Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T20:08:44.038Z Has data issue: false hasContentIssue false
  • English
  • Français

Symbolic and Non-Symbolic Number Magnitude Processing in Children with Developmental Dyscalculia

Published online by Cambridge University Press:  10 January 2013

Danilka Castro Cañizares ,
Vivian Reigosa Crespo  and
Eduardo González Alemañy
Danilka Castro Cañizares*
Affiliation:
Centro de Neurociencias (Cuba)
Vivian Reigosa Crespo
Affiliation:
Centro de Neurociencias (Cuba)
Eduardo González Alemañy
Affiliation:
Centro de Neurociencias (Cuba)
*
Correspondence concerning this article should be addressed to Danilka Castro Cañizares. Centro de Neurociencias de Cuba. Ave 25 No. 15202 esq. 158. Cubanacán, Playa. Ciudad Habana. (Cuba). E-mail: danilkac@cneuro.edu.cu
Get access Rights & Permissions [Opens in a new window]

Abstract

The aim of this study was to evaluate if children with Developmental Dyscalculia (DD) exhibit a general deficit in magnitude representations or a specific deficit in the connection of symbolic representations with the corresponding analogous magnitudes. DD was diagnosed using a timed arithmetic task. The experimental magnitude comparison tasks were presented in non-symbolic and symbolic formats. DD and typically developing (TD) children showed similar numerical distance and size congruity effects. However, DD children performed significantly slower in the symbolic task. These results are consistent with the access deficit hypothesis, according to which DD children's deficits are caused by difficulties accessing magnitude information from numerical symbols rather than in processing numerosities per se.

El objetivo de este estudio fue evaluar si los niños con Discalculia del Desarrollo (DD) presentan un déficit general en la representación de las magnitudes o un déficit específico en la conexión de las representaciones simbólicas con sus correspondientes magnitudes análogas. La DD fue diagnosticada mediante una tarea aritmética con control del tiempo de reacción. Las tareas experimentales de comparación de magnitudes se presentaron en formato no-simbólico y simbólico. Los resultados muestran que en los discalcúlicos la representación numérica parece estar intacta, lo cual se expresa en efectos de distancia numérica y congruencia de la magnitud, similares a los que exhiben los niños con un desarrollo típico. Las diferencias respecto a este grupo se encuentran solo en la velocidad de procesamiento en las tareas simbólicas. Se concluye que los datos se ajustan a la hipótesis del déficit en el acceso, por lo que las dificultades de los niños discalcúlicos parecen producto de un trastorno en la conexión entre las representaciones simbólicas y las análogas y no en la representación numérica per se.

Keywords

size congruity effectdistance effectdyscalculiareaction timesize effectdiscalculiaefecto de distanciaefecto de congruencia de la magnitudefecto de magnitudtiempo de reacción
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 15 , Issue 3 , November 2012 , pp. 952 - 966
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ashkenazi, N., Mark-Zigdon, N., & Henik, A. (2009). Numerical distance effect in developmental dyscalculia. Cognitive Development, 24, 387–400. http://dx.doi.org/10.1016/j.cogdev.2009.09.006CrossRefGoogle Scholar
Bachot, J., Gevers, W., Fias, W., & Roeyers, H. (2005). Number sense in children with visuospatial disabilities: Orientation of the mental number line. Special Issue of Psychology Science, 47, 172–183.Google Scholar
