Sistema instruccional de apoyo a la enseñanza del sentido numérico

  1. Estíbaliz Aragón Mendizábal 1
  2. Manuel Aguilar Villagrán 1
  3. José Ignacio Navarro Guzmán 1
  1. 1 Universidad de Cádiz
    info

    Universidad de Cádiz

    Cádiz, España

    ROR https://ror.org/04mxxkb11

Journal:
Revista de educación

ISSN: 0034-8082

Year of publication: 2017

Issue: 375

Pages: 14-35

Type: Article

DOI: 10.4438/1988-592X-RE-2016-375-333 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista de educación

Abstract

Number sense is regarded as a strong predictor of mathematics achievement at formal school. This paper describes the improvement of early math skills using computer-assisted instruction and the effectiveness of an intervention program. An experimental design with control and experimental groups, and pre- and postintervention measurement was used. Participants were 48 preschool students (aged from 4.91 to 5.91; 21 were males and 27 were female), whose relational and numeracy skills were assessed before and after training. Differences between groups were analyzed. Participants were students from four schools (two public and two private). Schools were in middle-class neighborhood, in 100.000 inhabitants towns. Descriptive analysis, discriminant analysis and hypothesis test were calculated. Null hypothesis of equality between groups was rejected (Wilks¿ Lambda = .468; X2 = 31.46; p < .001). Therefore, the difference between the experimental and control groups was statistically significant. Also, discriminant analysis indicated that 83.3% of students were classified correctly in their group. Significant differences between control and experimental group in classifications (p < .001), correspondence (p < .001), counting structured (p < .001) and resulting (p < .001) skills, were found. Results supported the effectiveness of the intervention program, and indicated math skills that were significantly improved by training: classifications and correspondence as relational skills, and counting structured and resulting as numerical skills. Educational implications and future lines of action are discussed.

€ View funding

Funding information

Trabajo financiado con los proyectos EDU2011-22747 y PSI2015-63856-P (MINECO/FEDER), y P09- HUM7918 del PAIDI.

Funders

  • FEDER
    • EDU2011-22747
    • PSI2015-63856-P
  • MINECO Spain
    • EDU2011-22747
    • PSI2015-63856-P
  • PAIDI
    • P09- HUM7918

