The Neurocognitive Architecture of Individual Differences in Math Anxiety in Typical Children

Abstract

Math Anxiety (MA) is characterized by a negative emotional response when facing math-related situations. MA is distinct from general anxiety and can emerge during primary education. Prior studies
typically comprise adults and comparisons between high- versus low-MA, where neuroimaging work has focused on differences in network activation between groups when completing numerical tasks. The
present study used voxel-based morphometry (VBM) to identify the structural brain correlates of MA in a sample of 79 healthy children aged 7–12 years. Given that MA is thought to develop in later primary
education, the study focused on the level of MA, rather than categorically defining its presence. Using a battery of cognitive- and numerical-function tasks, we identified that increased MA was associated with reduced attention, working memory and math achievement. VBM highlighted that increased MA was associated with reduced grey matter in the left anterior intraparietal sulcus. This region was also associated with attention, suggesting that baseline differences in morphology may underpin attentional differences. Future studies should clarify whether poorer attentional capacity due to reduced grey matter density results in the later emergence of MA. Further, our data highlight the role of working memory in propagating reduced math achievement in children with higher MA.

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The Neurocognitive Architecture
of Individual Dierences in Math
Anxiety in Typical Children
Charlotte E. Hartwright
1,2, Chung Yen Looi2,3, Francesco Sella2, Alberto Inuggi
4,
Flávia Heloísa Santos5, Carmen González-Salinas6, Jose M. García Santos7,
Roi Cohen Kadosh
2 & Luis J. Fuentes
5
Math Anxiety (MA) is characterized by a negative emotional response when facing math-related
situations. MA is distinct from general anxiety and can emerge during primary education. Prior studies
typically comprise adults and comparisons between high- versus low-MA, where neuroimaging work
has focused on dierences in network activation between groups when completing numerical tasks. The
present study used voxel-based morphometry (VBM) to identify the structural brain correlates of MA in
a sample of 79 healthy children aged 7–12 years. Given that MA is thought to develop in later primary
education, the study focused on the level of MA, rather than categorically dening its presence. Using
a battery of cognitive- and numerical-function tasks, we identied that increased MA was associated
with reduced attention, working memory and math achievement. VBM highlighted that increased
MA was associated with reduced grey matter in the left anterior intraparietal sulcus. This region was
also associated with attention, suggesting that baseline dierences in morphology may underpin
attentional dierences. Future studies should clarify whether poorer attentional capacity due to
reduced grey matter density results in the later emergence of MA. Further, our data highlight the role of
working memory in propagating reduced math achievement in children with higher MA.
Math anxiety (MA) is characterised by negative emotional response such as fear and tension when facing
math-related situations, which cannot be reduced to either general anxiety or test anxiety1. It disrupts mathemat-
ical performance irrespective of gender2, and can emerge in the primary school years3,4. Depending on the extent
of MA, the negative impact of MA could have far-reaching consequences beyond academic achievements5. Given
that a signicant variation in the level of MA is contributed by genetic factors6, understanding the neurocognitive
basis of individual dierences in MA may shed light on its causal pathway.
To date, there are a limited number of neuroimaging studies, which are mainly based on adults and compar-
isons of neural response between groups of high and low levels of MA. In adults, high- compared with low-level
MA has been shown to be associated with increased activity in bilateral posterior insula, brain areas linked with
threat and pain processing, when anticipating mathematical tasks7. High- compared to low-level MA has also
been associated with stronger deactivation within the default mode network during tasks that require additional
inhibitory functions, possibly reecting depletion of working memory resources4. Further, increased activity in
frontoparietal regions in high-level MA adults when anticipating mathematical tasks has been shown to corre-
spond with reduced performance decits, suggesting the role of cognitive control in MA8. In children9, high-level
MA has been associated with hyperactivity in the right amygdala when solving mathematical problems, and
increased connectivity between this and the ventromedial prefrontal cortex, areas implicated in the process-
ing and regulation of negative emotions. Compared with low-level MA, high-level MA has been linked with
decreased activity in brain areas involved in working memory and attention, including the dorsolateral prefron-
tal cortex, and reduced activity in posterior parietal areas, critical to numerical processing. Furthermore, brain
1Aston Brain Centre, School of Life and Health Sciences, Aston University, Birmingham, UK. 2Department of
Experimental Psychology, University of Oxford, Oxford, UK. 3School of Experimental Psychology, University
of Bristol, Bristol, UK. 4Istituto Italiano di Tecnologia, Genova, Italy. 5Departamento de Psicología Básica y
Metodología, Facultad de Psicología, Universidad de Murcia, Murcia, Spain. 6Departamento de Psicología Evolutiva
y de la Educación, Facultad de Psicología, Universidad de Murcia, Murcia, Spain. 7Servicio de Radiología, Hospital
Morales Meseguer, Murcia, Spain. Charlotte E. Hartwright and Chung Yen Looi contributed equally to this work.
