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Reliability and Validity of Nonsymbolic and Symbolic Comparison Tasks in School-Aged Children

  • Danilka Castro (a1), Nancy Estévez (a2), David Gómez (a1) and Pablo Ricardo Dartnell (a1)


Basic numerical processing has been regularly assessed using numerical nonsymbolic and symbolic comparison tasks. It has been assumed that these tasks index similar underlying processes. However, the evidence concerning the reliability and convergent validity across different versions of these tasks is inconclusive. We explored the reliability and convergent validity between two numerical comparison tasks (nonsymbolic vs. symbolic) in school-aged children. The relations between performance in both tasks and mental arithmetic were described and a developmental trajectories’ analysis was also conducted. The influence of verbal and visuospatial working memory processes and age was controlled for in the analyses. Results show significant reliability (p < .001) between Block 1 and 2 for nonsymbolic task (global adjusted RT (adjRT): r = .78, global efficiency measures (EMs): r = .74) and, for symbolic task (adjRT: r = .86, EMs: r = .86). Also, significant convergent validity between tasks (p < .001) for both adjRT (r = .71) and EMs (r = .70) were found after controlling for working memory and age. Finally, it was found the relationship between nonsymbolic and symbolic efficiencies varies across the sample’s age range. Overall, these findings suggest both tasks index the same underlying cognitive architecture and are appropriate to explore the Approximate Number System (ANS) characteristics. The evidence supports the central role of ANS in arithmetic efficiency and suggests there are differences across the age range assessed, concerning the extent to which efficiency in nonsymbolic and symbolic tasks reflects ANS acuity.


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*Correspondence concerning this article should be addressed to Danilka Castro Cañizares. Área de Investigación de Neurociencia y Cognición del Centro de Investigación Avanzada en Educación. Santiago (Chile). E-mail:


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Funding from PIA-CONICYT Basal Funds for Centers of Excellence Project FB0003 is gratefully acknowledged.

How to cite this article:

Castro, D., Estévez, N., Gómez, D., & Dartnell, P. R. (2017). Reliability and validity of nonsymbolic and symbolic comparison tasks in school-aged children. The Spanish Journal of Psychology, 20. e75. Doi:10.1017/sjp.2017.68



