Ir al menú de navegación principal Ir al contenido principal Ir al pie de página del sitio

Artículos

Vol. 18 Núm. 2 (2015): Julio

RACIOCÍNIO GEOMÉTRICO VERSUS DEFINIÇÃO DE CONCEITOS: A DEFINIÇÃO DE QUADRADO COM ALUNOS DE 6.º ANO DE ESCOLARIDADE

DOI
https://doi.org/10.12802/relime.13.1821
Enviado
julio 1, 2023
Publicado
2023-07-04

Resumen

La geometría a pesar de ser considerada un tema de gran importancia sigue siendo, sin embargo, un tópico en el cual los estudiantes muestran, todavía, muchas dificultades. En este trabajo, hemos analizado la forma en cómo visualizan y presenta la idea de cuadrado un grupo de estudiantes del sexto grado. Esta investigación ha permitido caracterizar la posición del razonamiento geométrico de cada estudiante teniendo como base los niveles de van Hiele. Los resultados obtenidos permiten concluir que el nivel de razonamiento geométrico de los alumnos es menor de lo deseable y necesario a esta fase de aprendizaje en Geometría. Además, la definición del cuadrado presentada por la mayoría de los estudiantes está basada solamente en la congruencia de los lados. Así ambos resultados muestran que los alumnos tienen dificultades en la jerarquía de las propiedades geométricas, hecho que los autores consideran pertinente para seguir investigando, sea en el campo de las posibles causas, sea en cómo intervenir en el aula, así como la formación inicial y continua de los profesores.

Citas

  1. Battista, M. T. (2007). The Development of Geometric and Spatial Thinking. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 843-908).Second Handbook of Research on Mathematics Teaching and Learning (pp. 843-908).Second Handbook of Research on Mathematics Teaching and Learning NY, United States: NCTM.
  2. Bogdan, R. e Biklen, S. (1994). Investigação qualitativa em educação: uma introdução à teoria e aos métodos. Porto, Portugal: Porto Editora.
  3. Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp.151-178). Reston, United States: National Council of Teacher of Mathematics.
  4. Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). NewYork, UnitedHandbook of research on mathematics teaching and learning (pp. 420-464). NewYork, UnitedHandbook of research on mathematics teaching and learning States: Macmillan.
  5. Clements, D. H., Battista, M.T., & Sarama, J. (2001). Logo and Geometry. Journal for Research in Mathematics Education, 10, 1-177.
  6. Cohen, L., Manion, L., & Morrison, K. (2007). Research Methods in Education (6th Ed.). New York, United States: Routledge.
  7. de Villiers, M. (1998). To teach definitions in Geometry or teach to define? In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 248-255). Stellenbosch, South Africa: University of Stellenbosch.
  8. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, Netherlands: Reidel.
  9. Fuys, D., Geddes, D. & Tischler, R. (1988). The Van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education 3. New York, United States: NCTM.
  10. Gomes, A., Ribeiro, C. M., Martins, F., Aires, A. P., Campos, H., Caseiro, A., Poças, R. (2012). Tarefas em Geometria – Da sala de aula para a formação de formação de professores.
  11. Descrição de um projeto. In GTI-APM (Eds.), Atas do XXIIISIEM – Seminário de Investigação em Educação Matemática (pp. 761-763). Coimbra, Portugal: Associação de Professores de Matemática.
  12. Goulding, M., Rowland, T., & Barber, P. (2002). Does it matter? Primary teacher trainees’ subject knowledge in mathematics. British Educational Research Journal, 28(5), 689-704.
  13. Gray, E., & Tall, D. (2002). Abstraction as a natural process of mental compression. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th
  14. Proceedings of the 26th Proceedings of the 26 Conference of the Internacional
  15. Group for the Psychology of Mathematics Education (Vol. 1, pp. 115-120). Norwick, United Kingdom: University of East Anglia.
  16. Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: in search of a framework. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th Conference of the International
  17. Group for the Psychology of Mathematics Education (Vol. 1, pp. 3-19). Valencia, Spain: Universidad de Valencia.
  18. Gutiérrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to assess the acquisition of van Hiele levels. Journal for Research in Mathematics Education, 22(3), 237-251.
  19. Hiebert, J., & Wearne, D. (1993). Instructional Task, Classroom Discourse, and Students’Learning in Second Grade. American Educational Research Journal, 30, 393-425. doi: 10.3102/00028312030002393
  20. Jones, K. (2002). Issues in the teaching and learning of geometry. In L. Haggarty (Ed.), Aspects of Teaching Secondary Mathematics (121-139). London, United Kingdom: Routledge.
  21. NCTM. (1991). Professional standards for teaching mathematics. Reston, United States of America: National Council of Teachers of Mathematics.
  22. NCTM. (2007). Princípios e Normas para a Matemática Escolar. Lisboa, Portugal: Associação de Professores de Matemática.
  23. Pandiscio, E., & Orton, R. E. (1998). Geometry and metacognition: An analysis of Piaget’s and van Hiele’s perspectives. Focus on Learning Problems in Mathematics, 20(2-3), 78-87.
  24. Ponte, J. P., Serrazina, L., Guimarães, H., Breda, A., Guimarães, F., Sousa, H., & Oliveira, P. (2007). Programa de Matemática do Ensino Básico. Lisboa, Portugal: Ministério da Educação – Direção Geral da Inovação e Desenvolvimento Curricular.
  25. Rowan, B., Chiang, F. S., & Miller, R. J. (1997). Using research on employee’s performance to study the effects of teachers on student achievement. Sociology of Education, 70, 256-284.
  26. Rowland, T., Martyn, S., Barber, P., & Heal, C. (2000). Primary teacher trainees’mathematics subject knowledge and classroom performance. In T. Rowland & C. Morgan (Eds.), Research
  27. in Mathematics Education (Vol. 2, pp. 3-18). London, United Kingdom: British Society for Research into Learning Mathematics.
  28. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, United States: Routledge.
  29. Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309-321.
  30. Swafford, J., Jones, G. A., & Thorton, C. A. (1997). Increased knowledge in geometry and instructional practice. Journal for Research in Mathematics Education, 28(4), 467-483.
  31. Tall, D. (2004). Thinking through Three Worlds Of Mathematics. Proceedings of the 28th Conference of the Internacional Group for the Psychology of Mathematics Education, Bergen, Norway.
  32. van Hiele, P. M. (1986). Structure and insight: A Theory of Mathematics Education. Orlando, United States of America: Academic Press.
  33. van der Sandt, S. (2007). Pre-service geometry education in South-Africa: Atypical case? Issues in the Undergraduate Mathematics Preparation of School Teachers: The journal, I, 1-9. Acedido desde: http://www.k12prep.math.ttu.edu/journal/journal.shtml.
  34. Vygotsky, L. S. (1978). Mind in Society, The development of higher psychological processes. Cambridge, United Kingdom: Harvard University Press.

Descargas

Los datos de descargas todavía no están disponibles.

Artículos similares

1 2 3 4 5 6 7 > >> 

También puede {advancedSearchLink} para este artículo.