Correspondence and requests for materials should be addressed to C.E.H. (email: c.hartwright@aston.ac.uk)
Received: 13 July 2017
Accepted: 22 May 2018
Published: xx xx xxxx
OPEN
Correction: Publisher Correction
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stimulation over the dorsolateral prefrontal cortex has shown the ability to improve arithmetic performance
and reduced cortisol level in those with high-level MA10. To our knowledge, there are no prior published studies
assessing the link between brain structure and MA in children or adults.
A recent review11 highlighted that there are specic aspects of numerical and executive function that might
explain varying degrees of MA: lower working memory capacity, reduced attentional control, lower inhibitory
control and a decit in low-level numerical representations. Furthermore, increasing levels of MA may negatively
aect mathematical achievement, via disruption of core executive functions and/or decit in low-level numerical
representations. Using data collected from a larger study, we sought to test the strength of association made by
those predictions in that review, to better understand the neural and cognitive factors that are associated with the
degree of anxiety towards mathematics. We aimed to identify the structural brain correlates of the level of MA
in a typical school population, and to determine how brain structure mediates the relationship between those
cognitive functions that are most strongly predictive of the level of MA. Much of the prior literature has con-
sisted of between-group comparisons and, whilst these have provided important insights on the plausible neural
mechanisms of MA, the neural and cognitive architecture that contributes to individual dierences in MA, and
its association with mathematical achievement, remains unclear.
e present study comprises brain structure and MA data from 79 healthy, Spanish children. e Behavioural
Rating Inventory of Executive Function (BRIEF)12,13 was used to prole each child’s behavior in specic domains
of executive function. e BRIEF indices that were of primary interest for the present study were: inhibitory
control and impulsivity (INHBIT), ability to switch and alternate attention (SHIFT) and on-line, representational
memory (WORKING MEMORY). e BRIEF is regularly used in clinical and education settings, where higher
scores indicate greater diculty, and therefore lower capacity, in each domain. Numerical representation skills
were assessed using a number line task, consisting of positioning numbers on an analogue scale (PN)14, mathe-
matical achievement was determined using the Woodcock Johnson III Achievement (WJ)15 and the level of MA
was established via the Math Anxiety Scale (Math-AS)16. Voxel-based morphometry (VBM) was used to identify
brain-structure correlates of MA.
Method
Participants. Participants were recruited through two state primary schools in Murcia, Spain, as part of a
wider study17–19. e primary sample comprised 137 Spanish children, aged 7–12 years (2nd – 6th grade). Written,
informed consent was obtained from parents prior to acquiring any data, and verbal consent reobtained imme-
diately prior to data acquisition. Parents were advised that they would be informed by the hospital Radiologist
if any clinically relevant abnormalities were detected. T1-weighted structural MRI data were acquired from an
initial sample comprising 110 children whose parents gave previous informed consent. Two were not included in
the current study as they were reported to be bilingual, which may aect the measurement of math anxiety and
numerical achievement. A further 7 were excluded due to learning disabilities. Note that children with learning
disabilities were diagnosed before our study and were receiving special education from their schools. We admin-
istered tests on all children to ensure that no one felt excluded. We only analysed data of children without learning
disabilities. Following exclusion due to unsatisfactory image quality resulting from movement- or other imaging
artefacts (n = 21) or neuro-incidental ndings (n = 1), the nal sample comprised 79 children (age M = 115.20,
SD = 14.13; males = 50.6%; right-handed = 88.6%). e study was approved by the University of Murcia Ethics
Committee, and it was conducted in accordance with the approved guidelines and the Declaration of Helsinki.
Materials. Measures that were modeled in the current study include math anxiety, mathematical abilities and
working memory.