Barnes, M. A., Wilkinson, M., Khemani, E., Boudesquie, A., Dennis, M., & Fletcher, J. M. (2006). Arithmetic processing in children with spine bifida: Calculation accuracy, strategy use, and fact retrieval fluency. Journal of Learning Disabilities, 39, 174–187. http://dx.doi.org/10.1177/00222194060390020601CrossRefGoogle Scholar
Barth, H., La Mont, K., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences, 102, 14116–14121. http://dx.doi.org/10.1073/pnas.0505512102CrossRefGoogle ScholarPubMed
Bruandet, M., Molko, N., Cohen, L., & Dehaene, S. (2004). A cognitive characterization of dyscalculia in Turner syndrome. Neuropsychologia, 42, 288–298. http://dx.doi.org/10.1016/j.neuropsychologia.2003.08.007CrossRefGoogle ScholarPubMed
Butterworth, B. (1999). The mathematical brain. London, England: Macmillan.Google Scholar
Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46, 3–18. http://dx.doi.org/10.1111/j.1469-7610.2004.00374.xCrossRefGoogle ScholarPubMed
Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14, 534–541. http://dx.doi.org/10.1016/j.tics.2010.09.007CrossRefGoogle ScholarPubMed
Butterworth, B., Graná, A., Piazza, M., Girelli, L., Price, C., & Skuse, D. (1999). Language and the origins of number skills: karyotypic differences in Turner's syndrome. Brain and Language, 69, 486–488.Google Scholar
Butterworth, B., & Reigosa-Crespo, V. (2007). Information processing deficits in dyscalculia. In Berch, D. & Mazzocco, M. (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities. Baltimore, MD: Paul H Brookes Publishing Co.Google Scholar
Carey, S. (2001). Cognitive foundations of arithmetic: Evolution and ontogenesis. Mind & Language, 16, 37–55. http://dx.doi.org/10.1111/1468-0017.00155CrossRefGoogle Scholar
Carey, S. (2004). Bootstrapping and the origin of concepts. Daedalus, 133, 59–68. http://dx.doi.org/10.1162/001152604772746701CrossRefGoogle Scholar
Castro, D., Estévez, N., & Pérez, O. (2011). Typical development of quantity comparison in school-aged children. The Spanish Journal of Psychology, 14, 50–61. http://dx.doi.org/10.5209/rev_SJOP.2011.v14.n1.4Google Scholar
Chard, D. J., Clarke, B., Baker, S. Otterstedt, J., Braun, D., & Katz, R. (2005). Using measures of number sense to screen for difficulties in mathematics: Preliminary findings. Assessment for Effective Intervention, 30(2), 3–14. http://dx.doi.org/10.1177/073724770503000202CrossRefGoogle Scholar
Dantzig, T. (1967). Number: The language of science. New York, NY: The Free Press.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. http://dx.doi.org/10.1016/j.jecp.2010.09.003CrossRefGoogle ScholarPubMed
Dehaene, S. (1997). The number sense. New York, NY: Oxford University Press.Google Scholar
Dehaene, S. (2001). Précis of the number sense. Mind and Language, 16, 16–36. http://dx.doi.org/10.1111/1468-0017.00154CrossRefGoogle Scholar
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371–396. http://dx.doi.org/10.1037/0096-3445.122.3.371CrossRefGoogle Scholar
Dehaene, S., & Marques, J. F. (2002). Cognitive neuroscience: Scalar variability in price estimation and the cognitive consequences of switching to the euro. The Quarterly Journal of Experimental Psychology, 55, 705–731. http://dx.doi.org/10.1080/02724980244000044CrossRefGoogle Scholar
Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970–974. http://dx.doi.org/10.1126/science.284.5416.970CrossRefGoogle ScholarPubMed
Desoetea, A., Ceulemansa, A., Roeyersa, H., & Huylebroeck, A. (2009). Subitizing or counting as possible screening variables for learning disabilities in mathematics education or learning? Educational Research Review, 4, 55–66. http://dx.doi.org/10.1016/j.edurev.2008.11.003CrossRefGoogle Scholar
