There is extensive evidence for the involvement of working memory in mathematical attainment. This study aims to identify the relative contributions of verbal, spatial-simultaneous, and spatial-sequential working memory measures in written mathematics. Year 3 children (7–8 years of age, n = 214) in the United Kingdom were administered a battery of working memory tasks alongside a standardised test of mathematics. Confirmatory factor analyses and variance partitioning were then performed on the data to identify the unique variance accounted for by verbal, spatial-simultaneous, and spatial-sequential measures. Results revealed the largest individual contribution was that of verbal working memory, followed by spatial-simultaneous factors. This suggests the components of working memory underpinning mathematical performance at this age are those concerning verbal-numeric and spatial-simultaneous working memory. Implications for educators and further research are discussed.
AllenK.HigginsS.AdamsJ. (2019). The relationship between visuospatial working memory and mathematical performance in school-aged children: A systematic review. Educational Psychology Review. Advance online publication. doi:10.1007/s10648-019-09470-8
2.
AllowayT. P. (2012). Can interactive working memory training improve learning?Journal of Interactive Learning Research, 23, 197–207.
3.
AnderssonU. (2008). Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions. British Journal of Educational Psychology, 78, 181–203. doi:10.1348/000709907X209854
4.
AnderssonU.LyxellB. (2007). Working memory deficit in children with mathematical difficulties: A general or specific deficit?Journal of Experimental Child Psychology, 96, 197–228. doi:10.1016/j.jecp.2006.10.001
5.
AshkenaziS.Rosenberg-LeeM.MetcalfeA. W. S.SwigartA. G.MenonV. (2013). Visuo-spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition. Neuropsychologia, 51, 2305–2317. doi:10.1016/j.neuropsychologia.2013.06.031
6.
BaddeleyA. D.HitchG. J. (1974). Working memory. In BowerG. A. (Ed.), The psychology of learning and motivation (pp. 47-89). Cambridge, MA: Academic Press.
7.
BullR.JohnstonR. S.RoyJ. A. (1999). Exploring the roles of the visual-spatial sketch pad and central executive in children’s arithmetical skills: Views from cognition and developmental neuropsychology. Developmental Neuropsychology, 15, 421–442.
8.
CaviolaS.GerottoG.MammarellaI. C. (2016). Computer-based training for improving mental calculation in third- and fifth-graders. Acta Psychologica, 171, 118–127. doi:10.1016/j.actpsy.2016.10.005
9.
CaviolaS.MammarellaI. C.CornoldiC.LucangeliD. (2012). The involvement of working memory in children’s exact and approximate mental addition. Journal of Experimental Child Psychology, 112, 141–160. doi:10.1016/j.jecp.2012.02.005
10.
CaviolaS.MammarellaI. C.LucangeliD.CornoldiC. (2014). Working memory and domain-specific precursors predicting success in learning written subtraction problems. Learning and Individual Differences, 36, 92–100. doi:10.1016/j.lindif.2014.10.010
11.
CaviolaS.MammarellaI. C.PastoreM.LeFevreJ.-A. (2018). Children’s strategy choices on complex subtraction problems: Individual differences and developmental changes. Frontiers in Psychology, 9, 1209. doi:10.3389/fpsyg.2018.01209
12.
ChuahY. M.MayberyM. T. (1999). Verbal and spatial short-term memory: Common sources of developmental change?Journal of Experimental Child Psychology, 73, 7–44. doi:10.1006/jecp.1999.2493
13.
ClearmanJ.KlingerV.SzűcsD. (2017). Visuospatial and verbal memory in mental arithmetic. The Quarterly Journal of Experimental Psychology, 70, 1837–1855. doi:10.1080/17470218.2016.1209534
14.
CorsiP. M. (1972). Memory and the medial temporal region of the brain. Montreal, Quebec, Canada: McGill University.
15.
D’AmicoA.GuarneraM. (2005). Exploring working memory in children with low arithmetical achievement. Learning and Individual Differences, 15, 189–202. doi:10.1016/j.lindif.2005.01.002
16.
DengL.ChanW. (2016). Testing the difference between reliability coefficients Alpha and Omega. Educational and Psychological Measurement, 77, 185–203. doi:10.1177/0013164416658325
17.
DunningD. L.HolmesJ.GathercoleS. E. (2013). Does working memory training lead to generalized improvements in children with low working memory? A randomized controlled trial. Developmental Science, 16, 915–925. doi:10.1111/desc.12068
18.
FabbriS.CaviolaS.TangJ.ZorziM.ButterworthB. (2012). The role of numerosity in processing nonsymbolic proportions. The Quarterly Journal of Experimental Psychology, 65, 2435–2446. doi:10.1080/17470218.2012.694896
19.
