Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T05:35:44.436Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  10 January 2013

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: [email protected]

Abstract

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.

Type
Research Article
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

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. 457492). 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, 8391. 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, 1131. 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, 1636. 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. 191232). 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, 102110. 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, 840859.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, 4251.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, 177180. 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, 503521. 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, 2740. 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. 325340). 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, 15801587. 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, 212.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, 265281. 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, 242256. 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, 2437. 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, 1116. 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, 2533. 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, 4452. 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, 87101. 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, 669680. 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, 377388. 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, 160164.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, 171196. 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. 96118). 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, 6374. 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, 113.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, 615620. 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, 216231. 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, 28592865. 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, 15331547. 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, 421433. 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. 6980). 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. 125137). 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. 5771). 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, 169177.Google Scholar
Shalev, R. S., (2004). Developmental dyscalculia. Journal of Child Neurology, 19, 765771.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, 593601. 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, 973980. 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, 239264. 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, 169178.Google ScholarPubMed
von Aster, M., (2000). Developmental cognitive neuropsychology of number processing and calculation: Varieties of developmental dyscalculia. European Child and Adolescent Psychiatry, 9, 4157. 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, 151166.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, 868873. 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, 222230. 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