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

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.

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.

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.

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.

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

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.

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

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 Human memory and the medial temporal region of the brain (Unpublished doctoral dissertation).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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.