Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-06T12:12:58.654Z Has data issue: false hasContentIssue false
  • English
  • Français

Number Processing and Calculation in Brazilian Children Aged 7-12 Years

Published online by Cambridge University Press:  10 January 2013

Flávia Heloísa Dos Santos ,
Paulo Adilson Da Silva ,
Fabiana Silva Ribeiro ,
Ana Luiza Ribeiro Pereira Dias ,
Michele Cândida Frigério ,
Georges Dellatolas  and
Michael von Aster
Flávia Heloísa Dos Santos*
Affiliation:
Universidade Estadual Paulista (Brazil)
Paulo Adilson Da Silva
Affiliation:
Universidade Estadual Paulista (Brazil)
Fabiana Silva Ribeiro
Affiliation:
Universidade Estadual Paulista (Brazil)
Ana Luiza Ribeiro Pereira Dias
Affiliation:
Universidade Estadual Paulista (Brazil)
Michele Cândida Frigério
Affiliation:
Universidade Estadual Paulista (Brazil)
Georges Dellatolas
Affiliation:
Institut National de La Santé et de la Recherche Médicale (France)
Michael von Aster
Affiliation:
University of Zurich (Switzerland)
*
Correspondence concerning this article should be addressed to Flávia Heloísa Dos Santos. Universidade Estadual Paulista, UNESP/Assis. Laboratório de Neuropsicologia. Programa de Pós-Graduação em Psicologia. Departamento de Psicologia Experimental e do Trabalho. Avenida Dom Antônio 2100 - cep 19806-900, Assis - SP, (Brazil). Phone: + 55-18-33025902. Fax: + 55-18-33025804; E-mail: flaviahs@assis.unesp.br
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Numerical cognition is based on two components - number processing and calculation. Its development is influenced by biological, cognitive, educational, and cultural factors. The objectives of the present study were to: i) assess number processing and calculation in Brazilian children aged 7-12 years from public schools using the Zareki-R (Battery of neuropsychological tests for number processing and calculation in children, Revised; von Aster & Dellatolas, 2006) in order to obtain normative data for Portuguese speakers; ii) identify how environment, age, and gender influences the development of these mathematical skills; iii) investigate the construct validity of the Zareki-R by the contrast with the Arithmetic subtest of WISC-III. The sample included 172 children, both genders, divided in two groups: urban (N = 119) and rural (N = 53) assessed by the Zareki-R. Rural children presented lower scores in one aspect of number processing; children aged 7-8 years demonstrated an inferior global score than older; boys presented a superior performance in both number processing and calculation. Construct validity of Zareki-R was demonstrated by high to moderate correlations with Arithmetic subtest of WISC-III. The Zareki-R therefore is a suitable instrument to assess the development of mathematical skills, which is influenced by factors such as environment, age, and gender.

La cognición numérica se basa en dos componentes: el procesamiento numérico y el cálculo. Su desarrollo está influenciado por factores biológicos, cognitivos, educativos, y culturales. Los objetivos del presente trabajo fueron: a) evaluar el procesamiento numérico y el cálculo en niños brasileños de entre 7-12 años de escuelas públicas utilizando el Zareki-R (batería de pruebas neuropsicológicas para el procesamiento numérico y el cálculo en niños, revisada por von Aster y Dellatolas, 2006) con el fin de obtener datos normativos para los hablantes de portugués, b) determinar cómo el medio ambiente, la edad y el género influyen en el desarrollo de estas habilidades matemáticas, y c) investigar la validez de constructo del Zareki-R en contraste con el subtest de Aritmética WISC-III. La muestra incluyó a 172 niños evaluados por el Zareki-R, niños de ambos sexos, divididos en dos grupos: urbano (N = 119) y rural (N = 53). Los niños de origen rural presentaron puntuaciones más bajas en un aspecto de procesamiento numérico, los niños de 7-8 años demostraron una puntuación inferior global que los mayores; los varones presentaron un rendimiento superior tanto en el procesamiento numérico como en el cálculo. La validez del constructo del Zareki-R fue demostrada por las correlaciones de alta a moderada con el subtest de Aritmética WISC-III. El Zareki-R por lo tanto, es un instrumento adecuado para evaluar el desarrollo de habilidades matemáticas, que está influenciado por factores como el medio ambiente, la edad y el género.

