Working Memory in Children's Math Learning and Its Disruption In

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Working memory in children’s math learning and

its disruption in dyscalculia

Vinod Menon

Working memory (WM) plays an essential role in children’s WM components at different stages of mathematical skill

mathematical learning. WM inﬂuences both the early acquisition. Deﬁcits in WM in children with dyscalculia

foundational phases of number knowledge acquisition and contribute to weaknesses in the representation of quanti-

subsequent maturation of problem solving skills. The role of ty information, as well as the ability to manipulate this

individual WM components in mathematical cognition depends information during numerical problem solving [7 ]. Con-

not only on problem complexity but also on individual vergent ﬁndings from neuroimaging studies provide fun-

differences in mathematical abilities. Furthermore, the damental insights into the link between WM and

contributions of individual WM components change mathematical cognition, and the mechanisms by which

dynamically over development with visuospatial processes poor WM contributes to dyscalculia. A common neural

playing an increasingly important role in learning and enhancing locus of deﬁcits in visuospatial quantity representations

mathematical proﬁciency. Convergent ﬁndings from and visuospatial WM likely contributes to both numerical

neuroimaging studies are now providing fundamental insights magnitude judgment and arithmetic problem solving

into the link between WM and mathematical cognition, and the deﬁcits in children with dyscalculia.

mechanisms by which poor WM contributes to learning

disabilities. Evidence to date suggests that visuospatial WM is

Working memory in children’s mathematical

a speciﬁc source of vulnerability in children with mathematical

cognition and learning

learning disabilities and needs to be considered as a key

The particular emphasis on WM in developmental stud-

component in cognitive, neurobiological, and developmental

ies has its origins in children’s immature problem solving

models of typical and atypical mathematical skill acquisition.

abilities, which require them to break down numerical

Address problems into more basic components. The use of such

Stanford University, Stanford, CA, United States strategies necessitates greater reliance on WM systems

for problem solving in children. For example, children

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

rely more on counting strategies during simple arithmetic

problem solving and need to access multiple WM com-

Current Opinion in Behavioral Sciences 2016, 10:125–132 ponents including short-term storage and rule-based

manipulation and updating of the contents of stored

This review comes from a themed issue on Neuroscience of

education information [8]. With increased proﬁciency and a switch

to fact retrieval strategies there is less demand and need

Edited by De´ nes Szu¨ cs, Fumiko Hoeft and John DE Gabrieli

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

For a complete overview see the Issue and the Editorial

children’s mathematical cognition and learning has large-

Available online 7th June 2016

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

doi:10.1016/j.cobeha.2016.05.014 ticomponent model [11,12]. Brieﬂy, this model includes a

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

Introduction [13].

Many aspects of children’s academic skill acquisition

require access to working memory (WM) resources Developmental studies using the Baddeley and Hitch

[1–3]. In no academic domain is this truer than in math- model have predominantly reported a strong link

ematical cognition where problem solving abilities de- between the central executive and visuospatial WM

pend on the capacity to efﬁciently manipulate quantity components and math abilities [9,14–17] (Simmons

representations in WM [4 ,5]. Over three decades of et al., 2012). The effects of phonological WM have gen-

behavioral research have established that numerical prob- erally been much weaker, and are typically more evident

lem solving tasks place strong demands on the active during very early stages (ages 4–5), when phonological

maintenance and manipulation of task-relevant informa- representations for numbers are still weak and word-

tion in WM [5,6]. Cross-sectional and longitudinal studies based problem solving places greater demands on reading

are providing new insights into the role of individual comprehension. In a detailed cognitive analysis of the

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

126 Neuroscience of education

factors that contribute to mathematical abilities, Szucs Longitudinal studies have expanded on these ﬁndings

and colleagues found strong relations between visuospa- and shown that the central executive component predicts

tial WM measures, but not phonological WM measures, performance on single-digit addition tasks in grades 1 to

and mathematical abilities in a large well-characterized 3 as well as faster transitions from simple (e.g., counting)

group of 9 year-old children [18]. to sophisticated (e.g., decomposition) solution strategies

Figure 1

(a) Numerical L R (b) Arithmetic

(d) Visuospatial

Current Opinion in Behavioral Sciences

Common patterns of fronto-parietal network activations elicited by numerical, arithmetic, working memory and visuospatial processing tasks.

