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Arithmetic processing in children with

dyscalculia: an event-related potential

study

Sonia Y. Cárdenas

1

, Juan Silva-Pereyra

2

, Belén Prieto-Corona

2

,

Susana A. Castro-Chavira

1

and Thalía Fernández

1

1Departamento de Neurobiología Conductual y Cognitiva, Instituto de Neurobiología,

Universidad Nacional Autónoma de México, Querétaro, México

2Facultad de Estudios Superiores Iztacala, Universidad Nacional Autónoma de México,

Tlalnepantla, Estado de México, México

ABSTRACT

Introduction: Dyscalculia is a speciﬁc learning disorder affecting the ability to learn

certain math processes, such as arithmetic data recovery. The group of children with

dyscalculia is very heterogeneous, in part due to variability in their working memory

(WM) deﬁcits. To assess the brain response to arithmetic data recovery, we applied

an arithmetic veriﬁcation task during an event-related potential (ERP) recording.

Two effects have been reported: the N400 effect (higher negative amplitude for

incongruent than for congruent condition), associated with arithmetic incongruency

and caused by the arithmetic priming effect, and the LPC effect (higher positive

amplitude for the incongruent compared to the congruent condition), associated

with a reevaluation process and modulated by the plausibility of the presented

condition. This study aimed to (a) compare arithmetic processing between children

with dyscalculia and children with good academic performance (GAP) using ERPs

during an addition veriﬁcation task and (b) explore, among children with dyscalculia,

the relationship between WM and ERP effects.

Materials and Methods: EEGs of 22 children with dyscalculia (DYS group) and

22 children with GAP (GAP group) were recorded during the performance of

an addition veriﬁcation task. ERPs synchronized with the probe stimulus were

computed separately for the congruent and incongruent probes, and included only

epochs with correct answers. Mixed 2-way ANOVAs for response times and correct

answers were conducted. Comparisons between groups and correlation analyses

using ERP amplitude data were carried out through multivariate nonparametric

permutation tests.

Results: The GAP group obtained more correct answers than the DYS group.

An arithmetic N400 effect was observed in the GAP group but not in the DYS group.

Both groups displayed an LPC effect. The larger the LPC amplitude was, the higher

the WM index. Two subgroups were found within the DYS group: one with an

average WM index and the other with a lower than average WM index. These

subgroups displayed different ERPs patterns.

Discussion: The results indicated that the group of children with dyscalculia was very

heterogeneous and therefore failed to show a robust LPC effect. Some of these

children had WM deﬁcits. When WM deﬁcits were considered together with

dyscalculia, an atypical ERP pattern that reﬂected their processing difﬁculties

How to cite this article Cárdenas SY, Silva-Pereyra J, Prieto-Corona B, Castro-Chavira SA, Fernández T. 2021. Arithmetic processing in

children with dyscalculia: an event-related potential study. PeerJ 9:e10489 DOI 10.7717/peerj.10489

Submitted 4 September 2019

Accepted 13 November 2020

Published 27 January 2021

Corresponding author

Thalía Fernández,

thaliafh@yahoo.com.mx

Academic editor

Genevieve McArthur

Additional Information and

Declarations can be found on

page 23

DOI 10.7717/peerj.10489

Copyright

2021 Cárdenas et al.

Distributed under

Creative Commons CC-BY 4.0

emerged. Their lack of the arithmetic N400 effect suggested that the processing in

this step was not useful enough to produce an answer; thus, it was necessary to

reevaluate the arithmetic-calculation process (LPC) in order to deliver a correct

answer.

Conclusion: Given that dyscalculia is a very heterogeneous deﬁcit, studies examining

dyscalculia should consider exploring deﬁcits in WM because the whole group of

children with dyscalculia seems to contain at least two subpopulations that differ in

their calculation process.

Subjects Cognitive Disorders, Pediatrics

Keywords Dyscalculia, Event-related potentials, Arithmetic N400 effect, Late positive component

effect, Children, Learning disorders, Arithmetic veriﬁcation task, Working memory

INTRODUCTION

According to the Diagnostic and Statistical Manual of Mental Disorders, 5th Edition

(DSM-5; American Psychiatric Association, 2013), dyscalculia refers to difﬁculties with

number sense, number facts, and calculation (i.e. having a poor understanding of numbers,

their magnitudes and relationships, counting on ﬁngers to add single-digit numbers

instead of recalling math facts as peers do, becoming lost in the midst of arithmetic

computation and switching procedures). The academic skills of children with dyscalculia

are substantially below those expected for their chronological age, which can cause

signiﬁcant difﬁculties in academic performance and in activities of daily living (American

Psychiatric Association, 2013). Dyscalculia cannot be better accounted for by intellectual

disabilities, uncorrected visual or auditory acuity, other mental or neurological disorders,

psychosocial adversity, lack of proﬁciency in the language of academic instruction, or

inadequate educational instruction (American Psychiatric Association, 2013).

Dyscalculia is a heterogeneous cognitive disorder (Kaufmann et al., 2013). A known

source of this heterogeneity is working memory (WM), which varies markedly between

children with dyscalculia (Andersson & Lyxell, 2007;Geary, 1993;Mammarella et al.,

2017). The WM system provides online storage of information and its subsequent

manipulation through four subsystems: the phonological loop, the visuospatial sketchpad,

the episodic buffer, and the central executive (Baddeley, 2006). In the domain of

mathematics, the phonological loop holds intermediate arithmetic results in the form of

linguistic information, and plays a role in mathematical abilities that involve the

articulation of numbers, such as counting, problem-solving, and arithmetic fact retrieval

(Geary, 1993;Shen, Liu & Chen, 2018). The visuospatial sketchpad supports the

construction of visual representations of numerical information and is, thus, related to

spatial aspects of calculation, such as decomposition strategies (Foley, Vasilyeva & Laski,

2017;Simms et al., 2016). The episodic buffer provides a temporary storage that links

information from the two slave subsystems and long-term memory, allowing the

maintenance of multi-code number representations (Camos, 2018). Finally, the central

executive coordinates and monitors simultaneous processing and keeps track of math tasks

that have already been performed (DeStefano & LeFevre, 2004;Fuchs et al., 2005;Holmes &

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 2/29

Adams, 2006). Children with dyscalculia may show difﬁculty in verbal short-term memory

and verbal WM (Attout & Majerus, 2015;Berninger, 2008;Hitch & McAuley, 1991;Peng &

Fuchs, 2016;Shen, Liu & Chen, 2018;Swanson & Siegel, 2001), visuospatial short-term

memory and visuospatial WM (McDonald & Berg, 2018;Mammarella et al., 2017;Rotzer

et al., 2009;Schuchardt, Maehler & Hasselhorn, 2008), and the central executive

(Andersson & Lyxell, 2007;Meyer et al., 2010;Vanbinst & De Smedt, 2016). In addition,

these children have been reported to show a slower processing speed (Geary, Hoard &

Hamson, 1999;Landerl, Bevan & Butterworth, 2004;Shalev, Manor & Gross-Tsur, 2005).

