Working Memory and Mathematical Learning

  • Maria Chiara PassolunghiEmail author
  • Hiwet Mariam Costa


Working memory (WM) is a complex cognitive system responsible for the concurrent storage and processing of information. The WM plays a key role in everyday life as well as at school for typically developing children as much as for individuals with cognitive disabilities. Poor working memory skills are relatively commonplace in childhood and have a substantial advance impact on children’s learning. Recent studies show that complex cognitive tasks, such as mental arithmetic, clearly place demands on working memory: we have to remember partial results while monitoring the progress through a multistep calculation. This chapter describes the growing body of knowledge regarding the relationships between working memory and mathematical learning. In particular, we present the contribution of the three core components of working memory (phonological loop, visuospatial sketchpad, and central executive) to the development of mathematical skills such as calculation and problem-solving. Finally, the malleability of WM is discussed, with a focus on implication for mathematical development and mathematics curricula.


Working memory Mathematical precursors Problem-solving Calculation Working memory training Numeracy training 


  1. Alloway, T. P., Bibile, V., & Lau, G. (2013). Computerized working memory training: Can it lead to gains in cognitive skills in students? Computers in Human Behavior, 29(3), 632–638.CrossRefGoogle Scholar
  2. Baddeley, A. D. (1986). Working memory. Oxford, UK: Oxford University Press.Google Scholar
  3. Baddeley, A. D. (1990). Human memory: Theory and practice. Hove, UK: Lawrence Erlbaum Associates.Google Scholar
  4. Baddeley, A. D. (2000). The episodic buffer: A new component of working memory? Trends in Cognitive Sciences, 4(11), 417–423.CrossRefGoogle Scholar
  5. Baddeley, A. D., & Hitch, G. (1974). Working memory. Psychology of Learning and Motivation, 8, 47–89. CrossRefGoogle Scholar
  6. 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 : The Official Journal of the Ambulatory Pediatric Association, 5(5), 281–289. CrossRefGoogle Scholar
  7. Blair, C., & Razza, R. A. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78, 647–663.CrossRefGoogle Scholar
  8. Bull, R., Espy, K. A., & Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33(3), 205–228.CrossRefGoogle Scholar
  9. Bull, R., & Sherif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273–293.CrossRefGoogle Scholar
  10. Cargnelutti, E., Tomasetto, C., & Passolunghi, M. C. (2016). How is anxiety related to math performance in young students? A longitudinal study of Grade 2 to Grade 3 children. Cognition and Emotion, 1–10.Google Scholar
  11. Chiappe, P., Hasher, L., & Siegel, L. S. (2000). Working memory, inhibitory control, and reading disability. Memory & Cognition, 28, 8–17.CrossRefGoogle Scholar
  12. Cowan, N., & Alloway, T. P. (2008). The development of working memory in childhood. In M. Courage & N. Cowan (Eds.), Development of memory in infancy and childhood (2nd ed., pp. 303–342). Hove, UK: Psychology Press.Google Scholar
  13. Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19(4), 450–466.CrossRefGoogle Scholar
  14. De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (2001). Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved? Memory & Cognition, 29(2), 267–273.CrossRefGoogle Scholar
  15. De Smedt, B., Janssen, R., Bouwens, K., Verschaffel, L., Boets, B., & Ghesquière, P. (2009). Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade. Journal of Experimental Child Psychology, 103(2), 186–201. CrossRefGoogle Scholar
  16. Dunning, D. L., Holmes, J., & Gathercole, S. E. (2013). Does working memory training lead to generalized improvements in children with low working memory? A randomized controlled trial. Developmental Science, 16(6), 915–925.Google Scholar
  17. Engle, R. (2002). Working memory capacity as executive attention. Current Directions in Psychological Science, 11, 19–23.CrossRefGoogle Scholar
