Skip to main content
Published Online:https://doi.org/10.1027/2151-2604/a000210

Dyscalculia, or mathematics learning disability, has received growing attention in recent years. Working memory and number sense are hypothesized to form important determinants of dyscalculia, but longitudinal assessments of number sense in children with or at-risk for dyscalculia are scarce. The current study investigated number line development in first and second grade, in addition to kindergarten predictors and mathematical proficiency as an outcome. Children (n = 396) could be divided into three latent growth classes: at-risk, catch-up, and typical, based on their number line development. Growth was predicted by kindergarten number sense and verbal working memory. According to the class to which they were assigned, children differed in mathematical proficiency at the end of grade 2. The current study makes an important contribution to the understanding of risk for dyscalculia, showing that children at-risk can be distinguished based on their number line development, and that kindergarten variables are predictive of subsequent development.

References

  • Alloway, T. P. (2007). Automatic working memory assessment. Oxford, UK: Harcourt. First citation in articleGoogle Scholar

  • 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, 1698–1716. doi: 10.1111/j.1467-8624.2006.00968.x First citation in articleCrossrefGoogle Scholar

  • Baddeley, A. (2007). Working memory thought and action. Oxford, UK: Oxford University Press. First citation in articleCrossrefGoogle Scholar

  • Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. H. BowerEd., The psychology of learning and motivation, (Vol. 8, pp. 47–89). New York, NY: Academic Press. First citation in articleCrossrefGoogle Scholar

  • Barbaresi, W. J., Katusic, S. K., Colligan, R. C., Weaver, A. L., & Jacobsen, S. J. (2005). Math learning disorder: Incidence in a population-based birth cohort, 1976–82, Rochester Minn. Ambulatory Pediatrics, 5, 281–289. doi: 10.1367/A04-209R.1 First citation in articleCrossrefGoogle Scholar

  • Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8, 338–363. doi: 10.1037/1082-989X.8.3.338 First citation in articleCrossrefGoogle Scholar

  • Berteletti, I., Man, G., & Booth, J. R. (2015). How number line estimation skills relate to neural activations in single digit subtraction problems. NeuroImage, 107, 198–206. doi: 10.1016/j.neuroimage.2014.12.011 First citation in articleCrossrefGoogle Scholar

  • Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14, 534–541. doi: 10.1016/j.tics.2010.09.007 First citation in articleCrossrefGoogle Scholar

  • Cohen, D. J., & Sarnecka, B. W. (2014). Children’s number-line estimation shows development of measurement skills (not number-representations). Developmental Psychology, 50, 1640–1652. doi: 10.1037/a0035901 First citation in articleCrossrefGoogle Scholar

  • Cowan, R., & Powell, D. (2014). The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability. Journal of Educational Psychology, 106, 214–229. doi: 10.1037/a0034097 First citation in articleCrossrefGoogle 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, 278–292. doi: 10.1016/j.jecp. 2010.09.003 First citation in articleCrossrefGoogle Scholar

  • Friso-van den Bos, I., Kroesbergen, E. H., & Van Luit, J. E. H. (2014). Number sense in kindergarten children: Factor structure and working memory predictors. Learning and Individual Differences, 33, 23–29. doi: 10.1016/j.lindif.2014.05.003 First citation in articleCrossrefGoogle Scholar

  • Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4–15. doi: 10.1177/00222194040370010201 First citation in articleCrossrefGoogle Scholar

  • Geary, D. C., Bailey, D. H., Littlefield, A., Wood, P., Hoard, M. K., & Nugent, L. (2009). First-grade predictors of mathematical learning disability: A latent class trajectory analysis. Cognitive Development, 24, 4. doi: 10.1016/j.cogdev.2009.10.001 First citation in articleCrossrefGoogle Scholar

  • Geary, D. C., Hoard, M. K., & Bailey, D. H. (2012). Fact retrieval deficits in low achieving children and children with mathematical learning disability. Journal of Learning Disabilities, 45, 291–307. doi: 10.1177/0022219410392046 First citation in articleCrossrefGoogle Scholar

  • Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., … Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS One, 8, e67374. doi: 10.1371/journal.pone.0067374 First citation in articleGoogle Scholar

  • Janssen, J., Verhelst, N., Engelen, R., & Scheltens, F. (2010). Wetenschappelijke verantwoording van de toetsen LOVS rekenen-wiskunde voor groep 3 tot en met 8 [Scientific justification of the mathematics test for grades 1–6]. Arnhem, The Netherlands: Cito. First citation in articleGoogle Scholar

  • Jordan, N. C., Kaplan, D., Locuniak, M. N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22, 36–46. doi: 10.1111/j.1540-5826.2007.00229.x First citation in articleCrossrefGoogle Scholar

  • Jordan, N. C., Kaplan, D., Nabors Oláh, 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. doi: 10.1111/j.1467-8624.2006.00862.x First citation in articleCrossrefGoogle Scholar

