Working memory in children's math learning and its ... · memory in children’s math learning and its disruption in dyscalculia Vinod Menon Working memory (WM) plays an essential

Working memory in children’s math learning andits disruption in dyscalculiaVinod Menon

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Working memory (WM) plays an essential role in children’s

mathematical learning. WM influences both the early

foundational phases of number knowledge acquisition and

subsequent maturation of problem solving skills. The role of

individual WM components in mathematical cognition depends

not only on problem complexity but also on individual

differences in mathematical abilities. Furthermore, the

contributions of individual WM components change

dynamically over development with visuospatial processes

playing an increasingly important role in learning and enhancing

mathematical proficiency. Convergent findings from

neuroimaging studies are now providing fundamental insights

into the link between WM and mathematical cognition, and the

mechanisms by which poor WM contributes to learning

disabilities. Evidence to date suggests that visuospatial WM is

a specific source of vulnerability in children with mathematical

learning disabilities and needs to be considered as a key

component in cognitive, neurobiological, and developmental

models of typical and atypical mathematical skill acquisition.

Address

Stanford University, Stanford, CA, United States

Corresponding author: Menon, Vinod ([email protected])

Current Opinion in Behavioral Sciences 2016, 10:125–132

This review comes from a themed issue on Neuroscience of

education

Edited by Denes Szu cs, Fumiko Hoeft and John DE Gabrieli

For a complete overview see the Issue and the Editorial

Available online 7th June 2016

doi:10.1016/j.cobeha.2016.05.014

2352-1546/# 2016 Elsevier Ltd. All rights reserved.

IntroductionMany aspects of children’s academic skill acquisition

require access to working memory (WM) resources

[1–3]. In no academic domain is this truer than in math-

ematical cognition where problem solving abilities de-

pend on the capacity to efficiently manipulate quantity

representations in WM [4��,5]. Over three decades of

behavioral research have established that numerical prob-

lem solving tasks place strong demands on the active

maintenance and manipulation of task-relevant informa-

tion in WM [5,6]. Cross-sectional and longitudinal studies

are providing new insights into the role of individual

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WM components at different stages of mathematical skill

acquisition. Deficits in WM in children with dyscalculia

contribute to weaknesses in the representation of quanti-

ty information, as well as the ability to manipulate this

information during numerical problem solving [7��]. Con-

vergent findings from neuroimaging studies provide fun-

damental insights into the link between WM and

mathematical cognition, and the mechanisms by which

poor WM contributes to dyscalculia. A common neural

locus of deficits in visuospatial quantity representations

and visuospatial WM likely contributes to both numerical

magnitude judgment and arithmetic problem solving

deficits in children with dyscalculia.

Working memory in children’s mathematicalcognition and learningThe particular emphasis on WM in developmental stud-

ies has its origins in children’s immature problem solving

abilities, which require them to break down numerical

problems into more basic components. The use of such

strategies necessitates greater reliance on WM systems

for problem solving in children. For example, children

rely more on counting strategies during simple arithmetic

problem solving and need to access multiple WM com-

ponents including short-term storage and rule-based

manipulation and updating of the contents of stored

information [8]. With increased proficiency and a switch

to fact retrieval strategies there is less demand and need

for WM resources [9,10]. The link between WM and

children’s mathematical cognition and learning has large-

ly been based on Baddeley and Hitch’s influential mul-

ticomponent model [11,12]. Briefly, this model includes a

central executive component, responsible for high-level

control, monitoring, and task switching, along with two

subordinate, modality-dependent components, impor-

tant for short-term storage of verbal and visuospatial

information, respectively [11]. Crucially, all three com-

ponents of WM can be distinguished from an early age

[13].

Developmental studies using the Baddeley and Hitch

model have predominantly reported a strong link

between the central executive and visuospatial WM

components and math abilities [9,14–17] (Simmons

et al., 2012). The effects of phonological WM have gen-

erally been much weaker, and are typically more evident

during very early stages (ages 4–5), when phonological

representations for numbers are still weak and word-

based problem solving places greater demands on reading

comprehension. In a detailed cognitive analysis of the


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126 Neuroscience of education

factors that contribute to mathematical abilities, Szucs

and colleagues found strong relations between visuospa-

tial WM measures, but not phonological WM measures,

and mathematical abilities in a large well-characterized

group of 9 year-old children [18].