Results from meta-analysis conducted using Neurosynth (www.neurosynth.org) with the corresponding search terms.

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

Working memory in children’s math learning Menon 127

[16]. Similarly, in a large sample of 673 children, Lee and abilities in third graders [17]. Similarly, Li and Geary

Bull found that WM updating capacity in kindergarten reported individual differences in the growth rate of visuo-

predicted growth rate of math abilities (numerical opera- spatial WM during childhood. Notably, they found that

tions) in subsequent grades [19]. these differences became increasingly important for learn-

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

It is important to note that the role of individual WM tudinal changes associated with multiplication fact retrieval

components depends not only on task complexity but also [21 ]. They found that multiplication task performance was

on children’s developmental stage. The changing role of correlated with verbal WM in third graders but with visuo-

WM components can be detected even in a 1-year time- spatial WM in grade four. Taken together, these patterns of

window between ages 8 and 9. Meyer and colleagues found relationships suggest that the contributions of individual

that while the central executive and phonological compo- WM processes change dynamically over development with

nents of WM predicted mathematical abilities in second visuospatial WM processes playing an increasingly impor-

graders, it was the visuospatial component that predicted tant role in enhancing mathematical proﬁciency.

Figure 2

SMG IPS

SMG CE

PL VS

Overlap of VS and CE Overlap of PL and CE L SMG L IPS

Z = 34 Y = –43 Z = 54 Y = –47

CE r = .334 CE r = .417 1 VS r = .353 1 PL r = .374 ) ) β β 0 0

Activity ( –1 Activity ( –1

–2 –2 51015 2025 30 5 15 25 35 Working Memory Score Working Memory Score

Current Opinion in Behavioral Sciences

Functional dissociations and overlap between brain areas associated with each of the three components of working memory in 7 to 9-year-old

children (N = 74). The neural correlates of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of working memory

were examined by contrasting brain responses to two different types of addition problems that differed in complexity. Overlap between the CE

and VS components was observed only in left supramarginal gyrus (SMG); overlap between CE and PL components was observed only in the left

intra-parietal sulcus (IPS); no overlap was observed between VS and PL components. Negative correlation between activity and PL ability is not

depicted. No overlap for VS and PL (magenta) was observed. Bottom panel: coronal slices depict regions of interest selected as overlap in

correlations of activity and individual working memory components. Scatter plots are based on functional clusters identified using whole-brain

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

Source: [23 ].

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128 Neuroscience of education

Figure 3

(a) (a) TD R AIC L IPS R IPS L MFG L MFG R MFG R MFG

R Visual L IFG Cortex Y = 32 L IPS Z = 10 Precuneus R MFG

R Fusiform Gyrus

Cingulate Gyrus Cerebellum Cerebellum Y = –44 X = 0 Y = –56 X = 40 (b) DD

L Postcentral Gyrus Positive Correlations 2 4

Negative Correlations 2 4

TD > DD (b)

(a) Prefrontal

L IFG R MFG 4 4 ∗∗ 3 r = –.65 3 ∗ 2 r = –.23 2 r = –.29 r = –.60 1 1

T Score 0 T Score 0 –1 –1 –2 –2 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120 X = –42 Block Recall Z = 36 Block Recall (b) Parietal

L IPS R SMG 4 4 3 ∗ 3 ∗ 2 r = .55 r = –.50 r = –.21 2 r = –.15 1 1

T Score 0 T Score 0 –1 –1 –2 –2 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120 Block Recall Z = 20 Z = 36 Block Recall DD 2 4 TD

Current Opinion in Behavioral Sciences

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 in children’s math learning Menon 129