Keywords

Zareki-Rmathematical skillschildrenneuropsychological assessmentarithmeticZareki-Rhabilidades matemáticasniñosevaluación neuropsicológicaaritmética
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 15 , Issue 2 , July 2012 , pp. 513 - 525
Copyright
Copyright © Cambridge University Press 2012

References

Almeida, P. M., & Wickerhauser, H., (1991). O critério ABA/ABIPEME - Em busca de uma atualização [The criterion ABA / ABIPEME - In search of an update]. São Paulo, Brazil: Associação Brasileira de Anunciantes/Associação Brasileira dos Institutos de Pesquisas de Mercado.Google Scholar
American Psychiatric Association. (2002) Diagnostic and statistical manual of mental disordes (4th Ed.). Washington, DC: American Psychiatric Association.Google Scholar
Angelini, A. L., Alves, I. C. B., Custódio, E. M., Duarte, W. F., & Duarte, J. L. M., (1999). Manual: Matrizes progressivas coloridas de Raven [Manual: Raven's colored progressive matrices]. São Paulo, Brazil: Centro Editor de Testes e Pesquisas em Psicologia.Google Scholar
Campbell, J. I. D., & Clark, J. M., (1992). Cognitive number processing: An encoding-complex perspective. In Campbell, J. I. D. (Ed.), The nature and origins of mathematical skills (pp. 457–492). Amsterdam, The Netherlands: Elsevier.CrossRefGoogle Scholar
Cantlon, J. F., Platt, M. L., & Brannon, E. M., (2009). Beyond the number domain. Trends in Cognitive Sciences, 13, 83–91. http://dx.doi.org/10.1016/j.tics.2008.11.007CrossRefGoogle ScholarPubMed
Correa, J., & Meireles, E. S., (2000). A compreensão intuitiva da criança acerca da divisão partitiva de quantidades contínuas [Children's intuitive understanding of partitive division tasks using continuous quantities]. Estudos de Psicologia, 5, 11–31. http://dx.doi.org/10.1590/S1413-294X2000000100002CrossRefGoogle Scholar
Dehaene, S., (1997). The number sense. Oxford, England: 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., & Cohen, L., (2000). Un modèle arithmétique e fonctionnel de l'arithmétique mental [An arithmetic and functional model of mental arithmetic]. In Pesenti, M. & Seron, X. (Eds.), Neuropsychologie des troubles du cálculo e du traitementdêsnúmeros (pp. 191–232). Marseille, France Solal.Google Scholar
Dellatolas, G., von Aster, M., Willardino-Braga, L., Meier, M., & Deloche, G., (2000) Number processing and mental calculation in school children aged 7 to 10 years: Transcultural comparison. European Child & Adolescent Psychiatry, 9, 102–110. http://dx.doi.org/10.1007/s007870070003CrossRefGoogle ScholarPubMed
Dellatolas, G., Deloche, G., Basso, A., & Claros-Salinas, D (2001). Assessment of calculation and number processing using the EC301 battery: Cross-cultural normative data and application to left- and right-brain damaged patients. Journal of the International Neuropsychological Society, 7, 840–859.CrossRefGoogle ScholarPubMed
Deloche, G., (1995). Batterie standardisée d'evaluation du calcul et du traitement des nombres [Standardized battery of assessment of calculation and number processing]. Salvador, Brazil: Editora Sarahletras.Google Scholar
Deloche, G., von Aster, M., Dellatolas, G., Gaillard, F., Tieche, C., & Azema, D., (1995). Traitement des nombres et calcul en CE1 et CE2 [Number processing and calculation in Grades 1 and 2]. Approche Neuropsychologique des Apprentissages chez l'Enfant (A.N.A.E.), Hors Série, 42–51.Google Scholar
Deloche, G., Dellatolas, G., Vendrell, J., & Bergego, C., (1996). Calculation and number processing: Neuropsychological assessment and daily activities. Journal of the International Neuropsychological Society, 2, 177–180. http://dx.doi.org/10.1017/S1355617700001028CrossRefGoogle Scholar
Deloche, G., Souza, L., Willadino-Braga, L., & Dellatolas, G., (1999). Acalculation and number processing battery for clinical application in illiterates and semi-literates. Cortex, 35, 503–521. http://dx.doi.org/10.1016/S0010-9452(08)70815-3CrossRefGoogle ScholarPubMed