Figure 1

(a) Numerical

(b) Arithmetic

(c) Working Memory

(d) Visuospatial

L R

Common patterns of fronto-parietal network activations elicited by numerica

Results from meta-analysis conducted using Neurosynth (www.neurosynth.o


Longitudinal studies have expanded on these findings

and shown that the central executive component predicts

performance on single-digit addition tasks in grades 1 to

3 as well as faster transitions from simple (e.g., counting)

to sophisticated (e.g., decomposition) solution strategies

Current Opinion in Behavioral Sciences

l, arithmetic, working memory and visuospatial processing tasks.

rg) with the corresponding search terms.


http://www.neurosynth.org/

Working memory in children’s math learning Menon 127

[16]. Similarly, in a large sample of 673 children, Lee and

Bull found that WM updating capacity in kindergarten

predicted growth rate of math abilities (numerical opera-

tions) in subsequent grades [19].

It is important to note that the role of individual WM

components depends not only on task complexity but also

on children’s developmental stage. The changing role of

WM components can be detected even in a 1-year time-

window between ages 8 and 9. Meyer and colleagues found

that while the central executive and phonological compo-

nents of WM predicted mathematical abilities in second

graders, it was the visuospatial component that predicted

Figure 2

Overlap of VS and CE

L SMG

SMG

SMG

0

1

–1

–25 10 20 30

Act

ivit

y (β

)

2515

Z = 34 Y = –43

Working Memory Score

VS r = .353

CE r = .334

IPS

Functional dissociations and overlap between brain areas associated with e

children (N = 74). The neural correlates of the central executive (CE), phono

were examined by contrasting brain responses to two different types of add

and VS components was observed only in left supramarginal gyrus (SMG);

intra-parietal sulcus (IPS); no overlap was observed between VS and PL co

depicted. No overlap for VS and PL (magenta) was observed. Bottom pane

correlations of activity and individual working memory components. Scatter

regression analysis, and are provided for the purpose of visualization. L, lef

Source: [23��].


abilities in third graders [17]. Similarly, Li and Geary

reported individual differences in the growth rate of visuo-

spatial WM during childhood. Notably, they found that

these differences became increasingly important for learn-

ing over time [20]. Nuerk and colleagues examined longi-

tudinal changes associated with multiplication fact retrieval

[21�]. They found that multiplication task performance was

correlated with verbal WM in third graders but with visuo-

spatial WM in grade four. Taken together, these patterns of

relationships suggest that the contributions of individual

WM processes change dynamically over development with

visuospatial WM processes playing an increasingly impor-

tant role in enhancing mathematical proficiency.

L IPS

Overlap of PL and CE

1

0

–1

–25

Act

ivit

y (β

)

25 3515Working Memory Score

PL r = .374

CE r = .417

Z = 54 Y = –47

CE

PL VS


ach of the three components of working memory in 7 to 9-year-old

logical (PL) and visuo-spatial (VS) components of working memory

ition problems that differed in complexity. Overlap between the CE

overlap between CE and PL components was observed only in the left

mponents. Negative correlation between activity and PL ability is not

l: coronal slices depict regions of interest selected as overlap in

plots are based on functional clusters identified using whole-brain

t.



Figure 3


(a) (a)

(b)

TD

L MFG

L IFG

L IPS R IPS

R VisualCortex

Cerebellum Cerebellum

R FusiformGyrus

R MFG

Cingulate Gyrus

Precuneus

Y = –44 X = 0 Y = –56 X = 40

R MFG

L IPS

R MFGR AIC

Z = 10Y = 32

L MFG

DD

L Postcentral GyrusPositive Correlations

Negative Correlations

4

4

2

2

(b)TD > DD

(a)

(b)

Prefrontal

Parietal

X = –42Z = 36

Z = 36Z = 20

DDTD

42

L IFG

L IPS R SMG

R MFG

Block Recall

Block Recall Block Recall

Block Recall

T S

core

T S

core

T S

core

T S

core

50 60 70 80 90 100 110 120

50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120

50 60 70 80 90 100 110 120–2–1

0

1

23

4

–2–1

0

1

23

4

–2–1

0

1

23

4

–2–1

0

1

23

4r = –.65∗∗

r = .55∗ r = –.50∗

r = –.60∗r = –.23

r = –.21 r = –.15

r = –.29

Children with dyscalculia do not use visuospatial working memory resources appropriately during arithmetic problem solving. (A) Brain areas in

which activity during arithmetic problem solving was significantly correlated with visuo-spatial working memory abilities in the typically developing

