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

Published online by Cambridge University Press:  04 December 2017

Danilka Castro Open the ORCID record for Danilka Castro [Opens in a new window] ,
Nancy Estévez ,
David Gómez  and
Pablo Ricardo Dartnell Open the ORCID record for Pablo Ricardo Dartnell [Opens in a new window]
Danilka Castro*
Affiliation:
Centro de Investigación Avanzada en Educación (Chile)
Nancy Estévez
Affiliation:
Centro de Neurociencias de Cuba (Cuba)
David Gómez
Affiliation:
Centro de Investigación Avanzada en Educación (Chile)
Pablo Ricardo Dartnell
Affiliation:
Centro de Investigación Avanzada en Educación (Chile)
*
*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: danilka.castro@ciae.uchile.cl
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Abstract

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.

Keywords

ANSarithmeticreliabilityvalidityworking memory
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 20 , 2017 , E75
Copyright
Copyright © Universidad Complutense de Madrid and Colegio Oficial de Psicólogos de Madrid 2017 

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Footnotes

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

References

Alloway, T. P., & Passolunghi, M. C. (2011). The relationship between working memory, IQ, and mathematical skills in children. Learning and Individual Differences, 21(1), 133–137. https://doi.org/10.1016/j.lindif.2010.09.013 Google Scholar
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.Google Scholar
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), 2305–2317. https://doi.org/10.1016/j.neuropsychologia.2013.06.031 Google Scholar
Castro, D., Estévez, N., & Pérez, O. (2011). Typical development of quantity comparison in school-aged children. The Spanish Journal of Psychology, 14(1), 50–61. https://doi.org/10.5209/rev_SJOP.2011.v14.n1.4 Google Scholar
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), 952–966. https://doi.org/10.5209/rev_SJOP.2012.v15.n3.39387 Google Scholar
Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. ZDM: Mathematics Education, 47, 759–770. https://doi.org/10.1007/s11858-014-0655-2 Google Scholar
Cohen, R. J., & Swerdlik, M. (2009). Psychological testing and assessment:An introduction to tests and measurement (7 th ed.). New York, NY: McGraw-Hill.Google Scholar
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), 63–68. https://doi.org/10.1016/j.tine.2013.12.001 Google Scholar
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, 278–292. https://doi.org/10.1016/j.jecp.2010.09.003 Google Scholar
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, 508–520. https://doi.org/10.1111/j.1467-7687.2009.00897.x Google Scholar
Dehaene, S., & Changeux, J. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neurosciences, 5, 390–407. https://doi.org/10.1162/jocn.1993.5.4.390 Google Scholar
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, 64–81. https://doi.org/10.1348/2044-8279.002002 Google Scholar
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. https://doi.org/10.3389/fpsyg.2015.00295 Google Scholar
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), 136–148. https://doi.org/10.1111/desc.12013 Google Scholar
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, 50–58. https://doi.org/10.1016/j.lindif.2013.10.004 Google Scholar
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. https://doi.org/10.1371/journal.pone.0067374 Google Scholar
Gilmore, C., Attridge, N., & Inglis, M. (2011). Measuring the approximate number system. The Quarterly Journal of Experimental Psychology, 64(11), 2099–2109. https://doi.org/10.1080/17470218.2011.574710 Google Scholar
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 Google Scholar
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, 11116–11120. https://doi.org/10.1073/pnas.1200196109 Google Scholar
Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity correlate with maths achievement. Nature, 455, 665–668. https://doi.org/10.1038/nature07246 Google Scholar
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, 17–29. https://doi.org/10.1016/j.jecp.2008.04.001 Google Scholar
Inglis, M., & Gilmore, C. (2014). Indexing the approximate number system. Acta Psychologica, 145, 147–155. https://doi.org/10.1016/j.actpsy.2013.11.009 Google Scholar
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 Google Scholar
Izard, V., & Dehaene, S. (2007). Calibrating the mental number line. Cognition, 106(3), 1221–1247. https://doi.org/10.1016/j.cognition.2007.06.004 Google Scholar
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, 516–531. https://doi.org/10.1016/j.jecp.2009.03.009 Google Scholar
Landerl, K., & Kölle, C. (2009). Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology, 103(4), 546–565. https://doi.org/10.1016/j.jecp.2008.12.006 Google Scholar
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), 243–261. https://doi.org/10.1016/j.jecp.2012.10.005 Google Scholar
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. https://doi.org/10.1111/j.1467-7687.2011.01080.x Google Scholar
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, 583–591.Google Scholar
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, 154–161. https://doi.org/10.1016/j.actpsy.2010.01.006 Google Scholar
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. https://doi.org/10.1371/journal.pone.0023749 CrossRefGoogle ScholarPubMed
Milner, B. (1971). Interhemispheric differences in the localization of psychological processes in man. British Medical Bulletin , 27, 272–277. https://doi.org/10.1093/oxfordjournals.bmb.a070866 Google Scholar
Mussolin, C., Mejias, S., & Noël, M.-P. (2010). Symbolic and nonsymbolic number comparison in children with and without Dyscalculia. Cognition, 115, 10–25. https://doi.org/10.1016/j.cognition.2009.10.006 Google Scholar
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, 50–57. https://doi.org/10.1016/j.actpsy.2012.02.008 Google Scholar
Raven, J. C., Court, J., & Raven, J. (1992). Manual for Raven’s progressive matrices and vocabulary scales. Oxford, UK: Oxford Psychologists Press.Google Scholar
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. https://doi.org/10.1371/journal.pone.0079711 Google Scholar
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), 361–395. https://doi.org/10.1016/j.cognition.2006.01.005 Google Scholar
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, 73–80. https://doi.org/10.1016/j.actpsy.2010.10.004 Google Scholar
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, 418–431. https://doi.org/10.1016/j.jecp.2012.10.012 Google Scholar
Sattler, J. (1982). Assessment of children’s intelligence and special abilities. Boston, MA: Allyn & Bacon.Google Scholar
Swanson, H. L. (2011). Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children. Journal of Educational Psychology, 103(4), 821–837. https://doi.org/10.1037/a0025114 Google Scholar
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), 2674–2688. https://doi.org/10.1016/j.cortex.2013.06.007 Google Scholar
Waechter, S., Stolz, J. A., & Besner, D. (2010). Visual word recognition: On the reliability of repetition priming. Visual Cognition, 18(4), 537–558. https://doi.org/10.1080/13506280902868603 Google Scholar
Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Nonverbal counting in humans: The psychophysics of number representation. Psychological Science, 10, 130–137. https://doi.org/10.1111/1467-9280.00120 Google Scholar
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), 49–61. https://doi.org/10.1177/0022219415588851 Google Scholar