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Which skills predict computational estimation? A longitudinal study in 5- to 7-year-olds

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Abstract

Computational estimation is seen as an important mathematical competence. Little is known, however, about the mathematical skills that are predictive of early computational estimation development. The current study longitudinally followed a group of about 350 children at four time points: second (K2, 4-year-olds) and third grades of kindergarten (K3, 5-year-olds) and first (P1, 6-year-olds) and second (P2, 7-year-olds) grades of primary school. The computational estimation task was administered in two variants: a nonverbal variant, in which the problems were presented with manipulatives and children also answered using manipulatives was administered in K3 and P1; and a verbal variant, in which the problems were presented with Arabic numerals and children had to answer verbally was administered in P1 and P2. Furthermore, children’s basic numerical skills and exact and approximate arithmetic skills were assessed in K2 and K3, respectively. Path analysis showed a positive autoregressive relationship between the verbal variants of the computational estimation task but not between the nonverbal ones. Basic numerical skills were important predictors for computational estimation at all time points. Approximate arithmetic positively contributed to nonverbal estimation, while exact arithmetic positively predicted verbal estimation. In sum, solid basic numerical and arithmetic skills support children when performing computational estimation. Future intervention research should further unravel the causal contribution of each of these basic numerical and arithmetic skills.

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Notes

  1. See https://ppw.kuleuven.be/o_en_o/CIPenT/wis-co-start

References

  • Alloway, T. P., Gathercole, S. E., & Pickering, S. J. (2006). Verbal and visuospatial short-term and working memory in children: Are they separable? Child Development, 77(6), 1698–1716.

    Article  Google Scholar 

  • Andrews, P., & Sayers, J. (2015). Identifying opportunities for grade one children to acquire foundational number sense: Developing a framework for cross cultural classroom analysis. Early Childhood Education Journal, 43(4), 257–267.

    Article  Google Scholar 

  • Bailey, D. H., Duncan, G. J., Watts, T., Clements, D. H., & Sarama, J. (2017). Risky business: Correlation and causation in longitudinal studies of skill development. American Psychologist, 73(1), 81–94.

    Article  Google Scholar 

  • Bakker, M., Torbeyns, J., Wijns, N., Verschaffel, L., & De Smedt, B. (2018). Gender equality in 4- to 5-year-old preschoolers’ early numerical competencies. Developmental Science, 22(1), 1–7.

  • Barth, H., La Mont, K., Lipton, J., & Spelke, E. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences of the United States of America, 102(39), 14116–14112.

    Article  Google Scholar 

  • Berch, D. B. (2005). Making sense of number sense: implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–339.

    Article  Google Scholar 

  • Caviola, S., Mammarella, I. C., Cornoldi, C., & Lucangeli, D. (2012). The involvement of working memory in children’s exact and approximate mental addition. Journal of Experimental Child Psychology, 112(2), 141–160.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970.

    Article  Google Scholar 

  • Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/Math/

  • Corsi, P.M. (1972). Human memory and the medial temporal region of the brain (Unpublished doctoral dissertation). McGill University, Canada.

  • Cowan, R. (2003). Does it all add up? Changes in children’s knowledge of addition combinations, strategies and principles. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 35–74). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • De Smedt, B., & Gilmore, C. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278–292.

    Article  Google Scholar 

  • Department for Education. (2013). The national curriculum in England: Key stages 1 and 2 framework document. Retrieved from https://www.gov.uk/government/collections/national-curriculum

  • Departement Onderwijs en Vorming (2016). Onderzoek naar kleuterparticipatie. Eindrapport. [Research on kindergarten participation. Final report].Retrieved from: https://onderwijs.vlaanderen.be/sites/default/files/atoms/files/Eindrapport_Onderzoek_naar_kleuterparticipatie.pdf.

  • Deschuyteneer, M., De Rammelaere, S., & Fias, W. (2005). The addition of two-digit numbers: exploring carry versus no-carry problems. Psychology Science, 47(1), 74–83.

    Google Scholar 

  • Dowker, A. (2003). Young children’s estimates for addition: The zone of partial knowledge and understanding. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 243–265). Lawrence Erlbaum Associates.

  • Dowker, A. (1997). Young children’s addition estimates. Mathematical Cognition, 3(2), 141–153.

    Article  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, 44(1), 1428-1446.

  • Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43(4), 981–986.

    Article  Google Scholar 

  • Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648.

    Article  Google Scholar 

  • Gilmore, C. (2015). Approximate arithmetic abilities in childhood. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of mathematical cognition (pp. 309–329). University of Oxford.

  • Gilmore, C., Göbel, S. M., & Inglis, M. (2018). An introduction to mathematical cognition. London, United Kingdom: Routledge.

    Book  Google Scholar 

  • GO. (1998). Leerplan wiskunde lager onderwijs. [Math curriculum primary education] Retrieved from http://pro.g-o.be/pedagogische-begeleiding/basisonderwijs/leerplannen-basisonderwijs/wiskunde

  • Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79(4), 329–343.

    Article  Google Scholar 

  • Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive internet-based sample. PNAS, 109(28), 11116–11120.

    Article  Google Scholar 

  • Heck, R. H., Thomas, S. L., & Tabata, L. N. (2014). Multilevel and longitudinal modeling with IBM SPSS (2nd ed.). Routledge.

  • Hu, L., & Bentler, P. M. (2009). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55.

    Article  Google Scholar 

  • Jordan, J., Mulhern, G., & Wylie, J. (2009a). Individual differences in trajectories of arithmetical development in typically achieving 5- to 7-year olds. Journal of Experimental Child Psychology, 103(4), 455–468.

