Modelo Matemáticas 6º-11º

Pensamiento Algebraico

El Pensamiento Algebraico es la capacidad de generalizar, representar, justificar y razonar con estructuras y relaciones matemáticas abstractas. El Pensamiento Algebraico es importante para desarrollar una comprensión profunda de la aritmética y ayuda a los estudiantes a hacer conexiones entre muchos componentes de sus estudios matemáticos tempranos.

Ideas Principales

El Pensamiento Algebraico permite a los estudiantes pasar de pensar y trabajar con números y medidas particulares a entender y razonar con relaciones generalizadas entre ellos. Las prácticas de Pensamiento Algebraico ocurren en estos dominios matemáticos:

  • Equivalencia, expresiones, ecuaciones e inecuaciones: Incluye desarrollar una comprensión del signo igual como expresión de una relación entre cantidades equivalentes, representar y razonar con expresiones que incluyan cantidades desconocidas, y razonar y describir relaciones entre cantidades que pueden o no ser equivalentes.

  • Generalización y razonamiento con relaciones aritméticas: Incluye razonar sobre la estructura de expresiones y relaciones aritméticas, incluyendo propiedades básicas de número y Operaciones.

  • Pensamiento funcional: Incluye representar y razonar con relaciones generalizadas entre cantidades covariantes usando representaciones verbales, simbólicas, gráficas y tabulares (usando tablas).

  • Razonamiento Proporcional: Incluye razonar abstractamente sobre la relación entre dos cantidades generalizadas.

Barbieri, C. A., & Miller-Cotto, D. (2021). The importance of adolescents’ sense of belonging to mathematics for algebra learningLearning and Individual Differences87, 101993.

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 sampleLearning and Individual Differences21(4), 327–336.

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 gradeJournal for Research in Mathematics Education, 46(1), 39-87.

Blanton, M., Brizuela, B., Stephens, A., Knuth, E., Isler, I., Gardiner, A., … Stylianou, D. (2018). Implementing a framework for early algebra. In Teaching and Learning Algebraic Thinking with 5-12 Year Olds. ICME-13 Monographs. (pp. 27–49). Springer, Cham.

Blatto-Vallee, G., Kelly, R. R., Gaustad, M. G., Porter, J., & Fonzi, J. (2007). Visual-spatial representation in mathematical problem solving by deaf and hearing studentsThe Journal of Deaf Studies and Deaf Education12(4), 432–448.

Booker, G. (2009). Algebraic thinking: Generalising number and geometry to express patterns and properties succinctlyGriffith University, Brisbane.

Booth, J. L., Newton, K. J., & Twiss-Garrity, L. K. (2014). The impact of fraction magnitude knowledge on algebra performance and learningJournal of Experimental Child Psychology118(1), 110–118.

Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A reviewJournal of Mathematical Behavior32(3), 613–632.

Cai, J., & Knuth, E. (Eds.). (2011). Early algebraization: A global dialogue from multiple perspectives. Heidelberg, Germany: Springer.

Capraro, M. M., & Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology27(2–3), 147–164.

Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 669–705). Charlotte, NC: Information Age Publishing.

Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2008). Early algebra is not the same as algebra earlyAlgebra in the early grades, 235-272.

Dindyal, J. (2004). Algebraic thinking in geometry at high school level: Students’ use of variables and unknowns. In 27th Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (MERGA 2004) on “Mathematics Education for the Third Millennium, Towards 2010”, (pp. 183–190).

Fernandes, S. H. A. A., & Healy, L. (2014). Algebraic expressions of deaf students: Connecting visuo-gestural and dynamic digital representations. Proceedings of PME 38 and PME-NA, 36(3), 49-56.

Froiland, J. M., & Davison, M. L. (2016). The longitudinal influences of peers, parents, motivation, and mathematics course-taking on high school math achievementLearning and Individual Differences50, 252-259.

Geary, D. C., Hoard, M. K., Nugent, L., & Rouder, J. N. (2016). Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systemsJournal of Experimental Child Psychology15(4), 942–953.

Irwin, K. C., & Britt, M. S. (2005). The algebraic nature of students’ numerical manipulation in the New Zealand Numeracy ProjectEducational Studies in Mathematics58(2), 169-188.

Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). New York, NY: Lawrence Erlbaum Associates.

Kieran, C. (2007). Learning and teaching of algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 707–762). Reston, VA: NCTM.

Kyttälä, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligenceEuropean Journal of Psychology Education, 23(1), 77–94.

Lee, K., Ng, E. L., & Ng, S. F. (2009). The contributions of working memory and executive functioning to problem representation and solution generation in algebraic word problemsJournal of Educational Psychology101(2), 373–387.

Lee, K., Ng, S. F., Ng, E. L., & Lim, Z. Y. (2004). Working memory and literacy as predictors of performance on algebraic word problemsJournal of Experimental Child Psychology89(2), 140-158.

MacGregor, M., & Price, E. (1999). An exploration of aspects of language proficiency and algebra learningJournal for Research in Mathematics Education. 30, 449-467.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core standards mathematics. Washington, DC: Authors.

Nichols, J. D., & White, J. (2001). Impact of peer networks on achievement of high school algebra studentsThe Journal of Educational Research94(5), 267–273.

Star, J. R., Pollack, C., Durkin, K., Rittle-Johnson, B., Lynch, K., Newton, K., & Gogolen, C. (2015). Learning from comparison in algebraContemporary Educational Psychology40, 41-54.

Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solvingLearning and Instruction18(6), 565–579.

Stephens, A. C., Ellis, A. B., Blanton, M., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Compendium for Research in Mathematics Education. Reston, VA: National Council of Teachers of Mathematics.

Susac, A., Bubic, A., Vrbanc, A., & Planinic, M. (2014). Development of abstract mathematical reasoning: The case of algebraFrontiers in Human Neuroscience8(679), 1–10.

Trezise, K., & Reeve, R. A. (2014). Working memory, worry, and algebraic abilityJournal of Experimental Child Psychology121(1), 120–136.