáticos (recursos centro) | Lógica matemática | Procesos de justificación
Enfoque
Nivel educativo
Educación primaria, escuela elemental (6 a 12 años) | Educación secundaria básica (12 a 16 años)
Idioma
Revisado por pares
Formato del archivo
Nombre del evento
Lugar (evento)
Tipo de evento
Tipo de presentación
Referencias
Abdelfatah, H. (2011). A story-based dynamic geometry approach to improve attitudes toward geometry and geometric proof. ZDM - International Journal on Mathematics Education, 43(3), 441–450. http://doi.org/10.1007/s11858-011-0341-6 Barrera-Mora, F., & Reyes-Rodríguez, A. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments Barrera-Mora & Reyes-Rodríguez. The Mathematics Enthusiast, 10(1), 109–136. Beeson, M. (2013). Proof and Computation in Geometry. In T. Ida & J. Fleuriot (Eds.), Automated Deduction in Geometry (pp. 1–30). Retrieved from http://dx.doi.org/10.1007/978-3-642-40672-0_1 Bjuland, R. (2007). Adult Students’ Reasoning in Geometry: Teaching Mathematics through Collaborative Problem Solving in Teacher Education. The Montana Mathematics Enthusiast, 4(1), 1–30. Cai, J. (1994). A protocol-analytic study of metacognition in mathematical problem solving. Mathematics Education Research Journal, 6(2), 166–183. http://doi.org/10.1007/BF03217270 Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45–75. http://doi.org/10.1007/s10649-005-0808-x Dettori, G., Greco, S., & Lemut, E. (1998). Information Technology and problem solving in mathematics education. In G. Marshall & M. Ruohonen (Eds.), Capacity Building for IT in Education in Developing Countries (pp. 299–307). London: Chapman & Hall. http://doi.org/10.1007/978-0-387-35195-7_32 Duffield, J. a. (1991). Designing computer software for problem-solving instruction. Educational Technology Research and Development, 39(1), 50–62. http://doi.org/10.1007/BF02298106 Erbas, A. K., & Okur, S. (2012). Researching students’ strategies, episodes, and metacognitions in mathematical problem solving. Quality and Quantity, 46(1), 89–102. http://doi.org/10.1007/s11135-010-9329-5 Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education. http://doi.org/10.2307/748391 Goos, M., & Galbraith, P. (1996). Do it this way! Metacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30(3), 229–260. http://doi.org/10.1007/BF00304567 Guven, B., Baki, A., & Cekmez, E. (2012). Using dynamic geometry software to develop problem solving skills. Mathematics & Computer Education, 46(1), 6–17. Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.), Perspectives on the Teaching of Geometry for the 21st Century (pp. 121–128). Dordrecht: Kluwer. Retrieved from http://eprints.soton.ac.uk/41227/ Jurdak, M. (2000). Technology and problem solving in mathematics: Myths and Realities. In Proceedings of the International Conference on Technology in Mathematics Education (pp. 30–37). Beirut: Lebanese American University. Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40. Laborde, C. (2000). Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Educational Studies in Mathematics, 44, 151–161. Lárez, J. (2014). Las demostraciones geométricas como instancias de resolución de problemas. Paradigma, 35(2), 183–199. Leikin, R., & Grossman, D. (2013). Teachers modify geometry problems: from proof to investigation. Educational Studies in Mathematics, 82(3), 515–531. Mariotti, M. (2000). Introduction to proof: the mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1-2), 25–53. Matsuda, N., & Vanlehn, K. (2004). GRAMY: A geometry theorem prover capable of construction. Journal of Automated Reasoning, 32(1), 3–33. http://doi.org/10.1023/B:JARS.0000021960.39761.b7 Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1-2), 49– 63. http://doi.org/10.1023/A:1003088013286 Narboux, J. (2007). A graphical user interface for formal proofs in geometry. Journal of Automated Reasoning, 39(2), 161–180. http://doi.org/10.1007/s10817-007-9071-4 Özen, D., & Köse, N. Y. (2013). Investigating Pre-service Mathematics Teachers’ Geometric Problem Solving Process in Dynamic Geometry Environment. Turkish Online Journal of Qualitative Inquiry, 4(3), 61–74. Perry, P., Samper, C., Camargo, L., & Molina, O. (2013). Innovación en un aula de geometría de nivel universitario. In Geometría Plana: un espacio de aprendizaje (pp. 11–34). Bogotá: Fondo Editorial Universidad Pedagógica Nacional. Pitta-Pantazi, D., & Christou, C. (2009). Cognitive styles, dynamic geometry and measurement performance. Educational Studies in Mathematics, 70(1), 5–26. http://doi.org/10.1007/s10649-008-9139-z Pochulu, M. (2010). Significados atribuidos a la resolución de problemas con software de geometría dinámica durante un desarrollo profesional docente. Revista Latinoamericana de Investigación En Matemática Educativa, 13(3), 307–336. Robotti, E. (2012). Natural language as a tool for analyzing the proving process: The case of plane geometry proof. Educational Studies in Mathematics, 80(3), 433–450. http://doi.org/10.1007/s10649-012-9383-0 Sandoval, I. T., & Moreno, L. E. (2012). Tecnología digital y cognición matemática: retos para la educación. Horizontes Pedagógicos, 14(1), 21–29. Santos-Trigo, M. (2007). Mathematical problem solving: An evolving research and practice domain. ZDM - International Journal on Mathematics Education, 39(5-6), 523–536. http://doi.org/10.1007/s11858-007-0057-9 Santos-Trigo, M., & Cristóbal-Escalante, C. (2008). Emerging High School Students’ Problem Solving Trajectories Based on the Use of Dynamic Software. Journal of Computers in Mathematics and Science Teaching, 27(3), 325–340. Schoenfeld, A. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334–370). New York: MacMillan. Valencia, N., Sanabria, L., & Ibáñez, J. (2012). Procesos cognitivos y metacognitivos en la solución de problemas de movimiento de figuras en el plano a través de ambientes computacionales. Tecné, Episteme Y Didaxis, 31(1), 45–65. Vincent, J. (2002). Dynamic Geometry Software and Mechanical Linkages. In D. Watson & J. Andersen (Eds.), Networking the Learner SE - 42 (pp. 423–432). Springer US. http://doi.org/10.1007/978-0-387-35596-2_42 Wertheimer, R. (1990). The Geometry Proof Tutor: An “Intelligent” Computer-Based Tutor in the Classroom. Mathematics Teacher, 84(4), 308–317. Wong, W. K., Yin, S. K., Yang, H. H., & Cheng, Y. H. (2011). Using computer-assisted multiple representations in learning geometry proofs. Educational Technology and Society, 14(3), 43–54. Yang, K. L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics, 80(3), 307–326. http://doi.org/10.1007/s10649-011-9350-1 Yimer, A., & Ellerton, N. F. (2006). Cognitive and metacognitive aspects of mathematical problem solving: An emerging model. Identities, Cultures, and Learning Spaces, (1994), 575–582.
Dirección de correo electrónico de contacto
jcsuaf@pedagogica.edu.co