Feigenson, L., Dehaene, S., & Spelke, E. (2004) Core systems of number. Trends in Cognitive Sciences 8, 307–314. http://dx.doi.org/10.1016/j.tics.2004.05.002CrossRefGoogle ScholarPubMed
Feigenson, L., Carey, S., & Spelke, E. (2002). Infants' discrimination of number vs. continuous extent. Cognitive Psychology, 44, 33–66. http://dx.doi.org/10.1006/cogp.2001.0760Google ScholarPubMed
Gallistel, C. R., & Gelman, R. (2005). Mathematical cognition. In Holyoak, K. & Morrison, R. (Eds.), The Cambridge handbook of thinking and reasoning (pp. 559–588). Cambridge, MA: Cambridge University Press.Google Scholar
Geary, D. C., Brown, S. C., & Samaranayake, V. A. (1991). Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. Developmental Psychology, 27, 787–797. http://dx.doi.org/10.1037//0012-1649.27.5.787CrossRefGoogle Scholar
Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77, 236–263. http://dx.doi.org/10.1006/jecp.2000.2561CrossRefGoogle ScholarPubMed
Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In Campbell, J. I. D. (Ed.), Handbook of mathematical cognition (pp. 253–268). Hove, England: Psychology Press.Google Scholar
Geary, D. C., Hoard, M. K., & Hamson, C. O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk of mathematical disability. Journal of Experimental Child Psychology, 74, 213–239. http://dx.doi.org/10.1006/jecp.1999.2515CrossRefGoogle ScholarPubMed
Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity correlate with maths achievement. Nature, 455, 665–668. http://dx.doi.org/10.1038/nature07246CrossRefGoogle ScholarPubMed
Iuculano, T., Tang, J., Hall, Ch., & Butterworth, B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science, 11, 669–680. http://dx.doi.org/10.1111/j.1467-7687.2008.00716.xCrossRefGoogle ScholarPubMed
Ivanovic, R., Forno, H., Durán, M. C., Hazbún, J., Castro, C., & Ivanovic, D. (2000). Intellectual capacity study (Raven's Coloured Progressive Matrices) in Chilean children from 5 to 18 years of age. General background, standards and recommendations. IberPsicologia, 5, 5–30.Google Scholar
Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106, 1221–1247. http://dx.doi.org/10.1016/j.cognition.2007.06.004CrossRefGoogle ScholarPubMed
Jordan, N., Hanich, L., & Kaplan, B. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74, 834–850. http://dx.doi.org/10.1111/1467-8624.00571CrossRefGoogle ScholarPubMed
Jordan, N., & Montani, T. (1997). Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities, 30, 624–634. http://dx.doi.org/10.1177/002221949703000606CrossRefGoogle ScholarPubMed
Karmiloff-Smith, A. (1998). Development itself is the key to understanding developmental disorders. Trends in Cognitive Science, 2, 389–398. http://dx.doi.org/10.1016/S1364-6613(98)01230-3CrossRefGoogle ScholarPubMed
Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2(1), 1–24. http://dx.doi.org/10.1080/135467996387525CrossRefGoogle Scholar
Kucian, K., Loenneker, T., Dietrich, T., Dosch, M., Martin, E., & von Aster, M. (2006). Impaired neural networks for approximate calculation in dyscalculic children: A functional MRI study. Behavioral and Brain Functions, 2, 31. http://dx.doi.org/10.1186/1744-9081-2-31CrossRefGoogle ScholarPubMed
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8-9-year-old students. Cognition, 93, 99–125. http://dx.doi.org/10.1016/j.cognition.2003.11.004CrossRefGoogle ScholarPubMed
Landerl, K., Fussenegger, B., Moll, K., & Willburger, E. (2009). Dyslexia and dyscalculia: Two learning disorders with different cognitive profiles. Journal of Experimental Child Psychology, 103, 309–324. http://dx.doi.org/10.1016/j.jecp.2009.03.006CrossRefGoogle ScholarPubMed