Behavioural performance (accuracy and response time) in arithmetic tasks depends

on the arithmetic ability of the subject (Cipora & Nuerk, 2013;LeFevre & Kulak, 1994;

Núñez-Peña & Suárez-Pellicioni, 2012) as well as individual characteristics such as age

(De Smedt et al., 2009;Geary & Wiley, 1991;Geary, Bow-Thomas & Yao, 1992) and school

grade (Geary, 2004;Imbo & Vandierendock, 2008). Behavioural performance also

depends on the task features. In an arithmetic veriﬁcation task, in which the arithmetic

operation (context) is followed by a possible solution (probe) that may or may not match

the correct result of the operation, the priming phenomenon manifests as a shorter

response time in the presence of facilitation provided by the context, that is when the probe

digit coincides with the result of the proposed arithmetic operation (congruent condition).

One explanation for this phenomenon is that the congruent solution is more quickly

recovered from memory (Niedeggen & Rösler, 1999;Niedeggen, Rösler & Jost, 1999). Thus,

to provide a correct answer, a child needs to perform adequate arithmetic processing

(to choose the correct probe) as well as adequately maintain the result in verbal WM via

the verbal short-term memory, which leads to facilitation.

All previously mentioned studies used behavioural variables to draw their conclusions.

Although behavioural assessments of performance during tasks can yield data for variables

such as response time and percentage of correct answers, they ignore the subject’s cerebral

and cognitive processes. In contrast, the high temporal resolution of event-related

potentials (ERPs) can elucidate these processes by representing the processing through

each millisecond and thereby allowing chronologic analysis of brain function through

different cognitive processes.

Event-related potentials have previously been used to study arithmetic processing.

Evaluation of arithmetic veriﬁcation processing in healthy young adults by using ERPs

reported a negative wave with greater amplitude in an incongruent condition (i.e. when

there is no facilitation provided by the context) than in a congruent condition

(i.e. with facilitation provided by the context) (Dong et al., 2007;El Yagoubi, Lemaire &

Besson, 2003;Hinault & Lemaire, 2016;Prieto-Corona et al., 2010;Szűcs & Csépe, 2005).

The arithmetic N400 component is a negative waveform that begins at around 250 ms,

peaks at around 400 ms, and is maximal over the centroparietal area on the scalp

(Dickson & Federmeier, 2017;Hinault & Lemaire, 2016;Jost, Hennighausen & Rösler, 2004;

Niedeggen, Rösler & Jost, 1999;Niedeggen & Rösler, 1999;Prieto-Corona et al., 2010).

If the arithmetic N400 component in the incongruent is larger than in the congruent

condition, the signiﬁcant difference in amplitude between these components is known as

the arithmetic N400 effect, which reﬂects the strength of the probe’s relationship with the

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 3/29

context (i.e. arithmetic operation) (Niedeggen & Rösler, 1999). N400 is thought to reﬂect

the automatic retrieval of arithmetic facts from long-term memory and its magnitude

represents the strength of the probe’s relationship with the context (i.e. arithmetic

operation) (Niedeggen & Rösler, 1999). However, lack of concordance between automatic

recovery of the correct results and the probe may involve additional inhibitory processes

(Hinault & Lemaire, 2016).

Studies with different populations have indicated that the arithmetic N400 effect is

modulated by arithmetic abilities. For example the effect is greater in adults or teenagers

with better arithmetic abilities than in adults or teenagers, respectively, with poorer

arithmetic abilities (Núñez-Peña, Gracia-Bafalluy & Tubau, 2011;Núñez-Peña & Suárez-

Pellicioni, 2012,2015;Soltész et al., 2007;Soltész & Szűcs, 2009;Thevenot, Fanget & Fayol,

2007). Comparisons between children and adults have revealed differences in latency

and topographical distributions of the arithmetic N400 effect (Prieto-Corona et al., 2010).

Further, younger children show longer latencies than older children (Dong et al., 2007).

Another ERP component that has been used to investigate arithmetic processing in

adults and children is the late positive component (LPC). This follows the arithmetic N400

component, appearing between 500 and 700 ms. The LPC is a positive deﬂection in the

ERP waveform that shows a parietal (Jasinski & Coch, 2012;Niedeggen, Rösler & Jost, 1999;

Núñez-Peña & Suárez-Pellicioni, 2015;Xuan et al., 2007) or centro-parietal (Núñez-Peña &

Escera, 2007;Núñez-Peña & Suárez-Pellicioni, 2012;Prieto-Corona et al., 2010)

topography, mainly over the right hemisphere (Jasinski & Coch, 2012;Niedeggen &

Rösler, 1999;Niedeggen, Rösler & Jost, 1999). The signiﬁcant difference in amplitudes

between LPC components elicited by incongruent and congruent conditions is known as the

LPC effect when amplitude in an incongruent condition is larger than in a congruent

condition (Jost, Hennighausen & Rösler, 2004;Niedeggen, Rösler & Jost, 1999;Núñez-Peña &

Suárez-Pellicioni, 2012;Prieto-Corona et al., 2010;Szűcs & Csépe, 2005;Szűcs & Soltész,

2010). The LPC effect is associated with processing re-evaluation (Núñez-Peña & Suárez-

Pellicioni, 2012;Prieto-Corona et al., 2010;Szűcs & Soltész, 2010), and its amplitude is

modulated by the plausibility of a presented condition (Niedeggen & Rösler, 1999;

Núñez-Peña & Escera, 2007;Núñez-Peña & Honrubia-Serrano, 2004;Núñez-Peña & Suárez-

Pellicioni, 2015;Szűcs & Soltész, 2010). Some authors have proposed that the LPC effect

reﬂects surprise due to an out-of-context stimulus (Donchin & Coles, 1997;Núñez-Peña &

Suárez-Pellicioni, 2012;Polich, 2007). The LPC effect is greater in adults than in children

(Zhou et al., 2011) and in individuals with better arithmetic abilities than in those with

arithmetic deﬁcits (Iguchi & Hashimoto, 2000;Núñez-Peña, Gracia-Bafalluy & Tubau, 2011;

Núñez-Peña & Honrubia-Serrano, 2004;Núñez-Peña & Suárez-Pellicioni, 2012,2015;

Szűcs & Soltész, 2010).

In summary, children with dyscalculia may show deﬁcits in WM in addition to the

characteristic mathematical problems, making them a heterogeneous group. Although

ERPs have shown that neural processing in these children differs from that in children with

typical abilities, the effects of an additional WM deﬁcit on the processing of an arithmetic

veriﬁcation task at the neural level remain unknown. Since ERPs can reveal or highlight

mechanisms that remain undetected by behavioural measures, the body of knowledge

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 4/29

about dyscalculia may be enhanced by comparing ERPs of children with dyscalculia and

those with typical development while the children perform an arithmetic veriﬁcation

task. Thus, the ﬁrst aim of the current study was to compare the arithmetic processing

between children with dyscalculia and children with good academic performance (GAP)

by assessing their ERPs during an addition veriﬁcation task. The second aim was to explore

the relationship between WM and ERPs in children with dyscalculia. We hypothesised

that, in comparison with children with GAP, children with dyscalculia would show (1) less

accurate or slower behavioural responses on an arithmetic veriﬁcation task, (2) smaller or

later arithmetic N400 and LPC effects, and (3) poorer performance on WM tests.

In addition, we explored the possibility of a relationship between WM performance and

the N400 and LPC effects in children with dyscalculia.

METHODS

Ethics

This research was conducted in accordance with the ethical principles of the Declaration of

Helsinki. The Bioethics Committee of the Neurobiology Institute at the Universidad

Nacional Autónoma de México approved the experimental protocol (INEU/SA/CB/145).

Children and their parents gave written informed consent to participate in this study.

Participants

Forty-four right-handed children aged between 9 and 11 years participated in this study.

