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Ecuadorian Kindergartners’ Spontaneous Focusing on Numerosity Development: Contribution of Numerical Abilities and Quality of Mathematics Education

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Contemporary Research and Perspectives on Early Childhood Mathematics Education

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

Young children’s spontaneous focusing on numerosity (SFON) predicts their later mathematical competencies. In this study we investigated the development of SFON in Ecuadorian kindergartners as well as the contribution of early numerical abilities and the quality of mathematics education to this development. The participants were 100 kindergartners drawn from 10 classrooms. Children received two SFON tasks, one at the beginning and one at the end of the school year, and an early numerical abilities achievement test at the beginning of the school year. The quality of mathematics education was assessed twice via the COEMET instrument. Results demonstrated limited SFON development during the kindergarten year, with large individual differences in and highly consistent SFON performances. Additionally, children’s SFON development during the kindergarten year was predicted by their SFON tendency and early numerical abilities at the start of the year. The quality of mathematics education did not contribute to children’s SFON development. The scientific and practical implications of these results are discussed.

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References

  • Andrews, P., & Sayers, J. (2015). Identifying opportunities for grade one children to acquire foundational number sense: Developing a framework for cross cultural classroom analyses. Early Childhood Education Journal, 43, 257–267.

    Article  Google Scholar 

  • Aunio, P., & Niemivirta, M. (2010). Predicting children’s mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20(5), 427–435.

    Article  Google Scholar 

  • Bojorque, G., Torbeyns, J., Hannula-Sormunen, M., Van Nijlen, D., & Verschaffel, L. (2016). Development of SFON in Ecuadorian kindergartners. European Journal of Psychology of Education, 1–14.

    Google Scholar 

  • Bojorque, G., Torbeyns, J., Moscoso, J., Van Nijlen, D., & Verschaffel, L. (2015). Early number and arithmetic performance of Ecuadorian 4–5-year olds. Educational Studies, 41, 565–586.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal, 45(2), 443–494. https://doi.org/10.3102/0002831207312908.

  • Clements, D. H., & Sarama, J. (2013). Building blocks-SRA, pre-kindergarten. Columbus, OH: SRA/McGraw-Hill.

    Google Scholar 

  • Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42, 127–166.

    Article  Google Scholar 

  • Clements, D. H., Sarama, J., Wolfe, C. B., & Spitler, M. E. (2013). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies: Persistence of effects in the third year. American Educational Research Journal, 50, 812–850.

    Article  Google Scholar 

  • De Smedt, B., Verschaffel, L., & Ghesquiere, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103, 469–479.

    Article  Google Scholar 

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446.

    Google Scholar 

  • Edens, K. M., & Potter, E. F. (2013). An exploratory look at the relationships among math skills, motivational factors and activity choice. Early Childhood Education Journal, 41, 235–243.

    Article  Google Scholar 

  • Everitt, B. S., & Dunn, G. (2001). Applied multivariate data analysis (2nd ed.). Chichester: Wiley.

    Book  Google Scholar 

  • Fuson, K. (2004). Pre-K to grade 2 goals and standards: Achieving 21st century mastery for all. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 105–148). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Geary, D. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47, 1539–1552.

    Article  Google Scholar 

  • Griffin, S. (2004). Number worlds. A research-based mathematics program for young children. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 325–342). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusing on numerosity and mathematical skills of young children. Learning and Instruction, 15, 237–256.

    Article  Google Scholar 

  • Hannula, M. M., Lepola, J., & Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal of Experimental Child Psychology, 107, 394–406.

    Article  Google Scholar 

  • Hannula, M. M., Mattinen, A., & Lehtinen, E. (2005). Does social interaction influence 3 year-old children’s tendency to focus on numerosity? A quasi-experimental study in day-care. In L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds.), Powerful learning environments for promoting deep conceptual and strategic learning (Studia Paedagogica) (Vol. 41, pp. 63–80). Leuven: Leuven University Press.

    Google Scholar 

  • Hannula, M. M., Räsänen, P., & Lehtinen, E. (2007). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9, 51–58.