Math Anxiety. MA was assessed using the Math-AS (known also as the EAM, Escala de Ansiedade a
Matemática16). It consists of 25 items that describe situations that are commonly experienced by elementary and
high school students during their math lessons. is scale measures the variations in the degrees of math anxiety,
from absence to extreme math anxiety. is task was translated from Portuguese into European Spanish by a
speaker uent in both languages (FHS) to enable cross-cultural adaptation. Children indicated the intensity of
their response to each item on a ve-point Likert scale by crossing out one of the following: (1) None (2) Low (3)
Moderate (4) High and (5) Very High. e score was the sum of all points from the 25 questions. is measure has
been shown to have accurate validity and reliability when used with children20. Note that we could not control for
general anxiety in our analyses however, as we did not have normative data for children below 9 years old using
the State-Trait Anxiety Inventory for Children (STAI-CH)21. To be condent that we measured MA and not gen-
eral anxiety trait, we ran a correlation analysis on the standardised scores of the 50 out of 79 children. We found a
lack of correlation between general anxiety (STAI-CH) and MA, rp = 0.07, p = 0.63.
Numerical Cognition. Math Achievement. Children’s math abilities were assessed using the Spanish ver-
sion of the Woodcock-Johnson III (WJ-III) Achievement (ACH) battery15, which has been validated for the use
of children aged 6–13 years in Spain22. It comprises 4 subtests: calculation, math uency, quantitative concepts
and applied problems (see Supplementary Information: Method). e raw scores of each subtest were transformed
into W scores23 following the Rasch’s measurement model24,25. We used the composite score of all 4 subtests in
our analyses.
Numerical Representation. Numerical representation was assessed using a number line task, consisting of
positioning numbers on an analogue scale (PN)14. e participants were required to map numbers on a vertical
line that was marked with “0” at the bottom and “100” at the top. In half of the trials, the line was further marked
with 4 horizontal lines at dierent locations to assist children with number mapping. Children were required
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to indicate the position of an Arabic numeral, orally or visually presented by the experimenter, by pointing to a
specic location on the line. ere were 12 trials in this task.
Executive Function. We used parents’ rating of children’s online memory (WORKING MEMORY), atten-
tion (SHIFT) and inhibitory control (INHIBIT) using the Spanish version of the Behavioural Rating Inventory of
Executive Function, BRIEFTM 12,13, which assesses the executive functioning of children between 5–18 years old.
It contains 86 items in eight non-overlapping clinical scales and two validity scales.
Procedure. Cognitive and Achievement Testing. Children’s performance on a range of behavioural, cognitive
and achievement tasks was assessed prior to collecting the structural MRI scans. Testing was conducted during
the Autumn term by six trained assistants with children in groups of two.
Analysis of Demographic, Cognitive and Achievement Data. Several of the measures resulted in positively
skewed data. Parametric statistics were combined with permutation testing as this approach, in contrast with
non-parametric analyses, has been shown to maximally reduce type I and type II errors26. Condence inter-
vals (CIs) were estimated using the bias-corrected and accelerated (BCa) percentile bootstrap method (10,000
samples).
e cognitive and achievement data were analysed using SPSS, version 22. e mediation analysis was con-
ducted using the Process macro for SPSS (v2.16.3), available from http://www.processmacro.org/index.html fol-
lowing a published analysis pipeline27. Ten-thousand bootstrap resamples were used to generate bias-corrected,
95% condence intervals.
Neuroimaging Acquisition. e participants were tted with ear plugs and so foam padding used to minimize
head movement during the scan. Participants were asked to remain as still as possible for the duration of the
scan, and a parent sat beside their child throughout. A T1-weighted image was acquired for each participant
using a 1.5 T GE HDX scanner with an 8-channel, phased array, transmit-receive head coil. A 3D FSPGR BRAVO
sequence was used to achieve whole brain coverage, composed of 142 axially oriented slices with a reconstructed
voxel size of 1 × 1 × 1 mm3, where TR = 12.4 ms, TE = 5.2 ms, ip angle = 12°.
