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

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

ISSN: 0214-9877

Year of publication: 2021

Issue Title: LEARNING IN A POSITIVE MOOD: THE RESPONSE TO COVID-19

Volume: 2

Issue: 2

Pages: 163-172

Type: Article

DOI: 10.17060/IJODAEP.2021.N2.V2.2221 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

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

Sustainable development goals

Abstract

This study analyzed the arithmetic conceptual comprehension from a dual perspective (conceptual and strategic) of students in 4th, 5th and 6th grades of Elementary school, selected based on three achievement groups: mathematical learning disabilities (MLD; n=51), typical achievement (TA; n=60) and high achievement (HA; n=21). Specifically, it aimed to (1) characterize students based on their arithmetic conceptual knowledge and (2) analyze how the different achievement groups cope with more complex tasks based on their previous conceptual skills. The BANEVHAR battery was applied to assess conceptual understanding and the full scale of the CAS battery was used as a reliable estimator of intelligence. The results pointed out the conceptual deficits of students with MLD with respect to their peers with TA and HA, who seem to reach these educational levels with acquired conceptual skills. In addition, it was observed that there are differences between the groups not only in conceptual knowledge but also in the strategic coping of tasks when these are novel or complex. In this context, students with HA can solve tasks more efficiently. These findings highlight the importance of conceptual and strategic teaching of arithmetic and suggest its practical implementation at school.

Bibliographic References

  • 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