Quando as frações não São apenas partes de um todo…!
Tipo de documento
Autores
Lista de autores
Graça, Sofia, da-Ponte, João Pedro y Guerreiro, António
Resumen
Este estudo tem como objetivo analisar os conhecimentos de alunos do 5.º ano relativos aos significados das frações antes e após uma experiência de ensino que segue uma abordagem exploratória com ênfase na resolução de problemas. Os participantes são alunos de uma turma do referido ano. Para a recolha de dados foram usados dois testes, inicial e final, complementados com a realização de entrevistas semiestruturadas individuais. Os dados indicam que, antes da experiência de ensino, os alunos tinham um conhecimento muito limitado dos significados das frações, nomeadamente como medida e como quociente. Demonstravam apenas algumas ideias associadas à relação parte-todo e ao operador, mas este último apenas ao nível procedimental. Após a experiência de ensino, estes alunos mostraram alguma flexibilidade com todos os significados, embora o significado de medida ainda constitua um desafio para um dos alunos participantes.
Fecha
2020
Tipo de fecha
Estado publicación
Términos clave
Diseño | Estrategias de solución | Números racionales | Planteamiento de problemas | Reflexión sobre la enseñanza | Usos o significados
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Referencias
Alkhateeb, M. (2019). Common errors in fractions and the thinking strategies that accompany them. International Journal of Instruction, v. 12(2), p. 339-416. https://doi.org/10.29333/iji.2019.12226a Barnett-Clarke, C., Fisher, W., Marks, R., & Ross, S. (2010). Developing essential understanding of rational numbers: Grades 3-5. NCTM. Behr, M., Lesh, R., Post, T., & Silver, E. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.). Acquisition of mathematics concepts and processes, (pp. 91-125). Academic Press. Charalambous C., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understanding of fractions. Educational Studies in Mathematics, v. 64(3), p. 293-316. Erickson, F. (1986). Qualitative methods in research on teaching. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 119-161). Macmillan. Hunt, J., Westenskow, A., & Moyer-Packenham, P. (2017). Variations of reasoning in equal sharing of children who experience low achievement in mathematics: Competence in context. Education Sciences, v. 7(1), p. 1-14. https://doi.org/10.3390/educsci7010037 Lamon, S. (1996). The development of unitizing: Its role in children’s partitioning strategies. Journal for Research in Mathematics Education, v. 27(2), p. 170–193. https://doi.org/10.2307/749599 Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (629-668). Information Age Publishing. Lee, H., Dewolf, M., Bassok, M., & Holyoak, K. (2016). Conceptual and procedural distinctions between fractions and decimals: A cross-national comparison. Cognition, v. 147, p. 57-69. https://doi.org/10.1016/j.cognition.2015.11.005 Lewis, C., & Perry, R. (2014). Lesson study with mathematical resources: A sustainable model for locally-led teacher professional learning. Mathematics Teacher Education and Development, v. 16(1), p. 22-42. Llinares, S., & Sánchez, M. V. (1997). Fracciones: La relacion parte-todo. Sintesis. Moseley, B. (2005). Students’ early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, v. 60, p. 37-69. https://doi.org/10.1007/s10649-005-5031-2 Norton, A., Wilkins, J., & Xu, C. (2018). A progression of fraction schemes common to Chinese and U.S. students. Journal for Research in Mathematics Education, v. 49(2), p. 210-226. https://doi.org/10.5951/jresematheduc.49.2.0210 Ponte, J. P., & Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. Educational Studies in Mathematics, v. 93(1), p. 51-66. https://doi.org/10.1007/s10649-016-9681-z Post, T., Behr, M., & Lesh, R. (1986). Research-based observations about children’s learning of rational number concepts. Focus on Learning Problems in Mathematics, v. 8(1), p. 39-48. Post, T., Cramer, K., Behr, M., Lesh, T., & Harel, G. (1993). Curriculum implications of research on the learning, teaching and assessing of rational number concepts. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 327-358). Lawrence Erlbaum. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, v. 26(2), p. 114-145. https://doi.org/10.2307/749205 Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, v. 14, p. 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015 Toluk, Z., & Middleton, J. (2001). The development of children’s understanding of the quotient: a teaching experiment. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th annual meeting of the International Group for the Psychology of Mathematics Education (pp. 265-272). Hogrefe.