Number Sense Abilities, Working Memory and RANA Longitudinal Approximation of Typical and Atypical Development in Chilean Children.

  1. Bárbara Yaneth Guzmán Ayala 1
  2. Cristina Rodríguez Rodríguez 12
  3. Felipe Sepúlveda 1
  4. Roberto A. Ferreira 1
  1. 1 Universidad Católica de la Santísima Concepción

    Universidad Católica de la Santísima Concepción

    Concepción, Chile


  2. 2 Universidad de La Laguna

    Universidad de La Laguna

    San Cristobal de La Laguna, España


Revista de psicodidáctica

ISSN: 1136-1034

Year of publication: 2019

Volume: 24

Issue: 1

Pages: 9

Type: Article

DOI: 10.1016/J.PSICOD.2018.11.002 DIALNET GOOGLE SCHOLAR lock_openOpen access editor


The present study examined the contribution of working memory and Rapid Automatized Naming (RAN) to growth trajectories in number processing, measured using Curriculum-based Measurement (CBM). Participants were two groups of first grade children; one group were at risk of developing mathematics disabilities (MLD-at-risk, n=32), and the other included typically developing (non-MLD, n=32) children. Of all the cognitive measures, backward digit span (BDS) tasks and RAN-Letter made significant contributions to differentiating group performance. RAN-Letter provided differentiation of groups, and BDS provided differentiation of the growth rates of both groups in number processing skills. These results highlight the relevance of RAN and BDS for the development of number processing skills in first grade, especially for MLD-at-risk children. BDS is therefore a very important task to be measured during the early stages of mathematics instruction, because it predicts deficits in development of number skills.

