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Arithmetic processing in children with dyscalculia: an event-related potential study

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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 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.
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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 specic 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) decits. To assess the brain response to arithmetic data recovery, we applied
an arithmetic verication 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 verication 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 verication 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 decits. When WM decits were considered together with
dyscalculia, an atypical ERP pattern that reected their processing difculties
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 decit, studies examining
dyscalculia should consider exploring decits 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 verication 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 difculties with
number sense, number facts, and calculation (i.e. having a poor understanding of numbers,
their magnitudes and relationships, counting on ngers 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
signicant difculties 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 prociency 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 difculty 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 verication 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 subjects 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 verication 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 signicant difference in amplitude between these components is known as
the arithmetic N400 effect, which reects the strength of the probes 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 reect
the automatic retrieval of arithmetic facts from long-term memory and its magnitude
represents the strength of the probes 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 deection 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 signicant 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;ñez-Peña & Suárez-
Pellicioni, 2015;Szűcs & Soltész, 2010). Some authors have proposed that the LPC effect
reects 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 decits (Iguchi & Hashimoto, 2000;Núñez-Peña, Gracia-Bafalluy & Tubau, 2011;
Núñez-Peña & Honrubia-Serrano, 2004;ñez-Peña & Suárez-Pellicioni, 2012,2015;
Szűcs & Soltész, 2010).
In summary, children with dyscalculia may show decits 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 decit on the processing of an arithmetic
verication 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 verication
task. Thus, the rst 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 verication 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 verication 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 20152016.
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
deant disorder as identied 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, ve 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 signicantly
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/g-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 verication task. Flowchart of stimuli presentation during
individual trials. W, warning stimulus. Full-size
DOI: 10.7717/peerj.10489/g-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
1020 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 ampliers was 0.550 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 ofine 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 amplier 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 signicant 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 signicance for the statistical test (i.e. signicant 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 Workow of the statistical analyses of ERP data using non-parametric permutation tests.
(A) Denition of analysed time windows, where signicant 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 dened 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 signicant 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 dened 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. Signicant 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. Signicance for the statistical test
was reported (r
max
and its extreme p-value). Specic signicant 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 signicantly 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 signicantly 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 signicant group by
condition interaction was noted (F< 1).
The responses for all children were signicantly 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 signicant 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/g-3
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 11/29
times were not signicantly different between the groups (F< 1). No signicant group by
condition interaction (F
(1,42)
= 1.114, p= 0.297, η
p
2
= 0.026) was observed for this
assessment. This nding 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 signicant 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
signicant 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 signicant 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 signicant differences in the rst 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 ndings 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 verication
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/g-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 signicant
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 gure 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 305385 ms (arithmetic N400). (B) Differences
between conditions at 510630 ms (LPC effect). Bottom: DYS group. (C) Differences between conditions
at 680700 ms (LPC effect). Blue and red colours represent the t-values that were above the threshold of
signicance (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/g-5
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ERP difference waveforms in the DYS and GAP groups
Having identied 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 identied (305385 ms, 510630 ms and 680700 ms).
The GAP children showed a signicantly larger amplitude for the arithmetic N400 effect
over T5 (T
max
=3.58, extreme p= 0.007) and a signicantly 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 reected 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/g-6
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 14/29
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 signicant correlation was found between the WM index and
the difference wave in the N400 window. However, in both LPC windows, signicant
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 rst objective of this study was to compare arithmetic verication processing in
children with dyscalculia with that in children with GAP during an addition verication
task by using ERPs. To our knowledge, this is the rst 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 (305385 ms) at T5. (B) Statistical map of the comparison between groups based
on the difference between conditions (incongruent minus congruent) for the LPC (510630 ms) at Fp2.
The blue and red spots represent signicant differences between groups (t-values p< 0.05).
