Estudio longitudinal sobre procesamiento de magnitudes simbólicas y no-simbólicas y su relación con la competencia matemática

  1. Estívaliz Aragón 1
  2. M. Carmen Canto-López 1
  3. Manuel Aguilar 1
  4. Inmaculada Menacho 1
  5. José I. Navarro 1
  1. 1 Universidad de Cádiz

    Universidad de Cádiz

    Cádiz, España


Revista de psicodidáctica

ISSN: 1136-1034

Year of publication: 2023

Volume: 28

Issue: 1

Pages: 44-50

Type: Article

DOI: 10.1016/J.PSICOE.2022.08.001 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista de psicodidáctica


Research on cognitive development suggests that the human being has a number sense called “Approximate Number System” (ANS). There are also different characteristics for the representation system of symbolic numbers, called “Accuracy Number System”. In this context, the aims of the study were: (a) to identify and longitudinally evaluate the development of symbolic and non-symbolic magnitude representation skills; and (b) analyze the relationships between these skills and mathematical achievement. The present longitudinal study was carried out with a sample of 31 Early Childhood Education participants, for two years, with four evaluations timing. Results suggested that at the age of 4 years, symbolic magnitude processing abilities increased quickly until they surpass non-symbolic ones. On the other hand, the comparison of symbolic magnitudes had a higher predictive value on mathematical performance at the ages evaluated. It is discussed whether these skills may be of interest as detection and assessment tools in the field of mathematics, as well as for interventions in students with mathematics learning difficulties.