Working memory and fronto-parietal systems the fractionation of neurofunctional systems associated

associated with children’s mathematical with distinct WM components during numerical problem

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

Functional neuroimaging research has revealed signiﬁ- executive, phonological and visuospatial components of

cant overlap in multiple parietal and prefrontal cortex WM and brain activation during an arithmetic veriﬁcation

regions involved in WM and numerical problem solving task in a large (N = 74) group of 7 to 9-year-old children

[22–24]. Overlapping patterns of activation have most revealed that visuospatial WM is the strongest predictor

prominently been detected in the supramarginal gyrus of mathematical ability in children in this age group and is

and intraparietal sulcus in the posterior parietal cortex, associated with increased arithmetic complexity-related

the premotor cortex, and the ventral and dorsal aspects responses in left dorsolateral and right ventrolateral pre-

of the lateral prefrontal cortex (Figure 1). It is impor- frontal cortices as well as in the bilateral intra-parietal

tant to note, however, that the common patterns of sulcus and supramarginal gyrus in posterior parietal cortex

fronto-parietal cortex engagement during WM and nu- (Figure 2). This neurobiological ﬁnding conﬁrms a pivotal

merical problem solving cannot be conﬂated with role of visuospatial WM during arithmetic problem-solv-

shared neural mechanisms, and research on this topic ing in primary-school children.

has used both correlational and causative analyses

to gain a deeper understanding of the shared neural Metcalfe and colleagues also found that visuospatial WM

mechanisms [25]. and the central executive component were associated

with largely distinct patterns of brain responses during

Neuroimaging studies in typical and atypical develop- arithmetic problem-solving, and overlap was only ob-

ment are helping to provide a more mechanistic under- served in the ventral aspects of the left supramarginal

standing of the link between individual WM components gyrus in the posterior parietal cortex, suggesting that this

and brain responses associated with mathematical prob- region is an important locus for the integration of infor-

lem solving. The involvement of WM in mathematical mation in WM during numerical problem solving [29,31–

cognition had initially been surmised based on overlap- 35].

ping responses in posterior parietal cortex and prefrontal

cortex in the two domains [26–29]. Studies of typical Finally, there is also evidence that immature prefrontal

development provided initial evidence for the changing control systems associated with central executive func-

role of WM with age. For example, Rivera and colleagues tions may contribute to weaker math skills in children.

found that relative to adolescents and young adults, Supekar and colleagues used dynamic causal analysis to

children engage the posterior parietal cortex less, and probe interactions between the prefrontal and parietal

the prefrontal cortex more, when solving arithmetic pro- cortices in children and adults [36]. They found that

blems [29], likely reﬂecting the increased role of visuo- despite higher levels of activation, the strength of causal

spatial WM processes, and concurrent decrease in regulatory inﬂuences from the fronto-insular control net-

demands on cognitive control with age. Other studies work to the posterior parietal cortex was signiﬁcantly

have more directly addressed the link between WM weaker in children and weak signaling mechanisms con-

abilities and numerical problem solving skills. tributed to lower levels of performance in children, com-

Dumontheil and Klingberg [30] found that activity in pared to adults. More broadly, immature prefrontal

the intraparietal sulcus during a visuospatial WM task control systems may contribute to weaknesses in the

predicted arithmetic performance two years later in a ability to inhibit irrelevant information such as arithmetic

sample of 6- to 16-year-old children and adolescents. facts or operations during numerical problem solving

This ﬁnding further reinforces the link between visuo- [4 ,37,38,39 ].

spatial WM and numerical problem solving and suggests a

common underlying process in the intraparietal sulcus Working memory disruption in children with

subdivision of the posterior parietal cortex. dyscalculia

Studies of children with dyscalculia provide a unique

More detailed analyses of the neural correlates of indi- window into the role of WM in numerical cognition.

vidual components of WM have provided evidence for Dyscalculia is a speciﬁc deﬁcit in arithmetic ability in