Full-size
DOI: 10.7717/peerj.10489/g-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 (305385 ms) effect. (B) Box-
and-whisker plots of both groups of children using the amplitude values of the LPC (510630 ms)
effect. Full-size
DOI: 10.7717/peerj.10489/g-8
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Behavioural differences between the DYS and GAP groups
Our behavioural results partially conrmed our hypothesis. We observed a signicantly
lower percentage of correct answers in the DYS group than in the GAP group. This result
corroborates the ndings 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 signicant 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/g-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 510630 ms (LPC effect) across electrode sites. The red spot represents
the signicant 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 680700 ms (LPC effect for the DYS group) across electrode sites. The red spot
represents the signicant 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/g-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 ndings 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 ndings 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
verication 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 ndings with both methods,
with the nonparametric permutations appearing to be more sensitive to differences.
Since we are using an arithmetic verication task to evoke the ERPs, it is important to
determine which processes could manifest in it. Among the four processes involved in the
arithmetic verication 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 operandssemantic 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 signicant arithmetic N400 effect, and
when their ERPs were compared to those of the controls, signicant differences were
observed over the left posterior temporal region. This nding 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 signicant 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 deection is elicited in both conditions). Thus, they must revert to
conducting the arithmetic calculation. The group differences in the left temporal region
may reect 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 signicantly 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 verication task (Dickson & Federmeier, 2017). According to these authors,
after an initial period of evaluation of the provided response (probe), the left hemisphere
classies 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 nd the answer, they then
perform the arithmetic calculation. Although the topography recorded from the scalp
does not necessarily indicate the generatorslocation, 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 childrens 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 nding. Two main hypotheses have been proposed to
explain atypical brain functioning that is reected as neurobiological disorders of cognitive
processing (Silver et al., 2008) that underlie learning disorders (Landerl et al., 2009).
In addition to the domain-specic hypothesis, which refers to abilities specically related to
mathematical competencies, the common-decit 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 decits 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 verication process and nally provide an answer.
Therefore, the arithmetic verication task that we used is particularly efcient 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 nding 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 reects 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
classied 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 reect 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
difculties combined.
CONCLUSIONS
Children with dyscalculia did not show the arithmetic N400 effect found in children with
typical development during an arithmetic verication 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 decits were,
the lower the LPC effect was in the right posterior region. In children with dyscalculia
and WM decits, 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
beneciary 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 gures and/or tables, authored or reviewed drafts of the
paper, and approved the nal draft.
Juan Silva-Pereyra conceived and designed the experiments, performed the experiments,
analyzed the data, prepared gures and/or tables, authored or reviewed drafts of the
paper, and approved the nal draft.
Belén Prieto-Corona conceived and designed the experiments, performed the
experiments, analyzed the data, prepared gures and/or tables, authored or reviewed
drafts of the paper, and approved the nal draft.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 23/29
Susana A. Castro-Chavira performed the experiments, prepared gures and/or tables,
authored or reviewed drafts of the paper, and approved the nal draft.
Thalía Fernández conceived and designed the experiments, performed the experiments,
analyzed the data, prepared gures and/or tables, authored or reviewed drafts of the
paper, and approved the nal 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. gshare. Dataset. DOI 10.6084/m9.gshare.9739052.v1.
REFERENCES
American Psychiatric Association. 2013. Diagnostic and statistical manual of mental disorders,
DSM-5. Fifth Edition. Washington, D. C.: American Psychiatric Association.
Andersson U, Lyxell B. 2007. Working memory decit in children with mathematical difculties: a
general or specicdecit? Journal of Experimental Child Psychology 96(3):197228
DOI 10.1016/j.jecp.2006.10.001.
Attout L, Majerus S. 2015. Working memory decits in developmental dyscalculia: the importance
of serial order. Child Neuropsychology 21(4):432450 DOI 10.1080/09297049.2014.922170.
Avancini C, Galfano G, Szűcs D. 2014. Dissociation between arithmetic relatedness and distance
effects is modulated by task properties: an ERP study comparing explicit vs. implicit arithmetic
processing. Biological Psychology 103:305316 DOI 10.1016/j.biopsycho.2014.10.003.
Avancini C, Soltész F, Szűcs D. 2015. Separating stages of arithmetic verication: An ERP study
with a novel paradigm. Neuropsychologia 75:322329
DOI 10.1016/j.neuropsychologia.2015.06.016.