Bibliographic References

  • Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291.
  • Aragón, E. L., Navarro, J. I., Aguilar, M., y Cerda, G. (2015). Cognitive predictors of 5-year-old students’ early number sense. Revista de Psicodidáctica, 20(1), 83–97.
  • Butterworth, B., Varma, S., y Laurillard, D. (2011). Dyscalculia: From brainto education. Science, 332(6033), 1049–1053.
  • Cantlon, J. F., Libertus, M. E., Pinel, P., Dehaene, S., Brannon, E. M., y Pelphrey, K. A. (2009). The neural development of an abstract concept of number. Journal of Cognitive Neuroscience, 21(11), 2217–2229.
  • Cattell,R. B., y Cattell,A.K. S.(1989). Test de Factor “g”. Escala 1 and 2.(Seisdedos, De La Cruz, Cordero, y González, 1991). Madrid: T.E.A. Ediciones (Originally published in 1950).
  • Chu, F. W., vanMarle, K., y Geary, D. C. (2016). Predicting children’s reading and mathematics achievement from early quantitative knowledge and domain-general cognitive abilities. Frontiers in Psychology, 7, 1–14.
  • Cirino, P. T., Fuchs, L. S., Elias, J. T., Powell, S. R., y Schumacher, R. F. (2015). Cognitive and mathematical profiles for different forms of learning difficulties. Journal of Learning Disabilities, 48(2), 156–175.
  • Clarke, B., Doabler, C. T., Smolkowski, K., Baker, S. K., Fien, H., y Strand Cary, M. (2016). Examining the efficacy of a Tier 2 kindergarten mathematics intervention. Journal of Learning Disabilities, 49(2), 152–165.
  • Clarke, B., Gersten, R., Dimino, J., y Rolfhus, E. (2012). Assessing Student Proficiency in Early Number Sense (ASPENS) [Measurement instrument]. Longmont, CO: Cambium Learning Group.
  • Clarke, B., y Shinn, M. R. (2004). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review, 33(2), 234.
  • Cowan, R., y Powell, D. (2014). The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability. Journal of Educational Psychology, 106(1), 214–229.
  • Cui, J., Georgiou, G. K., Zhang, Y., Li, Y., y Shu H. (2017). Examining the relationship between rapid automatized naming and arithmetic fluency in Chinese kindergarten children. Journal of Experimental Child Psychology, 154, 146–163.
  • Cummings, K. D., y Petscher, Y. (2015). The Fluency Construct: CurriculumBased Measurement Concepts and Applications. New York: Springer.,
  • Dehaene, S. (1997). The number sense: how the mind creates mathematics. New York:: Oxford University Press.
  • Denckla, M. B., y Rudel, R. G. (1976). Rapid ‘automatized’ naming (R.A.N.): Dyslexia differentiated from other learning disabilities. Neuropsychologia, 14, 471–479.
  • De Smedt, B., y Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278–292.
  • Donker, M., Kroesbergen, E., Slot, E., van Viersen, S., y de Bree, E. (2016). Alphanumeric and non-alphanumeric Rapid Automatized Naming in children with reading and/or spelling difficulties and mathematical difficulties. Learning and Individual Differences, 47, 80–87.
  • Foegen, A., Jiban, C., y Deno, S. (2007). Progress monitoring measures in mathematics: A review of the literature. The Journal of Special Education, 41(2), 121–139.
  • Fuchs, D., y Fuchs, L. S. (2006). Introduction to response to intervention: What, why, and how valid is it? Reading Research Quarterly, 41(1), 93–99.
  • Fuchs, L. S., Fuchs, D., y Compton, D. L. (2012). The early prevention of mathematics: Its power and limitations. Journal of Learning Disabilities, 45(3), 257–269.
  • García Vidal, J., García, B., y González, D. (2013). EVAMAT - Prueba para la evaluación de la competencia matemática. Madrid: EOS.
  • Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539.
  • Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22(1), 23–27.
  • Geary, D. C., Hoard, M. K., Byrd-Craven, J., y de Soto, M. C. (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, 121–151.
  • Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., y Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343–1359.
  • Geary, D. C., Hoard, M. K., Nugent, L., y Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206–223,
  • Georgiou, G. K., Tziraki, N., Manolitsis, G., y Fella, A. (2013). Is rapid automatized naming related to reading and mathematics for the same reason(s)? A follow-up study from kindergarten to grade 1. Journal of Experimental Child Psychology, 115(3), 481–496.
  • Gersten, R., Clarke, B., Jordan, N. C., Newman-Gonchar, R., Haymond, K., y Wilkins, C. (2012). Universal screening in mathematics for the primary grades: Beginnings of a research base. Exceptional Children, 78(4), 423–445.
  • Henry, L., yMacLean,M.(2003).Relationships between workingmemory, expressive vocabulary and arithmetical reasoning in children with and without intellectual disabilities. Educational and Child Psychology, 20(3), 51–63.
  • Hernández, J. A., y Betancort M. (2016). ULLRtoolbox [consultado 10 Sep 2017]. Disponible en:
  • Hinton, V., Flores, M. M., y Shippen, M. (2014). Response to intervention and math instruction. International Journal of Education in Mathematics, Science and Technology, 1(3), 190–201. Disponible en:
  • Jiménez, J. E., y de León, S. D. C.(2017).Análisis factorial confirmatorio de Indicadores de Progreso de Aprendizaje en Matemáticas (IPAM) en escolares de primer curso de primaria. European Journal of Investigation in Health, Psychology and Education, 7(1), 31–45.
  • Jordan, N. C., y Hanich, L. B. (2000). Mathematical thinking in second-grade children with different forms of LD. Journal of Learning Disabilities, 33(6), 567–578.
  • 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.
  • Kaufmann, L., y von Aster, M. (2012). The diagnosis and management of dyscalculia. Deutsches Ärzteblatt International, 109(45), 767–777, discusión 778
  • Kolkman, M. E., Hoijtink, H. J., Kroesbergen, E. H., y Leseman, P. P. (2013). The role of executive functions in numerical magnitude skills. Learning and Individual Differences, 24, 145–151.
