The aim of this paper was to examine the role of phonological working memory in specific mental arithmetic difficulties and general arithmetic learning difficulties (ALD; difficulties presenting in both mental arithmetic and written arithmetic). In Study 1, we categorized 53 sixth graders into a control group, a group with specific mental arithmetic difficulties, and a group with general ALD. The findings indicated the group with specific mental arithmetic difficulties performed significantly worse on the task involving phonological working memory than did the control group. However, a significant difference was not found between the group with general ALD and the control group. In Study 2 involving 54 sixth graders, we decreased the load of phonological working memory by changing the format of the problems from horizontal (more reliance on phonological codes) to vertical (more reliance on visual resources). We found that the group with specific mental arithmetic difficulties performed comparably to the control group. In other words, when the working memory load is reduced, they no longer lag significantly behind on mental arithmetic. However, the group with general ALD still performed significantly worse than the control group when the problems were presented vertically, indicating that reduced phonological working memory load did not alleviate their arithmetic difficulties. The findings in both studies suggested that poor phonological working memory might contribute to the underlying mechanism for specific mental arithmetic difficulties but not as much for general ALD.
AdamsJ. W.HitchG. J. (1997).
Working memory and children’s mental addition. Journal of Experimental Child Psychology,
67(1), 21–38. https://doi.org/10.1006/jecp.1997.2397
AshcraftM. H.DonleyR. D.HalasM. A.VakaliM. (1992). Working memory, automaticity, and problem difficulty. In CampbellJ. I. D. (Ed.), The nature and origins of mathematical skill (pp. 301–329).
Elsevier Science Publishers. https://doi.org/10.1016/S0166-4115(08)60890-0
BaddeleyA. D. (2003).
Working memory: Looking back and looking forward. Nature Reviews Neuroscience,
4(10), 829–839. https://doi.org/10.1038/nrn1201
8.
BaddeleyA. D.HitchG. J. (1974). Working memory. In BowerG. A. (Ed.), Recent advances in learning and motivation (Vol.
8, pp. 47–90).
Academic Press. https://doi.org/10.1016/S0079-7421(08)60452-1
9.
BaddeleyA. D.LogieR. H. (1999). Working memory: The multiple-component model. In MiyakeA.ShahP. (Eds.), Models of working memory (pp. 28–61).
Cambridge University Press. https://doi.org/10.1017/CBO9781139174909.005
10.
BarnesM. A.WilkinsonM.KhemaniE.BoudesquieA.DennisM.FletcherJ. M. (2006).
Arithmetic processing in children with spina bifida: Calculation accuracy, strategy use, and fact retrieval fluency. Journal of Learning Disabilities,
39(2), 174–187. https://doi.org/10.1177/00222194060390020601
11.
BergD. H. (2008).
Working memory and arithmetic calculation in children: The contributory roles of processing speed, short-term memory, and reading. Journal of Experimental Child Psychology,
99(4), 288–308. https://doi.org/10.1016/j.jecp.2007.12.002
12.
BlairC.RazzaR. P. (2007).
Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development,
78, 647–663. https://doi.org/10.1111/j.1467-8624.2007.01019.x
ButterworthB. (2005). Developmental dyscalculia. In CampbellJ. I. D. (Ed.), Handbook of mathematical cognition (pp. 455–467).
Psychology Press.
15.
CampbellJ. I. D.AlbertsN. M. (2009).
Operation-specific effects of numerical surface form on arithmetic strategy. Journal of Experimental Psychology Learning Memory & Cognition,
35(4), 999–1011. https://doi.org/10.1037/a0015829
16.
CampbellJ. I. D.EppL. J. (2005). Architectures for arithmetic. In CampbellJ. I. D. (Ed.), Handbook of mathematical cognition (pp. 347–360).
Psychology Press.
17.
CampbellJ. I. D.FugelsangJ. (2001).