Baddeley AD. 2006. Working memory: an overview. In: Pickering SJ, ed. Working Memory and
Education. Burlington: Academic Press, 517552.
Berninger V. 2008. Dening and differentiating dysgraphia, dyslexia, and languagelearning
disability within a working memory model. In: Mody M, Silliman E, eds. Brain, behavior, and
learning in language and reading disorders. New York: The Guilford Press, 103134.
Camos V. 2018. Do not forget memory to understand mathematical cognition. In: Henik A,
Fias W, eds. Heterogeneity of Function in Numerical Cognition. London: Academic Press,
433447.
Castro DE, Reigosa-Crespo V. 2001. Calibrando la línea numérica mental. Evidencias desde el
desarrollo típico y atípico. Revista de Neuropsicología, Neuropsiquiatría y Neurociencias
11:1731.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 24/29
Cipora K, Nuerk HC. 2013. Is the SNARC effect related to the level of mathematics? No systematic
relationship observed despite more power, more repetitions, and more direct assessment of
arithmetic skill. Quarterly Journal of Experimental Psychology 66(10):19741991
DOI 10.1080/17470218.2013.772215.
De Smedt B, Janssen R, Bouwens K, Verschaffel L, Boets B, Ghesquière P. 2009. Working
memory and individual differences in mathematics achievement: a longitudinal study from rst
grade to second grade. Journal of Experimental Child Psychology 103(2):186201
DOI 10.1016/j.jecp.2009.01.004.
Dehaene S, Cohen L. 1997. Cerebral pathways for calculation: double dissociation between rote
verbal and quantitative knowledge of arithmetic. Cortex 33(2):219250
DOI 10.1016/S0010-9452(08)70002-9.
Dehaene S, Piazza M, Pinel P, Cohen L. 2003. Three parietal circuits for number processing.
Cognitive Neuropsychology 20(36):487506 DOI 10.1080/02643290244000239.
DeStefano D, LeFevre JA. 2004. The role of working memory in mental arithmetic. European
Journal of Cognitive Psychology 16(3):353386 DOI 10.1080/09541440244000328.
Dickson DS, Federmeier KD. 2017. The language of arithmetic across the hemispheres: an
event-related potential investigation. Brain Research 1662:4656
DOI 10.1016/j.brainres.2017.02.019.
Donchin E, Coles MGH. 1997. Context updating and the P300. Behavioral and Brain Sciences
11(3):357374 DOI 10.1017/S0140525X00058027.
Dong X, Wang SH, Yang YL, Ren YL, Meng P, Yang YX. 2007. Event-related potentials in
Chinese characters semantic priming and arithmetic tasks: comparative study between healthy
children and children with cognitive disorder. Zhonghua Yi Xue Za Zhi 87:28252828
DOI 10.3760/j.issn:0376-2491.2007.40.005.
El Yagoubi R, Lemaire P, Besson M. 2003. Different brain mechanisms mediate two strategies in
arithmetic: evidence from event-related brain potentials. Neuropsychologia 41(7):855862
DOI 10.1016/S0028-3932(02)00180-X.
Ferrando L, Bobes J, Gilbert M, Soto M, Soto O. 1998. M.I.N.I: Mini International
Neuropsychiatric Interviewversión en español 5.0.0. DSM-IV. Madrid: Instituto IAP Madrid.
Foley AE, Vasilyeva M, Laski EV. 2017. Childrens use of decomposition strategies mediates the
visuospatial memory and arithmetic accuracy relation. British Journal of Developmental
Psychology 35(2):303309 DOI 10.1111/bjdp.12166.
Fuchs LS, Compton DL, Fuchs D, Paulsen K, Bryant JD, Hamlett CL. 2005. The prevention,
identication, and cognitive determinants of math difculty. Journal of Educational Psychology
97(3):493513 DOI 10.1037/0022-0663.97.3.493.
Galán L, Biscay R, Rodríguez JL, Pérez-Abalo MC, Rodríguez R. 1998. Testing topographic
differences between event related brain potentials by using non-parametric combinations of
permutation tests. Electroencephalography and Clinical Neurophysiology 102(3):240247
DOI 10.1016/s0013-4694(96)95155-3.