The participants were selected from a sample of 167 children from public and private

elementary schools in Querétaro, México. The study was carried out in 2015–2016.

The interview, examinations and psychological and neuropsychological tests were

administered around 2 months before the ERPs. After completing a semi-structured

interview, we excluded 16 children due to low socioeconomic status (the mother had not

completed elementary school and/or per capita income was less than 100% of the

minimum wage; Harmony et al., 1990) and two children who presented with epilepsy.

In addition, we excluded six children with intellectual disability (i.e. IQ < 70; Wechsler

Intelligence Scale for Children, 4th Edition, Spanish version; Wechsler, 2007), 52 children

who showed psychiatric disorders (i.e. ADHD, behaviour disorder, and/or oppositional

deﬁant disorder as identiﬁed with MiniKid (Ferrando et al., 1998) and neuropsychiatric

assessments), and two children with uncorrected hypoacusis were excluded as well.

The remaining 89 children completed the arithmetic subtest of the Child

Neuropsychological Assessment (Matute et al., 2005), which is standardised and includes

norms for the Mexican population. Its arithmetic domain consists of three subdomains

(counting, number management and calculus). Thirty participants who performed at or

below the 9th percentile in at least one arithmetic subdomain were assigned to a group of

children with dyscalculia (DYS group), and 28 participants at or above the 37th percentiles

in all subdomains were assigned to a group with GAP group. The remaining 31

participants that did not belong to either of these two groups were excluded. Of the

selected children, ﬁve from the DYS group and two from the GAP group were excluded

because their correct answers were below the chance level (58%). Another three children

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 5/29

from the DYS group and four from the GAP group were later excluded due to poor ERP

data (see the ERP section below). Thus, the DYS and GAP groups were each represented by

22 participants (11 and 14 girls in the DYS and GAP groups, respectively). The groups

did not differ in age, gender (χ

2

(1) = 0.834, p= 0.361), or monthly family income

per capita.

Both groups underwent assessments for the four neuropsychological indices of the

Wechsler Intelligence Scale for Children: verbal comprehension index, WM index,

processing speed index, and perceptual reasoning index. The children in the GAP group

had scores of 85 or higher in all indices, while those in the DYS group showed signiﬁcantly

lower scores on all the indices except the processing speed index, as shown in Table 1.

Figure 1 shows the boxplots of the arithmetic subtests of the Child Neuropsychological

Assessment and the WM index of the Wechsler Intelligence Scale for Children.

All participants had normal or corrected-to-normal visual acuity, and they did not present

any history of neurological or psychiatric disorders. Children from both groups were

selected from the same schools and were therefore from the same educational

environments.

Stimuli

Each trial of the task started with a warning stimulus (a right-pointed arrow), which was

followed by an addition operation with two single-digit operands between 1 and 9.

Each addition operation combined the two Arabic digits using the plus sign (+), resulting

in 81 different addition operations. Every operation was presented once with each of

the correct and incorrect results (congruent and incongruent conditions). The incorrect

result was constructed by either adding 2 to the correct result (for 41 facts) or by

subtracting 2 from it (for the remaining 40 facts).

Arithmetic verification task

Figure 2 illustrates the time chart of the task. In each of the 162 trials, a white warning

stimulus was presented at the centre of the black screen for 200 ms, followed by a black

screen that lasted for 300 ms. A white addition operation then appeared for 1,500 ms,

followed by another black screen for 1,500 ms. Subsequently, a white number (probe

stimulus) was presented for 1,000 ms on a black screen, which either did or did not match

the sum of the numbers (for the congruent or incongruent conditions, respectively).

Finally, a black screen was presented for 500 ms. Half of the trials were congruent and half

incongruent. Trials were randomised and delivered by Mind-Tracer 2.0 software

(Neuronic Mexicana, S.A.; Mexico City, Mexico).

Procedure

Children were seated in a comfortable chair 70 cm from the computer screen in a

sound-attenuated dimly-lit Faraday recording chamber. The experiment began after a

training period to familiarise the children with the task, which consisted of 16 trials with

feedback. This was followed by 162 trials divided into four blocks (two with 40 and two

with 41 trials). Blocks were separated by 1-min rest periods.

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 6/29

All children were instructed to relax and maintain their gaze towards the centre of the

screen and to avoid blinking when the probe stimulus appeared. They were asked to blink

after the response was given, just before the warning stimulus. The children were

instructed to respond as quickly and accurately as possible when the probe stimuli were

presented. Half the children were instructed to press the mouse key with the right thumb if

they thought the probe was correct (congruent condition) and with the left thumb if they

20

0

40

60

80

100

GAP DYS

Counting

Number management

Calculus

8

40

60

80

100

120

140

GAP DYS

Group

A.

B.

Percentile

WM index

Standarized score

Figure 1 Variability of arithmetic subdomains and WM index in both groups. (A) Box-and-whisker

plots of the subdomains (counting, number management, and calculus) of the arithmetic subtest of the

Child Neuropsychological Assessment in both groups of children (GAP and DYS). (B) Box-and-whisker

plots of the working memory index of the Wechsler Intelligence Scale for Children, 4th Edition, Spanish

version. The error bars represent the standard deviation. Full-size

DOI: 10.7717/peerj.10489/ﬁg-1

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 7/29

Table 1 Differences between groups in terms of demographic features, arithmetic performance and

intelligence quotient.

Mean ±SD t(42) p-Value

GAP DYS

Age (years) 9.41 ± 1.182 9.77 ± 0.813 −1.189 0.241

Monthly economic income 2421 ± 1188.81 1983 ± 1209.76 1.211 0.233

ENI subscales (arithmetic domain)

Counting 65.27 ± 15.03 24.55 ± 23.86 6.772 <0.001

Number management 59.73 ± 23.03 13.91 ± 17.68 7.400 <0.001

Calculus 68.18 ± 20.99 20.91 ± 26.08 6.622 <0.001

Logical mathematical reasoning 68.45 ± 22.28 51.41 ± 35.02 1.926 0.061

WISC-IV indexes

Intelligence quotient 105.95 ± 10.86 89.55 ± 10.82 5.017 <0.001

Verbal comprehension index 102.41 ± 20.69 86.23 ± 21.62 2.536 0.015

Perceptual reasoning index 100.59 ± 18.71 85.68 ± 20.83 2.947 0.017

Working memory index 104.23 ± 11.48 89.36 ± 13.85 3.875 <0.001

Processing speed index 97.95 ± 20.71 91.68 ± 14.32 1.168 0.249

WISC-IV subtests

Similarities 10.77 ± 2.72 8.59 ± 4.22 2.035 0.048

Vocabulary 11.64 ± 2.82 8.55 ± 2.24 4.024 <0.001

Comprehension 10.82 ± 3.11 8.09 ± 2.87 3.019 0.004

Block design 10.86 ± 2.76 8.68 ± 2.62 2.684 0.010

Picture Concepts 10.59 ± 2.70 8.86 ± 2.66 2.137 0.038

Matrix reasoning 10.45 ± 2.28 8.41 ± 1.91 3.217 0.002

Digit span 10.73 ± 2.12 7.68 ± 2.41 4.442 <0.001

Letter-number sequencing 11.23 ± 2.20 8.14 ± 2.73 4.133 <0.001

Arithmetic 14.00 ± 3.14 9.75 ± 2.86 4.417 <0.001

Coding 10.23 ± 2.56 8.64 ± 1.94 2.322 0.025

Symbol search 10.41 ± 2.21 9.27 ± 2.18 1.711 0.094

Note:

ENI: Child Neuropsychological Assessment (Matute et al., 2005); WISC-IV: The Wechsler Intelligence Scale for

Children, 4th Edition Spanish version (WISC-IV; Wechsler, 2007); GAP: children with good academic performance;

DYS: children with dyscalculia.