Deloche, G., & Wilmes, K., (2000). Cognitive neuropsychological models of adult calculation and number processing: the role of the surface format numbers. European Child and Adolescent Psychiatry, 9, 27–40. http://dx.doi.org/10.1007/s007870070007CrossRefGoogle ScholarPubMed
Devilly, G. J., (2005). The effect size generator for Windows (Version 4.0) [computer programme]. Brain Sciences Institute, Swinburne University, Australia.Google Scholar
Dias, N. M., Trevisan, B. T., Menezes, A., Tortella, G., Hipólito, R., Montiel, J. M., … Seabra, A. G., (2009). Habilidade aritmética: Influências da memória de trabalho e raciocínio não verbal [Arithmetic skills: Influences of working memory and nonverbal reasoning.]. In Montiel, J. M. & Capovilla, F. C. (Org.), Atualização em transtornos de aprendizagem [Updates on learning disorders]. (pp. 325–340). São Paulo, Brazil: Artes Médicas.Google Scholar
Engel, P., Santos, F. H., & Gathercole, S. E., (2008). Are working memory measures free of socio-economic influence? Journal of Speech, Language, and Hearing Research, 51, 1580–1587. http://dx.doi.org/10.1044/1092-4388(2008/07-0210)CrossRefGoogle Scholar
Gathercole, S. E., & Alloway, T. P., (2004). Working memory and classroom learning. Professional Association for Teachers of Students with Specific Learning Difficulties, 17, 2–12.Google Scholar
Gathercole, S. E., Alloway, T. P., Willis, C., & Adams, A., (2006). Working memory in children with reading disabilities. Journal of Experimental Child Psychology, 93, 265–281. http://dx.doi.org/10.1016/j.jecp.2005.08.003CrossRefGoogle ScholarPubMed
Geary, D. C., Frensch, P. A., & Wiley, J. G., (1993). Simple and complex mental subtraction: Strategy choice and speed-of-processing differences in younger and older adults. Psychology and Aging, 8, 242–256. http://dx.doi.org/10.1037/0882-7974.8.2.242CrossRefGoogle ScholarPubMed
Geary, D. C., (1995). Reflections of evolution and culture in children's cognition: Implications for mathematical develop-ment and instruction. American Psychologist, 50, 24–37. http://dx.doi.org/10.1037/0003-066X.50.1.24CrossRefGoogle Scholar
Geary, D. C., (2000). From infancy to adulthood: The development of arithmetical abilities. European Child and Adolescent Psychiatry, 9, 11–16. http://dx.doi.org/10.1007/s007870070004CrossRefGoogle Scholar
Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
Gross-Tsur, V., Manor, O., & Shalev, R. S., (1996). Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine and Child Neurology, 38, 25–33. http://dx.doi.org/10.1111/j.1469-8749.1996.tb15029.xCrossRefGoogle ScholarPubMed
Haydu, V. B., Costa, L. P., & Pullin, E. M. M. P. (2006). Resolução de problemas aritméticos: Efeito de relações de equivalência entre três diferentes formas de apresentação dos problemas [Arithmetic problem-solving: Effect of equivalence relations between three different forms of presenting problems]. Psicologia Reflexão e Crítica, 19, 44–52. http://dx.doi.org/10.1590/S0102-79722006000100007CrossRefGoogle Scholar
Hein, J., Bzufka, M. W., & Neumärker, K. J. (2000). The specific disorder of arithmetic skills. Prevalence studies in a rural and an urban population sample and their clinico-neuropsycho-logical validation. European Child & Adolescent Psychiatry, 9, 87–101. http://dx.doi.org/10.1007/s007870070012CrossRefGoogle 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, 669–680. http://dx.doi.org/10.1111/j.1467-7687.2008.00716.xCrossRefGoogle ScholarPubMed
Koumoula, A., Tsironi, V., Stamouli, V., Bardani, I., Siapati, S., Graham, A., … von Aster, M., (2004). An epidemiological study of number processing and mental calculation in Greek schoolchildren. Journal of Learning Disabilities, 37, 377–388. http://dx.doi.org/10.1177/00222194040370050201CrossRefGoogle ScholarPubMed