Neuroimaging Analysis using Voxel-Based Morphometry. e MRI data were analyzed using the FMRIB Soware
Library (FSL, version 6.0.0; http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/). Non-brain tissue was removed from the struc-
tural images and an initial weak bias eld correction applied using FSL’s anatomy pipeline (http://fsl.fmrib.ox.ac.
uk/fsl/fslwiki/fsl_anat). ese brain extracted, bias corrected images were then fed into the second and subsequent
stages of FSL-VBM28 (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSLVBM), an optimised VBM protocol29. e images
were grey matter-segmented and registered to the MNI-152 standard space using non-linear registration30. e
resulting images were averaged and ipped along the x-axis to create a le-right symmetric, study-specic grey
matter template. All native grey matter images were then non-linearly registered to this study-specic template
and “modulated” to correct for local expansion (or contraction) due to the non-linear component of the spatial
transformation. e modulated grey matter images were then smoothed with an isotropic Gaussian kernel with
a sigma of 3 mm, Full-Width-Half-Maximum (FWHM) ~7 mm. Finally, voxelwise general linear modelling was
applied using Randomise31 (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Randomise), which permits permutation-based
non-parametric testing, correcting for multiple comparisons across space. Here, 10,000 permutations of the
data were generated to test against the null. reshold-free cluster enhancement (TFCE)32 was used to identify
cluster-like structures, taking family-wise error rate (FWE) corrected p-values < 0.05. To avoid any labelling bias,
probabilistic anatomical descriptors were determined using FSL Atlas Query (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/
Atlasquery). Anatomical labels were output for voxels that had survived multiple-comparison correction. Cluster
peak information was extracted using FSL’s Cluster tool. See Supplementary Information: Method for a detailed
description of the GLM analyses.
Data availability. e research meta-data supporting this publication are available on the Open Science
Framework repository, see DOI 10.17605/OSF.IO/PDFJE. e senior author, LJF, may be contacted regarding the
wider dataset.
Results
Math Anxiety and its Association with Demographic, Cognitive and Numerical Factors. Table1 out-
lines the sample’s demographic, numerical and cognitive characteristics (see also Supplementary Information: TableS1
for a detailed breakdown by grade). Typically, the level of MA within the sample was low. An independent-sam-
ples t-test determined that there was no dierence in the mean level of MA between the sexes (t(65.569) = −1.063,
p = 0.292, 95% CI −13.21, 3.569). Age was positively associated with the level of MA (r(79) = 0.237, p = 0.035, CI 0.031,
0.433), consistent with previous studies33 (see Supplementary Information: Fig.S1).
To assess the relationship between MA, numerical- and cognitive-function we conducted a series of partial
correlations. Each of the three BRIEF indices of interest (INHIBIT, SHIFT, WORKING MEMORY), plus the
PN and WJ were correlated with the Math-AS score (controlling for age and biological sex). SHIFT, WORKING
MEMORY and WJ were statistically signicant aer applying a Bonferroni correction (Table2).
Math Anxiety and its Association with the Brain. VBM was used to identify the structural correlates
of MA. A general linear model (GLM) comprising Math-AS score and the nuisance variables, age, biological
sex, recruitment source and handedness was created. Contrasts for positive and negative associations between
grey matter volume (GMV) and MA were computed, where corrections were applied for multiple comparisons
across the brain, and adjustment to correct for running two contrasts using a Bonferroni correction. A whole
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brain analysis did not identify any regions that were positively associated with MA. Four clusters demonstrated a
negative association between GMV and MA, which encompassed only cortical grey matter (Table3 and Fig.1).
e largest cluster spanned both hemispheres across occipital and parietal cortices, including a section running
anterior-posterior along the le anterior intraparietal sulcus (IPS), in areas hIP1 and hIP3, as dened by the
Juelich Histological Atlas. A second, smaller cluster was identied in the right visual cortices, encompassing
extrastriate areas and additionally encompassing the le anterior IPS. Lastly, a small, le lateralized cluster was
identied in the inferior parietal lobule. e Bonferroni correction had split this latter cluster, resulting in a fur-
ther cluster in the lateral occipital cortex. As this comprised a single voxel (MNI: −18, −88, 42), this voxel was
excluded from subsequent analyses.
To understand the function of these structural correlates of MA, a further GLM was constructed comprising
the Math-AS scores and nuisance variables as outlined previously, plus those variables that had earlier shown
the most robust associations with the level of MA: attentional control (SHIFT), online memory (WORKING
MEMORY) and mathematical achievement (WJ). is GLM was applied to those voxels that were previously
identied as being negatively associated with MA.
