Keywords
numerical cognition
computational fluency
Weber's fraction
ANS
primary education
computational fluency
Weber's fraction
ANS
primary education
How to Cite
Cognitive Components of the Numerical Approximation System and Computational Fluency in Primary School Children. (2019). Universitas Psychologica, 18(3), 1-14. https://doi.org/10.11144/Javeriana.upsy18-3.ccsa
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Abstract
The relationship between the two cognitive systems that contribute to quantity processing (the Approximate Number System -ANS - and the Symbolic Number System -SNS-) and their influence on mathematical performance and learning difficulties has been investigated in recent years. This study investigates the relationship between SAN accuracy and mathematical performance in a symbolic calculus fluency test in second and third cycle primary school students (3rd to 6th grades). A total of 229 students were assessed with a SAN accuracy test, consisting of a non-symbolic comparison of quantities and a computational fluency test. The descriptive results are within what is expected with respect to the evolutionary character of the estimation and calculation fluidity variables. The correlational analysis showed that there is a low correlation between calculation fluidity and comparison of magnitudes in third (p < 0.05) that disappeared in subsequent courses (p > 0.05).
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Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457-1465. https://doi.org/10.1037/a0012682
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Brannon, E. M., Jordan, K. E., & Jones, S. M. (2010). Behavioral signatures of numerical discrimination. En M. L. Platt & A. A. Ghazanfar (Eds.), Primate neuroethology (pp. 144-159). Oxford, UK: Oxford. Oxford University Press.
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Castronovo, J., & Göbel, S. M. (2012). Impact of high mathematics education on the number sense. PLoS ONE, 7(4), e33832. https://doi.org/10.1371/journal.pone.0033832
Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163-172. https://doi.org/10.1016/j.actpsy.2014.01.016
Cordes, S., Gallistel, C. R., Gelman, R., & Latham, P. (2007). Nonverbal arithmetic in humans: Light from noise. Attention, Perception, & Psychophysics, 69(7), 1185-1203. https://doi.org/10.3758/BF03193955
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De Smedt, B., Verschaffel, L., & Ghesquiere, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103, 469-479. https://doi.org/10.1016/j.jecp.2009.01.010
DeWind, N. K., & Brannon, E. M. (2012). Malleability of the approximate number system: Effects of feedback and training. Frontiers in Human Neuroscience, 6. https://doi.org/10.3389/fnhum.2012.00068
Dehaene, S. (2003). The neural basis for the Weber-Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7(4), 145-147. https://doi.org/10.1016/s1364-6613(03)00055-x
Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2010). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study: Mathematical learning disabilities in kindergarten. British Journal of
Educational Psychology, 82(1), 64-81. https://doi.org/10.1348/2044-8279.002002
Diamantopoulou, S., Pina, V., Valero-García, A. V., González-Salinas, C., & Fuentes, L. J. (2012). Validation of the Spanish version of the Woodcock Johnson mathematics achievement tests for children aged six to thirteen. Journal of Psychoeducational Assessment, 30, 466-477. https://doi.org/10.1177/0734282912437531
Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53-72. https://doi.org/10.1016/j.jecp.2014.01.013
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314. https://doi.org/10.1016/j.tics.2004.05.002
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4–15. https://doi.org/10.1177/00222194040370010201
Fonseca-Estupiñan, G. P., Rodríguez-Barreto, L. C., & Parra-Pulido, J. H. (2016). Relación entre funciones ejecutivas y rendimiento académico por asignaturas en escolares de 6 a 12 años. Revista hacia la Promoción de la Salud, 21(2). https://doi.org/10.17151/hpsal.2016.21.2.4
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Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115(3), 394-406. https://doi.org/10.1016/j.cognition.2010.02.002
Ginsburg, H., Baroody, A. J., del Río, M. C. N., & Guerra, I. L. (2007). Tema-3: test de competencia matemática básica. Madrid: Tea.
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457-1465. https://doi.org/10.1037/a0012682
Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences, 109(28), 11116-11120. https://doi.org/10.1073/pnas.1200196109
Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665-668. https://doi.org/10.1038/nature07246
Halberda, J., & Odic, D. (2014). The precision and internal confidence of our approximate number thoughts. En D. C. Geary, D. Berch & K. Koepke (Eds.), Evolutionary origins and early development of number processing (pp. 305-333). Londres: Academic Press.
Halberda, J., Sires, S. F., & Feigenson, L. (2006). Multiple spatially overlapping sets can be enumerated in parallel. Psychological Science, 17(7), 572-576. https://doi.org/10.1111/j.1467-9280.2006.01746.x
Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17-29. https://doi.org/10.1016/j.jecp.2008.04.001
Hyde, C., & Spelke, E S. (2009). All numbers are not equal: An electrophysiological investigation of small and large number representations. Journal Cognitive Neuroscience, 21(6), 1039-1053. https://doi.org/10.1162/jocn.2009.21090
Iglesias-Sarmiento, V., & Deaño, M. (2011). Cognitive processing and mathematical achievement: A study with schoolchildren between fourth and sixth grade of primary education. Journal of Learning Disabilities, 44(6), 570-583. https://doi.org/10.1177/0022219411400749
Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychonomic Bulletin & Review, 18(6), 1222-1229. https://doi.org/10.3758/ s13423-011-0154-1
Iuculano, T., Tang, J., Hall, C. W. B., & Butterworth, B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science, 11(5), 669-680. https://doi.org/10.1111/j.1467-7687.2008.00716.x
Libertus, M. E., & Brannon, E. M. (2009). Behavioral and neural basis of number sense in infancy: Number sense in infancy. Current Directions in Psychological Science, 18(6), 346-351. https://doi.org/10.1111/j.1467-8721.2009.01665.x
Libertus, M. E., & Brannon, E. M. (2010). Stable individual differences in number discrimination in infancy: Number discrimination in infants. Developmental Science, 13(6), 900-906. https://doi.org/10.1111/j.1467-7687.2009.00948.x
Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the Approximate Number System correlates with school math ability. Developmental Science, 14(6), 1292-1300. https://doi.org/10.1111/j.1467-7687.2011.01080.x
Libertus, M. E., Pruitt, L. B., Woldorff, M. G., & Brannon, E. M. (2009). Induced alpha-band oscillations reflect ratio-dependent number discrimination in the infant brain. Journal of Cognitive Neuroscience, 21(12), 2398-2406. https://doi.org/10.1162/jocn.2008.21162
Libertus, M. E., Woldorff, M. G., & Brannon, E. M. (2007). Electrophysiological evidence for notation independence in numerical processing. Behavioral and Brain Functions, 3(1), 1. https://doi.org/10.1186/1744-9081-3-1
Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense. Large-number discrimination in human infants. Psychological Science, 14(5), 396-401. https://doi.org/10.1111/1467-9280.01453
Lourenco, S. F., & Bonny, J. W. (2017). Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children. Developmental Science, 20, e12418. https://doi.org/10.1111/desc.12418
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