Figure 2 Depiction of a trial of the addition veriﬁcation task. Flowchart of stimuli presentation during

individual trials. W, warning stimulus. Full-size

DOI: 10.7717/peerj.10489/ﬁg-2

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thought it was incorrect (incongruent condition). The other half of the children were

instructed to do the opposite.

ERP acquisition and analysis

A 19-channel EEG (Ag/AgCl electrodes held in position with a cap according to the

10–20 International System; Electro-CapTM International, Inc.; OH, USA), referenced to

linked earlobes (A1A2), was recorded using a MEDICIDTM IV system (Neuronic S.A.;

Mexico City, Mexico) and a Track Walker v5.0 data system while the child was

performing the task. The bandwidth of the ampliﬁers was 0.5–50 Hz, and the sampling

frequency was 200 Hz. Impedances in all the recordings were maintained below 5 kΩ.

Electro-oculograms were recorded with electrodes located on the superciliary arch and

the external canthus of the right eye.

Event-related potentials were computed ofﬂine using 1,000 ms EEG epochs from each

subject in each experimental condition. The epochs consisted of a baseline period that

started 200 ms before the probe onset and ended 800 ms after the probe onset. Baseline

correction was performed using the 200 ms pre-stimulus period. An EEG epoch was

rejected if visual inspection revealed blinking or ocular movements, electrical activity

exceeding 100 microvolts, or ampliﬁer blocking for more than 50 ms at any electrode site.

Seven participants (three in the DYS group) had fewer than 20 artifact-free trials per

condition, so these participants were excluded. The number of EEG epochs per condition

was approximately equal per subject. On average, the DYS and GAP groups had 33 and

39 artifact-free epochs, respectively, for each condition. Accepted EEG epochs associated

with correct answers were averaged together to produce one ERP each for the congruent

and incongruent conditions for each child. The former was subtracted from the latter

(i.e. incongruent minus congruent) to produce one ERP difference wave per child.

Statistical analysis

Behavioural data analysis

Statistical analyses of behavioural data were performed using the statistical program SPSS

(IBM Statistic 20, Chicago, IL, USA). We conducted mixed 2-way ANOVAs for response

times and for correct answers. The percentage of correct answers was transformed by

arcsine (square root (percentage/100)) (Zar, 2010). Group (GAP, DYS) was included as the

between-subjects factor, and condition (congruent, incongruent) was included as the

within-subjects factor. The least signiﬁcant differences method was used for post-hoc

pairwise comparisons.

ERP data analysis

Figure 3 shows the scheme of statistical analyses for the ERP data. All assessments were

performed using nonparametric tests with permutations (Galán et al., 1998) due to the

multiplicity of comparisons and dependent variables and the consequently increased

probability of type I errors (Luck, 2014). Analyses were carried out using eLORETA

software (Pascual-Marqui et al., 2011). Five thousand permutations were performed.

Global signiﬁcance for the statistical test (i.e. signiﬁcant p-value level considering all the

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 9/29

-200 200 400 600 800

0

-200 200 400 600 800

0

-8

-4

4

8

-8

-4

4

8t-values

ms

GAP

DYS

Defining analysis time-window

A

.

Subject 01

Fp1 ...

Subject 02

Subject n

Subject 01

Fp1

...

Subject 02

Subject n

...

GAP

DYS ...

Between-group comparison of ERP effects C.

Mean amplitude value of the

...

VS

Fp1

t-testempirical

distributions

time 1

Comparison incongruent vs congruent

Subject 01

Fp1 ...

Subject 02

Subject n

t-test

Subject 01

Fp1

...

Subject 02

Subject n

...

GAP DYS

...

Topographical exploration of ERP effectsB.

mean

amplitude

value

...

VS

Subject 01

Fp1 ...

Subject 02

Subject n

Subject 01

Fp1

...

Subject 02

Subject n

...

...

...

VS

Congruent

Incongruent

Congruent

Incongruent

time 2

time 200

Pz

difference wave

(incongruent minus congruent)

Correlation analysesD.

Fp1 ...

Pz

Pz Pz

Pz

Permutation 1

. . .

Permutation 2

Permutation 5,000

. . .

Mean amplitude

WM index

...

t-test

Pz

...

Pz

t-test t-test

...

. . .

t-test

Pz

t-test

...

t-values

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

of the difference wave

V

µ

Arithmetic N400

(305 - 385 ms) (510 - 630 ms)

&LPC (680 - 700 ms)

LPC

Arithmetic N400

(305 - 385 ms) (510 - 630 ms)

&LPC

LPC1

(510 - 630 ms) (680 - 700 ms)

& LPC2

Figure 3 Workﬂow of the statistical analyses of ERP data using non-parametric permutation tests.

(A) Deﬁnition of analysed time windows, where signiﬁcant differences between incongruent and con-

gruent conditions (effects) were evinced; comparison between conditions using multiple t-tests, shown at

each point of time throughout the electrode sites (colour lines in the coordinate axis). Magenta horizontal

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 10/29

electrodes) was reported as T

max

and its extreme p-value. Because this statistical test is

based on an empirical probability distribution, extreme p-values were corrected by

multiple comparisons.

Time windows of the ERP components are usually deﬁned by the outcomes of previous

studies. However, most studies relevant to this experiment tested young adults, who have

faster processing than children. To determine appropriate time windows for the arithmetic

N400 and LPC effects in children, we performed a non-parametric permutation test to

identify signiﬁcant differences between the ERP waveforms for congruent and incongruent

conditions per time point between −200 to 800 ms at all electrode sites (Fig. 3A). In each

group of children, we deﬁned the time windows of the arithmetic N400 and LPC.

The next step was to explore the topography of the N400 and LPC effects per group

across all electrode sites (Fig. 3B). In addition, eLORETA was used to conduct three

analyses that compared the ERP difference waveforms (incongruent minus congruent)

between the two groups (GAP, DYS) (Fig. 3C). Five thousand permutations were

performed. Signiﬁcant t-values over electrode sites are represented in colour maps

(only t-values with p< 0.05).

We also used eLORETA to perform three correlation analyses in the DYS group

between each ERP difference wave form and the WM index across all electrode sites

(Fig. 3D). Five thousand permutations were performed. Signiﬁcance for the statistical test

was reported (r

max

and its extreme p-value). Speciﬁc signiﬁcant correlations (rvalue)

over electrode sites are represented in colour maps (only r-values with p< 0.05).

All statistical results for the ERPs were reported taking into consideration all 19

electrodes.

RESULTS

Behavioural results

The behavioural results are shown in Fig. 4. The participants in the GAP group

showed a signiﬁcantly higher percentage of correct answers than those in the DYS group

(F

(1, 42)

= 27.39, p< 0.0001, η

p

2

= 0.395). The percentage of correct answers in the

incongruent condition was signiﬁcantly higher than that in the congruent condition

(F

(1, 42)

= 8.67, p= 0.005, η

p

2

= 0.171), independently of the group. No signiﬁcant group by

condition interaction was noted (F< 1).

