Estratégias, representações e flexibilidade na resolução de tarefas de comparação multiplicativa
Tipo de documento
Autores
Lista de autores
Cebola, Graça y Brocardo, Joana
Resumen
Neste artigo analisamos, com base num quadro teórico sobre a comparação multiplicativa, a evolução conceitual de Bruno, aluno do 6.º ano (11 anos), focando-nos na articulação adaptativa e flexível de conceitos, estratégias, relações numéricas, propriedades das operações e representações. O modo como explora as cinco tarefas propostas no âmbito de uma experiência de ensino indica-nos que a construção conceitual da comparação multiplicativa de Bruno se situa na ligação entre fator multiplicativo e razão escalar. O seu conhecimento sobre os números e as suas relações permite-lhe usar diferentes representações dos racionais na tradução das estratégias que implementa. Estas variam entre aditivas e multiplicativas e, nas últimas, predomina a utilização da linha numérica dupla com apenas dois pontos. A análise da evolução de Bruno valida e amplia o quadro conceitual teórico adotado inicialmente.
Fecha
2019
Tipo de fecha
Estado publicación
Términos clave
Aprendizaje | Investigación de diseño | Proporcionalidad | Representaciones | Tareas
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
Volumen
33
Número
64
Rango páginas (artículo)
568-590
ISSN
19804415
Referencias
BERK, D. et al. Developing Prospective Elementary Teachers’ Flexibility in the domain of Proportional Reasoning. Mathematical Thinking and Learning, Philadelphia, v. 11, p. 113-135, 2009. BRUNER, J. S. The course of cognitive growth. American Psychologist, Washington, v. 19, p. 1-15, 1964. COBB, P. et al. Design experiments in education research. Educational Researcher, Washington, v. 32, n. 1, p. 9-13, 2003. CRAMER, K.; POST, T. Making connections: A case for proportionality. Arithmetic Teacher, Reston, v. 40, n. 6, p. 342-346, 1993. FREUDENTHAL, H. Didactical Phenomenology of Mathematical Structures. New York: Kluwer Academic Publishers, 2002. GRAVEMEIJER, K.; COBB, P. Design research from a learning design perspective. In: AKKER, J. van den et al. (Ed.). Educational Design Research. London: Routledge, 2006. p. 17-51. GRAY, E. M.; TALL, D. O. Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic. The Journal for Research in Mathematics Education, Reston, v. 26, n. 2, p. 115-141, 1994. GREER, B. Multiplication and Division as Models of Situations. In: GROUWS, D. A. (Ed.). Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan, 1992. p. 276-295. KILPATRICK, J.; SWAFFORD, J.; FINDELL, B. Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press, 2001. LAMON, S. Rational Numbers and Proportional Reasoning – Towards a Theoretical Framework for Research. In: LESTER, F. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning. Reston, VA: National Council of Teachers of Mathematics (NCTM), 2007. p. 629-667. LONG, C.; DUNNE T.; CRAIG, T. S. Proficiency in the multiplicative conceptual field: using Rasch measurement to identify levels of competence. African Journal of Research in MST Education, UK, v. 14, n. 3, p. 79-91, 2010. NCTM. Princípios e Normas para a Matemática Escolar. Lisboa: APM (versão portuguesa), 2007. NCTM. Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8. Reston: NCTM, 2010. PONTE, J. P. Gestão curricular em Matemática. In GTI (Ed.). O professor e o desenvolvimento curricular. Lisboa: APM, 2005. p. 11-34. RATHGEB-SCHNIERER, E.; GREEN, M. Flexibility in mental calculation in elementary students from different math classes. In: UBUZ, B.; HASER, Ç.; MARIOTTI, M. A. (Ed.). CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION, 8., 2013,Ankara. Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education. Ankara: Middle East Technical University, 2013. p. 353-362. RITTLE-JOHNSON, B.; STAR, J. R. Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge? An Experimental Study on Learning to Solve Equations. Journal of Educational Psychology, Washington, v. 99, n. 3, p. 561-574, 2007. ROBINSON, K.; LEFEVRE, J-A. The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework. Educational Studies in Mathematics, NL, v. 79, n. 3, p. 409- 428, 2012. SELTER, C. Creativity, flexibility, adaptivity, and strategy use in mathematics. ZDM Mathematics Education, Eggenstein-Leopoldshafen, v. 41, n. 5, p. 619-625, 2009. SFARD, A. On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, NL, v. 22, n. 1, p. 1-36, 1991. SOWDER, J. Estimation and Number Sense. In: GROUWS, D. A. (Ed.). Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan, 1992. p. 371-389. STAR, J. R.; NEWTON, K. J. The nature and development of experts’ strategy flexibility for solving equations. ZDM Mathematics Education, Eggenstein-Leopoldshafen, v. 41, n. 5, p. 557-567, 2009. THOMAS, N. D.; MULLIGAN, J. T.; GOLDIN, G. A. Children’s representation and structural development of the counting sequence 1–100. Journal of Mathematical Behaviour, UK, v. 21, p 117-133, 2002. THOMPSON, P. W. The development of the concept of speed and its relationship to concepts of rate. In: HAREL, G.; CONFREY, J. (Ed.). The development of multiplicative reasoning in the learning of mathematics. Albany, NY: SUNY Press, 1994. p. 181-234. THOMPSON, P. W.; SALDANHA, L. A. Fractions and Multiplicative Reasoning. In: KILPATRICK, J.; MARTIN, G.; SCHIFTER, D. (Ed.). Research Companion to the Principles and Standards for School Mathematics. Reston, VA: NCTM, 2003. p. 95-114. THRELFALL, J. Strategies and flexibility in mental calculation. ZDM Mathematics Education, Eggenstein-Leopoldshafen, v. 41, n. 5, p. 541-555, 2009. VAN GALEN, F. et al. Fractions, Percentages, Decimals and Proportions. Rotterdam: Sense Publishers, 2008. VERSCHAFFEL, L. et al. Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, Lisboa, v. XXIV, n. 3, p. 335-359, 2009.
Proyectos
Documentos relacionados
La mirada profesional al razonamiento proporcional y algebraico en la práctica estadística
- Gea, María Magdalena, Hernández, Luis Armando
- Aprendizaje, Contenido, Ejercicios rutinarios, Formativos, Funcional, Fundamentos de Educación Matemática, Incertidumbre y datos, Otro (estadística), Transversales
- Educación primaria, escuela elemental (6 a 12 años), Educación secundaria básica (12 a 16 años), Todos los niveles educativos