FlavellJ. H.BeachD. R.ChinskyJ. M. (1966). Spontaneous verbal rehearsal in a memory task as a function of age. Child Development, 37, 283–299. doi:10.1111/j.1467-8624.1966.tb05387.x
20.
GathercoleS. E. (1998). The development of memory. Journal of Child Psychology and Psychiatry, 39, 3–27. doi:10.1111/1469-7610.00301
21.
GiofrèD.DonolatoE.MammarellaI. C. (2018). Verbal and visuospatial WM & academic achievement. Trends in Neuroscience and Education, 12, 1–6. doi:10.1016/j.tine.2018.07.001
22.
GiofrèD.MammarellaI. C.CornoldiC. (2013). The structure of working memory and how it relates to intelligence in children. Intelligence, 41, 396–406. doi:https://doi.org/10.1016/j.intell.2013.06.006
23.
GiofrèD.MammarellaI. C.CornoldiC. (2014). The relationship among geometry, working memory, and intelligence in children. Journal of Experimental Child Psychology, 123, 112–128. doi:10.1016/J.JECP.2014.01.002
24.
GiofrèD.MammarellaI. C.RonconiL.CornoldiC. (2013). Visuospatial working memory in intuitive geometry, and in academic achievement in geometry. Learning and Individual Differences, 23, 114–122. doi:10.1016/J.LINDIF.2012.09.012
25.
GuérardK.TremblayS. (2008). Revisiting evidence for modularity and functional equivalence across verbal and spatial domains in memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34, 556–569. doi:10.1037/0278-7393.34.3.556
26.
HenryL. A.MesserD.Luger-KleinS.CraneL. (2012). Phonological, visual, and semantic coding strategies and children’s short-term picture memory span. The Quarterly Journal of Experimental Psychology, 65, 2033–2053. doi:10.1080/17470218.2012.672997
27.
HolmesJ.AdamsJ. W. (2006). Working memory and children’s mathematical skills: Implications for mathematical development and mathematics curricula. Educational Psychology, 26, 339–366. doi:10.1080/01443410500341056
28.
HolmesJ.AdamsJ. W.HamiltonC. J. (2008). The relationship between visuospatial sketchpad capacity and children’s mathematical skills. European Journal of Cognitive Psychology, 20, 272–289. doi:10.1080/09541440701612702
29.
HolmesJ.GathercoleS. E. (2014). Taking working memory training from the laboratory into schools. Educational Psychology, 34, 440–450. doi:10.1080/01443410.2013.797338
30.
HoyleR. H. (1995). Structural equation modeling: Concepts, issues, and applications. Thousand Oaks, CA: SAGE.
31.
HuL.BentlerP. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, 1–55. doi:10.1080/10705519909540118
32.
JonesD.FarrandP.StuartG.MorrisN. (1995). Functional equivalence of verbal and spatial information in serial short-term memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, 1008.
33.
JonesD. M.HughesR. W.MackenW. J. (2006). Perceptual organization masquerading as phonological storage: Further support for a perceptual-gestural view of short-term memory. Journal of Memory and Language, 54, 265–281. doi:10.1016/j.jml.2005.10.006
34.
Krousel-WoodM.MuntnerP.JannuA.HyreA.BreaultJ. (2006). Does waiver of written informed consent from the institutional review board affect response rate in a low-risk research study?Journal of Investigative Medicine, 54, 174–179.
35.
KyttäläM.LehtoJ. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23, 77–94.
36.
LiY.GearyD. C. (2013). Developmental gains in visuospatial memory predict gains in mathematics achievement. PLoS ONE, 8, e0070160. doi:10.1371/journal.pone.0070160
37.
LiY.GearyD. C. (2017). Children’s visuospatial memory predicts mathematics achievement through early adolescence. PLoS ONE, 12, e0172046. doi:10.1371/journal.pone.0172046
38.
LogieR. H. (2014). Visuo-spatial working memory. Taylor & Francis.
39.
MammarellaI. C.BorellaE.PastoreM.PazzagliaF. (2013). The structure of visuospatial memory in adulthood. Learning and Individual Differences, 25, 99–110. doi:10.1016/j.lindif.2013.01.014
40.
MammarellaI. C.CaviolaS.GiofrèD.SzűcsD. (2018). The underlying structure of visuospatial working memory in children with mathematical learning disability. British Journal of Developmental Psychology, 36, 220–235. doi:10.1111/bjdp.12202
41.
MammarellaI. C.CornoldiC.PazzagliaF.TosoC.GrimoldiM.VioC. (2006). Evidence for a double dissociation between spatial-simultaneous and spatial-sequential working memory in visuospatial (nonverbal) learning disabled children. Brain and Cognition, 62, 58–67. doi:10.1016/j.bandc.2006.03.007
42.
McLeanJ. F.HitchG. J. (1999). Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology, 74, 240–260. doi:10.1006/jecp.1999.2516
43.