  18. Espy, A. E., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A., & Senn, T. E. (2004). The contribution of executive functions to emergent mathematic skills in preschool children. Developmental Neuropsychology, 26, 465–486. CrossRefGoogle Scholar
  19. Fuerst, A. J., & Hitch, G. J. (2000). Separate roles for executive and phonological components of working memory in mental arithmetic. Memory & Cognition, 28, 774–782.CrossRefGoogle Scholar
  20. Gathercole, S. E., Brown, L., & Pickering, S. J. (2003). Working memory assessment at school entry as longitudinal predictors of National Curriculum attainment levels. Educational and Child Psychology, 20(3), 109–122.Google Scholar
  21. Geary, D. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental & Behavioral Pediatrics, 32, 250–263. CrossRefGoogle Scholar
  22. Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121–151. CrossRefGoogle Scholar
  23. 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(4), 1343–1359.CrossRefGoogle Scholar
  24. 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), e54651. CrossRefGoogle Scholar
  25. 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(6), e67374.CrossRefGoogle Scholar
  26. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668.CrossRefGoogle Scholar
  27. Holmes, J., & Adams, J. W. (2006). Working memory and children’s mathematical skills: Implications for mathematical development and mathematical curricula. Educational Psychology, 26, 339–366.CrossRefGoogle Scholar
  28. Holmes, J., Gathercole, S. E., & Dunning, D. L. (2009). Adaptive training leads to sustained enhancement of poor working memory in children. Developmental Science, 12(4), F9.CrossRefGoogle Scholar
  29. Imbo, I., & Vandierendonck, A. (2007). The role of phonological and executive working memory resources in simple arithmetic strategies. European Journal of Cognitive Psychology, 19, 910–933.CrossRefGoogle Scholar
  30. Kremen, W. S., Jacobsen, K. C., Xian, H., Eisen, S. A., Eaves, L. J., Tsuang, M. T., et al. (2007). Genetics of verbal working memory processes: A twin study of middle-aged men. Neuropsychology, 21, 569–580. CrossRefGoogle Scholar
  31. Kroesbergen, E. H., van’t Noordende, J. E., & Kolkman, M. E. (2014). Training working memory in kindergarten children: Effects on working memory and early numeracy. Child Neuropsychology, 20(1), 23–37.CrossRefGoogle Scholar
  32. Kuhn, J. T., & Holling, H. (2014). Number sense or working memory? The effect of two computer-based trainings on mathematical skills in elementary school. Advances in Cognitive Psychology, 10(2), 59–67.CrossRefGoogle Scholar
  33. Mazzocco, M. M., & Kover, S. T. (2007). A longitudinal assessment of executive function skills and their association with math performance. Child Neuropsychology, 13, 18–45.CrossRefGoogle Scholar
  34. Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disabilities Research and Practice, 20(3), 142–155. CrossRefGoogle Scholar
  35. McKenzie, B., Bull, R., & Gray, C. (2003). The effects of phonological and visual-spatial interference on children’s arithmetical performance. Educational and Child Psychology, 20(3), 93–108.Google Scholar
  36. Melby-Lervåg, M., & Hulme, C. (2013). Is working memory training effective? A meta-analytic review. Developmental Psychology, 49(2), 270.CrossRefGoogle Scholar
  37. Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., & Menon, V. (2010). Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders. Learning and Individual Differences, 20(2), 101–109.CrossRefGoogle Scholar
  38. Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: A latent variable analysis. Cognitive Psychology, 41(1), 49–100. CrossRefGoogle Scholar
  39. Morris, N., & Jones, D. M. (1990). Memory updating in working memory: The role of the central executive. British Journal of Psychology, 81(2), 111–121.CrossRefGoogle Scholar
  40. Passolunghi, M. C., Cargnelutti, E., & Pastore, M. (2014). The contribution of general cognitive abilities and approximate number system to early mathematics. British Journal of Educational Psychology, 84(4), 631–649.CrossRefGoogle Scholar
  41. Passolunghi, M. C., Cornoldi, C., & De Liberto, S. (1999). Working memory and intrusions of irrelevant information in a group of specific poor problem solvers. Memory & Cognition, 27(5), 779–790.CrossRefGoogle Scholar