  • Kolkman, M. E., Kroesbergen, E. H., y Leseman, P. P. (2014). Involvement of working memory in longitudinal development of number — magnitude skills. Infant and Child Development, 23(1), 36–50,
  • Landerl, K., y Wimmer, H. (2008). Development of word reading fluency and spelling in a consistent orthography: An 8-year follow-up. Journal of Educational Psychology, 100(1), 150–161.
  • Lembke, E., y Foegen, A. (2009). Identifying early numeracy indicators for Kindergarten and first grade students. Learning Disabilities Research y Practice, 24(1), 12–20.
  • Locuniak, M. N., y Jordan, N. C. (2008). Using kindergarten number sense to predict calculation fluency in second grade. Journal of Learning Disabilities, 41(5), 451–459.
  • Mazzocco, M. M. M., y Grimm, K. J.(2013). Growth in rapid automatized naming from grades K to 8 in children with math or reading disabilities. Journal of Learning Disabilities, 46(6), 517–533.
  • Mazzocco, M. M. M., y Rasanen, P. (2013). Contributions of longitudinal studies to evolving definitions and knowledge of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 65–73.
  • Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., y Menon, V. (2010). Differential contribution of specific working memory components to mathematics achievementin 2nd and 3rd graders. Learning and Individual Differences, 20(2), 101–109.
  • Mirman, D. (2014). Growth curve analysis and visualization using R. Florida, USA: Chapman y Hall/CRC.
  • Morsanyi, K., Devine, A., Nobes, A., y Szucs, D. (2013). The link between logic, mathematics and imagination: Evidence from children with developmental dyscalculia and mathematically gifted children. Developmental Science, 16(4), 542–553,
  • Mussolin, C., Mejias, S., y Noël, M. P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1) 10-25
  • Park, J., Hebrank, A., Polk, T. A., y Park, D. C. (2012). Neural dissociation of number from letter recognition and its relationship to parietal numerical processing. Journal of Cognitive Neuroscience, 24(1), 39–50. a 00085
  • Passolunghi, M. C., y Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348–367.
  • Pauly, H., Linkersdörfer, J., Lindberg, S., Woerner, W., Hasselhorn, M., y Lonnemann, J.(2011). Domain-specific Rapid Automatized Naming deficits in children at risk for learning disabilities. Journal of Neurolinguistics, 24(5), 602–610.
  • Peng, P., Namkung, J., Barnes, M., y Sun, C. (2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108(4), 455–473,
  • Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D. . . . Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.
  • Presentación-Herrero, M. J., Mercader-Ruiz, J., Siegenthaler-Hierro, R., FernándezAndrés, I., y Miranda-Casas, A. (2015). Funcionamiento ejecutivo y motivación en ninos ˜ de educación infantil con riesgo de dificultades en el aprendizaje de las matemáticas. Revista de Neurología, 60(1), 81–85.
  • R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria [consultado 10 Sep 2017]. Disponible en:
  • Raghubar, K. P., Barnes, M. A., y Hecht, S. A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20(2), 110–122.
  • Rasmussen, C., y Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91(2), 137–157.
  • Rodríguez, C., y Jiménez, J. E. (2016). What cognitive and numerical skills best define learning disabilities in mathematics? / ¿Qué habilidades cognitivas y numéricas definen mejor las dificultades de aprendizaje en matemáticas? Estudios de Psicología, 37(1), 115–134.
  • Rodríguez, C., van den Boer, M., Jiménez, J. E., y de Jong, P. F. (2015). Developmental changes in the relations between RAN, phonological awareness, and reading in Spanish children. Scientific Studies of Reading, 19(4), 273–288.
  • Seisdedos, N., de la Cruz, M. V., Cordero, A., y González, M. (1991). Test de Aptitudes Escolares. Madrid: TEA.
  • Simmons, F. R., y Singleton, C. (2008). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia, 14(2), 77–94,
  • Tobia, V., Bonifacci, P., y Marzocchi, G. M. (2016). Concurrent and longitudinal predictors of calculation skills in preschoolers. European Journal of Psychology of Education, 31(2), 155–174.
  • Toll, S. W., y van Luit, J. E. (2013). The development of early numeracy ability in kindergartners with limited working memory skills. Learning and Individual Differences, 25, 45–54.
  • Toll, S. W. M., van der Ven, S. H. G., Kroesbergen, E. H., y van Luit, J. E. H. (2011). Executive functions aspredictors ofmathlearningdisabilities.Journal of Learning Disabilities, 44(6), 521–532.
  • Träff, U. (2013). The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children. Journal of Experimental Child Psychology, 116(2), 139–156.
  • Träff, U., Olsson, L., Östergren, R., y Skagerlund, K. (2017). Heterogeneity of developmental dyscalculia: Cases with different deficit profiles. Frontiers in Psychology, 7(2000)
  • Van den Bos, K. P., Zijlstra, B. J. H., y Spelberg, H. C. (2002). Life-span data on continuous-naming speeds of numbers, letters, colors, and pictured objects, and word-reading speed. Scientific Studies of Reading, 6, 25–49. 0601 02
  • Van der Sluis, S., de Jong, P. F., y van der Leij, A. (2004). Inhibition and shifting in children with learning deficits in arithmetic and reading. Journal of Experimental Child Psychology, 87, 239–266.
  • Wechsler, D. (2003). Wechsler Intelligence Scale for Children (4th ed. (WISC-IV)). San Antonio, TX: The Psychological Corporation.
  • Wolf, M., y Denckla, M. B. (2005). Rapid Automatized Naming and Rapid Alternating Stimulus Tests (RAN/RAS). Austin: PRO-ED.
  • Xenidou-Dervou, I., van Luit, J. E., Kroesbergen, E. H., Friso-van den Bos, I., Jonkman, L. M., van der Schoot, M., y van Lieshout, E. C. (2018). Cognitive predictors of children’s developmentin mathematics achievement:Alatent growth modeling approach. Developmental Science,, e12671