Domain Scale/Index nmean SD min max
Demographic
Age (months) — 115.20 14.13 95.00 145.00
School grade — 4 — 2 6
Sex (M/F) 40/39 — — — —
Handedness (L/R) 9/70 — — — —
Numerical Cognition
Math Anxiety Scale 79 43.52 19.35 25 101
Woodcock-Johnson III Achievement 79 128.15 29.64 65 208
Number line task 73 7.51 2.18 2.00 10.50
Executive Function (BRIEF)
Initiate 71 12.92 2.99 8 22
Working Memory*71 17.49 4.62 10 27
Plan 71 19.87 5.43 12 33
Organization 71 10.75 3.28 6 18
Monitor 71 13.63 3.20 8 22
Inhibit*71 15.34 3.53 10 27
Shi*71 12.69 3.05 8 21
Emotional Control 71 16.49 4.21 10 28
Behavioral Regulation Index 71 43.96 9.41 18 69
Metacognition Index 71 74.69 16.70 48 118
Global Executive Composite 71 119.21 24.32 79 184
Table 1. Sample Characteristics. Note. * indicates BRIEF indices of primary interest due to prior published
associations with Math Anxiety.
Domain Math Anxiety
(MA)
Numerical
representation
(PN)
Math
Achievement
(WJ)
BRIEF indices
Inhibitory C ontrol
(INHIBIT) Attentional
Control (SHIFT) Online Memory
(WORKING MEMORY)
Math Anxiety (MA) Pe ar son’s r —−0.112 −0.302 0.278 0.320 0.313
p-value — 0.351 0.008*0.021 0.007*0.009*
Numerical Representation
(PN)
Pe ar so n’s r —0.384 −0.189 −0.155 −0.321
p-value — 0.002 0.138 0.226 0.010
Math Achievement
(WJ)
Pe ar so n’s r —−0.197 −0.127 −0.465
p-value — 0.104 0.299 <0.001
Inhibitory C ontrol
(INHIBIT)
Pe ar so n’s r —0.452 0.483
p-value — <0.001 <0.001
Attentional Control
(SHIFT)
Pe ar so n’s r —0.602
p-value — <0.001
Online Memory
(WORKING MEMORY)
Pe ar so n’s r —
p-value —
Table 2. Association between Math Anxiety, Numerical and Cognitive Indices. Note. p-values reect two-tailed
partial correlation analyses, where age and biological sex was held constant. Degrees of freedom (df) = 69 for
MA * PN; df = 75 for MA * WJ; df = 67 for all BRIEF indices. * indicates associations that survive Bonferroni
corrected alpha for the 5 primary analyses of interest (rst row; Bonferroni corrected alpha, p < 0.01). B Ca
Bootstrapped 95% CI (10,000 samples) for statistically signicant, primary MA analyses: MA * WJ lower −0.455
upper −0.133; MA * SHIFT lower 0.074, upper 0.512; MA * WORKING MEMORY lower 0.052, upper 0.529.
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When controlling for attention, working memory and mathematical achievement, a large number of those
voxels initially found to be negatively associated with MA were no longer statistically signicant, particularly
within the IPS. Although this result alone is insucient to determine a dierence, the data suggest that the asso-
ciation between MA and GMV in these voxels may be mediated by one or more of the newly modelled variables.
HO Anatomical Region Hemi
(L/R) Cluster Size
(voxels) p-value t-value
MNI Coordinates
of Cluster Peak
X Y Z
Lingual Gyrus*R 217 0.006 5.62 12 −66 −6
Intracalcarine Cortex R
Occipital Fusiform Gyrus R
Temporal Occipital Fusiform Cortex R
Precuneous Cortex R
Cuneal Cortex*L 1446 0.002 5.11 −8−82 20
Cuneal Cortex R
Lateral Occipital Cortex sup div (inc. anterior intraparietal sulcus hIP1&3a) L
Precuneous Cortex L & R
Occipital Pole L & R
Supracalcarine Cortex L & R
Intrcalcarine Cortex L
Superier Parietal Lobule (inc. anterior intraparietal sulcus hIP1&3a) L
Angular Gyrus L
Lingual Gyrus L
Lateral Occipital Cortex* (inc. anterior intraparietal sulcus hIP1&3a) L 76 0.017 4.91 −42 −64 34
Angular Gyrus L
Supramarginal Gyrus, posterior division L
Table 3. Probabilistic Labels for Brain Regions where Grey Matter Volume is Negatively Associated with Math
Anxiety. Note. Anatomical labels taken from the Harvard-Oxford (HO) Atlas bundled with FSL 6.0.0. *Cluster
peak. aReects anatomical label from Jeulich Histological Atlas available with FSL 6.0.0. p- and t-values reect
cluster peak. Labels are only reported from regions which survived correction at the voxel level, and subsequent
Bonferroni correction.