  42. Passolunghi, M. C., & Costa, H. M. (2016). Working memory and early numeracy training in preschool children. Child Neuropsychology, 22(1), 81–98.CrossRefGoogle Scholar
  43. Passolunghi, M. C., & Lanfranchi, S. (2012). Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. The British Journal of Educational Psychology, 82, 42–63. CrossRefGoogle Scholar
  44. Passolunghi, M. C., Lanfranchi, S., Altoè, G., & Sollazzo, N. (2015). Early numerical abilities and cognitive skills in kindergarten children. Journal of Experimental Child Psychology, 135, 25–42.CrossRefGoogle Scholar
  45. 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(4), 341–350.CrossRefGoogle Scholar
  46. 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(3), 229–250. CrossRefGoogle Scholar
  47. Passolunghi, M. C., & Pazzaglia, F. (2004). Individual differences in memory updating in relation to arithmetic problem solving. Learning and Individual Differences, 14(4), 219–230.CrossRefGoogle Scholar
  48. Passolunghi, M. C., & Siegel, L. (2001). Short-term memory, working memory and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80, 44–57.CrossRefGoogle Scholar
  49. Passolunghi, M. C., & Siegel, L. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88, 348–367.CrossRefGoogle Scholar
  50. Passolunghi, M. C., Vercelloni, B., & Schadee, H. (2007). The precursors of mathematics learning: Working memory, phonological ability and numerical competence. Cognitive Development, 22(2), 165–184. CrossRefGoogle Scholar
  51. Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91, 137–157.CrossRefGoogle Scholar
  52. Re, A. M., Lovero, F., Cornoldi, C., & Passolunghi, M. C. (2016). Difficulties of children with ADHD symptoms in solving mathematical problems when information must be updated. Research in Developmental Disabilities, 59, 186–193.CrossRefGoogle Scholar
  53. Shah, P., & Miyake, A. (2005). The Cambridge handbook of visuo-spatial thinking. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  54. Soltész, F., Szűcs, D., & Szűcs, L. (2010). Relationships between magnitude representation, counting and memory in 4-to 7-year-old children: A developmental study. Behavioral and Brain Functions, 6(1), 13.CrossRefGoogle Scholar
  55. St Clair-Thompson, H., Stevens, R., Hunt, A., & Bolder, E. (2010). Improving children’s working memory and classroom performance. Educational Psychology, 30(2), 203–219.CrossRefGoogle Scholar
  56. St Clair-Thompson, H. L., & Gathercole, S. E. (2006). Executive functions and achievements in school: Shifting, updating, inhibition, and working memory. The Quarterly Journal of Experimental Psychology, 59(4), 745–759.CrossRefGoogle Scholar
  57. Swanson, H. L. (2006). Cross-sectional and incremental changes in working memory and mathematical problem solving. Journal of Educational Psychology, 98(2), 265–281.CrossRefGoogle Scholar
  58. Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96(3), 471–491. CrossRefGoogle Scholar
  59. Szűcs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2014). Cognitive components of a mathematical processing network in 9-year-old children. Developmental Science, 17, 506–524.CrossRefGoogle Scholar
  60. Van Luit, J. E. H., Van de Rijt, B. A. M., & Pennings, A. H. (1994). Utrechtse Getalbegrip Toets [Early numeracy test]. Doetinchem, the Netherlands: Graviant.Google Scholar
  61. Wass, S. V., Scerif, G., & Johnson, M. H. (2012). Training attentional control and working memory–is younger, better? Developmental Review, 32(4), 360–387.CrossRefGoogle Scholar
  62. Wechsler, D. (1996). Wechsler Objective Number Dimensions (WOND). New York: Psychological Corporation.Google Scholar
  63. Witt, M. (2011). School based working memory training: Preliminary finding of improvement in children’s mathematical performance. Advances in Cognitive Psychology, 7, 7.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Maria Chiara Passolunghi
    • 1
    Email author
  • Hiwet Mariam Costa
    • 2
  1. 1.Department of Life SciencesUniversity of TriesteTriesteItaly
  2. 2.Department of PsychologyAnglia Ruskin UniversityCambridgeUK

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