Geary DC. 1993. Mathematical disabilities: cognitive, neuropsychological, and genetic
components. Psychological Bulletin 114(2):345362 DOI 10.1037/0033-2909.114.2.345.
Geary DC. 2004. Mathematics and learning disabilities. Journal of Learning Disabilities 37(1):415
DOI 10.1177/00222194040370010201.
Geary DC, Bow-Thomas CC, Yao Y. 1992. Counting knowledge and skill in cognitive addition: a
comparison of normal and mathematically disabled children. Journal of Experimental Child
Psychology 54(3):372391 DOI 10.1016/0022-0965(92)90026-3.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 25/29
Geary DC, Hoard MK, Hamson CO. 1999. Numerical and arithmetical cognition: Patterns of
functions and decits in children at risk for a mathematical disability. Journal of Experimental
Child Psychology 74(3):213239 DOI 10.1006/jecp.1999.2515.
Geary DC, Wiley JG. 1991. Cognitive addition: Strategy choice and speed-of-processing
differences in young and elderly adults. Psychology and Aging 6(3):474483
DOI 10.1037/0882-7974.6.3.474.
Harmony T, Marosi E, Díaz de León AE, Becker J, Fernández T. 1990. Effect of sex, psychosocial
disadvantages and biological risk factors on EEG maturation. Electroencephalography and
Clinical Neurophysiology 75(6):482491 DOI 10.1016/0013-4694(90)90135-7.
Hinault T, Lemaire P. 2016. What does EEG tell us about arithmetic strategies? A review.
International Journal of Psychophysiology 106:115126 DOI 10.1016/j.ijpsycho.2016.05.006.
Hitch GJ, McAuley E. 1991. Working memory in children with specic arithmetical learning
difculties. British Journal of Psychology 82(3):375386
DOI 10.1111/j.2044-8295.1991.tb02406.x.
Holmes J, Adams JW. 2006. Working memory and childrens mathematical skills: implications for
mathematical development and mathematics curricula. Educational Psychology 26(3):339366
DOI 10.1080/01443410500341056.
Iguchi Y, Hashimoto I. 2000. Sequential information processing during a mental arithmetic is
reected in the time course of event-related brain potentials. Clinical Neurophysiology
111(2):204213 DOI 10.1016/S1388-2457(99)00244-8.
Imbo I, Vandierendock A. 2008. Effects of problem size, operation, and working-memory span on
simple-arithmetic strategies: differences between children and adults? Psychological Research
72(3):331346 DOI 10.1007/s00426-007-0112-8.
Jasinski EC, Coch D. 2012. ERPs across arithmetic operations in a delayed answer verication task.
Psychophysiology 49(7):943958 DOI 10.1111/j.1469-8986.2012.01378.x.
Jost K, Hennighausen E, Rösler F. 2004. Comparing arithmetic and semantic fact retrieval: effects
of problem size and sentence constraint on event-related brain potentials. Psychophysiology
41(1):4659 DOI 10.1111/1469-8986.00119_41_1.
Kaufmann L, Mazzocco MM, Dowker A, von Aster M, Göbel SM, Grabner RH, Henik A,
Jordan NC, Karmiloff-Smith AD, Kucian K, Rubinsten O, Szucs D, Shalev R, Nuerk HC.
2013. Dyscalculia from a developmental and differential perspective. Frontiers in Psychology
4:516 DOI 10.3389/fpsyg.2013.00516.
Landerl K, Bevan A, Butterworth B. 2004. Developmental dyscalculia and basic numerical
capacities: a study of 89-year-old students. Cognition 93(2):99125
DOI 10.1016/j.cognition.2003.11.004.
Landerl K, Fussenegger B, Moll K, Willburger E. 2009. Dyslexia and dyscalculia: two learning
disorders with different cognitive proles. Journal of Experimental Child Psychology
103(3):309324 DOI 10.1016/j.jecp.2009.03.006.
LeFevre JA, Kulak AG. 1994. Individual differences in the obligatory activation of addition facts.
