Modelo Matemáticas 2º-5º
Razonamiento Proporcional
El Razonamiento Proporcional implica una comprensión de la razón y las relaciones entre razones. Las razones expresan una relación de parte a todo que puede representarse en forma de fracciones, porcentajes o tasas. El Razonamiento Proporcional es un componente esencial de la competencia aritmética en la escuela primaria y proporciona acceso a habilidades matemáticas superiores, incluyendo álgebra, geometría, y probabilidad y estadística.
Ideas Principales
Los estudiantes comienzan con una comprensión informal de las relaciones proporcionales (por ejemplo, repartir o compartir equitativamente, o relacionar proporciones en áreas sombreadas de formas). Este conocimiento informal se desarrolla a lo largo de varios años en una comprensión conceptual más formal a medida que conectan diferentes aspectos del Razonamiento Proporcional, incluyendo:
- Aprender a hacer comparaciones basadas en la multiplicación en lugar de la suma.
- Aprender qué aspectos de una proporción pueden cambiarse (es decir, los valores específicos) y cuáles deben ser constantes (es decir, la relación multiplicativa entre los valores).
- Aprender a hacer unidades compuestas —es decir, aprender a reconceptualizar una proporción como una sola entidad.
Aunque el Razonamiento Proporcional es desafiante para muchos estudiantes en los primeros años, aquellos con discalculia a menudo demuestran dificultades persistentes que no se resuelven sin intervención.
Referencias
Agostino, A., Johnson, J., & Pascual-Leone, J. (2010). Executive functions underlying multiplicative reasoning: Problem type matters. Journal of Experimental Child Psychology, 105(4), 286–305.
Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Developmental Science, 17(5), 775–785.
Booth, J. L., Newton, K. J., & Twiss-Garrity, L. K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118(1), 110–118.
Carney, M. B., Smith, E., Hughes, G. R., Brendefur, J. L., & Crawford, A. (2016). Influence of proportional number relationships on item accessibility and students’ strategies. Mathematics Education Research Journal, 28(4), 503–522.
Empson, S. B., & Turner, E. (2006). The emergence of multiplicative thinking in children’s solutions to paper folding tasks. Journal of Mathematical Behavior, 25(1), 46–56.
Hansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., & Micklos, D. (2015). General and math-specific predictors of sixth-graders’ knowledge of fractions. Cognitive Development, 35, 34–49.
Hecht S., Close L., & Santisi, M. (2003). Sources of individual differences in fraction skills. Journal of Experimental Child Psychology, (86), 277–302.
Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–859.
Jeong, Y., Levine, S. C., & Huttenlocher, J. (2007). The development of proportional reasoning: Effect of continuous versus discrete quantities. Journal of Cognition and Development, 8(2), 237–256.
Kleemans, T., Segers, E., & Verhoeven, L. (2018). Role of linguistic skills in fifth-grade mathematics. Journal of Experimental Child Psychology, 167, 404–413.
Lamon, S. J., (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. Lester (Ed.), Second handbook of research on teaching and learning mathematics, Vol. I (pp. 629 – 667). Reston, VA: National Council of Teachers of Mathematics.
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38, 201–221.
Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and “holes”: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681–691.
Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371–387.
Möhring, W., Newcombe, N. S., Levine, S. C., & Frick, A. (2016). Spatial proportional reasoning is associated with formal knowledge about fractions. Journal of Cognition and Development, 17(1), 67–84.
Namkung, J., Fuchs, L. S., & Koziol, N. (2018). Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill? Learning and Individual Differences, 61, 165–171.
National Research Council, & Mathematics Learning Study Committee. (2001). Adding it up: Helping children learn mathematics. National Academies Press.
Panaoura, A., Gagatsis, A., Deliyianni, E., & Elia, I. (2009). The structure of students’ beliefs about the use of representations and their performance on the learning of fractions. Educational Psychology, 29(6), 713–728.
Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of prealgebra understandings In algebraic concepts in the curriculum K-12. Reston, VA: National Council of Teachers of Mathematics.
Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13–19.
Thomas, N. (2004). The development of structure in the number system. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 4, 305-312.
Thompson, P. W., & Saldanha, L. A. (2003). Fractions and Multiplicative Reasoning. In J. Kilpatrick, G. Martin, & Schif (Eds.), Research companion to the Principles and Standards for School Mathematics (pp. 95–114).
Ye, A., Resnick, I., Hansen, N., Rodrigues, J., Rinne, L., & Jordan, N. C. (2016). Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge. Journal of Experimental Child Psychology, 152, 242–263.