CARACTERÍSTICAS EN LA CONSTRUCCIÓN DE LA FRACCIÓN IMPROPIA EN ESTUDIANTES DE 9-12 AÑOS
DOI:
https://doi.org/10.17921/2176-5634.2015v8n4p%25pResumo
El objetivo de esta investigación es caracterizar el uso de las acciones de dividir e iterar en la construcción del concepto de fracción impropia en un contexto continuo en estudiantes de Educación Primaria de 9 a 12 años de edad. 138 estudiantes de Educación Primaria contestaron a un cuestionario con tareas centradas en representar fracciones impropias. Los resultados indican que, los estudiantes deben coordinar las operaciones de dividir una cantidad en partes iguales e iterar la fracción unitaria para representar fracciones impropias. Los resultados obtenidos apoyan la hipótesis de que los estudiantes deben superar la idea de las fracciones como partes dentro de un todo para llegar a coordinar diferentes niveles de unidades necesario para representar fracciones impropias.
Referências
BATTISTA, M.T., (2012). Cognition-Based Assessment and Teaching of Fractions. Building on Students’ Reasoning. Portsmouth, NH: Heinemann.
BEHR, M., LESH, R., POST, T. Y SILVER, E. (1983). ‘Rational number concepts’. En R. Lesh y M. Landau (eds.), Acquisition of Mathematics Concepts and Processes, Academic Press, New York, pp. 91–125.
CHARALAMBOUS, CH. Y PITTA-PANTAZI, D. (2007). Drawing a Theoretical Model to Study Students’ Understanding of Fractions. Educational Studies in mathematics, 64, 293-316.
DEWOLF, M., Y VOSNIADOU, S. (2013). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, http://dx.doi.org/10.1016/j.learninstruc.2014.07.002
HACKENBERG, A. J. (2007). Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behavior, 26 (1), 27-47.
LLINARES, S. Y SÁNCHEZ, V. (1988). Fracciones. Madrid: Síntesis
MCMULLEN, J., LAAKKONEN, E., HANNULA-SORMUNEN, M., Y LEHTINEN, E. (2014). Modeling the developmental trajectories of rational number concept(s). Learning and Instruction, http://dx.doi.org/10.1016/j.learninstruc.2013.12.004
NORTON A. Y MCCLOSKEY A. (2008). Modeling Students’ mathematics using Steffe’s fraction schemes. Teaching Children Mathematics, 15 (1), 48-54.
NORTON A. Y MCCLOSKEY A. (2009). Using Steffe’s Advanced Fraction Schemes. Teaching Children Mathematics, 15 (1), 44-50.
OLIVE, J. (1999), From Fractions to Rational Numbers of Arithmetic: A Reorganization Hypothesis. Mathematical Thinking and Learning 1, no. 4, 279–314.
OLIVE, J., Y STEFFE, L. P. (2002). The construction of an iterative fractional scheme: The case of joe. Journal of Mathematical Behavior, 20(4), 413-437.
OBANDO, G.; VASCO, C., Y ARBOLEDA, L. (2014). Enseñanza y aprendizaje de la razón, la proporción y la proporcionalidad: un estado del arte. Relime-Revista Latinoamericana de Invetigación en Matemática Educativa, 17 (1), 59-81.
PANTZIARA, M. Y PHILIPPOU, G. (2012). Levels of Students’ « conceptions » of fractions. Educational Studies in mathematics, 79, 61-83.
RAMFUL A., (2014). Reversible reasoning in fractional situations: Theorems-in-action and constraints. Journal of Mathematical Behavior, 33, 119-130.
STEFFE, L. P. (2001). A new hypothesis concerning children's fractional knowledge. Journal of Mathematical Behavior, 20(3), 267-307.
STEFFE, L. P. (2003). Fractional commensurate, composition, and adding schemes. learning trajectories of Jason and Laura: Grade 5. Journal of Mathematical Behavior, 22(3), 237-295.
STEFFE, L. P. Y OLIVE, J., (2010). Children’s Fractional Knowledge. London: Springer-Verlag.
TUNÇ-PEKKAN, Z. (2015). An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations. Educational Studies in Mathematics, 89, 419-441.
TZUR, R. (1999). An integrated study of children’s construction of improper fractions and the teacher’s role in promoting that learning. Journal of Research in Mathematics Education, 30(4), 390-416.
VAN HOOF, J., VANDEWALLE, J., VERSCHAFFEL, L., Y VAN DOOREN, W. (2014). In search for the natural number bias in secondary school students' interpretation of the effect of arithmetical operations. Learning and Instruction,