Krinzinger, H., & Kaufmann, L., (2006). Rechenangst und rechenleistung [Math anxiety and arithmetic skills]. Sprache Stimme Gehor, 30, 160–164.CrossRefGoogle Scholar
Lepez, R., & Riquier, M., (1997). Test d'Acquisitions Scolaires Francais et mathematiques. CE1-CE2, CE2-CM1 [School Achievement Test: French and mathematics. CE1-CE2, CE2-CM1]. Paris, France: ECPA.Google Scholar
McCloskey, M., Caramazza, A., & Basili, A., (1985). Cognitive mechanisms in number processing and calculation: Evidence from discalculia. Brain and Cognition, 4, 171–196. http://dx.doi.org/10.1016/0278-2626(85)90069-7CrossRefGoogle Scholar
O'Hare, A. E. (1999). Dysgraphia and dyscalculia. In Whltmore, K., Hart, H., & Willems, G. (Ed.), Clinics in Developmental Medicine (Vol. 145, pp. 96–118). London, England: Mac Keith Press.Google Scholar
Oliveira, M. S., & Tourinho, E. Z., (2001). Desempenho de crianças do ensino fundamental na solução de problemas aritméticos [Performance of children of the elementary school in arithmetics problems solving]. Estudos de Psicologia, 6, 63–74. http://dx.doi.org/10.1590/S1413-294X2001000100007CrossRefGoogle Scholar
Raad, A. J., Pimentel, C. E., & Almeida, T. O., (2008). Avaliação neuropsicológica da aritmética em crianças [Neuropsycho-logical evaluation of arithmetic in children]. Psicologia em Foco, 1, 1–13.Google Scholar
Rice, M. E., & Harris, G. T., (2005). Comparing effect sizes in follow-up Studies: ROC Area, Cohen's d, and r. Law and human behavior, 29, 615–620. http://dx.doi.org/10.1007/s10979-005-6832-7CrossRefGoogle Scholar
Rosselli, M., Ardila, A., Matute, E., & Inozemtseva, O., (2009). Gender differences and cognitive correlates of mathematical skills in school-aged children. Child Neuropsychology, 15, 216–231. http://dx.doi.org/10.1080/09297040802195205CrossRefGoogle ScholarPubMed
Rotzer, S., Loenneker, T., Kucian, K., Martin, E., Klaver, P., & von Aster, M., (2009). Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia, 47, 2859–2865. http://dx.doi.org/10.1016/j.neuropsychologia.2009.06.009CrossRefGoogle ScholarPubMed
Santos, F. H., & Bueno, O. F. A., (2003). Validation of the Brazilian Children's Test of pseudoword repetition in Portuguese speakers aged 4 to 10 years. Brazilian Journal of Medical and Biological Research, 36, 1533–1547. http://dx.doi.org/10.1590/S0100-879X2003001100012CrossRefGoogle ScholarPubMed
Santos, F. H., Mello, C. B., Bueno, O. F. A., & Dellatolas, G., (2005) Cross-cultural differences for three visual memory tasks in Brazilian children. Perceptual Motor Skills, 101, 421–433. http://dx.doi.org/10.2466/pms.101.2.421-433CrossRefGoogle ScholarPubMed
Santos, F. H., Paschoalini, B., & Molina, J., (2006). Novos instrumentos para avaliação de habilidades matemáticas em crianças [New tools for assessment of mathematical skills in children]. In Sennyey, A. L., Mendonça, L. I. Z., Schlecht, B. B. G., Santos, E. F., & Macedo, E. C. (Org.), Neuro-psicologia e inclusão [Neuropsychology and inclusion] (pp. 69–80). São Paulo, Brazil: Artes Médicas.Google Scholar
Santos, F. H., & Silva, P. A. D., (2008). Avaliação da discalculia do desenvolvimento: Uma questão sobre o processamento numérico e o cálculo [Developmental dyscalculia assessment: A question of number processing and calculation]. In Senneyey, A. L., Capovilla, F. C., & Montiel, J. M. (Org.), Transtornos de aprendizagem: Da avaliação à reabilitação [Learning disorders: From assessment to rehabilitation] (pp. 125–137). São Paulo, Brazil: Artes Médicas.Google Scholar
Silva, P. A., & Santos, F. H., (2009). Prejuízos específicos em habilidades matemáticas de crianças com transtornos de aprendizagem [Specific impairments of mathematic skill in children with learning disorders]. In Montiel, J. M. & Capovilla, F. C. (Org.), Atualização em transtornos de aprendizagem [Updates on learning disorders] (pp. 57–71). São Paulo, Brazil: Artes Médicas.Google Scholar