The responses for all children were signiﬁcantly faster in the congruent condition than

in the incongruent condition (F

(1, 42)

= 131.922, p< 0.0001, η

p

2

= 0.759), but the response

Figure 3 (continued)

lines represent the threshold of t-values for p= 0.05, and grey shadowed boxes represent the analysed

time windows where signiﬁcant differences were found. Colour lines in the coordinate axis represent t-

values at different electrode sites. (B) Exploration of the topography of ERP effects (incongruent minus

congruent) obtained from (A); t- tests were computed using the mean amplitude values in each condition

for each analysed time window (N400 and LPC in the group GAP and LPC in the group DYS) across all

electrode sites. (C) Comparison of the ERP-difference wave between the DYS and GAP groups. Mean

amplitude values of the difference waves were used to compute the t-tests. (D) Correlation analyses

between the working memory index and ERP difference waves for the DYS group, for each electrode site

and each ERP window. Full-size

DOI: 10.7717/peerj.10489/ﬁg-3

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times were not signiﬁcantly different between the groups (F< 1). No signiﬁcant group by

condition interaction (F

(1,42)

= 1.114, p= 0.297, η

p

2

= 0.026) was observed for this

assessment. This ﬁnding could be attributed to the large age range of the participants, since

the automation of solutions to arithmetic problems is a developing process in children

of these ages. We tested this possibility by exploring the association between age and

response time using Spearman rank correlation analyses within groups. The GAP group

showed signiﬁcant negative correlations for congruent (r=−0.57, p= 0.006) and

incongruent (r=−0.60, p= 0.003) conditions; however, the DYS group showed no

signiﬁcant correlations for any condition (congruent: r=−0.29, p= 0.195; incongruent:

r=−0.22, p= 0.337).

Electrophysiological results

Time windows for the N400 and LPC effects in the DYS and GAP groups

The statistical results showed signiﬁcant differences between conditions from 305 to 385

ms and from 510 to 630 ms in the GAP group (T

max

=−3.387, extreme p= 0.0004).

Figures 5A and 5B show the topography of the signiﬁcant differences in the ﬁrst and

second windows, which correspond to the arithmetic N400 and LPC effects, respectively,

in terms of their latency and polarity (negative and positive, respectively). The LPC effect

elicited by the GAP group was named the LPC1 effect. The topographic distribution of

both ERP effects corresponds with the ﬁndings reported in previous studies in young

adults. The arithmetic N400 effect was localised over the frontal midline (Megías &

Macizo, 2016;Prieto-Corona et al., 2010) and left centroparietal area (Avancini, Galfano &

Szűcs, 2014;Avancini, Soltész & Szűcs, 2015;Dickson & Federmeier, 2017). The LPC effect

was observed over the centro-parieto-temporal area, mainly in the right hemisphere

GroupGroup

A

.

Congruent Incongruent

600

800

1000

110 0

GAP DYS

Response time

ms

20

40

60

80

100

GAP DYS

***

%

Correct answers

B.

*** ***

Figure 4 Behavioural data in both groups of children (GAP and DYS) in the arithmetic veriﬁcation

task. The correct answer (A) and mean response time (B) in both conditions (congruent and incon-

gruent) and both groups of children. Error bars represent the standard deviation. The DYS group showed

a lower percentage of correct answers than the GAP group. p< 0.0001.

Full-size

DOI: 10.7717/peerj.10489/ﬁg-4

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(Avancini, Soltész & Szűcs, 2015;Dickson & Federmeier, 2017;Jasinski & Coch, 2012;

Niedeggen & Rösler, 1999). In contrast, the DYS group only displayed a signiﬁcant

difference between 680 and 700 ms (T

max

= 4.84, extreme p= 0.021), as shown in Fig. 5C,

which could correspond to a late LPC effect (named the LPC2 effect).

The grand averages of the ERPs in the T3 and C3 electrodes in the two task conditions

for both groups are shown in Fig. 6. This ﬁgure clearly illustrates that the lack of arithmetic

N400 effect in the DYS group is not associated with a lack of response, but with similarly

large amplitudes for both arithmetic N400 components in each condition.

3.58

0

-3.60

0

t-values

Arithmetic N400 LPC

(305 - 385 ms) (510 - 630 ms)

3.68

0

t-values

GAP group

DYS group

A

.

C.

LPC

(680 - 700 ms)

B.

Figure 5 Statistical parametric maps of the arithmetic N400 and LPC effects in both groups. Top:

GAP group. (A) Differences between conditions at 305–385 ms (arithmetic N400). (B) Differences

between conditions at 510–630 ms (LPC effect). Bottom: DYS group. (C) Differences between conditions

at 680–700 ms (LPC effect). Blue and red colours represent the t-values that were above the threshold of

signiﬁcance (p< 0.001). In the GAP group, the arithmetic N400 effect was elicited at P3, O1, T4, T5, Fz,

and Pz and the LPC effect was elicited at C4, P4, O1, O2, T4, T6, Cz and Pz, while in the DYS group, the

LPC effect was observed at P3 and O1. All p< 0.001. Full-size

DOI: 10.7717/peerj.10489/ﬁg-5

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ERP difference waveforms in the DYS and GAP groups

Having identiﬁed appropriate time windows for the N400 and LPC effects in each group,

three statistical analyses for independent samples were performed using the permutation

technique (considering all electrodes) to compare the ERP difference waves in the GAP

and DYS groups per time window identiﬁed (305–385 ms, 510–630 ms and 680–700 ms).

The GAP children showed a signiﬁcantly larger amplitude for the arithmetic N400 effect

over T5 (T

max

=−3.58, extreme p= 0.007) and a signiﬁcantly larger LPC1 effect over Fp2

(global T

max

= 3.01, extreme p= 0.032) than the DYS children. In the LPC2 time window,

no differences between groups were observed (T

max

= 1.46, extreme p= 0.45). Figure 7

shows the statistical colour maps of the arithmetic N400 effect and LPC effect comparisons

between the two groups (GAP vs. DYS).

Associations between WM and ERPs

The heterogeneity that characterises behavioural performance in dyscalculia (Kaufmann

et al., 2013) is also likely reﬂected on ERPs since ERPs correspond to the brain processing

that underlies performance, which indicates that data dispersion is higher in the DYS

group. Moreover, the DYS group showed more outliers than the GAP group (Fig. 8).

One source of this heterogeneity has been proposed to be WM (Andersson & Lyxell, 2007;

Geary, 1993).

The children with dyscalculia were assessed according to their WM indices and

distributed into two subgroups: one with average WM indices (scores equal to 85 or higher;

-6

-4

-2

2

4

6

8

-6

-4

-2

2

4

6

8

200-200 600 200-200 600

T3 C3

arithmetic N400

GAP group DYS group

Congruent

Incongruent

ms

VµVµ

A. B.

Figure 6 ERP wave grand averages. (A) T3 electrode. (B) C3 electrode. The GAP group responses to

congruent and incongruent conditions are represented by the black continuous and discontinuous lines,

while the DYS group responses to congruent and incongruent conditions are represented by the red

continuous and discontinuous lines, respectively. Negativity is plotted downwards.

Full-size

DOI: 10.7717/peerj.10489/ﬁg-6

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n= 13, six girls) and the other with lower-than-average WM indices (scores < 85; n=8,

four girls). Figure 9 displays the grand average of the difference wave for these two

subgroups of children with dyscalculia, as well as children with GAP. The children with

dyscalculia and a low WM index score seemed to show one N200 peak, one arithmetic

N400 peak, and two LPC peaks, representing an atypical ERP pattern for this task.