  • Jung, T., & Wickrama, K. A. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2, 302–317. doi: 10.111/j.1751-9004.2007.00054.x First citation in articleCrossrefGoogle Scholar

  • Kolkman, M. E., Kroesbergen, E. H., & Leseman, P. P. M. (2013). Early numerical development and the role of non-symbolic and symbolic skills. Learning and Instruction, 25, 95–103. doi: 10.1016/j.learninstruc.2012.12.001 First citation in articleCrossrefGoogle Scholar

  • Landerl, K. (2013). Development of numerical processing in children with typical and dyscalculic arithmetic skills – a longitudinal study. Frontiers in Psychology, 4, 459. doi: 10.3389/fpsyg.2013.00459 First citation in articleCrossrefGoogle Scholar

  • Muthén, L. K., & Muthén, B. O. (1998–2011). Mplus user’s guide (6th ed.). Los Angeles, CA: Muthén & Muthén. First citation in articleGoogle Scholar

  • Nylund, K. L., Asparouhov, T., & Muthén, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modelling: A Monte Carlo simulation study. Structural Equation Modeling, 14, 535–569. doi: 10.1080/10705510701575396 First citation in articleCrossrefGoogle Scholar

  • Passolunghi, M.-C., & Mammarella, I. C. (2012). Selective spatial working memory impairment in a group of children with mathematics learning disabilities and poor problem-solving skills. Journal of Learning Disabilities, 45, 341–350. doi: 10.1177/0022219411400746 First citation in articleCrossrefGoogle Scholar

  • Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91, 137–157. doi: 10.1016/j.jecp.2005.01.004 First citation in articleCrossrefGoogle Scholar

  • Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and change in markers of core numerical competencies. Journal of Experimental Psychology: General, 141, 649–666. doi: 10.1037/a0027520 First citation in articleCrossrefGoogle Scholar

  • Rouder, J. N., & Geary, D. C. (2014). Children’s cognitive representations of the mathematical number line. Developmental Science, 17, 525–536. doi: 10.1111/desc.12166 First citation in articleCrossrefGoogle Scholar

  • Rousselle, L., & Noël, M.-P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs. non-symbolic number magnitude processing. Cognition, 102, 361–395. doi: 10.1016/j.cognition.2006.01.005 First citation in articleCrossrefGoogle Scholar

  • Sasanguie, D., Van den Bussche, E., & Reynvoet, B. (2012). Predictors for mathematics achievement? Evidence from a longitudinal study. Mind, Brain, and Education, 6, 119–128. doi: 10.1111/j.1751-228X.2012.01147.x First citation in articleCrossrefGoogle Scholar

  • Siegler, R. S., & 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 First citation in articleCrossrefGoogle Scholar

  • Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49, 2674–2688. doi: 10.1016/j.cortex.2013.06.007 First citation in articleCrossrefGoogle Scholar

  • Van der Sluis, S., Van der Leij, A., & De Jong, P. F. (2005). Working memory in Dutch children with reading- and arithmetic-related LD. Journal of Learning Disabilities, 38, 207–221. doi: 10.1177/00222194050380030301 First citation in articleCrossrefGoogle Scholar

  • Van Luit, J. E. H., Bloemert, J., Ganzinga, E. G., & Mönch, M. E. (2012). Protocol dyscalculie: Diagnostiek voor gedragsdeskundigen [Dyscalculia protocol: Diagnostics for behavioural experts]. Doetinchem, The Netherlands: Graviant. First citation in articleGoogle Scholar

  • Van Luit, J. E. H., & Van de Rijt, B. A. M. (2009). Utrechtse getalbegrip toets-Revised [Early numeracy test-Revised]. Doetinchem, The Netherlands: Graviant. First citation in articleGoogle Scholar

  • Van Viersen, S., Slot, E. M., Kroesbergen, E. H., Van ‘t Noordende, J. E., & Leseman, P. P. M. (2013). The added value of eye-tracking in diagnosing dyscalculia: A case study. Frontiers in Psychology, 4, 679. doi: 10.3389/fpsyg.2013.00679 First citation in articleCrossrefGoogle Scholar

  • Von Aster, M. G., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine & Child Neurology, 49, 868–873. doi: 10.1111/j.1469-8749.2007.00868.x First citation in articleCrossrefGoogle Scholar

  • 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. doi: 10.1016/j.lindif.2013.09.012 First citation in articleCrossrefGoogle Scholar

  • Xenidou-Dervou, I., Van Lieshout, E. C. D. M., & Van der Schoot, M. (2014). Working memory in nonsymbolic approximate arithmetic processing: A dual-task study with preschoolers. Cognitive Science, 38, 101–127. doi: 10.1111/cogs.12053 First citation in articleCrossrefGoogle Scholar