Silva, P. A., & Santos, F. H., (2011). Discalculia do desenvol-vimento: Avaliação da representação numérica pela Zareki-R [Developmental dyscalculia: Assessment of number representation by the Zareki-R]. Psicologia: TeoriaePesquisa, 27, 169–177.Google Scholar
Shalev, R. S., (2004). Developmental dyscalculia. Journal of Child Neurology, 19, 765–771.CrossRefGoogle ScholarPubMed
Shalev, R. S., Manor, O., Amir, N., & Gross-Tsur, V., (1993). Acquisition of arithmetic in normal children: Assessment by a cognitive model of dyscalculia. Developmental Medicine & Child Neurology, 35, 593–601. http://dx.doi.org/10.1111/j.1469-8749.1993.tb11696.xCrossRefGoogle 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
StatSoft, Inc. (1995). STATISTICA for Windows [Computer program manual]. Tulsa, OK: StatSoft, Inc.Google Scholar
Stein, L. M., (1994). TDE: Teste de Desempenho Escolar: Manual para aplicação e interpretação [TDE: School Achievent Test: Manual for application and interpretation]. São Paulo, Brazil: Casa do Psicólogo.Google Scholar
Swanson, H. L., (2006). Cognitive processes that underlie mathe-matical precociousness in young children. Journal of Experimental Child Psychology, 93, 239–264. http://dx.doi.org/10.1016/j.jecp.2005.09.006CrossRefGoogle Scholar
von Aster, M., (1994). Developmental dyscalculia in children: Review of the literature and clinical validation. Acta Paedopsychiatrica, 56, 169–178.Google ScholarPubMed
von Aster, M., (2000). Developmental cognitive neuropsychology of number processing and calculation: Varieties of developmental dyscalculia. European Child and Adolescent Psychiatry, 9, 41–57. http://dx.doi.org/10.1007/s007870070008CrossRefGoogle ScholarPubMed
von Aster, M., (2001). Die neuropsychologische Testbatterie für Zahlenverarbeitung und Rechnen bei Kindern (ZAREKI). [The neuropsychological test battery for number processing and calculation in children (NUCALC)]. Frankfurt, Germany: Swets & Zeitliger.Google Scholar
von Aster, M., Deloche, G., Dellatolas, G., & Meier, M., (1997). Number processing and calculation in 2nd and 3rd grade school children: Acomparative study of French-speaking and German-speaking children. Zeitschrift fur Entwicklungspsychologie und padagogische Psychologie, 29, 151–166.Google Scholar
von Aster, M., & Dellatolas, G., (2006). Zareki-R: Batterie pour l'évaluation du traitement des nombres et du calcul chez l'enfant. Adaptation Francaise [Zareki-R: Neuropsychological Test Battery for Number Processing and Calculation in Children. French adaptation]. Paris, France: ECPA.Google Scholar
von Aster, M., & Shalev, R. S., (2007). Number development and developmental dyscalculia. Developmental Medicine & Child Neurology, 49, 868–873. http://dx.doi.org/10.1111/j.1469-8749.2007.00868.xCrossRefGoogle ScholarPubMed
von Aster, M. G., Weinhold Zulauf, M., & Horn, R., (2006). Zareki-R Neuropsychologische Testbatterie für Zahlenverarbeitung und Rechnen bei Kindern [Neuropsychological Test Battery for Number Processing and Calculation in Children]. Frankfurt A.M., Germany: Harcourt Test Services.Google Scholar
Wechsler, D., (2002). WISC-III: Escala de Inteligência Wechsler para Crianças: Manual [WISC-III: Wechsler Intelligence Scale for Children: Manual] (3rd Ed.). São Paulo, Brazil: Casa do Psicólogo.Google Scholar
Weinhold Zulauf, M., Schweiter, M., & von Aster, M. G., (2003). Das Kindergartenalter: Sensitive periode für die entwicklung numerischer fertigkeiten [The preschool year: A sensitive period for the development of numerical abilities]. Kindheit und Entwicklung, 12, 222–230. http://dx.doi.org/10.1026//0942-5403.12.4.222CrossRefGoogle Scholar
World Health Organization (2005). ICD-10.Internationalstatistical classification of diseases and related health problems. Chapter V: Mental and behavioural disorders (F81.2). Geneva, Switzerland: World Health Organization.Google Scholar