(Figure 3 continued) correlations were observed in the TD group. (b) In the DD group, Block Recall was negatively correlated with activity in left

postcentral gyrus. No positive correlations were observed in the DD group. (B) Fronto-parietal cortical areas where the relation between activity

during arithmetic problem solving and visuo-spatial working memory abilities differed significantly between the TD and DD groups. (a) Prefrontal

cortex. In TD children, left inferior frontal gyrus (IFG) and right middle frontal gyrus (MFG) showed significant positive correlation between

activation during Complex addition problems and Block Recall, a measure of visuo-spatial working memory. In contrast, correlations were

nonsignificant in children with DD. (b) Parietal cortex. In TD children, the left intra-parietal sulcus (IPS), and right supramarginal gyrus (SMG)

showed significant positive correlation between activation during arithmetic problem solving and Block Recall. In the DD group there were no

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

Source: [52 ].

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130 Neuroscience of education

the presence of preserved intellectual and verbal abilities and dorsolateral and ventrolateral prefrontal cortices were

[40–43]. Children with dyscalculia show poor perfor- positively correlated with visuospatial WM ability in

mance on a broad range of numerical tasks, including typically developing children, but no such relation was

magnitude judgment [44–47] and enumeration seen in children with dyscalculia. This result suggests

[4 ,48,49]. They also lag behind their typically develop- that children with dyscalculia fail to appropriately exploit

ing peers in basic arithmetic problem solving skills visuospatial WM resources during problem solving. While

[4 ,50]. There is growing evidence that deﬁcits in still preliminary, extant ﬁndings point to the intraparietal

WM can contribute to multiple aspects of dyscalculia, sulcus as a common locus of visuospatial WM deﬁcits and

encompassing not only complex arithmetic problem solv- arithmetic problem solving deﬁcits in children with dys-

ing but also basic quantity representation [4 ,51 ]. calculia. On the basis of these and other related ﬁndings,

we have suggested that parietal cortex mechanisms for

Multiple experimental paradigms across extended peri- storing and manipulating quantity representations are

ods of early skill acquisition in the domains of number impaired in dyscalculia [23 ,55 ,56 ].

sense and arithmetic have highlighted the involvement of

visuospatial WM in developmental models of dyscalculia. Conclusion

At a more fundamental level, deﬁcits in visuospatial WM WM plays an integral role in children’s math learning and

can inﬂuence the ability to engage and manipulate repre- development of problem solving abilities. The role of

sentations of magnitude on a mental number line and individual WM components in mathematical cognition is

estimate non-symbolic quantity. Furthermore, other learning-stage dependent, both in terms of proﬁciency and

areas of difficulty that define the profile of children with age. Behavioral and neuroimaging studies are converging

dyscalculia, such as counting and subitizing, may have on the idea that the contributions of individual WM

their roots in visuospatial WM deﬁcits [4 ,49]. Conver- processes and their neural substrates change dynamically

gent with these observations, several lines of evidence over development, with visuospatial WM processes play-

point to disruptions in visuospatial WM in children with ing an increasingly important role in learning and enhanc-

dyscalculia. Even when they are matched with typically ing mathematical proﬁciency. Although the role of the

developing children on general intelligence, reading and visuospatial component of WM has often been considered

other cognitive measures, children with dyscalculia dem- secondary to that of the central executive component in

onstrate lower visuospatial WM despite preserved pho- typical arithmetic skill acquisition, and has generally been

nological and central executive WM abilities [52 ]. neglected in prior accounts of dyscalculia and math learn-

Furthermore, Swanson et al. [53] found deﬁcits in visuo- ing disabilities, recent studies suggest that visuospatial

spatial, but not in other WM components, differentiating WM is a critical component for successfully building

children with dyscalculia from children with reading quantity representations and efﬁciently manipulating

difﬁculties. Consistent with these ﬁndings, Rotzer et al. them during problem solving. These processes are impor-

[54] found that children with dyscalculia had lower scores tant at all stages of learning and skill acquisition, and are

than typically developing children on a Corsi Block- signiﬁcantly disrupted in children with dyscalculia.

