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Typical Development of Quantity Comparison in School-Aged Children

Published online by Cambridge University Press:  10 January 2013

Danilka Castro Cañizares ,
Nancy Estévez Pérez  and
Otmara Pérez Marrero
Danilka Castro Cañizares*
Affiliation:
Centro de Neurociencias de Cuba (Cuba)
Nancy Estévez Pérez
Affiliation:
Centro de Neurociencias de Cuba (Cuba)
Otmara Pérez Marrero
Affiliation:
Universidad de la Habana (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: [email protected]
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Abstract

Although basic numerical skills have been widely studied in the last years, very few studies have undertaken a developmental approach. The present study evaluated the development of the magnitude comparison basic numerical ability, in children from first, third and sixth grades by means of the subject's response time in numerical tasks presented in symbolic and non-symbolic formats. The results showed a significant decrease on quantities processing speed as age increases, which suggests numerical skills tend to become automatic with instruction. The differences found, concerning the general achievement pattern in each school year, might express the maturational specificities of the numerical representation system through development.

Aunque las capacidades numéricas básicas han sido ampliamente investigadas en los últimos años, muy pocos estudios han tenido en cuenta una perspectiva del desarrollo de las mismas. En este estudio se evaluó el desarrollo de la capacidad numérica básica de comparación de cantidades en escolares de primero, tercero y sexto grados, a través del análisis del tiempo de reacción de los sujetos en tareas numéricas presentadas en formatos simbólico y no simbólico. Los resultados mostraron una disminución significativa en la velocidad de procesamiento de las cantidades con el incremento de la edad, lo cual apunta a una automatización de las habilidades numéricas con el aumento del nivel escolar. Las diferencias encontradas en el patrón de rendimiento general en cada grado escolar podrían expresar las particularidades de la maduración del sistema de representación numérica en las diferentes etapas del desarrollo.

Keywords

developmentdistance effectmagnitude comparisonpresentation formatcomparación de magnitudesdesarrolloefecto de distanciaformato de presentación
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 14 , Issue 1 , May 2011 , pp. 50 - 61
Copyright
Copyright © Cambridge University Press 2011