(TD) and developmental dyscalculia (DD) groups. (a) In the TD group, Block Recall, a measure of visuo-spatial working memory, was correlated

with activity in bilateral middle frontal gyrus (MFG), left inferior frontal gyrus (IFG), right anterior insula (AIC), anterior, middle and posterior

cingulate cortex and precuneus, bilateral intraparietal sulcus (IPS), right fusiform gyrus, left temporal pole and the cerebellum. No negative

Current Opinion in Behavioral Sciences 2016, 10:125–132 www.sciencedirect.com


Working memory and fronto-parietal systemsassociated with children’s mathematicalcognitionFunctional neuroimaging research has revealed signifi-

cant overlap in multiple parietal and prefrontal cortex

regions involved in WM and numerical problem solving

[22–24]. Overlapping patterns of activation have most

prominently been detected in the supramarginal gyrus

and intraparietal sulcus in the posterior parietal cortex,

the premotor cortex, and the ventral and dorsal aspects

of the lateral prefrontal cortex (Figure 1). It is impor-

tant to note, however, that the common patterns of

fronto-parietal cortex engagement during WM and nu-

merical problem solving cannot be conflated with

shared neural mechanisms, and research on this topic

has used both correlational and causative analyses

to gain a deeper understanding of the shared neural

mechanisms [25].

Neuroimaging studies in typical and atypical develop-

ment are helping to provide a more mechanistic under-

standing of the link between individual WM components

and brain responses associated with mathematical prob-

lem solving. The involvement of WM in mathematical

cognition had initially been surmised based on overlap-

ping responses in posterior parietal cortex and prefrontal

cortex in the two domains [26–29]. Studies of typical

development provided initial evidence for the changing

role of WM with age. For example, Rivera and colleagues

found that relative to adolescents and young adults,

children engage the posterior parietal cortex less, and

the prefrontal cortex more, when solving arithmetic pro-

blems [29], likely reflecting the increased role of visuo-

spatial WM processes, and concurrent decrease in

demands on cognitive control with age. Other studies

have more directly addressed the link between WM

abilities and numerical problem solving skills.

Dumontheil and Klingberg [30] found that activity in

the intraparietal sulcus during a visuospatial WM task

predicted arithmetic performance two years later in a

sample of 6- to 16-year-old children and adolescents.

This finding further reinforces the link between visuo-

spatial WM and numerical problem solving and suggests a

common underlying process in the intraparietal sulcus

subdivision of the posterior parietal cortex.

More detailed analyses of the neural correlates of indi-

vidual components of WM have provided evidence for

(Figure 3 continued) correlations were observed in the TD group. (b) In the

postcentral gyrus. No positive correlations were observed in the DD group.

during arithmetic problem solving and visuo-spatial working memory abilitie

cortex. In TD children, left inferior frontal gyrus (IFG) and right middle fronta

activation during Complex addition problems and Block Recall, a measure o

nonsignificant in children with DD. (b) Parietal cortex. In TD children, the lef

showed significant positive correlation between activation during arithmetic

significant correlations (*P < .05, **P < .01).

Source: [52�].


the fractionation of neurofunctional systems associated

with distinct WM components during numerical problem

solving [23��]. Analysis of the relation between the central

executive, phonological and visuospatial components of

WM and brain activation during an arithmetic verification

task in a large (N = 74) group of 7 to 9-year-old children

revealed that visuospatial WM is the strongest predictor

of mathematical ability in children in this age group and is

associated with increased arithmetic complexity-related

responses in left dorsolateral and right ventrolateral pre-

frontal cortices as well as in the bilateral intra-parietal

sulcus and supramarginal gyrus in posterior parietal cortex

(Figure 2). This neurobiological finding confirms a pivotal

role of visuospatial WM during arithmetic problem-solv-

ing in primary-school children.