MoreyC. C.MarevaS.LelonkiewiczJ. R.ChevalierN. (2018). Gaze-based rehearsal in children under 7: A developmental investigation of eye movements during a serial spatial memory task. Developmental Science, 21, e12559. Retrieved from https://doi.org/10.1111/desc.12559
44.
MorrisonA. B.CheinJ. M. (2011). Does working memory training work? The promise and challenges of enhancing cognition by training working memory. Psychonomic Bulletin and Review, 18, 46–60. doi:10.3758/s13423-010-0034-0
45.
PassolunghiM. C.CornoldiC. (2008). Working memory failures in children with arithmetical difficulties. Child Neuropsychology, 14, 387–400. doi:10.1080/09297040701566662
46.
PassolunghiM. C.MammarellaI. C. (2010). Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving. European Journal of Cognitive Psychology, 22, 944–963. doi:10.1080/09541440903091127
47.
PassolunghiM. C.MammarellaI. 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
48.
PengP.NamkungJ.BarnesM.SunC. (2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108, 455–473. doi:10.1037/edu0000079
49.
PetersG. -J. Y. (2014). The alpha and the omega of scale reliability and validity: Why and how to abandon Cronbach’s alpha and the route towards more comprehensive assessment of scale quality. European Health Psychologist, 16, 56–69. doi:10.31234/osf.io/h47fv
50.
RaghubarK. P.BarnesM. A.HechtS. A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20, 110–122. doi:10.1016/j.lindif.2009.10.005
51.
R Core Team. (2018). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
52.
RohrkemperM. (1986). The functions of inner speech in elementary school students’ problem-solving behavior. American Educational Research Journal, 23, 303–313. Retrieved from https://doi.org/10.3102/00028312023002303
SchneiderW. (2008). The development of metacognitive knowledge in children and adolescents: Major trends and implications for education. Mind, Brain, and Education, 2, 114–121. doi:10.1111/j.1751-228X.2008.00041.x
55.
SimmonsF. R.WillisC.AdamsA.-M. (2012). Different components of working memory have different relationships with different mathematical skills. Journal of Experimental Child Psychology, 111, 139–155. doi:10.1016/j.jecp.2011.08.011
56.
SoltanlouM.PixnerS.NuerkH.-C. (2015). Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: A longitudinal investigation. Frontiers in Psychology, 6, 1062. doi:10.3389/fpsyg.2015.01062
57.
SwansonH. L.Beebe-FrankenbergerM. (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, 471–491. doi:10.1037/0022-0663.96.3.471
58.
SwansonH. L.Sachse-LeeC. (2001). Mathematical problem solving and working memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology, 79, 294–321. doi:10.1006/JECP.2000.2587
59.
SwansonL.KimK. (2007). Working memory, short-term memory, and naming speed as predictors of children’s mathematical performance. Intelligence, 35, 151–168. doi:10.1016/J.INTELL.2006.07.001
60.
SzűcsD.CsépeV. (2004a). Access to numerical information is dependent on the modality of stimulus presentation in mental addition: A combined ERP and behavioral study. Brain Research: Cognitive Brain Research, 19, 10–27. doi:10.1016/j.cogbrainres.2003.11.002
61.
SzűcsD.CsépeV. (2004b). Similarities and differences in the coding of numerical and alphabetical order using acoustic stimulation as revealed by event-related potentials in humans. Neuroscience Letters, 360, 65–68. doi:10.1016/j.neulet.2004.02.038
62.
SzűcsD.DevineA.SolteszF.NobesA.GabrielF. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex; A Journal Devoted to the Study of the Nervous System and Behavior, 49, 2674–2688. doi:10.1016/j.cortex.2013.06.007
63.
TremblayS.Saint-AubinJ.JalbertA. (2006). Rehearsal in serial memory for visual-spatial information: Evidence from eye movements. Psychonomic Bulletin & Review, 13, 452–457.
64.
Van de Weijer-BergsmaE.KroesbergenE. H.Van LuitJ. E. H. (2015). Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school. Memory & Cognition, 43, 367–378. doi:10.3758/s13421-014-0480-4
65.
WilsonK. M.SwansonH. L. (2001). Are mathematics disabilities due to a domain-general or a domain-specific working memory deficit?Journal of Learning Disabilities, 34, 237–248. doi:10.1177/002221940103400304
ZhengX.SwansonH. L.MarcoulidesG. A. (2011). Working memory components as predictors of children’s mathematical word problem solving. Journal of Experimental Child Psychology, 110, 481–498. doi:10.1016/J.JECP.2011.06.001
68.
ZinbargR. E.RevelleW.YovelI.LiW. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ωH: Their relationship with each other and two alternative conceptualizations of reliability. Psychometrika, 70, 123–133.
