Involvement of Working Memory in Longitudinal Development of Number-Magnitude Skills

Infant and Child Development

Volumn 23, Issue 1, 2014, Pages 36-50

  Kolkman, Meijke E ^a   Kroesbergen, Evelyn H ^a   Leseman, Paul P M ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Comparison; Number magnitude skills; Number to position; Working memory

Indexed keywords

EID: 84893799714     PISSN: 15227227     EISSN: 15227219     Source Type: Journal    
DOI: 10.1002/icd.1834     Document Type: Article

References (49)

1. Alloway, T. P. (2007). Automated working memory assessment. London, UK: Pearson Assessment.
2. Alloway, T. P., Gathercole, S. E., Kirkwood, H., & Elliott, J. (2008). Evaluating the validity of the automated working memory assessment. Educational Psychology, 28, 725-734. doi: 10.1080/01443410802243828
3. 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
4. Alloway, T. P., Gathercole, S. E., Willis, C. S., & Adams, A.-M. (2004). A structural analysis of working memory and related cognitive skills in young children. Journal of Experimental Child Psychology, 87, 85-170. doi: 10.1016/j.jecp.2003.10.002
5. Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278-91. doi: 10.1038/nrn2334
6. Baddeley, A. D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49A, 5-28. doi: 10.1080/713755608
7. Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4, 417-423. doi: 10.1016/S1364-6613(00)01538-2
8. Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. H. Bower (Ed.), The psychology of learning and motivation (pp. 47-89). New York, NY: Academic Press.
9. Blunch, N. J. (2008). Introduction to structural equation modelling using SPSS and AMOS. London, UK: SAGE Publications Ltd.
10. Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189-201. doi: 10.1037/0012-1649.41.6.189
11. Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence math learning. Child Development, 79, 1016-1031. doi: 10.1111/j.1467-8624.2008.01173.x
12. Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children's mathematics ability. Inhibition, switching and working memory. Developmental Neuropsychology, 19, 273-293. doi: 10.1207/S15326942DN1903_3
13. CBS Statistics Netherlands. (2007). Personen van 15 tot 65 jaar die geen onderwijs volgen, naar opleidingsniveau. [Data file]. Retrieved from http://www.cbs.nl/nlNL/menu /themas/onderwijs/cijfers/incidenteel/maatwerk/2008-2436-maatwerk.htm
14. IBM Corp. (2011). IBM SPSS Sta$tistics for Windows, Version 20.0. Armonk, NY: IBM Corp.
15. Cowan, N. (2010). Multiple concurrent thoughts: The meaning and developmental neuropsychology of working memory. Developmental Neuropsychology, 35, 447-474. doi: 10.1080/87565641.2010.494985
16. De Smedt, B., & Gilmore, C. K. (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
17. De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103, 469-479. doi: 10.1016/j.jcep.2009.01.010
18. Dehaene, S. (2001). Précis of the number sense. Mind & Language, 16, 16-36. doi: 10.1111/1468-0017.00154
19. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396. doi: 10.1037/0096-3445.122.3.371
20. Durand, M., Hulme, C., Larkin, R., & Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds. Journal of Experimental Child Psychology, 91, 113-136. doi: 10.1016/j.jecp.2005.01.003
21. Field, A. (2005). Discovering statistics using SPSS. London, UK: Sage.
22. Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555-556. doi: 10.1038/nn1066
23. Friso-Van Den Bos, I., Kolkman, M. E., Kroesbergen, E. H., & Leseman, P. P. M. (2014). Explaining variability: Numerical representations in 4- to 8-year old children. Journal of Cognition and Development. doi: 10.1080/15248372.2012.742900
24. Gathercole, S. E., Pickering, S. J., Ambridge, B., & Wearing, H. (2004). The structure of working memory from 4 to 15years of age. Developmental Psychology, 40, 177-190. doi: 10.1037/0012-1649.40.2.177
25. 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, 34, 411-429. doi: 10.1016/j.cogdev.2009.10.001
26. Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343-1360. doi: 10.1111/j.1467-8624.2007.01069.x
27. Geary, D. C., Hoard, M. K., Nugent, L., & Byrd-Craven, J. (2008). Development of number-line representations in children with mathematical learning disability. Developmental Neuropsychology, 33, 277-299. doi: 10.1080/87565640801982361
28. Gevers, W., Lammertyn, J., Notebaert, W., Verguts, T., & Fias, W. (2006). Automatic response activation of implicit spatial information: Evidence from the SNARC effect. Acta Psychologica, 122, 221-233. doi: 10.1016/j.actpsy.2005.11.004
29. Henik, A., Leibovich, T., Naparstek, S., Diesendruck, L., & Rubinsten, O. (2012). Quantities, amounts, and the numerical core system. Frontiers in Human Neuroscience, 5, 1-4. doi: 10.3389/fnhum.2011.00186
30. Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology, 103, 17-29. doi: 10.1016/j.jecp.2008.04.001
31. Kolkman, M. E., Hoijtink, H., Kroesbergen, E. H., & Leseman, P. P. M. (2013). The role of executive functions in numerical skills. Learning and Individual Differences, 24, 145-151. doi: 10.1016/j.lindiff.2013.01.004
32. 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
33. Krajewski, K., & Schneider, W. (2009). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study. Journal of Experimental Child Psychology, 103, 516-531. doi: 10.1016/j.jecp.2009.03.009
34. Kroesbergen, E. H., Van de Rijt, B. A. M., & Van Luit, J. E. H. (2007). Working memory and early mathematics: Possibilities for early identification of mathematics learning disabilities. In T. E. Scruggs, & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities: International perspectives (pp. 1-19). Oxford, UK: JAI Press.
35. Laski, E. V., & Siegler, R. S. (2007). Is 27 a big number? Correlational and causal connection among numerical categorization, number-line estimation and numerical magnitude comparison. Child Development, 78, 1723-1744. doi: 10.1111/j.1467-8624.2007.01087.x
36. rd graders. Learning and Individual Differences, 20, 101-109. doi: 10.1016/j.lindif.2009.08.004
37. Noël, M. P. (2009). Counting on working memory when learning to count and to add: A preschool study. Developmental Psychology, 45, 1630-1643. doi: 10.1037/a0016224
38. Opfer, J. E., & Siegler, R. S. (2007). Representational change and children's numerical estimation. Cognitive Psychology, 55, 169-195. doi: 10.1016/j.cogpsych.2006.09.002
39. Passolunghi, M. -C., Mammarella, I. C., & Altoè, G. (2008). Cognitive abilities as precursors of the early acquisition of mathematical skills during first through second grades. Developmental Neuropsychology, 33, 229-250. doi: 10.1080/87565640801982320
40. Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children's numerical knowledge trough playing number board games. Child Development, 97, 375-394. doi: 10.1111/j.1467-8624.2007.01131.x
41. Raven, J. (1962). Coloured progressive matrices. New York, NY: The Psychological Corporation.
42. Raven, J. C., Court, J. H., & Raven, J. (1995). Coloured progressive matrices. Oxford, UK: Psychologists Press.
43. Rousselle, L., & Noel, 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
44. Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75, 428-444. doi: 10.1111/j.1467-8624.2004.00684.x
45. 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
46. Van Dijck, J.-P., & Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition, 119, 114-119. doi: 10.1016/j.cognition.2010.12.013
47. Welch, G. W. (2007). Model Fit and Interpretation of Non-linear Latent Growth Curve Models (Doctoral dissertation, University of Pittsburgh). Retrieved from http://d-scholarship.pitt.edu/8769/
48. Wood, G., Willmes, K., Nuerk, H. C., & Fischer, M. H. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50, 489-525.
49. Xenidou-Dervou, I., Van Lieshout, E. C. D. M., & Van der Schoot, M. (2013). Working memory in nonsymbolic approximate arithmetic processing: A dual-task study with preschoolers. Cognitive Science. Online first doi: 10.1111/cogs.12053