Landerl, K., & Kölle, C. (2009). Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology, 103, 546–565. http://dx.doi.org/10.1016/j.jecp.2008.12.006CrossRefGoogle ScholarPubMed
Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia, 41, 1942–1958. http://dx.doi.org/10.1016/S0028-3932(03)00123-4CrossRefGoogle ScholarPubMed
Leslie, A., Xu, F., Tremoulet, P., & Scholl, B. (1998). Indexing and the object concept: Developing ‘what’ and ‘where’ systems. Trends in Cognitive Sciences, 2, 10–18. http://dx.doi.org/10.1016/S1364-6613(97)01113-3CrossRefGoogle ScholarPubMed
Logan, G. D. (1988). Towards an instance theory of automatization. Psychological Review, 95, 492–527. http://dx.doi.org/10.1037//0033-295X.95.4.492CrossRefGoogle Scholar
Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 111, 1–22. http://dx.doi.org/10.1037/0096-3445.111.1.1CrossRefGoogle ScholarPubMed
McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetical difficulties. Journal of Experimental Child Psychology, 74, 240–260. http://dx.doi.org/10.1006/jecp.1999.2516CrossRefGoogle Scholar
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519–1520. http://dx.doi.org/10.1038/2151519a0CrossRefGoogle ScholarPubMed
Mussolin, Ch., Mejias, S., & Nöel, M-P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115, 10–25. http://dx.doi.org/10.1016/j.cognition.2009.10.006CrossRefGoogle ScholarPubMed
Nöel, M-P., Rousselle, L., & Mussolin, C. (2005). Magnitude representation in children: Its development and dysfunction.In Campbell, J. I. D. (Ed.), Handbook of mathematical cognition. New York, NY: Psychology Press.Google Scholar
Paterson, S. J. (2001) Language and number in Down syndrome: The complex developmental trajectory from infancy to adulthood. Down Syndrome. Research and Practice, 7, 79–86. http://dx.doi.org/10.3104/reports.117CrossRefGoogle ScholarPubMed
Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503. http://dx.doi.org/10.1126/science.1102085CrossRefGoogle Scholar
Raven, J. C., Court, J. H., & Raven, J. (1992). Standard progressive matrices. Oxford, England: Oxford Psychologists Press.Google Scholar
Reigosa-Crespo, V., Valdés Sosa, M., Butterworth, B., Torres, P., Santos, E., Lage, A., … Rodríguez, M. (2012). Basic numerical capacities and prevalence of developmental dyscalculia: The Havana Survey. Developmental Psychology. 48(1), 123–135. http://dx.doi.org/10.1037/a0025356CrossRefGoogle ScholarPubMed
Rousselle, L., & Nöel, M. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs. non-symbolic number magnitude processing. Cognition, 102, 361–395. http://dx.doi.org/10.1016/j.cognition.2006.01.005CrossRefGoogle ScholarPubMed
Rousselle, L., Palmers, E., Nöel, M-P. (2004). Magnitude comparison in preschoolers: What counts? Influence of perceptual variables. Journal of Experimental Child Psychology, 87, 57–84. http://dx.doi.org/10.1016/j.jecp.2003.10.005CrossRefGoogle ScholarPubMed
Rubinsten, O., & Henik, A. (2005). Automatic activation of internal magnitudes: A study of developmental dyscalculia. Neuropsychology, 19, 641–648. http://dx.doi.org/10.1037/0894-4105.19.5.641CrossRefGoogle ScholarPubMed
Rubinsten, O., & Henik, A. (2006). Double dissociation of functions in developmental dyslexia and dyscalculia. Journal of Educational Psychology, 98, 854–867. http://dx.doi.org/10.1037/0022-0663.98.4.854CrossRefGoogle Scholar
Rubinsten, O., Henik, A., Berger, A., & Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology, 81, 74–92. http://dx.doi.org/10.1006/jecp.2001.2645CrossRefGoogle ScholarPubMed
Sattler, J. M. (1982). Assessment of children's intelligence and special abilities. Boston, MA: Allyn & Bacon.Google Scholar