Metcalfe and colleagues also found that visuospatial WM

and the central executive component were associated

with largely distinct patterns of brain responses during

arithmetic problem-solving, and overlap was only ob-

served in the ventral aspects of the left supramarginal

gyrus in the posterior parietal cortex, suggesting that this

region is an important locus for the integration of infor-

mation in WM during numerical problem solving [29,31–35].

Finally, there is also evidence that immature prefrontal

control systems associated with central executive func-

tions may contribute to weaker math skills in children.

Supekar and colleagues used dynamic causal analysis to

probe interactions between the prefrontal and parietal

cortices in children and adults [36]. They found that

despite higher levels of activation, the strength of causal

regulatory influences from the fronto-insular control net-

work to the posterior parietal cortex was significantly

weaker in children and weak signaling mechanisms con-

tributed to lower levels of performance in children, com-

pared to adults. More broadly, immature prefrontal

control systems may contribute to weaknesses in the

ability to inhibit irrelevant information such as arithmetic

facts or operations during numerical problem solving

[4��,37,38,39�].

Working memory disruption in children withdyscalculiaStudies of children with dyscalculia provide a unique

window into the role of WM in numerical cognition.

Dyscalculia is a specific deficit in arithmetic ability in

DD group, Block Recall was negatively correlated with activity in left

(B) Fronto-parietal cortical areas where the relation between activity

s differed significantly between the TD and DD groups. (a) Prefrontal

l gyrus (MFG) showed significant positive correlation between

f visuo-spatial working memory. In contrast, correlations were

t intra-parietal sulcus (IPS), and right supramarginal gyrus (SMG)

problem solving and Block Recall. In the DD group there were no



the presence of preserved intellectual and verbal abilities

[40–43]. Children with dyscalculia show poor perfor-

mance on a broad range of numerical tasks, including

magnitude judgment [44–47] and enumeration

[4��,48,49]. They also lag behind their typically develop-

ing peers in basic arithmetic problem solving skills

[4��,50]. There is growing evidence that deficits in

WM can contribute to multiple aspects of dyscalculia,

encompassing not only complex arithmetic problem solv-

ing but also basic quantity representation [4��,51��].

Multiple experimental paradigms across extended peri-

ods of early skill acquisition in the domains of number

sense and arithmetic have highlighted the involvement of

visuospatial WM in developmental models of dyscalculia.

At a more fundamental level, deficits in visuospatial WM

can influence the ability to engage and manipulate repre-

sentations of magnitude on a mental number line and

estimate non-symbolic quantity. Furthermore, other

areas of difficulty that define the profile of children with

dyscalculia, such as counting and subitizing, may have

their roots in visuospatial WM deficits [4��,49]. Conver-

gent with these observations, several lines of evidence

point to disruptions in visuospatial WM in children with

dyscalculia. Even when they are matched with typically

developing children on general intelligence, reading and

other cognitive measures, children with dyscalculia dem-

onstrate lower visuospatial WM despite preserved pho-

nological and central executive WM abilities [52�].Furthermore, Swanson et al. [53] found deficits in visuo-

spatial, but not in other WM components, differentiating

children with dyscalculia from children with reading

difficulties. Consistent with these findings, Rotzer et al.[54] found that children with dyscalculia had lower scores

than typically developing children on a Corsi Block-

Tapping Test. Thus, visuospatial WM deficits appear

to be a specific source of mathematical difficulty in

dyscalculia.

Visuospatial working memory and fronto-parietal impairments in children withdyscalculiaThe importance of visuospatial WM and associated

fronto-parietal processing during arithmetic problem-

solving is further highlighted by neuroimaging studies

in children with dyscalculia. Rotzer et al. [54] found that

compared to typically developing children, children with

low math abilities had lower visuospatial abilities and

lower activity levels in the right anterior intraparietal

sulcus, inferior frontal gyrus, and insular cortex during

a visuospatial WM task. Ashkenazi and colleagues [52�]identified impaired WM components in children with

dyscalculia and then examined their role in modulating

brain responses to numerical problem solving (Figure 3).