Memory and Cognition 22(2):188220 DOI 10.3758/BF03208890.
Luck SJ. 2014. An introduction to the event-related potential technique. Second Edition. Cambridge:
MIT Press.
Mammarella IC, Caviola S, Giofrè D, Szűcs D. 2017. The underlying structure of visuospatial
working memory in children with mathematical learning disability. British Journal of
Developmental Psychology 36(2):220235 DOI 10.1111/bjdp.12202.
Matute E, Rosselli M, Ardila A, Ostrosky-Solís F. 2005. Evaluación neuropsicológica infantil.
Primera Ed. México DF: Manual Moderno.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 26/29
McDonald PA, Berg DH. 2018. Identifying the nature of impairments in executive functioning
and working memory of children with severe difculties in arithmetic. Child Neuropsychology
24(8):10471062 DOI 10.1080/09297049.2017.1377694.
Megías P, Macizo P. 2016. Simple arithmetic: electrophysiological evidence of coactivation and
selection of arithmetic facts. Experimental Brain Research 234(11):33053319
DOI 10.1007/s00221-016-4728-z.
Meiri H, Sela I, Nesher P, Izzetoglu M, Izzetoglu K, Onaral B, Breznitz Z. 2012. Frontal lobe role
in simple arithmetic calculations: an fNIR study. Neuroscience Letters 510(1):4347
DOI 10.1016/j.neulet.2011.12.066.
Meyer ML, Salimpoor VN, Wu SS, Geary DC, Menon V. 2010. Differential contribution of
specic working memory components to mathematics achievement in 2nd and 3rd graders.
Learning and Individual Differences 20(2):101109 DOI 10.1016/j.lindif.2009.08.004.
Niedeggen M, Rösler F. 1999. N400 effects reect activation spread during retrieval of arithmetic
facts. Psychological Science 10(3):271276 DOI 10.1111/1467-9280.00149.
Niedeggen M, Rösler F, Jost K. 1999. Processing of incongruous mental calculation problems:
evidence for an arithmetic N400 effect. Psychophysiology 36(3):307324
DOI 10.1017/S0048577299980149.
Nunez PL, Srinivasan R. 2006. Electrical elds of the brain: the neurophysics of EEG. Oxford:
Oxford University Press.
Núñez-Peña MI, Escera C. 2007. An event-related brain potential study of the arithmetic split
effect. International Journal of Psychophysiology 64(2):165173
DOI 10.1016/j.ijpsycho.2007.01.007.
Núñez-Peña MI, Gracia-Bafalluy M, Tubau E. 2011. Individual differences in arithmetic skill
reected in event-related brain potentials. International Journal of Psychophysiology
80(2):143149 DOI 10.1016/j.ijpsycho.2011.02.017.
Núñez-Peña MI, Honrubia-Serrano ML. 2004. P600 related to rule violation in an arithmetic task.
Cognitive Brain Research 18(2):130141 DOI 10.1016/j.cogbrainres.2003.09.010.
Núñez-Peña MI, Suárez-Pellicioni M. 2012. Processing false solutions in additions: differences
between high-and lower-skilled arithmetic problem-solvers. Experimental Brain Research
218(4):655663 DOI 10.1007/s00221-012-3058-z.
Núñez-Peña MI, Suárez-Pellicioni M. 2015. Processing of multi-digit additions in high
math-anxious individuals: psychophysiological evidence. Frontiers in Psychology 6:1268
DOI 10.3389/fpsyg.2015.01268.
Pascual-Marqui RD, Lehmann D, Koukkou M, Kochi K, Anderer P, Saletu B, Tanaka H,
Hirata K, John ER, Prichep L, Biscay-Lirio R, Kinoshita T. 2011. Assessing interactions in the
brain with exact low-resolution electromagnetic tomography. Philosophical Transactions of the
Royal Society A: Mathematical, Physical and Engineering Sciences 369(1952):37683784
DOI 10.1098/rsta.2011.0081.
Peng P, Fuchs D. 2016. A meta-analysis of working memory decits in children with learning
difculties: is there a difference between verbal domain and numerical domain? Journal of
Learning Disabilities 49(1):320 DOI 10.1177/0022219414521667.