Schwarz, W., & Ischebeck, A. (2003). On the relative speed account of the number-size interference in comparative judgments of numerals. Journal of Experimental Psychology: Human Perception and Performance, 29, 507–522. http://dx.doi.org/10.1037/0096-1523.29.3.507Google ScholarPubMed
Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60, 973–980. http://dx.doi.org/10.2307/1131037CrossRefGoogle ScholarPubMed
Simon, T. J. (1997). Reconceptualizing the origins of number knowledge: A “non-numerical” account. Cognitive Development, 12, 349–372. http://dx.doi.org/10.1016/S0885-2014(97)90008-3CrossRefGoogle Scholar
Simon, T. J. (1999). The foundations of numerical thinking in a brain without numbers. Trends in Cognitive Sciences, 3, 363–365. http://dx.doi.org/10.1016/S1364-6613(99)01383-2CrossRefGoogle Scholar
Soltész, F., Szücs, D., Dékány, J., Márkus, A., & Csépe, V. (2007). A combined event-related potential and neuropsychological investigation of developmental dyscalculia. Neuroscience Letters, 417, 181–186. http://dx.doi.org/10.1016/j.neulet.2007.02.067CrossRefGoogle ScholarPubMed
Spelke, E. S., & Tsivkin, S. (2001). Language and number: A bilingual training study. Cognition, 78, 45–88. http://dx.doi.org/10.1016/S0010-0277(00)00108-6CrossRefGoogle ScholarPubMed
Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96, 471–491. http://dx.doi.org/10.1037/0022-0663.96.3.471CrossRefGoogle Scholar
Trick, L. M., & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerated differently. A limited-capacity preattentive stage in vision. Psychological Review, 101, 80–102. http://dx.doi.org/10.1037//0033-295X.101.1.80CrossRefGoogle ScholarPubMed
Tzelgov, J., Meyer, J., & Henik, A. (1992). Automatic and intentional processing of numerical information. Journal of Experimental Psychology: Learning, Memory and Cognition, 18, 166–179. http://dx.doi.org/10.1037//0278-7393.18.1.166Google Scholar
Udwin, O., Davies, M., & Hosylin, P. (1996) A longitudinal study of cognitive and education attainment in Williams syndrome. Developmental Medicine and Child Neurology, 38, 1020–1029. http://dx.doi.org/10.1111/j.1469-8749.1996.tb15062.xCrossRefGoogle ScholarPubMed
van der Sluis, S., de Jong, P. F., & 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. http://dx.doi.org/10.1016/j.jecp.2003.12.002CrossRefGoogle ScholarPubMed
van Loosbroek, E., Dirkx, G. S. M. A., Hulstijn, W., & Janssen, F. (2009). When the mental number line involves a delay: The writing of numbers by children of different arithmetical abilities. Journal of Experimental Child Psychology, 102, 26–39. http://dx.doi.org/10.1016/j.jecp.2008.07.003CrossRefGoogle Scholar
Wilson, A., & Dehaene, S. (2007). Number Sense and Developmental Dyscalculia. In Coch, D., Dawson, G., & Fischer, K. (Eds.), Human behavior, learning, and the developing brain: Atypical development. New York, NY: Guilford Press.Google Scholar
Wilson, K. M., & Swanson, H. L. (2001). Are mathematics disabilities due to a domain- general or a domain-specific working memory deficit? Journal of Learning Disabilities, 34, 237–248. http://dx.doi.org/10.1177/002221940103400304CrossRefGoogle ScholarPubMed
Wynn, K. (1990). Children's understanding of counting. Cognition, 36, 155–193. http://dx.doi.org/10.1016/0010-0277(90)90003-3CrossRefGoogle ScholarPubMed
Wynn, K. (1992). Children's acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251. http://dx.doi.org/10.1016/0010-0285(92)90008-PCrossRefGoogle Scholar
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, 1–11. http://dx.doi.org/10.1016/S0010-0277(99)00066-9CrossRefGoogle Scholar