Strategy choice for arithmetic verification: Effects of numerical surface form. Cognition,
80(3), B21–B30. https://doi.org/10.1016/S0010-0277(01)00115-9
18.
CampbellJ. I. D.ParkerH. R.DoetzelN. L. (2004).
Interactive effects of numerical surface form and operand parity in cognitive arithmetic. Journal of Experimental Psychology Learning Memory & Cognition,
30(1), 51–64. https://doi.org/10.1037/0278-7393.30.1.51
19.
CampbellJ. I. D.XueQ. (2001).
Cognitive arithmetic across cultures. Journal of Experimental Psychology: General,
130(2), 299–315. https://doi.org/10.1037/0096-3445.130.2.299
20.
CavdarogluS.KnopsA. (2016).
Mental subtraction and multiplication recruit both phonological and visuospatial resources: Evidence from a symmetric dual-task design. Psychological Research,
80(4), 608–624. https://doi.org/10.1007/s00426-015-0667-8
21.
ChenY.-H.WangM.-Y. (2006).
The influence of working memory span on children’s arithmetical cognitive strategies. Psychological Development and Education,
22(2), 29–35. https://doi.org/10.3969/j.issn.1001-4918.2006.02.006
22.
CostaA. J.SilvaJ. B.ChagasP. P.KrinzingerH.LonnemanJ.WillmesK., . . . HaaseV. G. (2011).
A hand full of numbers: A role for offloading in arithmetics learning?Frontiers in Psychology,
2(4), 368. https://doi.org/10.3389/fpsyg.2011.00368
23.
D’AmicoA.GuarneraM. (2005).
Exploring working memory in children with low arithmetical achievement. Learning & Individual Differences,
15(3), 189–202. https://doi.org/10.1016/j.lindif.2005.01.002
24.
D’AmicoA.PassolunghiM. C. (2009).
Naming speed and effortful and automatic inhibition in children with arithmetic learning disabilities. Learning & Individual Differences,
19(2), 170–180. https://doi.org/10.1016/j.lindif.2009.01.001
25.
De RammelaereS.StuyvenE.VandierendonckA. (1999).
The contribution of working memory resources in the verification of simple mental arithmetic sums. Psychological Research,
62(1), 72–77. https://doi.org/10.1007/s004260050041
26.
De RammelaereS.StuyvenE.VandierendonckA. (2001).
Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved?Memory & Cognition,
29(2), 267–273. https://doi.org/10.3758/BF03194920
DehaeneS.CohenL. (1995).
Towards an anatomical and functional model of number processing. Mathematical Cognition,
1, 83–120.
29.
DeStefanoD.LeFevreJ. A. (2004).
The role of working memory in mental arithmetic. European Journal of Cognitive Psychology,
16(3), 353–386. https://doi.org/10.1080/09541440244000328
Fuchs, L. S., Fuchs,D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., et al. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 29–43.
33.
FurstA. J.HitchG. J. (2000).
Separate roles for executive and phonological components of working memory in mental arithmetic. Memory & Cognition,
28(5), 774–782. https://doi.org/10.3758/BF03198412
34.
GaoB.-C. (2011). The relations between multiplication learning strategies, working memory, and multiplication of primary school students [Unpublished doctoral dissertation]. Beijing Normal University.
35.
GearyD. C. (1993).
Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin,
114, 345–362.
36.
GearyD. C. (2003). Learning disabilities in arithmetic: Problem-solving differences and cognitive deficits. In SwansonH. L.HarrisK. R.GrahamS. (Eds.), Handbook of learning disabilities (pp. 199–212).
Guilford Press.
GearyD. C. (2011).
Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology,
47, 1539–1552. https://doi.org/10.1037/a0025510
39.
GearyD. C.BrownS. C. (1991).
Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology,
27(3), 398–406. https://doi.org/10.1037/0012-1649.27.3.398
40.
GearyD. C.HamsonC. O.HoardM. K. (2000).
Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology,
77, 236–263. https://doi.org/10.1006/jecp.2000.2561
41.