Children with dyscalculia had specific deficits in visuo-

spatial WM in addition to deficits in arithmetic task

performance. Crucially, activations in intraparietal sulcus,


and dorsolateral and ventrolateral prefrontal cortices were

positively correlated with visuospatial WM ability in

typically developing children, but no such relation was

seen in children with dyscalculia. This result suggests

that children with dyscalculia fail to appropriately exploit

visuospatial WM resources during problem solving. While

still preliminary, extant findings point to the intraparietal

sulcus as a common locus of visuospatial WM deficits and

arithmetic problem solving deficits in children with dys-

calculia. On the basis of these and other related findings,

we have suggested that parietal cortex mechanisms for

storing and manipulating quantity representations are

impaired in dyscalculia [23��,55��,56��].

ConclusionWM plays an integral role in children’s math learning and

development of problem solving abilities. The role of

individual WM components in mathematical cognition is

learning-stage dependent, both in terms of proficiency and

age. Behavioral and neuroimaging studies are converging

on the idea that the contributions of individual WM

processes and their neural substrates change dynamically

over development, with visuospatial WM processes play-

ing an increasingly important role in learning and enhanc-

ing mathematical proficiency. Although the role of the

visuospatial component of WM has often been considered

secondary to that of the central executive component in

typical arithmetic skill acquisition, and has generally been

neglected in prior accounts of dyscalculia and math learn-

ing disabilities, recent studies suggest that visuospatial

WM is a critical component for successfully building

quantity representations and efficiently manipulating

them during problem solving. These processes are impor-

tant at all stages of learning and skill acquisition, and are

significantly disrupted in children with dyscalculia.

Phonological WM appears most prominently in the earli-

est stages of learning the verbal mapping of quantity

representations and later gives way to visuospatial WM

processes important for the representation and manipu-

lation of quantity information in short-term memory. The

central executive system helps scaffold the early stages of

learning by providing support for building new semantic

representations. The central executive component is also

required at subsequent stages for more complex problem

solving procedures, including the active maintenance of

intermediate results and rule-based problem solving.

Within the neurocognitive framework highlighted in this

review, the engagement of the intraparietal sulcus and

supramarginal gyrus in the posterior parietal cortex, and

the ventral and dorsal aspects of the lateral prefrontal

cortex changes dynamically with problem complexity and

developmental stage. Findings to date suggest that the

intraparietal sulcus plays an essential role not only in

quantity representations but also in maintaining quantity-

related information in short-term WM. Rule-based



manipulation of these representations in WM is in turn

supported by multiple prefrontal cortical areas, with the

supramarginal gyrus as a key locus for integrating frontal

control systems with quantity representations supported

by the intraparietal sulcus. Together, they provide mul-

tiple functional circuits that support essential WM pro-

cesses in children’s mathematical cognition.

A challenging question for future research is to under-

stand how WM processes are used dynamically to support

different types of mathematical learning and how they

change with different stages of development. Addressing

this question will require developing appropriate compu-

tational models of dynamic causal interactions between

brain regions, analyzing different stages of information

processing, and utilizing more appropriate experimental

designs that involve the controlled manipulation of quan-

tity representations in WM [57]. Finally, training studies

also have the potential to inform causal links between

WM processing and mathematical learning [55��].

Conflict of interest statementNothing declared.

AcknowledgementsIt is a pleasure to thank Teresa Iuculano, Rachel Rehert and Se Ri Bae forvaluable feedback and careful proof-reading, and Se Ri Bae for assistancewith the figures. I also thank two anonymous reviewers for valuable feedback.

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38. Cho S, Metcalfe AWS, Young CB, Ryali S, Geary DC, Menon V:Hippocampal-prefrontal engagement and dynamic causalinteractions in the maturation of children’s fact retrieval. JCognit Neurosci 2012, 24(9):1849-1866.

39.�

Szucs D, Devine A, Soltesz F, Nobes A, Gabriel F: Developmentaldyscalculia is related to visuo-spatial memory and inhibitionimpairment. Cortex 2013, 49(10):2674-2688.

Identifies weaknesses in visuospatial working memory and inhibitioncontrol as key cognitive factors contributing to developmental dyscalcu-lia.

40. Butterworth B, Varma S, Laurillard D: Dyscalculia: from brain toeducation. Science 2011, 332(6033):1049-1053.

41. Rubinsten O, Henik A: Developmental dyscalculia:heterogeneity might not mean different mechanisms. TrendsCognit Sci 2009, 13(2):92-99.