Figure 1. Grey matter correlates of Math Anxiety. Surface rendered image reects a t-statistic cluster map
rendered onto a template brain. All coloured areas reect those grey matter voxels that were signicantly
negatively associated with MA aer multiple comparison corrections as outlined in the method. e top right
panel illustrates the results transformed and rendered onto a single participant’s annoymised T1-structural
image. All images are presented in neurological convention, where the le of the image reects the le of the
brain. Surface rendering created using Surf Ice42; Individual subject rendering created using Mango43.
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To assess this possibility, the linear directional contrasts for each newly modelled variable werecomputed. ese
data suggested that, of the additional variables added, attentional control was negatively associated with a large
proportion of those voxels that were no longer associated with MA (see Supplementary Information: Fig.S2).
However, this result did not survive correction for multiple-comparisons. Working memory and math achieve-
ment did not explain the association with MA (see Supplementary Information for detailed modelling procedure).
To further assess this, the mean GMV was extracted for each of the 3 clusters identied in the earlier VBM
analysis. ough large, the spatial arrangement of these clusters may demarcate dierentiation of function, as
each comprised relatively distinct anatomical regions: lingual gyrus, cuneal cortex and the intraparietal sulcus.
SHIFT, WORKING MEMORY and WJ were entered into a series of partial correlations to examine their rela-
tionship with GMV within each of the 3 clusters. When controlling for age, biological sex and Math-AS score,
attentional control (SHIFT) was shown to be negatively associated with GMV across the IPS, although this result
did not survive a Bonferroni correction for 9 tests. All other tests were non-signicant at the uncorrected level
(see Table4).
The Cognitive Architecture of MA and Resultant Outcomes in Numerical Achievement.
Suárez-Pellicioni and colleagues11 outline a model, the processing eciency theory34 in which intrusive thoughts
resultant from MA consume working memory. This, in turn, is argued to expend already limited attentional
resources in high MA individuals, leading to diminished performance when complex mathematical operations are
performed. Such a relationship provides a causal explanation for the association between MA (Math-AS) and mathe-
matical achievement (WJ). We tested this theoretical model using mediation analysis. When controlling for working
memory and the nuisance variables age and biological sex, the relationship between MA and math achievement was
no longer signicant (c′) (see Table5 and Fig.2). e overall mediation model found that MA, working memory, age
and biological sex explained approximately 55% of the variance in math achievement, (R2 = 0.5527, F(4, 66) = 20.39,
p < 0.0001). Consistent with this model, the mediation analysis suggested that higher levels of MA (Math-AS) were
associated with slightly elevated diculty with holding appropriate information in mind (WORKING MEMORY),
which in turn resulted in reduced math achievement (WJ).
Discussion
e current study sought to examine the neurocognitive bases of MA in typically developing children. Unlike
most prior work, however, the analyses focused on the level of MA, which is a more rigorous approach than
making comparisons based on the presence or absence or of it35. is work therefore provides both a descrip-
tion of how MA might manifest itself across a cohort of typical children, as well as a detailed evaluation of
theoretically-driven factors that might inuence the degree of MA.
Most of the children in the sample demonstrated low-levels of MA. Around 10% of the entire sample reported
moderate to high-levels of MA, and prevalence increased linearly with age. Aside from numerical representations,
all other cognitive variables that were of theoretical interest were associated with the degree of MA: the more
math anxious children demonstrated reduced inhibitory and attentional control, as well as lower working mem-
ory capacity and math achievement. ough MA appears to be associated with dierences in baseline executive
functions in children with MA, working memory was also shown to mediate the relationship between MA and
math achievement suggesting that, possibly in addition to baseline dierences, capacity issues may be exacerbated
‘online’ when working with mathematics by the physiological response to anxiety, which in turn leads to poorer
learning and performance in mathematics.