GearyD. C.HoardM. K.Byrd-CravenJ.DeSotoM. 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(2), 121–151. https://doi.org/10.1016/j.jecp.2004.03.002
42.
GearyD. C.HoardM. K.HamsonC. O. (1999).
Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk of mathematical disability. Journal of Experimental Child Psychology,
74, 213–239. https://doi.org/10.1006/jecp.1999.2515
43.
GrantJ. D.DagenbachD. (2000).
Further considerations regarding inhibitory processes, working memory, and cognitive aging. The American Journal of Psychology,
113(1), 69–94. https://doi.org/10.2307/1423461
44.
GreiffensteinM. F.BakerW. J. (2002).
Neuropsychological and psychosocial correlates of adult arithmetic deficiency. Neuropsychology,
16(4), 451–458. https://doi.org/10.1037/0894-4105.16.4.451
45.
HanichL. B.JordanN. C.KaplanD.DickJ. (2001).
Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology,
93, 615–626. https://doi.org/10.1037//0022-0663.93.3.615
46.
HalfordG. S. (1993). Children’s understanding: The development of mental models.
Lawrence Erlbaum.
47.
HeathcoteD. (1994).
The role of visuo-spatial working memory in the mental addition of multi-digit addends. Cahiers De Psychologie Cognitive Current Psychology of Cognition,
13(2), 207–245.
48.
HechtS. A. (2002).
Counting on working memory in simple arithmetic when counting is used for problem solving. Memory & Cognition,
30(3), 447–455. https://doi.org/10.3758/BF03194945
49.
HechtS. A.TorgesenJ. K.WagnerR. K.RashotteC. A. (2001).
The relations between phonological processing abilities and emerging individual differences in mathematical computational skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology,
79(2), 192–227. https://doi.org/10.1006/jecp.2000.2586
50.
HitchJ. G.McAuleyE. (1991).
Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology,
82(3), 375–386. https://doi.org/10.1111/j.2044-8295.1991.tb02406.x
51.
HuttenlocherJ.JordanN. C.LevineS. C. (1994).
A mental model for early arithmetic. Journal of Experimental Psychology: General,
123, 377–380. https://doi.org/10.1037/0096-3445.123.3.284
52.
ImboI.LeFevreJ.-A. (2010).
The role of phonological and visual working memory in complex arithmetic for Chinese- and Canadian-educated adults. Memory & Cognition,
38(2), 176–185. https://doi.org/10.3758/MC.38.2.176
53.
JordanN. C.HanichL. B. (2003).
Characteristics of children with moderate mathematics deficiencies: A longitudinal perspective. Learning Disabilities Research and Practice,
18, 213–221. https://doi.org/10.1111/1540-5826.00076
54.
JordanN. C.HanichL. B.KaplanD. (2003).
A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development,
74, 834–850. https://doi.org/10.1111/1467-8624.00571
55.
JordanN. C.MontaniT. O. (1997).
Cognitive arithmetic and problem solving: A comparison of children with specific and general mathematics difficulties. Journal of Learning Disabilities,
30(6), 624–634. https://doi.org/10.1177/002221949703000606
56.
Johnson-LairdP. N. (1983). Mental models.
Harvard University Press.
57.
KayeD. B.DeWinstanleyP.ChenQ.BonnefilV. (1989).
Development of efficient arithmetic computation. Journal of Educational Psychology,
81(4), 467–480. https://doi.org/10.1037/0022-0663.81.4.467
58.
KuangH. (2008). Working memory and mental addition and subtraction in children [Unpublished master’s thesis]. Central China Normal University.
LemaireP. (1996).
The role of working memory resources in simple cognitive arithmetic. Journal of Cognitive Psychology,
8(1), 73–104. https://doi.org/10.1080/095414496383211
61.
LevineS. C.JordanN. C.HuttenlocherJ. (1992).
