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Early mathematical competencies and later achievement: insights from the Longitudinal Study of Australian Children

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Abstract

International research suggests that early mathematical competence predicts later mathematical achievement. In this article, we explore the relationship between mathematical competencies at 4–5 years, as measured by teacher ratings, and later results on Years 3, 5, 7 and 9 National Assessment Program – Literacy and Numeracy (NAPLAN) numeracy tests. Data from a nationally representative sample of 2343 children participating in the Longitudinal Study of Australian Children (LSAC) are examined. In line with international studies, we report moderate correlations between preschool-entry mathematics and later NAPLAN numeracy test results. However, analysis of individual growth trajectories indicates that early mathematics predicts the initial (Year 3) level, but not subsequent growth. This suggests that early mathematical competencies are important for enhancing achievement in early schooling, but that the quality of mathematics education provided in the schooling years is critical for future development.

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Notes

  1. This was the age when children’s parents completed the survey. Teacher data were obtained once parental permission was obtained.

  2. Using the interaction term in Model B, with Time = 3, SEP = 1 and β = 2.7, giving an increase of 8.1 points.

  3. Using the interaction term in Model C2, with Time = 3, Competency = 1 and β = − 6.2.

References

  • Atweh, B., Vale, C., & Walshaw, M. (2012). Equity, diversity, social justice and ethics in mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Research in mathematics education in Australasia 2008–2011 (pp. 39–65). Rotterdam: Sense Publishers.

    Chapter  Google Scholar 

  • Aubrey, C. (1993). An investigation of the mathematical knowledge and competencies which young children bring into school. British Educational Research Journal, 19(1), 27–41.

    Article  Google Scholar 

  • Australian Curriculum, Assessment and Reporting Agency. (2013). Australian curriculum: mathematics (Version 5.1). Retrieved from http://www.australiancurriculum.edu.au/mathematics/Rationale.

  • Baxter, J. A. (2015). Child care and early childhood education in Australia (facts sheet 2015). Melbourne: Australian Institute of Family Studies.

    Google Scholar 

  • Biddle, B. J. (1997). Foolishness, dangerous nonsense, and real correlates of state differences in achievement. Phi Delta Kappa, 79(1), 8–13.

    Google Scholar 

  • Björklund, C. (2008). Toddlers’ opportunities to learn mathematics. International Journal of Early Childhood, 40(1), 81–95.

    Article  Google Scholar 

  • Blakemore, T. J., Strazdins, L., & Gibbings, J. (2009). Measuring family socio-economic position. Australian Social Policy, 8, 121–169.

    Google Scholar 

  • Bliese, P. (2012). Multilevel modelling in R (2.4): a brief introduction to R, the multilevel package and the nlme package. R Development Team.

  • Bryk, A. S., & Raudenbush, S. W. (1987). Application of hierarchical linear models to assessing change. Psychological Bulletin, 101(1), 147–158.

    Article  Google Scholar 

  • Carmichael, C., MacDonald, A., & McFarland-Piazza, L. (2014). Predictors of numeracy performance in national testing programs: Insights from the Longitudinal Study of Australian Children. British Educational Research Journal, 40, 637–659.

  • Claessens, A., Duncan, G., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: evidence from the ECLS-K. Economics of Education Review, 28(4), 415–427.

    Article  Google Scholar 

  • Clarke, B., Clarke, D., & Cheeseman, J. (2006). The mathematical knowledge and understanding young children bring to school. Mathematics Education Research Journal, 18(1), 78–102.

    Article  Google Scholar 

  • Council of Australian Governments. (2009). Investing in the early years—a national early childhood development strategy. Barton: Commonwealth of Australian Available online from: https://www.coag.gov.au/sites/default/files/national_ECD_strategy.pdf.

    Google Scholar 

  • Darling-Hammond, L. (1999). Teacher quality and student achievement: a review of state policy evidence. Seattle: Center for the Study of Teaching and Policy.

    Google Scholar 

  • Department of Education, Employment and Workplace Relations. (2009). Belonging, being and becoming: the Early Years Learning Framework for Australia. Barton: Commonwealth of Australia.

    Google Scholar 

  • Doig, B., McRae, B., & Rowe, K. (2003). A good start to numeracy: effective numeracy strategies from research and practice in early childhood. Canberra: Commonwealth Department of Education, Science and Training.