In contrast, children with dyscalculia, but with average WM index scores, showed a similar

ERP pattern to children with GAP.

For the children with dyscalculia, correlation analyses between the WM index scores

and the amplitude values of the difference wave at each electrode site were performed

in every ERP window. No signiﬁcant correlation was found between the WM index and

the difference wave in the N400 window. However, in both LPC windows, signiﬁcant

positive correlations were found between the WM index and LPC difference waves. In the

LPC1 time window, a greater WM index correlated with a greater amplitude in the

LPC effect over O2 and T6 (r

max

= 0.68, extreme p= 0.0056) and, in the LPC2 time

window, a greater WM index correlated with a greater amplitude of the LPC effect over T6

(r

max

= 0.61, extreme p= 0.0178). Figure 10 shows statistical colour maps for the

correlations between the WM index and the LPC effects.

DISCUSSION

The ﬁrst objective of this study was to compare arithmetic veriﬁcation processing in

children with dyscalculia with that in children with GAP during an addition veriﬁcation

task by using ERPs. To our knowledge, this is the ﬁrst study to compare the ERPs of these

two populations of children. We expected poorer behavioural performance (lower

percentage of correct answers and/or longer response times) in the children with

-2.73

02.81

0

t-values

Arithmetic N400 effect LPC effect

(305 - 385 ms) (510 - 630 ms)

GAP > DYS GAP > DYS

t-values

A

.B.

Figure 7 Differences between groups in arithmetic N400 and LPC effects. (A) Statistical map of the

comparison between groups based on the difference between conditions (incongruent minus congruent)

for the arithmetic N400 (305–385 ms) at T5. (B) Statistical map of the comparison between groups based

on the difference between conditions (incongruent minus congruent) for the LPC (510–630 ms) at Fp2.

The blue and red spots represent signiﬁcant differences between groups (t-values p< 0.05).

Full-size

DOI: 10.7717/peerj.10489/ﬁg-7

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dyscalculia than in the children with GAP. For the ERP patterns, we hypothesised that the

children with dyscalculia would display longer latencies and smaller arithmetic N400 and

LPC effects than the children with GAP.

-20

-10

10

0

20

GAP

7

1

18

3

6

34

34

41

42

42

44 37

41 41

41

*

41

DYS

µV

8

8

11

13 13

19

20

77

8

8

11 18

*

34

42

34 34

34

34

24

35

25

27

30

-20

-10

10

0

20

GAP DYS

Group

µV

(305 - 385 ms)

(510 - 630 ms)

Arithmetic N400

LPC

A

.

B.

Figure 8 Variability of arithmetic N400 and LPC effects. (A) Box-and-whisker plots of both groups of

children (GAP and DYS) using the amplitude values of the arithmetic N400 (305–385 ms) effect. (B) Box-

and-whisker plots of both groups of children using the amplitude values of the LPC (510–630 ms)

effect. Full-size

DOI: 10.7717/peerj.10489/ﬁg-8

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Behavioural differences between the DYS and GAP groups

Our behavioural results partially conﬁrmed our hypothesis. We observed a signiﬁcantly

lower percentage of correct answers in the DYS group than in the GAP group. This result

corroborates the ﬁndings of other behavioural studies (Castro & Reigosa-Crespo, 2001;

Geary, 1993;Geary, Bow-Thomas & Yao, 1992;Geary, Hoard & Hamson, 1999;Landerl,

Bevan & Butterworth, 2004). The poor performance of children with dyscalculia has been

explained by their use of procedural strategies such as counting on, counting all, and

decomposition, which are more prone to errors, instead of the long-term-memory retrieval

strategies that are used by children with typical arithmetic abilities when facing one-digit

addition problems (Geary, 2004). Unfortunately, in the present study, the strategies used

were not systematically recorded for each child. This constitutes a limitation of the study

because it precludes us from proving that the observed differences were attributable to the

strategies used. On the other hand, there was no signiﬁcant group difference in response

times. This could be explained by the high dispersion in the data in both groups,

Fp1 Fp2

F3

C3

P3

F4

O1

O2

C4

P3

F7 F8

T3

T5

T4

T6

Fz

Cz

Pz

GAP

DYS H WM

DYS L WM

8

4

-4

-200 600 800

Vµ

ms

A. B.

C. D.

E. F.

G. H.

I. J.

K. L.

M. N.

O. P.

Q.

R.

S.

Figure 9 Grand averages of the difference waves (i.e. incongruent minus congruent condition). Blue

solid lines represent the ERPs for the GAP group. Red solid lines represent the ERPs for the DYS group

with high WM index scores and red dotted lines represent those for the DYS group with low WM index

scores. Positive is plotted up. The arithmetic N400 effect and the LPC effect in the GAP group are marked

with grey-shadow boxes. Black arrows indicate double-negative peaks (195 ms and 405 ms) and dou-

ble-positive peaks (525 ms and 685 ms) in the DYS group with low WM scores at P3 and C3, but such

effects can be observed over other electrode sites. Each letter represents an electrode. (A) Fp1. (B) Fp2.

(C) F3. (D) F4. (E) C3. (F) C4. (G) P3. (H) P4. (I) O1. (J) O2. (K) F7. (L) F8. (M) T3. (N) T4. (O) T5. (P)

T6. (Q) Fz. (R) Cz and (S) Pz. Full-size

DOI: 10.7717/peerj.10489/ﬁg-9

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50 90 110

2

6

10

14

-6

R2=0.4686

A. B.

O2

WM Index

µV

2

6

10

14

-6

µV

50 90 110

WM Index

R2=0.4426

0.65

0

LPC

(510 - 630 ms)

r-values

T6

C.

D.

2

6

10

14

-6

50 90 110

R2=0.3568

0.60

0

LPC

(680 - 700 ms)

r-values

WM Index

µVT6

E.

Figure 10 Relationship between working memory and LPC effect in the DYS group. (A) Statistical

map of the correlations between the WM index and the ERP amplitude difference between conditions

(incongruent minus congruent) at 510–630 ms (LPC effect) across electrode sites. The red spot represents

the signiﬁcant rvalues (p< 0.05) over the T6 and O2 electrodes. (B) Ascending regression line showing

that higher values of the working memory index (Xaxis) are associated with greater LPC effects in the

electrode T6 (Yaxis). (C) Ascending regression line showing that higher values of the working memory

index (Xaxis) are associated with greater LPC effect in the electrode O2 (Yaxis). (D) Statistical map of the

correlations between the WM index and the ERP amplitude difference between conditions (incongruent

minus congruent) at 680–700 ms (LPC effect for the DYS group) across electrode sites. The red spot

represents the signiﬁcant r values (p< 0.05) over the T6 electrode. (E) Ascending regression line showing

that higher values of the working memory index (Xaxis) are associated with greater LPC effects for the

DYS group in the electrode T6 (Yaxis). Full-size

DOI: 10.7717/peerj.10489/ﬁg-10

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mainly in the DYS group (see Fig. 4). As expected, in the GAP group, older children

showed shorter response times, perhaps because the automation of arithmetic facts tested

herein is still developing in that age range. Interestingly, children with dyscalculia did not

show this association of performance with age. This may be because, independently of

age-related maturational process, children with dyscalculia experience problems in this

automation process.