Tapping Test. Thus, visuospatial WM deﬁcits appear

to be a speciﬁc source of mathematical difﬁculty in Phonological WM appears most prominently in the earli-

dyscalculia. est stages of learning the verbal mapping of quantity

representations and later gives way to visuospatial WM

Visuospatial working memory and fronto- processes important for the representation and manipu-

parietal impairments in children with lation of quantity information in short-term memory. The

dyscalculia central executive system helps scaffold the early stages of

The importance of visuospatial WM and associated learning by providing support for building new semantic

fronto-parietal processing during arithmetic problem- representations. The central executive component is also

solving is further highlighted by neuroimaging studies required at subsequent stages for more complex problem

in children with dyscalculia. Rotzer et al. [54] found that solving procedures, including the active maintenance of

compared to typically developing children, children with intermediate results and rule-based problem solving.

low math abilities had lower visuospatial abilities and

lower activity levels in the right anterior intraparietal Within the neurocognitive framework highlighted in this

sulcus, inferior frontal gyrus, and insular cortex during review, the engagement of the intraparietal sulcus and

a visuospatial WM task. Ashkenazi and colleagues [52 ] supramarginal gyrus in the posterior parietal cortex, and

identiﬁed impaired WM components in children with the ventral and dorsal aspects of the lateral prefrontal

dyscalculia and then examined their role in modulating cortex changes dynamically with problem complexity and

brain responses to numerical problem solving (Figure 3). developmental stage. Findings to date suggest that the

Children with dyscalculia had speciﬁc deﬁcits in visuo- intraparietal sulcus plays an essential role not only in

spatial WM in addition to deﬁcits in arithmetic task quantity representations but also in maintaining quantity-

performance. Crucially, activations in intraparietal sulcus, related information in short-term WM. Rule-based

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

Working memory in children’s math learning Menon 131

Review addressing challenges of deﬁning and diagnosing dyscalculia,

manipulation of these representations in WM is in turn

emphasizing its heterogeneous nature and developmental sequela.

supported by multiple prefrontal cortical areas, with the

8. Bull R, Lee K: Executive functioning and mathematics

supramarginal gyrus as a key locus for integrating frontal

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by the intraparietal sulcus. Together, they provide mul-

and preference for use of retrieval-based processes for

tiple functional circuits that support essential WM pro- solving addition problems: individual and sex differences from

ﬁrst to sixth grades. J Exp Child Psychol 2012, 113(1):78-92.

cesses in children’s mathematical cognition.

10. Geary DC, Hoard M, Nugent L, Byrd-Craven J, Berch D,

Mazzocco M: Strategy use, long-term memory, and working

A challenging question for future research is to under-

memory capacity. In Why is math so hard for some children?.

stand how WM processes are used dynamically to support Edited by Anonymous. Baltimore, MD: Paul H. Brookes Publishing

Co.; 2007:83-105.

different types of mathematical learning and how they

change with different stages of development. Addressing 11. Baddeley AD: Working memory: theories, models, and

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this question will require developing appropriate compu-

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Conﬂict of interest statement

15. De Smedt B, Janssen R, Bouwens K, Verschaffel L, Boets B,

Nothing declared. Ghesquiere P: Working memory and individual differences in

mathematics achievement: a longitudinal study from ﬁrst

grade to second grade. J Exp Child Psychol 2009, 103(2):186-

Acknowledgements 201.

It is a pleasure to thank Teresa Iuculano, Rachel Rehert and Se Ri Bae for

16. Geary DC, Hoard MK, Nugent L: Independent contributions of

valuable feedback and careful proof-reading, and Se Ri Bae for assistance

the central executive, intelligence, and in-class attentive

with the figures. I also thank two anonymous reviewers for valuable feedback.

behavior to developmental change in the strategies used to

solve addition problems. J Exp Child Psychol 2012, 113(1):49-65.

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