    Google Scholar 

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446.

    Article  Google Scholar 

  • Dunn, L. M., Dunn, L., & Dunn, D. M. (1997). Peabody picture vocabulary test (3rd ed.). Detroit: AGS Publishing.

    Google Scholar 

  • Elliott, A. (2006). Early childhood education: pathways to quality and equity for all children. Camberwell: Australian Council for Educational Research.

    Google Scholar 

  • English, L., & Mulligan, J. (Eds.). (2013). Reconceptualising early mathematics learning. Dordrecht: Springer.

    Google Scholar 

  • Faraway, J. (2006). Extending the linear model with R: generalized linear, mixed effects and non-parametric regression models. New York: Chapman and Hall/CRC.

    Google Scholar 

  • Fielding-Wells, J., & Makar, K. (2015). Inferring to a model: using inquiry-based argumentation to challenge young children’s expectations of equally likely outcomes. In A. Zieffler (Ed.), Reasoning about uncertainty: learning and teaching informal inferential reasoning (pp. 1–28). Minneapolis: Catalyst Press.

    Google Scholar 

  • Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2013). Adolescents’ functional numeracy is predicted by their school entry number system knowledge. PloS ONE, 8(1).

  • Gervasoni, A., & Perry, P. (2013). Children’s mathematical knowledge prior to starting school. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: yesterday, today and tomorrow. Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 338–345). Melbourne: MERGA.

  • Gervasoni, A., & Perry, B. (2015). Children’s mathematical knowledge prior to starting school and implications for transition. In B. Perry, A. MacDonald, & A. Gervasoni (Eds.), Mathematics and transition to school: international perspectives (pp. 47–64). Singapore: Springer.

    Google Scholar 

  • Gould, P. (2012). What number knowledge do children have when starting kindergarten in NSW? Australasian Journal of Early Childhood, 37(3), 105–110.

    Google Scholar 

  • Harris, P., Chinnappan, M., Castleton, G., Carter, J., De Courcy, M., & Barnett, J. (2013). Impact and consequence of Australia’s National Assessment Program - Literacy and Numeracy (NAPLAN): using research evidence to inform improvement. TESOL in Context, 23(1 & 2), 30–52.

    Google Scholar 

  • Jordan, N. C., Kaplan, D., Olah, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: a longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153–175.

    Article  Google Scholar 

  • Karoly, L. A., Kilburn, M. R., & Cannon, J. S. (2006). Early childhood intervention: proven results, future promise. Santa Monica: RAND Corp.

    Google Scholar 

  • Kinnear, V., & Clark, J. (2014). Probabilistic reasoning and prediction with young children. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: research guided practice. Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 335–342). Sydney: MERGA.

  • Kwok, O., West, S. G., & Green, S. B. (2007). The impact of misspecifying the within-subject covariance structure in multiwave longitudinal multilevel models: a Monte Carlo study. Multivariate Behavioral Research, 43(3), 557–592.

    Article  Google Scholar 

  • Levine, S. C., Suriyakham, L. W., Rowe, M. L., Huttenlocher, J., & Gunderson, E. A. (2010). What counts in the development of young children’s number knowledge? Developmental Psychology, 46(5), 1309–1319.

    Article  Google Scholar 

  • MacDonald, A. (2010). Young children’s measurement knowledge: Understandings about comparison at the commencement of schooling. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33 rd annual conference of the Mathematics Education Research Group of Australasia (pp. 375–382). Fremantle: MERGA.

  • MacDonald, A. (2012). Young children’s photographs of measurement in the home. Early Years, 32(1), 71–85.

  • Makar, K. (2014). Young children’s explorations of average through informal inferential reasoning. Educational Studies in Mathematics, 86(1), 61–78.

    Article  Google Scholar 

  • Mensah, F. K., & Kiernan, K. E. (2010). Gender differences in educational attainment: influences of the family environment. British Educational Research Journal, 36, 239–260.

    Article  Google Scholar 

  • Peter-Koop, A., & Scherer, P. (2012). Early childhood mathematics teaching and learning. Journal für Mathematik-Didaktik, 33, 175–179.

    Article  Google Scholar 

  • Ponitz, C. C., Rimm-Kaufman, S. E., Brock, L. L., & Nathanson, L. (2009). Early adjustment, gender differences, and classroom organizational climate in first grade. The Elementary School Journal, 110, 142–162.

