La comprensión conceptual aritmética en la escuela elemental

  1. Pérez Pérez, Leire 1
  2. Núñez López, Andrea 1
  3. Iglesias Sarmiento, Valentín
  1. 1 Universidade de Vigo
    info

    Universidade de Vigo

    Vigo, España

    ROR https://ror.org/05rdf8595

Revista:
International Journal of Developmental and Educational Psychology: INFAD. Revista de Psicología

ISSN: 0214-9877

Ano de publicación: 2021

Título do exemplar: LEARNING IN A POSITIVE MOOD: THE RESPONSE TO COVID-19

Volume: 2

Número: 2

Páxinas: 163-172

Tipo: Artigo

DOI: 10.17060/IJODAEP.2021.N2.V2.2221 DIALNET GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: International Journal of Developmental and Educational Psychology: INFAD. Revista de Psicología

Resumo

Este estudio analizó la comprensión conceptual aritmética desde una doble vía, (conceptual y estratégica) del alumnado escolarizado en 4º, 5º y 6º de Educación Primaria, seleccionado en base a tres grupos de logro: dificultades de aprendizaje en matemáticas (DAM; n=51), competencia normal (CN; n=60) y alto rendimiento (AR; n=21). Concretamente, pretendió (1) caracterizar al alumnado en base a su conocimiento conceptual aritmético y (2) analizar cómo los distintos grupos de logro afrontan tareas más complejas en base a sus habilidades conceptuales previas. Se utilizó la batería BANEVHAR para evaluar la comprensión conceptual y la escala completa de la batería CAS como estimador fiable de inteligencia. Los resultados señalaron los déficits conceptuales del alumnado con DAM respecto a sus iguales de CN y AR que parecen llegar a estos niveles educativos con las habilidades conceptuales adquiridas. Además, se observó que existen diferencias entre los tres grupos en el afrontamiento estratégico de las tareas cuando estas son novedosas o complejas. En este contexto, el alumnado con AR es capaz de resolver las tareas de forma más eficiente. Estos hallazgos resaltan la importancia de la enseñanza conceptual y estratégica de la aritmética y sugieren su implementación práctica en la escuela.

