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

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 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 (χ²(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.

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 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-Cap^™ International, Inc.; OH, USA), referenced to linked earlobes (A1A2), was recorded using a MEDICID^™ 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

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 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 (r value) 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.

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_p² = 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_p² = 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_p² = 0.759), but the response 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_p² = 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 (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.

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; 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.

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, 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

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 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.