ERP differences between the DYS and GAP groups

N400 effect

Only the GAP group exhibited the arithmetic N400 effect (a higher amplitude for the

incongruent condition than for the congruent condition). This effect was observed over the

left temporo-parieto-occipital and right fronto-temporal regions and peaked earlier than

400 ms. The ﬁndings for the frontal region coincide with the topography observed in

some studies in young adults (Megías & Macizo, 2016;Prieto-Corona et al., 2010) and

the left posterior localisation coincides with those found in other studies (Avancini,

Galfano & Szűcs, 2014;Avancini, Soltész & Szűcs, 2015;Dickson & Federmeier, 2017).

This more-distributed effect in children corresponds with the ﬁndings reported by

Prieto-Corona et al. (2010), who observed that the N400 effect in children involves more

cortical regions than that in adults to perform the same task, and by Dong et al. (2007),

who compared younger and older children during the performance of arithmetic

veriﬁcation tasks.

Only a few studies have assessed these effects in children, and the majority of them used

different arithmetic operations, which activate different brain regions (Zhou et al., 2011).

Another point of difference from these studies is that we obtained ERPs time-locked to

the onset of the probe stimuli, whereas almost all studies obtained ERPs time-locked to the

arithmetic problem or equation (Van Beek et al., 2014;Xuan et al., 2007). Only the study by

Xuan et al. (2007) shows the same characteristics as ours; however that study observed

the N400 effect over the vertex. One concern regarding ERP topography could be the use

of non-parametric statistics because they are not commonly used. However, Picton et al.

(2000) has argued that this is a better approach for ERP assessment than parametric

analyses because it makes no assumptions about the distribution of the data, and is

especially useful in the analysis of multichannel scalp distributions, as in our study. This is

supported by Megías & Macizo (2016) who analysed their ERP data by using parametric

and nonparametric statistical analysis and obtained similar ﬁndings with both methods,

with the nonparametric permutations appearing to be more sensitive to differences.

Since we are using an arithmetic veriﬁcation task to evoke the ERPs, it is important to

determine which processes could manifest in it. Among the four processes involved in the

arithmetic veriﬁcation task proposed by Avancini, Soltész & Szűcs (2015), two were

controlled in our task: (1) the number of congruent and incongruent probes was equal,

so violations of strategic expectations should not have manifested as ERP effects; and

(2) precisely the same probe stimuli were used for both conditions, so the physical

characteristics of the visual stimuli would not have affected the ERPs. The other two effects

are the magnitude effect and the violation of the operands’semantic constraints when an

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 19/29

incongruent probe is shown. Although all the incongruent probes were two units away

from the correct solution in our paradigm, a magnitude effect may have been present;

therefore, the priming effect and the magnitude effect could be mixed. A stronger left

posterior effect related to distance was observed by Avancini, Galfano & Szűcs (2014),

consistent with the studies indicating the association of this area with the verbal code

according to the triple-code model (Dehaene & Cohen, 1997). In our study, the GAP group

showed a higher N400 effect than the DYS group precisely in the left posterior temporal

area (Fig. 8).

In contrast, children with dyscalculia showed no signiﬁcant arithmetic N400 effect, and

when their ERPs were compared to those of the controls, signiﬁcant differences were

observed over the left posterior temporal region. This ﬁnding is consistent with those of

studies reporting a smaller arithmetic N400 effect in adults or teenagers with dyscalculia

compared to age-matched controls (Núñez-Peña & Suárez-Pellicioni, 2012;Soltész

et al., 2007). The lack of a signiﬁcant N400 effect in children with dyscalculia could be

explained as a failure to process congruent results. In these children, any probe (congruent

or incongruent) is perceived as a mismatch with what is stored in the arithmetic lexicon

(in Fig. 6A negative deﬂection is elicited in both conditions). Thus, they must revert to

conducting the arithmetic calculation. The group differences in the left temporal region

may reﬂect the fact that simple addition problems activate phonological processes, as has

been described for multiplication problems (Zhou et al., 2009).

LPC effect

The LPC effect was displayed in both groups, but with different latencies and topographies.

The DYS group showed a delayed LPC effect of shorter duration. Since the LPC effect

is modulated by the expectation or plausibility of the solution and children with dyscalculia

had lower arithmetic abilities, we expected a smaller LPC effect in the DYS group than

in the GAP group. Our results support this hypothesis because a signiﬁcantly lower

amplitude of the LPC effect was observed in the DYS group in the right frontopolar region.

Like other studies (Iguchi & Hashimoto, 2000;Núñez-Peña, Gracia-Bafalluy & Tubau,

2011;Núñez-Peña & Honrubia-Serrano, 2004;Núñez-Peña & Suárez-Pellicioni, 2012,

2015;Szűcs & Soltész, 2010), we observed that the LPC effect is greater in individuals with

better performance, and that this difference was located in the right frontal region.

Meiri et al. (2012), who used functional near-infrared spectroscopy, observed that the right

frontal region is activated during simple additions, and this region is believed to be

responsible for holistic arithmetic processing (Dehaene et al., 2003;El Yagoubi, Lemaire &

Besson, 2003). This suggests that children in the GAP group perform a greater

re-evaluation of incorrectness when the proposed result was incongruent than when it

was congruent, while children with dyscalculia, perhaps due to the lack of arithmetic

knowledge, re-evaluated almost all the results without distinction between congruent and

incongruent conditions.

Differences in topography were also observed between groups: The GAP group showed

the LPC effect in the expected right posterior location, while the DYS group exhibited

this effect in the left posterior region (see Fig. 5). The right lateralisation of the LPC effect

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 20/29

in children with GAP is consistent with the more deliberative and prolonged role of the

right hemisphere during probe evaluation, which has been found in adults during a

multiplication veriﬁcation task (Dickson & Federmeier, 2017). According to these authors,

after an initial period of evaluation of the provided response (probe), the left hemisphere

classiﬁes it as correct or incorrect and no longer performs follow-up evaluations, while

the right hemisphere engages in a deliberate assessment of the additional features of the

probe, perhaps using spatial skills, to provide an evaluation that is less categorical. It is

therefore possible that children with dyscalculia intentionally search for the correct answer

from their long-term memory (left hemisphere), but failing to ﬁnd the answer, they then

perform the arithmetic calculation. Although the topography recorded from the scalp

does not necessarily indicate the generators’location, different topographies indicate the

presence of distinct generators (Nunez & Srinivasan, 2006). Our results may suggest that

the left lateralisation of the LPC effect observed in children with dyscalculia is a

compensatory phenomenon to obtain the correct answer.

Heterogeneity within the DYS group

In contrast to our expectations, we found few differences between groups in the arithmetic

N400 and LPC effects. The heterogeneity in the children’s behaviour (Figs. 1 and 4), which

was enhanced in the WM behavioural scores (Fig. 1B), and ERP patterns (Fig. 7) of the

DYS group, could explain this ﬁnding. Two main hypotheses have been proposed to

explain atypical brain functioning that is reﬂected as neurobiological disorders of cognitive

processing (Silver et al., 2008) that underlie learning disorders (Landerl et al., 2009).