Development of calculation abilities in young children. Journal of Experimental Child Psychology,
53, 72–103. https://doi.org/10.1016/S0022-0965(05)80005-0
62.
LiD.-M.LiuC.LiG.-Y. (2003).
Development in digit working memory span across life span and its influential factors. Acta Psychologica Sinica,
35(1), 63–68.
63.
LiuR.-D.DingY.XuL.WangJ. (2017).
Involvement of working memory in mental multiplication in Chinese elementary students. The Journal of Educational Research,
110(4), 380–390. https://doi.org/10.1080/00220671.2015.1103689
64.
LogieR. H.GilhoolyK. J.WynnV. (1994).
Counting on working memory in arithmetic problem solving. Memory & Cognition,
22(4), 395–410. https://doi.org/10.3758/BF03200866
McCloskeyM.HarleyW.SokolS. M. (1991).
Models of arithmetic fact retrieval: An evaluation in light of findings from normal and brain-damaged subjects. Journal of Experimental Psychology Learning Memory & Cognition,
17(3), 377–397. https://doi.org/10.1037/0278-7393.17.3.377
67.
McLeanJ. F.HitchG. J. (1999).
Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology,
74(3), 240–260. https://doi.org/10.1006/jecp.1999.2516
68.
MetcalfeA. W.CampbellJ. I. (2008).
Spoken numbers versus Arabic numerals: Differential effects on adults’ multiplication and addition. Canadian Journal of Experimental Psychology,
62(1), 56–61. https://doi.org/10.1037/1196-1961.62.1.56
MiyakeA.ShahP. (Eds.). (1999). Models of working memory: Mechanisms of active maintenance and executive control.
Cambridge University Press. https://doi.org/10.1017/CBO9781139174909
71.
MorsanyiK.van BersB. M.O’ConnorP. A.McCormackT. (2018).
Developmental dyscalculia is characterized by order processing deficits: Evidence from numerical and non-numerical ordering tasks. Developmental Neuropsychology,
43, 595–621. https://doi.org/10.1080/87565641.2018.1502294
72.
NoëlM. P.FiasW.BrysbaertM. (1997).
About the influence of the presentation format on arithmetical-fact retrieval processes. Cognition,
63(3), 335–374. https://doi.org/10.1016/S0010-0277(97)00009-7
73.
ParlatoV.LopezO. L.PanissetM.IavaroneA.GrafmanJ.BollerF. (1992).
Mental calculation in mild Alzheimer’s disease: A pilot study. International Journal of Geriatric Psychiatry,
7(8), 599–602. https://doi.org/10.1002/gps.930070810
74.
PassolunghiM. C.MammarellaI. C. (2010).
Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving. Journal of Cognitive Psychology,
22(6), 944–963. https://doi.org/10.1080/09541440903091127
75.
PassolunghiM. C.SiegelL. S. (2001).
Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology,
80(1), 44–57. https://doi.org/10.1006/jecp.2000.2626
76.
PengP.NamkungJ.BarnesM.SunC. Y. (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. https://doi.org/10.1037/edu0000079
77.
RasmussenC.BisanzJ. (2005).
Representation and working memory in early arithmetic. Journal of Experimental Child Psychology,
91, 137–157. https://doi.org/10.1016/j.jecp.2005.01.004
RémyF.MirrashedF.CampbellB.RichterW. (2004).
Mental calculation impairment in Alzheimer’s disease: A functional magnetic resonance imaging study. Neuroscience Letters,
358(1), 25–28. https://doi.org/10.1016/j.neulet.2003.12.122
80.
RourkeB. P. (1993).
Arithmetic disabilities, specific and otherwise: A neuropsychological perspective. Journal of Learning Disabilities,
26(4), 214–226. https://doi.org/10.1177/002221949302600402
81.
RousselleL.NoëlM. P. (2008).
Mental arithmetic in children with mathematics learning disabilities: The adaptive use of approximate calculation in an addition verification task. Journal of Learning Disabilities,
41(6), 498–513. https://doi.org/10.1177/0022219408315638
82.