42. Szucs D, Goswami U: Developmental dyscalculia: freshperspectives. Trends Neurosci Educ 2013, 2(2):33-37.

43. von Aster M, Shalev R: Number development anddevelopmental dyscalculia. Dev Med Child Neurol 2007,49(11):868-873.


44. Geary DC, Hamson CO, Hoard MK: Numerical and arithmeticalcognition: a longitudinal study of process and concept deficitsin children with learning disability. J Exp Child Psychol 2000,77(3):236-263.

45. Mussolin C, De Volder A, Grandin C, Schlogel X, Nassogne MC,Noel MP: Neural correlates of symbolic number comparison indevelopmental dyscalculia. J Cogn Neurosci 2010, 22(5):860-874.

46. Piazza M, Facoetti A, Trussardi AN, Berteletti I, Conte S,Lucangeli D, Dehaene S, Zorzi M: Developmental trajectory ofnumber acuity reveals a severe impairment in developmentaldyscalculia. Cognition 2010, 116(1):33-41.

47. Price GR, Holloway I, Rasanen P, Vesterinen M, Ansari D:Impaired parietal magnitude processing in developmentaldyscalculia. Curr Biol 2007, 17(24):R1042-R1043.

48. Landerl K, Bevan A, Butterworth B: Developmental dyscalculiaand basic numerical capacities: a study of 8–9-year-oldstudents. Cognition 2004, 93(2):99-125.

49. Schleifer P, Landerl K: Subitizing and counting in typical andatypical development. Dev Sci 2011, 14(2):280-291.

50. Shalev R, Manor O, Gross-Tsur V: Developmental dyscalculia: aprospective six-year follow-up. Dev Med Child Neurol 2005,47(2):121-125.

51.��

Fias W, Menon V, Szucs D: Multiple components ofdevelopmental dyscalculia. Trends Educ Neurosci 2013, 2(2):43-47.

Provides a fresh perspective on unresolved controversies regarding thefunctional impairments at the origin of dyscalculia, including workingmemory, approximate number system and attention. Argues for a neu-rocognitive network framework involving multiple functional componentsthat contribute to inefficient numerical problem solving and dyscalculia.

52.�

Ashkenazi S, Rosenberg-Lee M, Metcalfe AW, Swigart AG,Menon V: Visuo-spatial working memory is an importantsource of domain-general vulnerability in the development ofarithmetic cognition. Neuropsychologia 2013, 51(11):2305-2317.

Demonstrates that children with dyscalculia do not use visuospatialworking memory resources appropriately during problem solving, andidentifies the neural correlates of this deficit.

53. Swanson HL, Howard CB, Saez L: Do different components ofworking memory underlie different subgroups of readingdisabilities? J Learn Disabil 2006, 39(3):252-269.

54. Rotzer S, Loenneker T, Kucian K, Martin E, Klaver P, von Aster M:Dysfunctional neural network of spatial working memorycontributes to developmental dyscalculia. Neuropsychologia2009, 47(13):2859-2865.

55.��

Iuculano T, Rosenberg-Lee M, Richardson J, Tenison C, Fuchs L,Supekar K, Menon V: Cognitive tutoring induces widespreadneuroplasticity and remediates brain function in children withmathematical learning disabilities. Nat Commun 2015:6.

First demonstration that cognitive training in children with mathematicallearning disabilities can normalize aberrant responses in fronto-parietalresponses that support problem solving and working memory.

56.��

Jolles DD, Ashkenazi S, Kochalka J, Evans T, Richardson J,Rosenberg-Lee M, Zhao H, Supekar K, Chen T, Menon V: Parietalhyper-connectivity, aberrant brain organization, and circuit-based biomarkers in children with mathematical disabilities.Dev Sci 2016. (in press).

Identifies hyper-connectivity of the intraparietal sulcus with multiplefrontal and parietal areas, as well as higher levels of spontaneous lowfrequency fluctuations in fronto-parietal cortex, in children with dyscal-culia. Provides novel evidence for the view that dyscalculia is a network-level deficit.

57. Luck SJ, Vogel EK: Visual working memory capacity: frompsychophysics and neurobiology to individual differences.Trends Cognit Sci 2013, 17(8):391-400.
















































































































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Working memory in children's math learning and its ... · memory in children’s math learning and its disruption in dyscalculia Vinod Menon Working memory (WM) plays an essential