Modelo Matemáticas 2º-5º
Operaciones
Los estudiantes generalmente comienzan pensando en las Operaciones como instrucciones para realizar cálculos o computaciones procedimentales, como encontrar la suma o la diferencia entre dos números. Sin embargo, es crítico que los estudiantes también desarrollen una comprensión conceptual de las Operaciones. Esta base conceptual apoya a los estudiantes en la estimación de cálculos aproximados, además de calcular rápida y correctamente usando procedimientos.
Ideas Principales
La habilidad de los estudiantes con las Operaciones se apoya en estos componentes conceptuales críticos:
- Comprender las propiedades algebraicas de las Operaciones involucradas en el problema: Por ejemplo, los estudiantes deberían ser capaces de transformar la suma más difícil 3+8+7 en la suma más fácil 3+7+8 (es fácil ver que 3+7 = 10, y luego es fácil sumar 8 a 10).
- Comprender el sistema de Valor Posicional y descomposición: Por ejemplo, un estudiante también podría transformar 3+8+7 en 3+7+1+7 (haciendo más fácil sumar hasta 10, antes de sumar 1 y 7).
- Comprender cómo las relaciones en una situación del mundo real pueden expresarse mediante Operaciones (es decir, modelado).
Los estudiantes que tienen dificultad específica para conceptualizar números y realizar Operaciones aritméticas pueden tener discalculia, un trastorno de aprendizaje que afecta muchos aspectos fundamentales del pensamiento matemático.
Referencias
Andersson, U. (2008). Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions. The British Journal of Educational Psychology, 78(2), 181–203.
Best, J. R., Miller, P. H., & Naglieri, J. A. (2011). Relations between executive function and academic achievement from ages 5 to 17 in a large, representative national sample. Learning and Individual Differences, 21(4), 327–336.
Berg, D. H. (2008). Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory, and reading. Journal of Experimental Child Psychology, 99(4), 288–308.
Berry III, R. Q., Thunder, K., & McClain, O. L. (2011). Counter narratives: Examining the mathematics and racial identities of Black boys who are successful with school mathematics. Journal of African American Males in Education, 2(1).
Blanton, M., Stephens, A., Knuth, E., Gardiner, A., Isler, I., & Kim, J. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39-87.
Butterworth, B, Sashank V, & Laurillard, D. (2011). Dyscalculia: From brain to education. Science 332 (6033), 1049-105.
Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 37–50.
Chaddock-Heyman, L., Erickson, K. I., Kienzler, C., King, M., Pontifex, M. B., Raine, L. B., … & Kramer, A. F. (2015). The role of aerobic fitness in cortical thickness and mathematics achievement in preadolescent children. PloS one, 10(8), e0134115.
De Smedt, B., Holloway, I. D., & Ansari, D. (2011). Effects of problem size and arithmetic operation on brain activation during calculation in children with varying levels of arithmetical fluency. NeuroImage, 57(3), 771–781.
De Visscher, A., & Noël, M. P. (2014). The detrimental effect of interference in multiplication facts storing: Typical development and individual differences. Journal of Experimental Psychology: General, 143(6), 2380–2400.
Green, C. T., Bunge, S. A., Briones Chiongbian, V., Barrow, M., & Ferrer, E. (2017). Fluid reasoning predicts future mathematical performance among children and adolescents. Journal of Experimental Child Psychology, 157, 125–143.
Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills : A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79, 192–227.
Imbo, I., & Vandierendonck, A. (2008). Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: Differences between children and adults? Psychological Research, 72(3), 331–346.
Keller, J. (2007). Stereotype threat in classroom settings: The interactive effect of domain identification, task difficulty and stereotype threat on female students’ maths performance. British journal of educational psychology, 77(2), 323-338.
Kleemans, T., Segers, E., & Verhoeven, L. (2012). Naming speed as a clinical marker in predicting basic calculation skills in children with specific language impairment. Research in Developmental Disabilities, 33, 882–889.
Linsen, S., Verschaffel, L., Reynvoet, B., & De Smedt, B. (2014). The association between children’s numerical magnitude processing and mental multi-digit subtraction. Acta Psychologica, 145, 75–83.
Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. (2011). Early place-value understanding as a precursor for later arithmetic performance — A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837–1851.
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.
Parham, Diane, L. (1998). The relationship of sensory integrative development to achievement in elementary students: Four-year longitudinal patterns. The Occupational Therapy Journal of Research, 18(3), 105–127.
Pieters, S., Desoete, A., Roeyers, H., Vanderswalmen, R., & Van Waelvelde, H. (2012). Behind mathematical learning disabilities: What about visual perception and motor skills? Learning and Individual Differences, 22(4), 498–504.
Pixner, S., Leyrer, M., & Moeller, K. (2014). Number processing and arithmetic skills in children with cochlear implants. Frontiers in Psychology, 5, 1479.
Ramdass, D., & Zimmerman, B. J. (2008). Effects of self correction strategy training on middle school student’s self-efficacy, self-evaluation, and mathematics division learning. Journal of Advanced Academics, 20(1), 18–41.
Robinson, K. M., & Dubé, A. K. (2009). Children’s understanding of the inverse relation between multiplication and division. Cognitive Development, 24(3), 310–321.
Robinson, K. M., Arbuthnott, K. D., Rose, D., McCarron, M. C., Globa, C. A., & Phonexay, S. D. (2006). Stability and change in children’s division strategies. Journal of Experimental Child Psychology, 93(3), 224–238.
Rosenberg-Lee, M., Ashkenazi, S., Chen, T., Young, B., Geary, D. C., & Menon, V. (2015). Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia. Developmental Science, 18(3), 351–372.
Rubinsten, O., & Tonnock, R. (2010). Mathematics anxiety in children with developmental dyscalculia. Behavioral and Brain Functions, 6(46), 1–13.
Seethaler, P. M., & Fuchs, L. S. (2006). The cognitive correlates of computational estimation skill among third-grade students. Learning Disabilities Research and Practice, 21(4), 233–243.
Skagerlund, K., & Träff, U. (2016). Processing of space, time, and number contributes to mathematical abilities above and beyond domain-general cognitive abilities. Journal of Experimental Child Psychology, 143, 85–101.
Star, J. R., & Rittle-Johnson, B. (2009). It pays to compare: An experimental study on computational estimation. Journal of Experimental Child Psychology, 102(4), 408–426.
Vanbinst, K., Ceulemans, E., Ghesquière, P., & De Smedt, B. (2015). Profiles of children’s arithmetic fact development: A model-based clustering approach. Journal of Experimental Child Psychology, 133, 29–46.
van der Ven, S. H. G., Straatemeier, M., Jansen, B. R. J., Klinkenberg, S., & van der Maas, H. L. J. (2015). Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems. Learning and Individual Differences, 43, 48–62.
Vasilyeva, M., Casey, B. M., Dearing, E., & Ganley, C. M. (2009). Measurement skills in low-income elementary school students: Exploring the nature of gender differences. Cognition and Instruction, 27(4), 401–428.
Vukovic, R. K., Kieffer, M. J., Bailey, S. P., & Harari, R. R. (2013). Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance. Contemporary Educational Psychology, 38, 1–10.
Wechsler, D. (2009). Wechsler Individual Achievement Test 2nd Edition (WIAT III). San Antonio, TX: The Psychological Corp.
Witacre, I., Schoen, R., Champagne, Z., & Goddard, A. (2017). Relational thinking: What’s the difference? Teaching Children Mathematics, 23(5), 302–308.