Contrary to previous studies36,37, we found no association between MA and low-level numerical representa-
tions. ere has been considerable debate regarding the presence of a low-level decit in math ability in MA11.
It may be that the task used here was not ne-grained enough to highlight any association, although note that
the data from the task used did correlate with the measure of math achievement, suggesting that the task was
tapping into numerical cognition to some degree. e current pattern of results is also indicative of experiential
dierences between high and low math anxious individuals, as MA may result in avoidance of exposure to math
Domain Math Achievement
(WJ)
BRIEF INDICES
Attentional
Control (SHIFT) Online Memory
(WORKING MEMORY)
Lingual Gyrus*Pe ar so n’s r −0.086 −0.070 0.051
p-value 0.460 0.572 0.678
Cuneal Cortex*Pe ar so n’s r −0.168 −0.123 0.086
p-value 0.148 0.318 0.487
Lateral Occipital Cortex*Pe ar son ’s r −0.112 −0.318 −0.066
/anterior Intraparietal Sulcus hIP1&3** p-value 0.334 0.008 0.592
Table 4. Partial Correlation Results for Regional Grey Matter Volume, Numerical and Cognitive Indices. Note.
p-values reect two-tailed partial correlation analyses, where MAS score, age and biological sex is held constant.
Degrees of freedom (df) = 74 for WJ; df = 66 for BRIEF indices. BCa Bootstrapped 95% CI (10,000 samples)
for SHIFT * IPS, lower −0.513, upper −0.108. No analyses survive Bonferroni corrected alpha for 9 tests of
interest (corrected alpha, p < 0.0056). *Anatomical descriptors reect VBM cluster peak and are taken from the
Harvard-Oxford (HO) Atlas bundled with FSL 6.0.0. **Reects anatomical label from Jeulich Histological Atlas
available with FSL 6.0.0.
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problems38. Moreover, an experientially-driven reduction in math achievement does not discount a primary,
causal decit in numerical representation; it may be that more extreme levels of MA reect both causal (rep-
resentational) and aectual (experiential) mechanisms. Indeed, cross-sectional work strongly suggests the pres-
ence of a less precise representation of numerical representation in adults with high MA37.
e present study also identied that reduced grey matter volume in the IPS, lingual gyrus and cuneal
cortex was associated with increased MA. e identication of a structural correlate in relatively young chil-
dren suggests that there may be dierences in early brain structure that underpin the development of MA.
us, whilst prior functional imaging studies demonstrate how network functionality can explain dierences
in mathematical performance in people with math anxiety8,9, these data provide the rst evidence of a possible
underlying structural basis. Genetic modelling suggests that around 40% of variance in MA6 can be explained
Path Estimate p-value
BCa 95% CI
Lower Upper
Total eect (c)−0.3639 0.0058 −0.6188 −0.1091
Direct eect (c’)−0.2247 0.0743 −0.4721 0.0227
a 0.0758 0.0088 0.0197 0.1318
b−1.8378 0.0006 −2.8603 −0.8154
Indirect eect
ab −0.1392 — −0.3074 −0.0282
Table 5. Mediation Path Coecients and Condence Intervals for Math Anxiety Predicting Math
Achievement. Note. BCa condence intervals (CI) reect 10,000 samples.
Figure 2. Summary coecients for mediation model. Note. Path a = unstandardised IV to mediator; path
b = unstandardised mediator to DV; path c = unstandardised total eect (IV to DV); path c′ = unstandardised
direct eect. Coecient values rounded to 2 decimal places; full values reported in accompanying table (3).
ns = non-signicant *p < 0.01; **p < 0.001. Note. Higher working memory values indicate lower working
memory.