Picton TW, Bentin S, Berg P, Donchin E, Hillyard SA, Johnson R Jr, Miller GA, Ritter W,
Ruchkin DS, Rugg MD, Taylor MJ. 2000. Guidelines for using human event-related potentials
to study cognition: recording standards and publication criteria. Psychophysiology
37(2):127152 DOI 10.1111/1469-8986.3720127.
Polich J. 2007. Updating P300: an integrative theory of p3a and P3b. Clinical Neurophysiology
118(10):21282148 DOI 10.1016/j.clinph.2007.04.019.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 27/29
Prieto-Corona B, Rodríguez-Camacho M, Silva-Pereyra J, Marosi E, Fernández T, Guerrero V.
2010. Event-related potentials ndings differ between children and adults during arithmetic-fact
retrieval. Neuroscience Letters 468(3):220224 DOI 10.1016/j.neulet.2009.10.094.
Rotzer S, Loenneker T, Kucian K, Martin E, Klaver P, Von Aster M. 2009. Dysfunctional neural
network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia
47(13):28592865 DOI 10.1016/j.neuropsychologia.2009.06.009.
Schmajuk M, Liotti M, Busse L, Woldorff MG. 2006. Electrophysiological activity underlying
inhibitory control processes in normal adults. Neuropsychologia 44(3):384395
DOI 10.1016/j.neuropsychologia.2005.06.005.
Schuchardt K, Maehler C, Hasselhorn M. 2008. Working memory decits in children with
specic learning disorders. Journal of Learning Disabilities 41(6):514523
DOI 10.1177/0022219408317856.
Shalev RS, Manor O, Gross-Tsur V. 2005. Developmental dyscalculia: a prospective six-year
follow-up. Developmental Medicine & Child Neurology 47(2):121125
DOI 10.1017/S0012162205000216.
Shen I, Liu P, Chen C. 2018. Neural correlates underlying spatial and verbal working memory in
children with different mathematics achievement levels: an event-related potential study.
International Journal of Psychophysiology 133:149158 DOI 10.1016/j.ijpsycho.2018.07.006.
Silver CH, Ruff RM, Iverson GL, Barth JT, Broshek DK, Bush SS, Kofer SP, Reynolds CR,
Policy NAN, Planning Committee. 2008. Learning disabilities: the need for neuropsychological
evaluation. Archives of Clinical Neuropsychology 23(2):217219 DOI 10.1016/j.acn.2007.09.006.
Simms V, Clayton S, Cragg L, Gilmore C, Johnson S. 2016. Explaining the relationship between
number line estimation and mathematical achievement: the role of visuomotor integration and
visuospatial skills. Journal of Experimental Child Psychology 145:2233
DOI 10.1016/j.jecp.2015.12.004.
Soltész F, Szűcs D. 2009. An electro-physiological temporal principal component analysis of
processing stages of number comparison in developmental dyscalculia. Cognitive Development
24(4):473485 DOI 10.1016/j.cogdev.2009.09.002.
Soltész F, Szűcs D, Dékány J, Márkus A, Csépe V. 2007. A combined event-related potential and
neuropsychological investigation of developmental dyscalculia. Neuroscience Letters
417(2):181186 DOI 10.1016/j.neulet.2007.02.067.
Swanson HL. 1987. Information processing theory and learning disabilities: a commentary and
future perspective. Journal of Learning Disabilities 20(3):155166
DOI 10.1177/002221948702000303.
Swanson HL. 2015. Intelligence, working memory, and learning disabilities. In: Papadopoulos TC,
Parrila RK, Kirby JR, eds. Cognition, Intelligence, and Achievement. Amsterdam: Academic
Press, 175196.
Swanson HL, Siegel L. 2001. Learning disabilities as a working memory decit. Issues in Education
7:148.
Szűcs D, Csépe V. 2005. The effect of numerical distance and stimulus probability on ERP
components elicited by numerical incongruencies in mental addition. Cognitive Brain Research
22(2):289300 DOI 10.1016/j.cogbrainres.2004.04.010.