In addition to the domain-speciﬁc hypothesis, which refers to abilities speciﬁcally related to

mathematical competencies, the common-deﬁcit hypothesis postulates that certain

processing patterns are common to all children with learning disorders. Supporting this

hypothesis, Swanson (1987) proposed that children with learning disorders experience

failures in executive functioning mechanisms, which also points to WM deﬁcits as essential

problems (Berninger, 2008;Swanson, 2015;Swanson & Siegel, 2001). In children with

arithmetic disabilities, WM has been frequently reported to play an essential role in the

arithmetic domain (Swanson, 2015). In our study, once children had performed the

addition operation, they had to store the result in WM until the probe digit appeared

(1,500 ms later) to perform the response veriﬁcation process and ﬁnally provide an answer.

Therefore, the arithmetic veriﬁcation task that we used is particularly efﬁcient for

highlighting WM problems.

WM and dyscalculia

Consistent with our hypothesis, the children with dyscalculia showed a lower WM index

than those in the GAP group. This ﬁnding aligns with previous studies where WM was

found to predict learning arithmetic (Meyer et al., 2010;Vanbinst & De Smedt, 2016), as

well as a study by Mammarella et al. (2017), which reported that children with dyscalculia

had low scores for WM. Since the arithmetic N400 effect reﬂects a facilitation for the

probe stimulus that matches the correct answer, it may be the case that the absence of this

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 21/29

effect is associated with poor WM. Keeping the information of the addition in WM, as

children with GAP likely do, facilitates recognition or rejection of the proposed result.

However, it is important to emphasise that the WM performance in the DYS group was

not homogeneous. And while exploring the relationship between WM and arithmetic

processing in the DYS group, we discovered that children with higher WM index scores

showed a greater amplitude of the LPC effect in the right posterior region. This region

coincides with the LPC topography observed in previous studies (Niedeggen & Rösler,

1999;Núñez-Peña & Escera, 2007;Núñez-Peña & Honrubia-Serrano, 2004) and in our

control participants.

This relationship between WM and the LPC effect was elucidated in the present study

and contributes to the understanding of dyscalculia in children. For a more thorough

exploration of the WM effect in children with dyscalculia, children in the DYS group were

classiﬁed into two groups (average and lower-than-average) according to their WM

index. Visual inspection of ERP patterns from these two groups showed that the children

with dyscalculia and an average WM index had a similar ERP pattern to that in the

children with GAP, while the children with dyscalculia and a lower-than-average WM

index showed an atypical ERP pattern (Fig. 9). Visual inspection of the ERPs suggests that

this atypical pattern consisted of two negative peaks (at 195 ms and 405 ms) over the

parieto-occipital and centro-parieto-temporal regions and two positive peaks (at 525 ms

and 685 ms) over the parietal regions. The two negativities could correspond to the

N200 and arithmetic N400 effects, while the two positivities may correspond to the two

LPC effects. The N200 effect might be interpreted as evidence that children with

dyscalculia and poor WM engaged additional attentional resources (Xuan et al., 2007).

However, this N200 effect had a posterior topography; which may instead reﬂect a strong

early sensory attention (Schmajuk et al., 2006) before the comparison between the

probe stimulus and the sum result, which produces an arithmetic N400 effect. Later, the

children probably re-evaluated the arithmetic error (Núñez-Peña & Suárez-Pellicioni,

2012) twice.

It is noteworthy that the categorisation of the ERP patterns of the DYS group into two

subgroups was based on visual inspection. Ideally, we would have compared the ERPs

of the children with dyscalculia with poor WM and typical WM statistically, but the

sample sizes of these two subgroups were too small. It would be useful if future studies

could conduct these statistical comparisons to help clarify whether the atypical ERP

pattern that we observed is reliably association with dyscalculia, poor WM, or both

difﬁculties combined.

CONCLUSIONS

Children with dyscalculia did not show the arithmetic N400 effect found in children with

typical development during an arithmetic veriﬁcation task; however, both groups showed

an LPC effect. The great heterogeneity within the group of children with dyscalculia

precluded a robust LPC effect in these children; however, the higher the WM deﬁcits were,

the lower the LPC effect was in the right posterior region. In children with dyscalculia

and WM deﬁcits, an atypical ERP pattern (i.e. N200, N400 and two LPC effects) was

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 22/29

evinced. Therefore, future studies of both WM and ERPs in children with dyscalculia must

be mindful of the heterogeneous nature of dyscalculia at both the level of behaviour and

the brain function.

ACKNOWLEDGEMENTS

The authors are grateful for the cooperation of the children and parents who participated

in this study. The authors also acknowledge the administrative support provided by Bertha

Esquivel, Iva´n Negrete, Leonor Casanova, Lourdes Lara, and Teresa Alvarez, and the

technical assistance provided by Benito Martínez-Briones, Daniel Villareal, Enrique

Cabral, Héctor Belmont, Lucero Albarrán-Cárdenas, María del Carmen Rodríguez,

Maria do Carmo Carvalho, María Elena Juárez, Marisa Oar, Mauricio Cervantes-Romero,

Milene Roca Stappung, Minerva Berenice Rojas, Roberto Riveroll, Saulo Hernández, and

Sergio Sánchez-Moguel. We also thank Angelica Acosta for her comments on the

manuscript.

ADDITIONAL INFORMATION AND DECLARATIONS

Funding

This work was supported by the Programa de Apoyo a Proyectos de Investigación e

Innovación Tecnológica (IN204613, IN205520, and IN207520) and the Consejo Nacional

de Ciencia y Tecnología (CONACYT; CB-2015-01-251309). Sonia Y Cárdenas is a

beneﬁciary of the CONACYT scholarship (No. 336175). The funders had no role in study

design, data collection and analysis, decision to publish, or preparation of the manuscript.

Grant Disclosures

The following grant information was disclosed by the authors:

Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica: IN204613,

IN205520 and IN207520.

Consejo Nacional de Ciencia y Tecnología (CONACYT): CB-2015-01-251309.

CONACYT scholarship: 336175.

Competing Interests

The authors declare that they have no competing interests.

Author Contributions

Sonia Y. Cárdenas conceived and designed the experiments, performed the experiments,

analyzed the data, prepared ﬁgures and/or tables, authored or reviewed drafts of the

paper, and approved the ﬁnal draft.

Juan Silva-Pereyra conceived and designed the experiments, performed the experiments,

analyzed the data, prepared ﬁgures and/or tables, authored or reviewed drafts of the

paper, and approved the ﬁnal draft.

Belén Prieto-Corona conceived and designed the experiments, performed the

experiments, analyzed the data, prepared ﬁgures and/or tables, authored or reviewed

drafts of the paper, and approved the ﬁnal draft.

Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 23/29

Susana A. Castro-Chavira performed the experiments, prepared ﬁgures and/or tables,

authored or reviewed drafts of the paper, and approved the ﬁnal draft.

Thalía Fernández conceived and designed the experiments, performed the experiments,

analyzed the data, prepared ﬁgures and/or tables, authored or reviewed drafts of the

paper, and approved the ﬁnal draft.

Human Ethics

The following information was supplied relating to ethical approvals (i.e. approving body

and any reference numbers):

The Bioethics Committee of the Instituto de Neurobiología at the Universidad Nacional

Autónoma de México (UNAM) approved the experimental protocol (INEU/SA/CB/145).

Data Availability

The following information was supplied regarding data availability:

Raw data is available at Figshare:

Cárdenas-Sánchez, Sonia Y; Fernandez, Thalia; Silva-Pereyra, Juan; Prieto-Corona,

Belén (2020): Arithmetic Processing in Children with Dyscalculia. An Event-Related

Potentials Study. ﬁgshare. Dataset. DOI 10.6084/m9.ﬁgshare.9739052.v1.

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