    Article  Google Scholar 

  • R Development Core Team. (2011). R 2.14.1. Vienna: R Foundation for Statistical Computing.

    Google Scholar 

  • Reikerås, E., Løge, I. K., & Knivsberg, A. (2012). The mathematical competencies of toddlers expressed in their play and daily life activities in Norwegian kindergartens. International Journal of Early Childhood, 44, 91–114.

    Article  Google Scholar 

  • Rimm-Kaufman, S. E., Pianta, R. C., Cox, M. J., & Bradley, R. H. (2003). Teacher-rated family involvement and children’s social and academic outcomes in kindergarten. Early Education & Development, 14(2), 179–198.

    Article  Google Scholar 

  • Robinson, G., Silburn, S. R., & Arney, F. (2011). The value of investment in the early years: balancing costs of childhood services. Darwin: Northern Territory Government.

    Google Scholar 

  • Rogosa, D. R., & Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50(2), 203–228.

    Article  Google Scholar 

  • Rothman, S. (2005). Report on adapted PPVT-III and Who Am I? (LSAC data issues paper no. 2). Available online from: http://www.growingupinaustralia.gov.au/pubs/issues/ip2.pdf

  • Sammons, P., Sylva, K., Melhuish, E. C., Siraj-Blatchford, I., Taggart, B., & Elliot, K. (2002). Measuring the impact of pre-school on children’s cognitive progress over the preschool period (Technical Paper8a). London: Institute of Education, University of London.

  • Sanson, A., Nicholson, J., Ungerer, J., Zubrick, S., Wilson, K., Ainley, J., Berthelsen, D., Bittman, M., Broom, D., Harrison, L., Rodgers, B., Sawyer, M., Silburn, S., Strazdins, L., Vimpani, G., & Wake, M. (2002). Introducing the longitudinal study of Australian children (LSAC discussion paper no. 1). Melbourne: Australian Institute of Family Studies.

  • Sarama, J., & Clements, D. H. (2015). Scaling up early childhood mathematics interventions: transitioning with trajectories and technologies. In B. Perry, A. MacDonald, & A. Gervasoni (Eds.), Mathematics and transition to school: international perspectives (pp. 153–169). Dordrecht: Springer.

    Google Scholar 

  • Sirin, S. R. (2005). Socioeconomic status and academic achievement: a meta-analytic review of research. Review of Educational Research, 75(3), 417–453.

    Article  Google Scholar 

  • Watts, T., Duncan, G., Siegler, R., & Davis-Kean, P. (2014). What’s past is prologue: relations between early mathematics knowledge and high school achievement. Educational Researcher, 43(7), 352–360.

    Article  Google Scholar 

  • Weis, M., Heikamp, T., & Trommsdorff, G. (2013). Gender differences in school achievement: the role of self-regulation. Frontiers in Psychology, 4, Article 442.

  • Williams, K. E., White, S. J., & MacDonald, A. (2016). Early mathematics achievement of boys and girls: Do differences in early self-regulation pathways explain later achievement? Learning and Individual Differences, 51, 199–209.

  • Wright, R. J. (1994). A study of the numerical development of 5-year-olds and 6-year-olds. Educational Studies in Mathematics, 26, 25–44.

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank all involved in the LSAC study. Growing Up in Australia: The Longitudinal Study of Australian Children was initiated and funded as part of the Australian Government Stronger Families and Communities Strategy by the Australian Government Department of Families, Housing, Community Services and Indigenous Affairs (FaHCSIA). The study is being undertaken in partnership with the Australian Institute of Family Studies (AIFS), with advice being provided by a consortium of leading researchers at research institutions and universities throughout Australia. The data collection is undertaken by the Australian Bureau of Statistics. All views expressed in this paper are the authors’ own and do not represent the views of FaHCSIA or AIFS.

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  1. School of Education, Charles Sturt University, PO Box 789, Albury, NSW, 2640, Australia

    Amy MacDonald & Colin Carmichael

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  1. Amy MacDonald
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  2. Colin Carmichael
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Correspondence to Amy MacDonald.

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MacDonald, A., Carmichael, C. Early mathematical competencies and later achievement: insights from the Longitudinal Study of Australian Children. Math Ed Res J 30, 429–444 (2018). https://doi.org/10.1007/s13394-017-0230-6

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