Bibliographic References

  • Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.
  • Barroso, C., Ganley, C. M., McGraw, A. L., Geer, E., Hart, S. A., & Daucourt, M. (2021). A meta-analysis of the relation between math anxiety and math achievement. Psychological Bulletin, 147(2), 134–168.
  • Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency? Journal of Experimental Child Psychology, 117, 12–28.
  • Barth, H., Starr, A., & Sullivan, J. (2009). Children’s mappings of large number words to numerosities. Cognitive Development, 24(3), 248–264.
  • Braeuning, D., Hornung, C., Hoffmann, D., Lambert, K., Ugen, S., Fischbach, A., Schiltz, C., Hübner, N., Nagengast, B., & Moeller, K. (2021). Long-term relevance and interrelation of symbolic and non-symbolic abilities in mathematical–numerical development: Evidence from large-scale assessment data. Cognitive Development, 58, Article 101008.
  • Bryer, M. A., Koopman, S. E., Cantlon, J. F., Piantadosi, S. T., MacLean, E. L., Baker, J. M., Beran, M. J., Jones, S. M., Jordan, K. E., Mahamane, S., Nieder, A., Perdue, B. M., Range, F., Stevens, J. R., Tomonaga, M., Ujfalussy, D. J., & Vonk, J. (2022). The evolution of quantitative sensitivity. Philosophical Transactions of the Royal Society B, 377(1844), Article 20200529.
  • Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118, 32–44.
  • 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.
  • Dehaene, S. (2011). The number sense: How the mind creates mathematics. Oxford University Press.
  • Devlin, D., Moeller, K., & Sella, F. (2022). The structure of early numeracy: Evidence from multi-factorial models. Trends in Neuroscience and Education, 26, Article 100171.
  • 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.
  • Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2007). Symbolic arithmetic knowledge without instruction. Nature, 447, 589–591.
  • Ginsburg, H. P., & Baroody, A. J. (2003). Test of early mathematics ability. Pro-Ed.
  • Gobel, S. M., Watson, S. E., Lervag, A., & Hulme, C. (2014). Children’s arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25, 789–798.
  • Goffin, C., & Ansari, D. (2019). How are symbols and non-symbolic numerical magnitudes related? Exploring bidirectional relationships in early numeracy. Mind, Brain, and Education, 13(3), 143–156.
  • Heckman, J. J. (2011). The economics of inequality: The value of early childhood education. American Educator, 31–36.
  • Hutchison, J. E., Ansari, D., Zheng, S., De Jesus, S., & Lyons, I. M. (2020). The relation between subitizable symbolic and non-symbolic number processing over the kindergarten school year. Developmental Science, 23(2), Article e12884.
  • Hyde, D. C., Khanum, S., & Spelke, E. S. (2014). Brief non-symbolic. Approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131, 92–107.
  • Kolkman, M. E., Kroesbergen, E. H., & Leseman, P. P. M. (2013). Early numerical development and the role of non-symbolic and symbolic skills. Learning and Instruction, 25, 95–103.
  • Lau, N. T. T., Merkley, R., Tremblay, P., Zheng, S., De Jesus, S., & Ansari, D. (2021). Kindergartners’ symbolic number abilities predict non-symbolic number abilities and math achievement in grade 1. Developmental Psychology, 57, 471–488.
  • Li, Y., Zhang, M., Chen, Y., Deng, Z., Zhu, X., & Yan, S. (2018). Children’s non-symbolic and symbolic numerical representations and their associations with mathematical ability. Frontiers in Psychology, 9, 1035.
  • Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the Approximate Number System correlates with school math ability. Developmental Science, 14, 1292–1300.
  • Lyons, I. M., Ansari, D., & Beilock, S. L. (2012). Symbolic estrangement: Evidence against a strong association between numerical symbols and the quantities they represent. Journal of Experimental Psychology: General, 141(4), 635.
  • Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., & Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714–726.
  • Malone, S. A., Pritchard, V. E., & Hulme, C. (2021). Separable effects of the approximate number system, symbolic number knowledge, and number ordering ability on early arithmetic development. Journal of Experimental Child Psychology, 208, Article 105120.
  • Matejko, A. A., & Ansari, D. (2016). Trajectories of symbolic and nonsymbolic magnitude processing in the first year of formal schooling. PLoS One, 11(3), Article e0149863.
  • Mussolin, C., Nys, J., Content, A., & Leybaer, J. (2014). Symbolic number abilities predict later approximate number acuity in preschool children. PLoS One, 9(3), Article e91839.
  • Nosworthy, N., Bugden, S., Archibald, L., Evans, B., & Ansari, D. (2013). A two-minute paper-and-pencil test of symbolic and nonsymbolic numerical magnitude processing explains variability in primary school children’s arithmetic competence. PLoS One, 8(7), Article e67918.
  • Odic, D., & Starr, A. (2018). An introduction to the approximate number system. Child Development Perspective, 12(4), 223–229.
  • Praet, M., & Desoete, A. (2014). Number line estimation from kindergarten to grade 2: A longitudinal study. Learning and Instruction, 33, 19–28.
  • Sasanguie, D., Defever, E., Maertens, B., & Reynvoet, B. (2014). The approximate number system is not predictive for symbolic number processing in kinder-garteners. The Quarterly Journal of Experimental Psychology, 67(2), 271–280.
  • Scalise, N. R., & Ramani, G. B. (2021). Symbolic magnitude understanding predicts preschoolers’ later addition skills. Journal of Cognition and Development, 22(2), 185–202.
  • Schneider, M., Beeres, K., Coban, L., Merz, S., Susan-Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A metaanalysis. Developmental Science, 20(3), Article e12372.
  • Toll, S. W., VanViersen, S., Kroesberge, E. H., & Van Van Luit, J. E. H. (2015). The development of (non-)symbolic comparison skills throughout kindergarten and their relations with basic mathematical skills. Learning and Individual Differences, 38, 10–17.
  • Van Marle, K., Chu, F. W., Li, Y., & Geary, D. C. (2014). Acuity of the approximate number system and preschoolers’ quantitative development. Developmental Science, 17, 492–505.
  • Wang, J., Halberda, J., & Feigenson, L. (2021). Emergence of the link between the approximate number system and symbolic math ability. Child Development, 92(2), e186–e200.
  • Wong, B., Bull, R., Ansari, D., Watson, D. M., & Liem, G. A. D. (2022). Order processing of number symbols is influenced by direction, but not format. Quarterly Journal of Experimental Psychology, 75(1), 98–117.
  • Xenidou-Dervou, I., Gilmore, C., Van der Schoot, M., & Van Lieshout, E. C. D. (2015). The developmental onset of symbolic approximation: Beyond nonsymbolic representations. The language of numbers matters. Frontiers in Psychology, 6, 487.
  • Xenidou-Dervou, I., Molenaar, D., Ansari, D., Van der Schoot, M., & Van Lieshout, E. C. D. (2017). Nonsymbolic and symbolic magnitude comparison skills as a longitudinal predictors of mathematical achievement. Learning and Instruction, 50, 1–13.