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Alloway, T. P., & Passolunghi, M. C. (2011). The relationship between working memory, IQ, and mathematical skills in children. Learning and Individual Differences, 21(1), 133137.
American Educational Research Association, American Psychological Association y National Council on Measurement in Education (1999). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
Ashkenazi, S., Rosenberg-Lee, M., Metcalfe, A. W. S., Swigart, A. G., & Menon, V. (2013). Visuo-spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition. Neuropsychologia, 51(11), 23052317.
Castro, D., Estévez, N., & Pérez, O. (2011). Typical development of quantity comparison in school-aged children. The Spanish Journal of Psychology, 14(1), 5061.
Castro, D., Reigosa, V., & González, E. (2012). Non-symbolic and symbolic number magnitude processing in children with developmental dyscalculia. The Spanish Journal of Psychology, 15(3), 952966.
Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. ZDM: Mathematics Education, 47, 759770.
Cohen, R. J., & Swerdlik, M. (2009). Psychological testing and assessment:An introduction to tests and measurement (7 th ed.). New York, NY: McGraw-Hill.
Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 6368.
De Smedt, B., & 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, 278292.
De Smedt, B., Taylor, J., Archibald, L., & Ansari, D. (2010). How is phonological processing related to individual differences in children´s arithmetic skills. Developmental Sciences, 13, 508520.
Dehaene, S., & Changeux, J. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neurosciences, 5, 390407.
Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology, 82, 6481.
Dietrich, J. F., Huber, S., & Nuerk, H. C. (2015). Methodological aspects to be considered when measuring the approximate number system (ANS) – a research review. Frontiers in Psychology, 6, 295.
Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: Contributions of inhibitory control. Developmental Science, 16(1), 136148.
Gilmore, C., Attridge, N., De Smedt, B., & Inglis, M. (2014). Measuring the approximate number system in children: exploring the relationships among different tasks. Learning and Individual Differences, 29, 5058.
Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., ... Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS ONE 8(6), e67374.
Gilmore, C., Attridge, N., & Inglis, M. (2011). Measuring the approximate number system. The Quarterly Journal of Experimental Psychology, 64(11), 20992109.
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), 14571465.
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, 1111611120.
Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity correlate with maths achievement. Nature, 455, 665668.
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, 1729.
Inglis, M., & Gilmore, C. (2014). Indexing the approximate number system. Acta Psychologica, 145, 147155.
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), 669680.
Izard, V., & Dehaene, S. (2007). Calibrating the mental number line. Cognition, 106(3), 12211247.
Krajewski, K., & Schneider, W. (2009). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study. Journal of Experimental Child Psychology, 103, 516531.
Landerl, K., & Kölle, C. (2009). Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology, 103(4), 546565.
LeFevre, J., Berrigan, L., Vendetti, C., Kamawar, D., Bisanz, J., Skwarchuk, S., & Smith-Chant, B. (2013). The role of executive attention in the acquisition of mathematical skills for children in grades 2 through 4. Journal of Experimental Child Psychology, 114(2), 243261.
Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14, 12921300.
Lonnemann, J., Linkersdörfer, J., Hasselhorn, M., & Lindberg, S. (2011). Symbolic and non-symbolic distance effects in children and their connection with arithmetic skills. Journal of Neurolinguistics, 24, 583591.
Maloney, E. A., Risko, E. F., Preston, F., Ansari, D., & Fugelsang, J. (2010). Challenging the reliability and validity of cognitive measures: The case of the numerical distance effect. Acta Psychologica, 134, 154161.
Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS ONE, 6, e23749.
Milner, B. (1971). Interhemispheric differences in the localization of psychological processes in man. British Medical Bulletin , 27, 272277.
Mussolin, C., Mejias, S., & Noël, M.-P. (2010). Symbolic and nonsymbolic number comparison in children with and without Dyscalculia. Cognition, 115, 1025.
Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140, 5057.
Raven, J. C., Court, J., & Raven, J. (1992). Manual for Raven’s progressive matrices and vocabulary scales. Oxford, UK: Oxford Psychologists Press.
Reigosa-Crespo, V., González-Alemañy, E., León, T., Torres, R., Mosquera, R., & Valdés-Sosa, M. (2013). Numerical capacities as domain-specific predictors beyond early mathematics learning: A longitudinal study. PLoS ONE, 8(11), e79711.
Rousselle, L., & Noël, M-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs. non-symbolic number magnitude processing. Cognition, 102(3), 361395.
Sasanguie, D., Defever, E., van den Bussche, E., & Reynvoet, B. (2011). The reliability of and the relation between non-symbolic numerical distance effects in comparison, same-different judgments and priming. Acta Psychologica, 136, 7380.
Sasanguie, D., Göbel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number–space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114, 418431.
Sattler, J. (1982). Assessment of children’s intelligence and special abilities. Boston, MA: Allyn & Bacon.
Swanson, H. L. (2011). Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children. Journal of Educational Psychology, 103(4), 821837.
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 26742688.
Waechter, S., Stolz, J. A., & Besner, D. (2010). Visual word recognition: On the reliability of repetition priming. Visual Cognition, 18(4), 537558.
Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Nonverbal counting in humans: The psychophysics of number representation. Psychological Science, 10, 130137.
Wong, T. T. Y., Ho, C. S. H., & Tang, J. (2017). Defective number sense or impaired access? Differential impairments in different subgroups of children with mathematics difficulties. Journal of learning disabilities, 50(1), 4961.


Reliability and Validity of Nonsymbolic and Symbolic Comparison Tasks in School-Aged Children

  • Danilka Castro (a1), Nancy Estévez (a2), David Gómez (a1) and Pablo Ricardo Dartnell (a1)


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