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by heredity, thus, a neurodevelopmental precursor is not implausible. Prior work has implicated the IPS in a
network of regions showing aberrant activity in young, math anxious children, where these patterns of activa-
tion were unrelated to intelligence, general anxiety, reading ability or working memory9. Our data suggest that
the IPS region identied in the current study might serve an attentional function, where children with reduced
grey matter in this area had lower reported attentional resources, and this reduced attentional capacity was
associated with increased MA. is is consistent with the assumption of the processing eciency theory34 that
high MA individuals may already have a limited attentional resource, and MA would further consume work-
ing memory, contributing to lower performance on complex mathematical operations. Future studies could
investigate whether this reduced grey matter in the IPS is a structural adaptation due to reduced attentional
capacity or compensatory strategies associated with MA39, or a potential biomarker on the causal pathway of
the development of MA. One model that should be examined in future research is that children with MA, or
who go on to develop MA, start o with dierences in IPS structure, which translate into a decit in baseline
attentional capacity. According to this view, a limited ability to attend to stimuli, particularly mathematical
stimuli – where demands on attentional resources are oen high due to the nature of arithmetic problems –
could result in general feelings of anxiety, which later become habitually associated with doing math, causing
the development of MA.
In addition to providing a rich description of the neurocognitive bases of the level of math anxiety, the current
study provides testable hypotheses regarding the emergence and maintenance of MA. Having a more nuanced
understanding of the neurocognitive prole of MA, including any impairments that may cause, contribute to,
or result from MA, has important implications for the development of targeted, individualized intervention.
Longitudinal and cross-sectional work to prole MA against developmental dyscalculia, which may appear qual-
itatively similar40, is required, however, to assess the validity of these assertions.
Limitations and Suggested Future Directions. e review by Suárez-Pellicioni and colleagues11 out-
lines three core explanations of MA: (1) Task-related competition for working memory resources (2) A decit
in low-level numerical representation (3) Math anxiety as an inhibition/attentional-control decit. Using data
collected from a wider study, we evaluated each of these, combining paediatric MRI data from typically develop-
ing children to advance a neurocognitive model of the level of MA. Whilst our results address some of the core
areas of interest in the cognitive literature, the present study does not, however, provide an assessment across
all cognitive domains, so cannot be considered an exhaustive evaluation of the neurocognitive architecture of
MA. Moreover, our executive function measures were derived from parental report. Although the measure of
executive function administered is used extensively in education and clinical settings, a standardized, automated
neurocognitive test battery may provide more valid data regarding performance and capacity.
Future work should include measures sampled ‘online’ whilst performing numerical tasks, based on
event-related potentials, functional magnetic resonance imaging or autonomic measurement, for example. Whilst
such work has been conducted with adults, there has been little progress towards developing a dynamic view of
how individual dierences in children’s physiological responses to numerical stimuli vary as a function of MA.
Importantly, such an approach could identify further potential antecedents of MA; thus, permitting directed
early intervention ideally to prevent, or at least reduce, the negative consequences of MA. Similarly, multimodal
approaches could achieve deeper evidence regarding the functional properties of MA and, if approached longi-
tudinally, its emergence could be evaluated. Still, though longitudinal approaches permit causal inference, they
attract signicant technical and practical challenges41.
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Acknowledgements
Authors CEH FS, and RCK were supported by the European Research Council (Learning and Achievement,
award number 338065). Authors LJF, FHS, JMGS and CGS were supported by grant PSI2017-84556-P from
Ministry of Economy, Industry and Competitiveness (FEDER funding).
Author Contributions
L.J.F. conceived and designed the over-arching study. All authors contributed to the math anxiety study concept.
F.H.S. translated the Math-AS into Spanish and organized and interpreted the Math-AS scores. C.G.S. organized
and interpreted the BR.IEF questionnaire. L.J.F., A.I. and J.M.G.S. designed and implemented the MRI protocol.
L.JF., A.I., F.H.S., C.G.S. and J.M.G.S. oversaw the testing and data collection. C.E.H., C.Y.L., F.S. and R.C.K.
were given access to the subset of data described in this article to examine math anxiety, following L.J.F. taking a
sabbatical within RCK’s laboratory at the Department of Experimental Psychology, University of Oxford. C.Y.L.
contributed to the organization of test measures and raw data. C.E.H., C.Y.L. and F.S. conducted the behavioural
analysis. C.E.H. conducted the neuroimaging analyses. C.E.H. and C.Y.L. draed the manuscript. L.J.F., R.C.K.,
F.S., A.I., F.H.S., C.G.S. and J.M.G.S. provided critical revisions of the manuscript. All authors approved the nal
version of the manuscript for submission.
Additional Information
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-018-26912-5.
Competing Interests: e authors declare no competing interests.
Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and
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