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References

Álvarez, A., & del Río, P. (1990). Educación y desarrollo: la teoría de Vigostky y la zona de desarrollo próximo [Education and Development: Vigostky's theory and the zone of proximal development]. In Coll, C., Palacios, J., & Marchesi, A. (comps.), Desarrollo Psicológico y educación [Psychological development and education II] (Vol II, pp. 93–119). Madrid: Alianza.Google Scholar
Ansari, D., Dhital, B., & Siong, S. Ch. (2006). Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes. Brain Research, 1067, 181–188. doi:10.1016/j.brainres.2005.10.083CrossRefGoogle ScholarPubMed
Ansari, D., Fugelsang, J., Dhital, B., & Venkatraman, V. (2006). Dissociating response conflict from numerical magnitude processing in the brain: an event-related fMRI study. NeuroImage, 32(2), 799–805. doi:10.1016/j.neuroimage.2006.04.184CrossRefGoogle Scholar
Antell, S. E., & Keating, D P. (1983). Perception numerical invariance in neonates. Child Development, 54, 695–701.doi:10.1111/j.1467-8624.1983.tb00495.xCrossRefGoogle ScholarPubMed
Banks, W. P., Fujii, M., & Kayra-Stuart, F. (1976). Semantic congruity effects in comparative judgments of magnitudes of digits. Journal of Experimental Psychology: Human Perception and Performance, 2, 435–447. doi:10.1037/0096-1523.2.3.435Google Scholar
Barth, H., Kanwisher, N., & Spelke, E. (2003). The construction of large number representations in adults. Cognition, 86, 201–221. doi:10.1016/S0010-0277(02)00178-6CrossRefGoogle ScholarPubMed
Barth, H., La Mont, K., Lipton, J., Dehaene, S., Kanwisher, N., & Spelke, E. S. (2006). Non symbolic arithmetic in adults and young children. Cognition, 98, 199–222. doi:10.1016/j.cognition.2004.09.011CrossRefGoogle ScholarPubMed
Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016–1031. doi:10.1111/j.1467-8624.2008.01173.xCrossRefGoogle ScholarPubMed
Brannon, E. M. (2006). The representation of numerical magnitude. Current Opinion in Neurobiology, 16, 222–229. doi:10.1016/j.conb.2006.03.002CrossRefGoogle ScholarPubMed
Buckley, P. B., & Gilman, C. B. (1974). Comparison of digits and dot patterns. Journal of Experimental Psychology, 103, 1131–. doi:10.1037/h0037361CrossRefGoogle ScholarPubMed
Butterworth, B. (1999). The mathematical brain. London: Macmillan.Google Scholar
Cordes, S., Gelman, R., Gallistel, C. R., & Whalen, J. (2001). Variability signatures distinguish verbal from nonverbal counting for both large and small numbers. Psychological Bulletin, 8(4), 698–707. doi:10.3758/BF03196206CrossRefGoogle ScholarPubMed
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42. doi:10.1016/0010-0277(92)90049-NCrossRefGoogle ScholarPubMed
Dehaene, S. (1996). The organization of brain activations in number comparison: Event-related potentials and the additivefactors methods. Journal of Cognitive Neuroscience, 8, 47–68. doi:10.1162/jocn.1996.8.1.47CrossRefGoogle Scholar
Dehaene, S. (1997). The number sense. New York, NY: Oxford University Press.Google Scholar
Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21, 355–361. doi:10.1016/S0166-2236(98)01263-6CrossRefGoogle ScholarPubMed
Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16, 626–641. doi:10.1037//0096-1523.16.3.626Google ScholarPubMed
Duncan, E. M., & McFarland, C. E. (1980). Isolating the effects of symbolic distance and semantic congruity in comparative judgments: An additive-factors analysis. Memory & Cognition, 8, 612–622. doi:10.3758/BF03213781CrossRefGoogle ScholarPubMed
Estévez, N. (2005). Developmental Dyscalculia. A neuropsychological and morphometric study. (Unpublished master's thesis). Universidad de la Habana, La Habana, Cuba.Google Scholar
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345–362. doi:10.1037//0033-2909.114.2.345CrossRefGoogle ScholarPubMed
Geary, D. C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.CrossRefGoogle 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. doi:10.1037//0012-1649.27.5.787CrossRefGoogle Scholar
Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76, 104–122. doi:10.1006/jecp.2000.2564CrossRefGoogle ScholarPubMed
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. doi:10.1037/a0012682CrossRefGoogle ScholarPubMed
Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in nonverbal number acuity correlate with maths achievement. Nature, 455, 665–668. doi:10.1038/nature07246CrossRefGoogle ScholarPubMed
Hasher, L., & Zacks, R. T. (1979). Automatic and effortful processes in memory. Journal of Experimental Psychology: General, 108, 356–388. doi:10.1037//0096-3445.108.3.356CrossRefGoogle Scholar
Holloway, I., & Ansari, D. (2008). Domain-specific and domain-general changes in children's development of number comparison. Developmental Science, 11, 644–649. doi:10.1111/j.1467-7687.2008.00712.xCrossRefGoogle ScholarPubMed
Holloway, I., & 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. doi:10.1016/j.jecp.2008.04.001CrossRefGoogle ScholarPubMed
Huntley-Fenner, G., & Cannon, E. (2000). Preschoolers' magnitude comparisons are mediated by a preverbal analog mechanism. Psychological Science, 11, 147–152. doi:10.1111/1467-9280.00230CrossRefGoogle ScholarPubMed
Ivanovic, R., Forno, H., Durán, M. C., Hazbún, J., Castro, C., & Ivanovic, D. (2000). Estudio de la capacidad intelectual (test de matrices progresivas de Raven) en escolares chilenos de 5 a 18 años. Antecedentes generales, normas y Recomendaciones [Intellectual capacity study (Raven's Coloured Progressive Matrices) in chilean children from 5 to 18 years of age. General background, standards and recommendations]. IberPsicologia, 53(1), 5–30.Google Scholar
Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221–1247. doi:10.1016/j.cognition.2007.06.004CrossRefGoogle ScholarPubMed
Johnson, D. M. (1939). Confidence and speed in the two-category judgment. Archives of Psychology, 34, 1–53.Google Scholar
Kaufmann, L., Handl, P., & Thoeny, B. (2003). Evaluation of a numeracy intervention program focusing on basic numerical knowledge and conceptual knowledge. A pilot study. Journal of Learning Disabilities, 36, 564–573. doi:10.1177/00222194030360060701CrossRefGoogle ScholarPubMed
Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2(1), 1–23. doi:10.1080/135467996387525CrossRefGoogle Scholar
Lander, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8–9-year-old students. Cognition, 93, 99–125. doi:10.1016/j.cognition.2003.11.004CrossRefGoogle Scholar
Landerl, K., Fussenegger, B., Moll, K., & Willburger, E. (2008). Dyslexia and dyscalculia: Two learning disorders with different cognitive profiles. Unpublished manuscript, University of Tübingen, Tübingen, Germany.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.doi:10.1016/j.jecp.2008.12.006CrossRefGoogle ScholarPubMed
Lipton, J. S., & Spelke, E. S. (2005). Preschool children's mapping of number words to nonsymbolic numerosities. Child Development, 76, 978–988. doi:10.1111/j.1467-8624.2005.00891.xCrossRefGoogle ScholarPubMed
Logan, G. D. (1988). Towards an instance theory of automatization. Psychological Review, 95, 492–527. doi:10.1037/0033-295X.95.4.492CrossRefGoogle Scholar
Luculano, T., Tang, J., Hall, Ch., & Butterworth, B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science, 11(5), 669–680. doi:10.1111/j.1467-7687.2008.00716.xCrossRefGoogle Scholar
McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetical difficulties. Journal of Experimental Child Psychology, 74, 240–260. doi:10.1006/jecp.1999.2516CrossRefGoogle Scholar
Mix., K. S., Huttenlocher, J., & Levine, S. C. (2002). Multiple cues for quantification in infancy: Is number one of them?. Psychological Bulletin, 128, 278–294. doi:10.1037//0033-2909.128.2.278CrossRefGoogle ScholarPubMed
Mover, R. S. (1973). Comparing objects in memory: Evidence suggesting an internal psychophysics. Perception & Psychophysics, 13, 180–184.Google Scholar
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519–1520. doi:10.1038/2151519a0CrossRefGoogle ScholarPubMed
Noël, M.-P., Rousselle, L., & Mussolin, C. (2005). Magnitude representation in children: Its development and dysfunction. In Campbell, J. (Ed.), Handbook of mathematical cognition (pp. 179–195). New York, NY: Psychology Press.Google Scholar
Passolunghi, M. Ch., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88, 348–367. doi:10.1016/j.jecp.2004.04.002CrossRefGoogle ScholarPubMed
Pérez, O. (2009). Basic numerical processing in Cuban schoolers: Quantity comparison development. (Unpublished B.Sc. thesis). Universidad de la Habana, La Habana, Cuba.Google Scholar
Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503. doi:10.1126/science.1102085CrossRefGoogle Scholar
Pinel, P., Dehaene, S., Riviere, D., & LeBihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage, 14(5), 1013–1026. doi:10.1006/nimg.2001.0913CrossRefGoogle Scholar
Pinel, P., Piazza, M., LeBihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number size and luminance during comparative judgments. Neuron, 41(6), 983–993. doi:10.1016/S0896-6273(04)00107-2CrossRefGoogle ScholarPubMed
Raven, J. C., Court, J. H., & Raven, J. (1992). Standard progressive matrices. Oxford, UK: Oxford Psychologists Press.Google Scholar
Rico, P., Santos, E. M., & Martin-Viana, V. (2004). Proceso de enseñanza– aprendizaje desarrollador en la escuela primaria. Teoría y práctica [Potentiation of learning processes through formal instruction in primary school. Theory and Practice]. La Habana: Pueblo y educación.Google Scholar
Rousselle, L., & Noël, M. (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. doi:10.1016/j.cognition.2006.01.005CrossRefGoogle ScholarPubMed
Rousselle, L., Palmers, E., & Noël, M. (2004). Magnitude comparison in preschoolers: What counts? Influence of perceptual variables. Journal of Experimental Child Psychology, 87, 57–84. doi:10.1016/j.jecp.2003.10.005CrossRefGoogle ScholarPubMed
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(1), 74–92. doi:10.1006/jecp.2001.2645CrossRefGoogle ScholarPubMed
Sattler, J. M. (1982). Assessment of children's intelligence and special abilities. Boston, MA: Allyn & Bacon.Google Scholar
Sekuler, R., & Mierkiewicz, D. (1977). Children's judgments of numerical equality. Child Development, 48, 630–633. doi:10.2307/1128664CrossRefGoogle Scholar
Strauss, M. S., & Curtis, L. E. (1981). Infant perception of numerosity. Child Development, 52, 1146–1152. doi:10.1111/j.1467-8624.1981.tb03160.xCrossRefGoogle ScholarPubMed
Temple, E., & Posner, M. I. (1998). Brain mechanisms of quantity are similar in 5-year-olds and adults. Proceedings of the National Academy of Sciences of the USA, 95, 7836–7841. doi:10.1073/pnas.95.13.7836CrossRefGoogle Scholar
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. doi:10.1037//0278-7393.18.1.166Google Scholar
Vigotsky, S. L. (1987). Historia del Desarrollo de las Funciones Psíquicas Superiores [History of the Higher Psychological Functions Development]. La Habana: Científico Técnica.Google Scholar
Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483–488. doi:10.1016/j.tics.2003.09.002CrossRefGoogle ScholarPubMed
Whalen, J., Gallistel, C. R., & Gelman, R. (1999). Nonverbal counting in humans: the psychophysics of number representation. Psychological Science, 10, 130–137. doi:10.1111/1467-9280.00120CrossRefGoogle 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