Szűcs D, Soltész F. 2010. Event-related brain potentials to violations of arithmetic syntax
represented by place value structure. Biological Psychology 84(2):354367
DOI 10.1016/j.biopsycho.2010.04.002.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 28/29
Thevenot C, Fanget M, Fayol M. 2007. Retrieval or nonretrieval strategies in mental arithmetic?
An operand recognition paradigm. Memory & Cognition 35(6):13441352
DOI 10.3758/BF03193606.
Van Beek L, Ghesquière P, De Smedt B, Lagae L. 2014. The arithmetic problem size effect in
children: an event-related potential study. Frontiers in Human Neuroscience 8(437):756
DOI 10.3389/fnhum.2014.00756.
Vanbinst K, De Smedt B. 2016. Individual differences in childrens mathematics achievement: the
roles of symbolic numerical magnitude processing and domain-general cognitive functions.
Progress in Brain Research 227:105130 DOI 10.1016/bs.pbr.2016.04.001.
Wechsler D. 2007. Wechsler intelligence scale for children-WISC-IV. México: Manual Moderno.
Xuan D, Wang S, Yang Y, Meng P, Xu F, Yang W, Sheng W, Yang Y. 2007. Age difference in
numeral recognition and calculation: an event-related potential study. Child Neuropsychology
13(1):117 DOI 10.1080/09297040600760465.
Zar JH. 2010. Biostatistical analysis. New York: Prentice Hall International Inc.
Zhou X, Booth JR, Lu J, Zhao H, Butterworth B, Chen C, Dong Q. 2011. Age-independent and
age-dependent neural substrate for single-digit multiplication and addition arithmetic problems.
Developmental Neuropsychology 36(3):338352 DOI 10.1080/87565641.2010.549873.
Zhou X, Chen C, Qiao S, Chen C, Chen L, Lu N, Dong Q. 2009. Event-related potentials for
simple arithmetic in Arabic digits and Chinese number words: a study of the mental
representation of arithmetic facts through notation and operation effects. Brain Research
1302:212224 DOI 10.1016/j.brainres.2009.09.024.
Cárdenas et al. (2021), PeerJ, DOI 10.7717/peerj.10489 29/29
... Recently, Cárdenas et al. (2021) reported a lack of the arithmetic N400 effect in a group of 9-to-11 years-old children with dyscalculia, suggesting that the processing step signalled by N400 (N270) might be insufficient to produce a correct response, thus lying on a reevaluation of the arithmetic-calculation process (as reflected by the LPC component). In our study, the so-called N400 effect appeared in L-children, but it was limited to distant solutions, probably suggesting that L-children represents an intermediate step between typical primary students and children with dyscalculia, thus signalling L-children as a group at risk of failure in calculus domain. ...
... Focusing on the ERP components of interest and their most typical topographic distribution, the amplitude of three main components was analyzed at different recording sites: early frontal negativity peaking at 330 ms (N270-like component analyzed at F3, F4, and Fz; see Rivera & Soylu, 2021 for reference), a subsequent positive component with a maximum at 375 ms (P300-like evaluated at P3, P4, and Pz; locations commonly considered when analyzing P300 component -Polich, 2011;Rivera & Soylu, 2021-), and a late central positive component with a maximum at 600 ms (LPC studied at C3, C4, and Cz; seeCárdenas et al., 2021), all of them elicited ...
Article
Fact retrieval deficits have been documented in children with mathematical learning disabilities. We assessed the retrieval of arithmetic facts in neurotypical 9-to-10-year-old children with different mathematical achievement levels using event-related potential methods while performing an arithmetic verification task (addition, subtraction, and multiplication). Forty-eight participants were divided into High (H), Average (A), and Low (L) mathematics performance according to their scores on The Wide Range Achievement Test 4 (WRAT4). Children determined whether appearing digits matched or not the correct solution of the preceding problem. L group showed a lower number of correct responses, prolonged reaction times, and poorer performance on working memory (WM) tasks. P300 component showed significantly higher amplitudes for correct solutions in H, while N270 showed higher amplitudes for incorrect solutions. L children showed difficulty in recovering arithmetic facts and poorly modulated N270 and P300 components, probably reflecting WM processing problems affecting the construction and retrieval of numerical information. ARTICLE HISTORY
... On the other side are works that explore the problems and difficulties in the process of learning mathematics. The article by S. Cardenas et al. [10] considers the features of arithmetic processing in an addition task in children with good academic performance and children with dyscalculia. The main criterion was the ERP, in particular, the N400 and LPC components. ...