Referencias bibliográficas

  • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. En A. J. Baroody y A. Dowker (Ed.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1–33). Erlbaum.
  • Baroody, A. J. (2006). Why children have difficulty mastering the basic number combinations and how to help them. Teaching Children Mathematics, 13(1), 22- 31.
  • Baroody, A. J., y Snyder, P. (1983). A cognitive analysis of basic arithmetic abilities of TMR children. Education and Training of the Mentally Retarded, 18(4), 253-259. Canobi, K. H. (2004). Individual differences in children’s addition and subtraction knowledge. Cognitive Development, 19(1), 81–93. https://doi.org/10.1016/j.cogdev.2003.10.001
  • Cowan, R., Donlan, C., Shepherd, D.-L., Cole-Fletcher, R., Saxton, M., y Hurry, J. (2011). Basic calculation proficiency and mathematics achievement in elementary school children. Journal of Educational Psychology, 103(4), 786–803. http://dx.doi.org/10.1037/a0024556
  • Crooks, N. M., y Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34 (4), 344-377. http://dx.doi.org/10.1016/j.dr.2014-10-001
  • Deaño, M. (2005). D.N: CAS (Das-Naglieri: Sistema de Evaluación Cognitiva) Adaptación Española. Gersam.
  • Dowker, A. (2003). Young children’s estimates for addition: The zone of partial knowledge and understanding. En A. J. Baroody (Ed.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 243–265). Erlbaum. Dowker, A. D. (2005). Individual differences in arithmetic. Implications for Psychology, Neuroscience and Education. Psychology Press.
  • Geary, D. C. (2011). Cognitive predictors of individual differences in achievement growth in mathematics: A five year longitudinal study. Developmental Psychology, 47(6), 1539-1552. http://dx.doi.org/10.1037/a0025510
  • Geary, D. C., Bow-Thomas, C. C., y Yao, Y. (1992). Counting knowledge and skill in cognitive addition: A comparison of normal and mathematically disabled children. Journal of Experimental Child Psychology, 54(3), 372–391. https://doi.org/10.1016/0022-0965(92)90026-3
  • Geary, D. C., Hoard, M. K., Byrd-Craven, J., y Catherine DeSoto, M. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121–151. https://doi.org/10.1016/j.jecp.2004.03.002
  • Gilmore, C. K., y Bryant, P. (2006). Individual differences in children’s understanding of inversion and arithmetical skill. The British Journal of Educational Psychology, 76(2), 309-331. https://doi.org/10.1348/000709905X39125
  • Gilmore, C., Keeble, S., Richardon, S., y Cragg, L. (2017). The interaction ofprocedural skill, conceptual understanding and working memory in early mathematics achievement. Journal of Numerical Cognition, 3(2), 400-416. https://doi.org/10.5964/jnc.v3i2.51
  • Gilmore, C. K., y Papadatou-Pastou, M. (2009). Patterns of individual differences in conceptual understanding and arithmetical skill: A meta-analysis. Mathematical Thinking and Learning, 11(1-2), 25-40. http://dx.doi.org/10.1080/10986060802583923
  • Hanich, L. B., Jordan, N. C., Kaplan, D., y Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93(3), 615–626. https://doi.org/10.1037/0022-0663.93.3.615
  • Iglesias-Sarmiento, V. (2009). Dificultades de aprendizaje en el dominio aritmético y en el procesamiento cognitivo subyacente [Learning difficulties in the mastery of arithmetic and in the underlying cognitive processing]. (Doctoral dissertation). Available from ProQuest database. (UMI No. AAT 3386296)
  • Iglesias-Sarmiento, V., Alfonso, S., Conde, A., Pérez, L., y Deaño, M. (2020).Mathematical difficulties vs. high achievement: An analysis of arithmetical cognition in elementary school. Developmental Neuropsychology, 45(2), 49-65. https://doi.org/10.1080/87565641.2020.1726920
  • International Association for the Evaluation of Educational Achievement (IEA, 2016). TIMMS 2015. Student achievement. Chestnut Hill, MA: TIMSS & PIRLS International Study Center.
  • Jordan, N. C., Hanich, L. B., y Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85(2), 103-119. https://doi.org/10.1016/S0022-0965(03)00032-8
  • Jordan, N. C., Huttenlocher, J., y Levine, S. C. (1994). Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle-and low-income children. Learning and Individual Differences, 6(4), 413–432. https://doi.org/10.1016/1041-6080(94)90003-5
  • Jordan, J.-A., Mulhern, G., y Wylie, J. (2009). Individual differences in trajectories of arithmetical development in typically achieving 5- to 7-year-olds. Journal of Experimental Child Psychology, 103(4), 455–468. https://doi.org/10.1016/j.jecp.2009.01.011
  • LeFevre, J.- A., Greenham, S. L., y Waheed, N. (1993). The development of procedural and conceptual knowledge in computational estimation. Cognition and Instruction, 11(2), 95–132. http://dx.doi.org/10.1207/s1532690xci1102_1
  • Lemaire, P., y Lecacheur, M. (2002). Children’s strategies in computational estimation. Journal of Experimental Child Psychology, 82(4), 281–304. https://doi.org/10.1016/S0022-0965(02)00107-8
  • Mabbott, D. J., y Bisanz, J. (2008). Computational skills, working memory, and conceptual knowledge in older children with mathematics learning disabilities. Journal of Learning Disabilities, 41(1), 15-28. https://doi.org/10.1177/0022219407311003
  • Macaruso, P., y Sokol S. M. (1998). Cognitive neuropsychology and developmental dyscalculia. En C. Donlan (Ed.), The development of mathematical skills (pp. 201- 205). Psychology Press.
  • Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., y Carraher, J. (2007). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology, 25(1), 147– 166. https://doi.org/10.1348/026151006X153127
  • Ploger, D., y Hecht, S. (2009). Enhancing children’s conceptual understanding of mathematics through Chartworld software. Journal of Research in Childhood Education, 23(3), 267–277. https://doi.org/10.1080/02568540909594660
  • Sherman, J., y Bisanz, J. (2007). Evidence for use of mathematical inversion by three- year-old children. Journal of Cognition and Development, 8(3), 333–344. https://doi.org/10.1080/15248370701446798
  • Siegler, R. S., y Booth, J. L. (2005). Development of numerical estimation: A review. En J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197–212). Psychology Press.
  • Star, J. R., Rittle-Johnson, B., Lynch, K., y Perova, N. (2009). The role of prior knowledge in the development of strategy flexibility: the case of computational estimation. Mathematics Education, 41 (5), 569-579. http://dx.doi.org/10.1007/s11858-009-0181-9
Fonte de datos: Dialnet