Bibliographic References

  • Aragón, E. L., Navarro, J. I., Aguilar, M. y Cerda, G. (2015). Cognitive predictors of 5-year-olds students’ early number. Journal of Psychodidactic, 20(1), 83-97. doi:10.1387/RevPsicodidact.11088.
  • Araújo, A., Aragón, E., Aguilar, M., Navarro, J.I. y Ruiz, G. (2014). Un estudio exploratorio para la adaptación de la versión española revisada del «Early Numeracy Test-R» para evaluar el aprendizaje matemático temprano. European Journal of Education and Psychology, 7, 83-93. doi:10.1989/ejep.v7i2.181
  • Aunio, P. y Niemvirta, M. (2010). Predicting children´s mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20, 427-435. doi: 10.1016/j.lindif.2010.06.003
  • Aunio, P., Hautamäki, J. y Van Luit, J. E. H. (2005). Mathematical thinking intervention programmes for preschool children with normal and low number sense. European Journal of Special Needs Education, 20(2), 131-146. doi:10.1080/08856250500055578
  • Ayvaci, H. S. y Devecioglu, Y. (2010). Computer-assisted instruction to teach concepts in pre-school education. Procedia Social and Behavioral Sciences, 2, 2083-2087. doi:10.1016/j.sbspro.2010.03.285
  • Baroody, A. J. y Rosu, L. (2006). Adaptive expertise with basic addition and subtraction combinations – The number sense view. Paper presented at the Meeting of the American Educational Research Association, San Francisco, CA.
  • Berch, D. B. (1998). Mathematical cognition: From numerical thinking to mathematics education. Conferencia presentada al National Institute of Child Health and Human Development. Bethesda, MD.
  • Berch, D. B. (2005) Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333–339.
  • Booth, J.L. y Siegler, R.S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016-1031. doi: 10.1111/j.1467-8624.2008.01173.x
  • Bryant, P. y Nunes, T. (2002). Children’s understanding of mathematics (pp. 412-439). In U. Goswami (Ed.). Blackwell handbook of childhood cognitive development. Sussex, UK: Blackwell.
  • Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14(12), 534-541. doi: 10.1016/j.tics.2010.09.007
  • Clements, D. H. y Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38, 136–163. doi: 10.3102/0002831207312908
  • Clements, D. H. y Sarama, J. (2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal, 45, 443–494. doi: 10.3102/00028312 07312908
  • Clements, D. H. y Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. doi: 10.1126/science.1204537
  • De Smedt, B. Verschaffel, L., y Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103, 469-479. doi: 10.1016/j.jecp.2009.01.010
  • Döst, S., Saglam, Y. y Ugur Altay, A. (2011). Use of computer algebra systems in mathematics teaching at university: a teaching experiment. H. U. Journal of Education, 40, 140-151
  • Duncan, G. J., Claessens, A., Huston, A. C., Pagani, L., Engel, M., Sexton, H., …y Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. doi:10.1037/00121649.43.6.1428
  • Fernández, C. y Ortiz, A. (2008). La evolución del pensamiento ordinal en los escolares de 3 a 6 años. Infancia y Aprendizaje, 31(1), 107-130. doi:10.1174/021037008783487066
  • Fuson, K. (1991). Children’s early counting: Saying the number word sequence, counting objects and understanding cardinality. In K. Durkin, y B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 27-40). Buckingham: Open University Press.
  • Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15. doi: 10.1177/00222194040370010201
  • Gersten, R., Jordan, N. C. y Flojo, J. R. (2005). Early identi?cation and interventions for students with mathematics dif?culties. Journal of Learning Disabilities, 38, 293–304. doi: 10.1177/00222194050380040301
  • Griffin, S. (2004). Building number sense with Number Worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173–180. doi:10.1016/j.ecresq.2004.01.012
  • Halpern, D. F., Millis, K., Graesser, A. C., Butler, H., Forsyth, C. y Cai, Z. (2012). Operation ARA: A computerized learning game that teaches critical thinking and scientific reasoning. Thinking Skills and Creativity, 7(2), 93-100. doi: 10.1116.j.tsc.2012.03.00
  • Hannula, M. M., Lepola, J. y Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal of Experimental Child Psychology, 107, 394-406. doi:10.1016/j.jecp.2010.06.004
  • Jordan, N. C., Glutting, J. y Ramineni, C. (2008). A number sense assessment tool for identifying children at risk for mathematical difficulties. In A. Dowker (Ed.), Mathematical difficulties: Psychology and intervention (pp. 45-58). San Diego, CA: Academic Press. doi:10.1016/B978-012373629-1.50005-8
  • Jordan, N. C., Kaplan, D., Locuniak, M. N. y Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research y Practice, 22(1), 36-46. doi:10.1111/j.1540-5826.2007.00229.x
  • Jordan, N. C., Kaplan, D., Ramineni, C. y Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850-867. doi:10.1037/a0014939
  • Judge, S., Puckett, K. y Cabuk, B. (2004). Digital equity: New findings from the early childhood longitudinal study. Journal of Research on Technology in Education, 36(4), 383-396.
  • Le Corre, M., Van de Walle, G., Brannon, E. M. y Carey, S. (2006). Revisiting the Competence/Performance Debate in the Acquisition of Counting as a Representation of the Positive Integers. Cognitive Psychology, 52(2), 130-169. doi:10.1016/j.cogpsych.2005.07.002
  • Lipton, J. S. y Spelke, E. S. (2005). Discrimination of large and small numerosities by human infants. Infancy, 5, 271–290. doi:10.1207/s15327078in0503_2
  • Mazzocco, M. M. M., Feigenson, L. y Halberda, J. (2011). Preschoolers’ Precision of the Approximate Number System Predicts Later School Mathematics Performance. PLoS ONE, 6(9), e23749. doi:10.1371/journal.pone.0023749
  • Navarro, J. I., Ruiz, G., Alcalde, C., Aguilar, M. y Marchena, E. (2007). Jugando con los números 2. Software educativo. Cádiz: Departamento de Psicología.
  • Passolunghi, M. C. y Lanfranchi, S. (2012). Domain-specific and domaingeneral precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. British Journal of Educational Psychology, 82, 42–63. doi:10.1111/j.2044-8279.2011.02039.x
  • Piaget, J. y Szeminska, A. (1941). Génesis del número en el niño. Buenos Aires: Guadalupe.
  • Piazza, M., Facoetti, A., Trussardi, A.N., Berletti, I., Conte, S., Lucangeli, D., Dehaene, S. y Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33-41. doi:10.1016/j.cognition.2010.03.012.
  • Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist 44(2), 69-162. doi:10.1037//0003-066X.44.2.162
  • Resnick, L. B. (1992). From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam, y R. A. Hattrup (Eds.), Analyses of arithmetic for mathematics teaching (pp. 373-429). Hillsdale, NJ: Erlbaum.
  • Sarama, J., Clements, D. H., Starkey, P., Klein, A. y Wakeley, A. (2008). Scaling up the implementation of a pre-kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1, 89– 119. doi:10.1080/19345740801941332
  • Siegler, R. S. y Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444. doi:10.1111/j.14678624.2004.00684.x
  • Siegler, R. S. y Opfer, J. E. (2003). The development of numerical estimation: evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243. doi: 10.1111/1467-9280.02438
  • Van Luit, J. E. H. y Van de Rijt, B. A. M. (2009). The Early Numeracy Test Revised. Graviant, Doetinchem: The Netherlands.
  • Van Luit, J. E. H., Van de Rijt, B.A.M., Araújo, A., Aguilar, M., Aragón, E., Ruiz… y García-Sedeño, M. (2015). TEMT-i. Test de Evaluación Matemática Temprana Informatizado. Madrid: EOS
  • Van Viersen, S., Slot, E. M., Kroesbergen, E. H., Van’t Noordende, J. E. y Leseman, P. M. (2013). The added value of eye-tracking in diagnosing dyscalculia: a case study. Frontiers in Psichology, 4(679). doi: 10.3389/fpsyg.2013.00679
  • Von Aster, M. G., y Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine and Child Neurology, 49, 868–873. doi:10.1111/j.1469-8749.2007.00868.x
  • Xenidou-Dervou, I., De Smedt, B., Van der Schoot, M. y Van Lieshout, E. C. D. M. (2013). Individual differences in kindergarten math achievement: The integrative roles of approximation skills and working memory. Learning and Individual Differences, 28, 119-129. doi: 10.1016/j.lindif.2013.09.012
Data source: Dialnet