SalthouseT. A.BabcockR. L. (1991).
Decomposing adult age differences in working memory. Developmental Psychology,
27(27), 763–776. https://doi.org/10.1037/0012-1649.27.5.763
83.
SchunnC. D.RederL. M.NhouyvanisvongA.RichardsD. R.StroffolinoP. J. (1996).
To calculate or not to calculate: A source activation confusion model of problem familiarity’s role in strategy selection. Journal of Experimental Psychology Learning Memory & Cognition,
23(1), 3–29. https://doi.org/10.1037/0278-7393.23.1.3
84.
SeitzK.Schumann-HengstelerR. (2002).
Phonological loop and central executive processes in mental addition and multiplication. Psychologische Beitrage,
44(2, 8 Supplement), 275–302.
85.
SeylerD. J.KirkE. P.AshcraftM. H. (2003).
Elementary subtraction. Journal of Experimental Psychology: Learning, Memory, and Cognition,
29(6), 1339–1352. https://doi.org/10.1037/0278-7393.29.6.1339
86.
SwansonH. L. (2011).
Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children. Journal of Educational Psychology,
103, 821–837. https://doi.org/10.1037/a0025114
87.
SwansonH. L.JermanO. (2006).
Math disabilities: A selective meta-analysis of the literature. Review of Educational Research,
76, 249–274. https://doi.org/10.3102/00346543076002249
88.
TempleC. M.SherwoodS. (2002).
Representation and retrieval of arithmetical facts: Developmental difficulties. Quarterly Journal of Experimental Psychology,
55A, 733–752. https://doi.org/10.1080/02724980143000550
89.
Thevenot, C., & Castel, C. (2012). Relationship and transfer between mental and written arithmetic. Journal of Cognitive Psychology, 24(3), 286–294. http://doi.org/10.1080/20445911.2011.617302
90.
ThevenotC.FangetM.FayolM. (2007).
Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm. Memory & Cognition,
35(6), 1344–1352. https://doi.org/10.3758/BF03193606
91.
TrbovichP. L.LeFevreJ.-A. (2003).
Phonological and visual working memory in mental addition. Memory & Cognition,
31(5), 738–745. https://doi.org/10.3758/BF03196112
Van der SluisS.van der LeijA.de JongP. F. (2005).
Working memory in Dutch children with reading- and arithmetic-related LD. Journal of Learning Disabilities,
38(3), 207–221. https://doi.org/10.1177/00222194050380030301
WangE.-G.LiuC.ZhaoG.-X. (2008).
Processing speed and working memory in children with mathematical disabilities. Psychological Science,
31(4), 856–860.
96.
WuC.-Z. (2010). The influence of working memory and mathematic anxiety on children’s mental arithmetic cognitive strategies [Unpublished master’s thesis]. Henan University.
97.
XingQ.XiaJ.-J.WangC.-Y. (2016).
The influence of working memory capacity and content relevance on category learning. Psychological Development and Education,
32(3), 324–329. https://doi.org/10.16187/j.cnki.issn1001-4918.2016.03.09
98.
ZbrodoffN. J.LoganG. D. (2005). What everyone finds: The problem size effect. In CampbellJ. I. D. (Ed.), Handbook of mathematical cognition (pp. 331–345).
Psychology Press.
99.
ZhangQ.LinC.-D.ZhaoD.-M.WangX.-L. (2002).
The developmental study of the speed and span of mental addition of pupils. Psychological Development and Education,
1, 16–21. https://doi.org/10.3969/j.issn.1001-4918.2002.01.004
100.
ZhouS.-J.YangJ.ZhangL.-Y. (2006).
Working memory, executive function, processing speed and reasoning and mental arithmetic in children with mathematical disabilities. Chinese Journal of Clinical Psychology,
14(6), 574–577. https://doi.org/10.3969/j.issn.1005-3611.2006.06.008