    Article  Google Scholar 

  • Jordan, N. C., Kaplan, D., Oláh, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153–175.

    Article  Google Scholar 

  • Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009b). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45(3), 850–867.

    Article  Google Scholar 

  • Katholiek Onderwijs Vlaanderen. (2018). Zin in leren, zin in leven: Generieke doelen. [Pleasure for learning. Pleasure for leaving. Curriculum standards.] Retrieved from https://zill.katholiekonderwijs.vlaanderen/#!/

  • Lemaire, P., & Brun, F. (2014). Effects of strategy sequences and response-stimulus intervals on children’s strategy selection and strategy execution: A study in computational estimation. Psychological Research, 78(4), 506–519.

    Article  Google Scholar 

  • Lemaire, P., & Lecacheur, M. (2002). Children’s strategies in computational estimation. Journal of Experimental Child Psychology, 82(4), 281–304.

    Article  Google Scholar 

  • Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., & Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714–726.

    Article  Google Scholar 

  • Ministerie van Onderwijs, Cultuur en Wetenschap. (2006). Kerndoelen primair onderwijs. [Key objectives primary education]. Retrieved from http://www.slo.nl/primair/kerndoelen/Kerndoelenboekje.pdf/

  • Muthén, L. K., & Muthén, B. O. (1998-2017). Mplus User’s guide (8th ed.). Muthén & Muthén.

  • NCTM. (2000). Principles and standards for school Mathematics. The National Council of Teachers of Mathematics, Inc..

  • Nesbitt, K. T., Fuhs, M. W., & Farran, D. C. (2019). Stability and instability in the co-development of mathematics, executive function skills, and visual-motor integration from prekindergarten to first grade. Early Childhood Research Quarterly, 46, 262–274.

    Article  Google Scholar 

  • Northcote, M., & McIntosh, A. (1999). What mathematics do adults really do in everyday life? Australian Primary Mathematics Classroom, 4(1), 19–21.

    Google Scholar 

  • Purpura, D. J., & Lonigan, C. J. (2013). Informal numeracy skills: The structure of and relations among numbering, relations, and arithmetic operations in preschool. American Educational Research Journal, 50(1), 178–209.

    Article  Google Scholar 

  • Reys, R. E., Bestgen, B. J., Rybolt, J. F., & Wyatt, J. W. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13(3), 183–201.

    Article  Google Scholar 

  • Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive of goodness-of-fit measures. Methods of Psychological Research Online, 8(2), 23–74.

    Google Scholar 

  • Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), 1–16.

    Article  Google Scholar 

  • Seethaler, P. M., & Fuchs, L. S. (2006). The cognitive correlates of computational estimation skills among third-grade students. Learning Disabilities Research & Practice, 21(4), 233–243.

    Article  Google Scholar 

  • Sekeris, E., Verschaffel, L., & Luwel, K. (2020a). Exact arithmetic, computational estimation, and approximate arithmetic are different skills: Evidence from a study with 5-year-olds. Manuscript submitted for publication.

  • Sekeris, E., Empsen, M., Verschaffel, L., & Luwel, K. (2020b). The development of computational estimation in the transition from informal to formal mathematics education. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-020-00507-z.

  • Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 192–212). Psychology Press.

  • Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012). Early predicts of high-school mathematics achievement. Psychological Science, 23(7), 691–697.

    Article  Google Scholar 

  • Sowder, J. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–389). Macmillan.

  • Tavakol, M., & Dennick, R. (2011). Making sense of Cronbach’s alfa. International Journal of Medical Education, 2, 53–55.

    Article  Google Scholar 

  • van den Heuvel-Panhuizen, M. (2000). Schattend rekenen. In van den Heuvel-Panhuizen, M., Buys, K., & Treffers, A. (Red.), Kinderen leren rekenen. Tussendoelen annex leerlijnen. Hele getallen. Bovenbouw basisschool (pp. 91-121) [Children learn mathematics. Standards. Whole numbers. Upper primary school.]. Utrecht, The Netherlands: Freudenthal Instituut.

  • Wechsler, D., Hendriksen, J., & Hurks, P. (2011). Wechsler preschool and primary scale of intelligence – III – NL. Pearson.

  • Xenidou-Dervou, I., De Smedt, B., van der Schoot, M., & 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.

    Article  Google Scholar 

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Funding

This research was supported by Grant KU Leuven project C16/16/001 “Development and stimulation of core mathematical competencies.”

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Authors and Affiliations

  1. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, box 3773, B-3000, Leuven, Belgium

    Elke Sekeris, Lieven Verschaffel & Koen Luwel

  2. Centre for Educational Research and Development, KU Leuven – Campus Brussels, Leuven, Belgium

    Koen Luwel

Authors
  1. Elke Sekeris
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  2. Lieven Verschaffel
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Contributions

- Elke Sekeris: conceptualization, formal analysis, investigation, methodology, writing — original draft;

- Lieven Verschaffel: conceptualization, methodology, supervision, writing — reviewing and editing; and

- Koen Luwel: conceptualization, methodology, supervision, writing — reviewing and editing.

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Correspondence to Elke Sekeris.

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Appendix

Appendix

Table 5 Items and corresponding number size from the computational estimation task
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Sekeris, E., Verschaffel, L. & Luwel, K. Which skills predict computational estimation? A longitudinal study in 5- to 7-year-olds. Eur J Psychol Educ 37, 19–38 (2022). https://doi.org/10.1007/s10212-021-00553-1

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