    Article  Google Scholar 

  • Hannula-Sormunen, M. M. (2015). Spontaneous focusing on numerosity and its relation to counting and arithmetic. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 275–290). Oxford, UK: Oxford University Press.

    Google Scholar 

  • Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Children’s preschool subitizing, spontaneous focusing on numerosity and counting skills as predictors of mathematical performance 6–7 years later at school. Mathematical Thinking and Learning, 17, 155–177.

    Article  Google Scholar 

  • Hayes, A. F. (2006). A primer on multilevel modeling. Human Communication Research, 32(4), 385–410. https://doi.org/10.1111/j.1468-2958.2006.00281.x.

  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on student’s learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age.

    Google Scholar 

  • Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850–867.

    Article  Google Scholar 

  • Kilday, C. R., & Kinzie, M. B. (2009). An analysis of instruments that measure the quality of mathematics teaching in early childhood. Early Childhood Education Journal, 36, 365–372.

    Article  Google Scholar 

  • Ministerio de Educación. (2012). Rendición de cuentas 2011 [Accountability 2011]. Ecuador: Quito.

    Google Scholar 

  • Ministerio de Educación. (2013). Archivo maestro de instituciones educativas AMIE [Master file of educational institutions AMIE. Educational Records Report 2013–2014]. Reporte de registros educativos 2013–2014. Quito, Ecuador.

    Google Scholar 

  • Mulligan, J., Verschaffel, L., Baccaglini-Frank, A., Coles, A., Gould, P., Obersteiner, A., Sinclair, N., & Roberts, N. (in press). Whole number thinking, learning and development. In M. G. Bartolini Bussi, & X. Sun (Eds.), Building the foundation: Whole numbers in the primary grades. The ICMI Study 23. New York: Springer.

    Google Scholar 

  • Perkins, D. N., Tishman, S., Ritchhart, R., Donis, K., & Andrade, A. (2000). Intelligence in the wild: A dispositional view of intellectual traits. Educational Psychology Review, 12, 269–293.

    Article  Google Scholar 

  • PREAL. (2006). Calidad con equidad: El desafío de la educación ecuatoriana. Informe del progreso educativo [Quality with Equity: The challenge of Ecuadorian education. Educational progress report]. Ecuador. ISBN–9978–45–344–X.

    Google Scholar 

  • Rathé, S., Torbeyns, J., Hannula-Sormunen, M. M., De Smedt, B., & Verschaffel, L. (2016). Spontaneous focusing on numerosity: A review of recent research. Mediterranean Journal for Research in Mathematics Education, 15, 1–25.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2009a). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.

    Google Scholar 

  • Sarama, J., & Clements, D. H. (2009b). Manual for Classroom Observation (COEMET)-Version 3. Unpublished version.

    Google Scholar 

  • Sarama, J., Lange, A. A., Clements, D. H., & Wolfe, C., B. (2012). The impacts of an early mathematics curriculum on oral language and literacy. Early Childhood Research Quarterly, 27, 489–502.

    Google Scholar 

  • UNESCO. (2015). Tercer estudio regional comparativo y explicativo. Logros de aprendizaje, Ecuador [Third regional comparative and explanatory study. Learning achievements, Ecuador]. Santiago, Chile: Oficina Regional de Educación de la UNESCO para América Latina y el Caribe. http://unesdoc.unesco.org/images/0024/002435/243532S.pdf. Accessed: July 15, 2016.

  • United Nations. (2016). World economic situation and prospects 2016. New York.

    Google Scholar 

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Correspondence to Gina Bojorque .

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Bojorque, G., Torbeyns, J., Hannula-Sormunen, M., Van Nijlen, D., Verschaffel, L. (2018). Ecuadorian Kindergartners’ Spontaneous Focusing on Numerosity Development: Contribution of Numerical Abilities and Quality of Mathematics Education. In: Elia, I., Mulligan, J., Anderson, A., Baccaglini-Frank, A., Benz, C. (eds) Contemporary Research and Perspectives on Early Childhood Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-73432-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-73432-3_5

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