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This study aimed at exploring the time course of processes underlying the associative confusion effect. We also evaluated the consequences of selecting arithmetic facts to resolve addition problems. We gathered electrophysiological evidence when participants performed a verification task. Simple addition problems were presented in blocks of two trials and participants decided whether they were correct or not. The N400-like component was considered an index of semantic access (i.e., the retrieval of arithmetic facts), and the P200 component was used to determine the difficulty associated with encoding after the answer to an addition problem. When an addition problem was incorrect but the result presented to the participant was that of multiplying the operands (e.g., 2 + 4 = 8), N400-like amplitude was reduced relative to an unrelated condition (e.g., 2 + 4 = 10). This finding suggested that the coactivation of addition and multiplication facts took place. Furthermore, the P200 amplitude was more positive when participants answered to addition problems whose result was that of multiplying the operands of the previous trial (e.g., 2 + 6 = 8). This suggests that irrelevant results were inhibited and it was difficult to encode them later.
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An age-matched achievement-matched design was used to examine whether the executive functioning and working memory impairments exhibited by children with severe difficulties in arithmetic (SDA) are better viewed as developmental lags or as cognitive deficits. Three groups of children were included: 20 SDA children, 20 typically achieving children (CM) matched in chronological age with the SDA children, and 20 younger typically achieving children (AM) matched in achievement with the SDA group. While children with SDA did not exhibit impairments in color-word inhibition and verbal working memory, they did demonstrate impairments in shifting, quantity-digits inhibition, and visuospatial working memory. As children with SDA did not perform more poorly than their AM counterparts on any of these tasks, impairments in specific areas of executive functioning and working memory appear to reflect developmental lags rather than cognitive deficits.
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This contribution reviewed the available evidence on the domain-specific and domain-general neurocognitive determinants of children's arithmetic development, other than nonsymbolic numerical magnitude processing, which might have been overemphasized as a core factor of individual differences in mathematics and dyscalculia. We focused on symbolic numerical magnitude processing, working memory, and phonological processing, as these determinants have been most researched and their roles in arithmetic can be predicted against the background of brain imaging data. Our review indicates that symbolic numerical magnitude processing is a major determinant of individual differences in arithmetic. Working memory, particularly the central executive, also plays a role in learning arithmetic, but its influence appears to be dependent on the learning stage and experience of children. The available evidence on phonological processing suggests that it plays a more subtle role in children's acquisition of arithmetic facts. Future longitudinal studies should investigate these factors in concert to understand their relative contribution as well as their mediating and moderating roles in children's arithmetic development.
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Arithmetic strategies refer to the set of procedures used to solve arithmetic problems. Previous studies revealed that participants can solve arithmetic problems by using several arithmetic strategies. In this review, we discuss the added value of using electroencephalography (EEG) to investigate such strategies. Indeed, this technique enables to delineate different aspects of information processing, and can further our understanding of arithmetic strategies. The investigation of processes involved within arithmetic strategies with event-related potentials (ERPs) and frequency analyses allows to discover how participants solve different types of problems by enabling to distinguish arithmetic strategies on the bases of their electrophysiological signatures. Moreover, this technique is fruitful to investigate the time course of arithmetic strategy selection and execution. EEG can also help to investigate the role of general cognitive processes during execution of arithmetic strategies. Finally, EEG is also a powerful tool to specify how strategy use differs between groups of different skills or ages. Overall, by addressing these ends, EEG further our understanding of variations in participants’ arithmetic performance as a function of different characteristics, such as participants’ (e.g., age, skills), problems’ (e.g., problem or split size, rule violation), or situations’ (e.g., strategy execution on previous problems, correctness of proposed answers) characteristics.