Identificación y análisis del índice de competencia matemática a temprana edad
ISSN: 0214-9877
Year of publication: 2014
Issue Title: CONVIVIR Y CONDUCTA
Volume: 7
Issue: 1
Pages: 495-506
Type: Article
More publications in: International Journal of Developmental and Educational Psychology: INFAD. Revista de Psicología
Abstract
The theory and practice on the development and teaching of mathematical concepts in young children has been strongly influenced by this logical operations model of Piaget and Szeminska (1941). The Piagetian position points to a strong relationship between logical operations and numerical concepts and also with arithmetic operations. The Piagetian model has received various criticisms calling into question the logical model of the number, since it would provide an incomplete explanation of the numerical competences in the child. Mayer et al., (2002) point out the importance of counting in mathematical development. On the other hand, Bryant and Nunes (2002) have suggested that the basis of mathematical development is logical thinking, the teaching of the conventional numbering system and the significant and contextualized learning of mathematical contents. Another point of view that we call interactionist assumes that Piagetian operations and counting together contribute to the development of the number. With this approach, the development of the number is reformulated by the construct called early mathematical competence (CMT). A sufficient level of CMT is a requirement to be able to follow a formal mathematics education (Kroesbergen, et al., 2009), hence it is of high interest to be able to achieve a procedure for evaluating this type of competence. In this sense, the Van Luit group has developed a successful evaluation procedure through the Early Numeracy Test-R (Van Luit et al., 2009). This test evaluates 9 components in children from 4 to 7 years old: Comparison, Classification, One-to-one correspondence, Seriation, Verbal count, Structured count, Resulting count or counting result (without pointing), General knowledge of numbers and Estimation. For this work the computerized Spanish version has been used, with the aim of standardizing it. A total of 1391 students participated in this study (747 boys and 644 girls). The evaluated participants had an age range between 48 and 95 months. The test, (Alpha = 0.902) allows to establish an index of the CMT in 6 levels, taking into account the evolutionary characteristics of the participants, concentrated in 10 age groups. For each of the levels, the test places the student according to the result in a quantitative and qualitative value with respect to the reference age group. The advantage of this CMT index is that it has a considerable predictive value with respect to mathematical performance, allowing an early detection of learning difficulties.
Bibliographic References
- Aunio, P., Hautamäki, J., Heiskari, P., & Van Luit, J. E. H. (2006). The early numeracy test in finnish: Children’s norms. Scandinavian Journal of Psychology, 47, 369-378. doi:10.1111/j.1467-9450.2006.00538.x.
- Berch, D. B. (2005). Making Sense of Number Sense: Implications for Children with Mathematical Disabilities. Journal of Learning Disabilities, 4, 333-339.
- Bryant, P. & Nunes, T. (2002). Children’s understanding of mathematics. En U. Goswami (Ed.), Blackwell handbook of childhood cognitive development (pp. 412-439). Malden: Blackwell.
- Cardeñoso, J. M. & Peñas, M. (2009). Investigación en el aula de Matemáticas. Sentido Numérico (pp. 117-184). Granada: Thales.
- Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty. Journal of Educational Psychology, 97(3), 493-513. doi:10.1037/0022-0663.97.3.493
- Gersten, R., C., Jordan, N. C. &. Flojo, J. R. (2005). Early Identification and Interventions for Students with Mathematics Difficulties. Journal of Learning Disabilities, 4, 293-304
- Kroesbergen, E., Van Luit, J, Van Lieshout, E., Van Loosbroek, E. y Van De Rijt, B. (2009). Individual differences in early numeracy: The role of executive functions and subitizing. Journal of Psychoeducational Assessment, 27 (3), 226-236.
- Mayer, R. E., Tajika, H. & Stanley, C. (2002). Mathematical problem solving in Japan and the United States: A controlled comparison. Journal of Educational Psychology, 83, 69-72.
- Navarro, J. I., Aguilar, M., Alcalde, C., Marchena, E., Ruiz, G., Menacho, I., & Sedeño, M. G. (2009). Estimación del aprendizaje matemático mediante la versión española del test de evaluación matemática temprana de Utrecht. European Journal of Education and Psychology, 2, 131-143.
- Navarro, J. I., Aguilar, M., Marchena, E., Ruiz, G., Menacho, I. & Van Luit, H. (2012). Longitudinal study of low and high achievers in early mathematics. British Journal of Educational Psychology, 82, 28-41. doi:10.1111/j.2044-8279.2011.02043.x.
- Pérez-Echeverría, M. P. & Scheuer, N. (2005). Desde el sentido numérico al número con sentido. Infancia y Aprendizaje, 28, (4), 393-407.
- Piaget, J. & Szeminska, A. (1943). Génesis del número en el niño. Buenos Aires: Guadalupe.
- Van de Rijt, B. A. M., Van Luit, J. E. H. (1998). Effectiveness of the Additional Early Mathematics program for teaching children early mathematics. Instructional Science, 26, 337-358. doi:10.1023/A:1003180411209.
- Van Luit, J. E. H., & Van de Rijt, B. A. M. (2009). The Early Numeracy Test Revised. Graviant, Doetinchem: The Netherlands.
- Van Nieuwenhoven, C., Grégoire, C.J. y Noël, M.P. (2005). Test para el diagnóstico de las competencias en Matemáticas. (TEDI-MATH). Adaptación española. Madrid: TEA. Versión original: Van Nieuwenhoven, C., Grégoire, C.J. y Noël, M.P. (2001). Le TEDI-MATH. Test diagnostique des compétences de base en mathématiques. Paris: ECPA.