Age-independent and age-dependent neural substrate for single-digit multiplication and addition arithmetic problems

Development is in the details: Event-related theta oscillations reveal children and adults verify multiplication facts differently

When verifying the correctness of single-digit multiplication problems, children and adults show a robust ERP correctness effect thought to reflect similar cognitive processes across groups. Recent studies suggest that this effect is instead a modulation of the negative-going N400 component in children, reflecting access to semantic memory, and the positive-going P300 component in adults, reflecting stimulus categorization. However, the relative difference in ERP amplitude is the same for both components, more positive for correct than incorrect solutions, presenting a challenge to ascertaining the appropriate interpretation. Time-frequency analysis (TFA) of the N400/P300 window provides an objective approach to dissociating these effects. TFA measured from solution onset during single-digit multiplication verification revealed significant modulations of event-related as theta power (3-6 Hz) in both groups. Correct trials elicit less power in children (9-12 years) and more power in adults relative to incorrect trials. These findings are consistent with modulations of the N400 and P300, respectively, where opposite effects were predicted for spectral power. The ERP results further support a reinterpretation of the multiplication correctness effect. In contrast, TFA of the N400 effect elicited to a word-picture verification task revealed the same event-related theta effect in both groups, with increased power for mismatched than matched pictures. Together, these findings provide evidence for a developmental shift in cognitive processing specific to the multiplication task. Models of arithmetic should account for this overlooked difference in cognitive processing between children and adults.

Longitudinal relations between self-regulatory skills and mathematics achievement in early elementary school children from Chinese American immigrant families

Drawing from two waves (∼1.5-2.5 years apart) of longitudinal data, the current study investigated the bidirectional associations between self-regulatory skills and mathematics achievement among a socioeconomically diverse sample of school-age Chinese American children from immigrant families (N = 258; 48.1% girls; ages 5.8-9.1 years; first to third grades at Wave 1). Children's self-regulatory skills were assessed with task-based measures of attention focusing, inhibitory control, behavioral persistence, and comprehensive executive function as well as parent- and teacher-reported effortful control. Multiple regressions showed that behavioral persistence and parent-reported effortful control positively predicted math achievement over time. Math achievement positively predicted comprehensive executive function over time. These effects were found when controlling for child age, sex, generation status, family socioeconomic status, parents' cultural orientations, and prior levels of math achievement or self-regulation. The prospective relation of math achievement predicting comprehensive executive function remained significant after a false discovery rate correction.

Effect of Obesity on Arithmetic Processing in Preteens With High and Low Math Skills: An Event-Related Potentials Study

Preadolescence is an important period for the consolidation of certain arithmetic facts, and the development of problem-solving strategies. Obese subjects seem to have poorer academic performance in math than their normal-weight peers, suggesting a negative effect of obesity on math skills in critical developmental periods. To test this hypothesis, event-related potentials (ERPs) were collected during a delayed-verification math task using simple addition and subtraction problems in obese [above 95th body mass index (BMI) percentile] and non-obese (between 5th and 90th BMI percentile) preteens with different levels of math skill; thirty-one with low math skills (14 obese, mean BMI = 26.40, 9.79 years old; 17 non-obese, BMI = 17.45, 9.76 years old) and thirty-one with high math skills (15 obese, BMI = 26.90, 9.60 years old; 16 non-obese, BMI = 17.13, 9.63 years old). No significant differences between weight groups were observed in task accuracy regardless of their mathematical skill level. For ERPs, electrophysiological differences were found only in the subtraction condition; participants with obesity showed an electrophysiologic pattern associated with a reduced ability to allocate attention resources regardless of their math skill level, these differences were characterized by longer P300 latency than their normal-weight peers. Moreover, the participants with obesity with high math skills displayed hypoactivity in left superior parietal lobule compared with their normal-weight peers. Additionally, obese preteens with low math skills displayed smaller arithmetic N400 amplitude than non-obese participants, reflecting difficulties in retrieving visual, semantic, and lexical information about numbers. We conclude that participants with obesity are less able than their normal-weight peers to deploy their attention regardless of their behavioral performance, which seems to have a greater effect on obese participants with low math skills because they also show problems in the retrieval of solutions from working memory, resulting in a delay in the development of mathematical skills.

Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Arithmetic performance is modulated by cognitive reappraisal and expression suppression: Evidence from behavioral and ERP findings

Previous studies have shown that negative emotional experiences are detrimental to individual's arithmetic performance, and no study has investigated whether such negative influence can be improved through emotional regulation. This study aimed to explore the relationship between emotion regulation and individual's performance in completing arithmetic problem verification task. Participants were asked to complete arithmetic problem verification task using the down-up strategy (e.g., doing 30 × 70 = 2100 for 34 × 67), under neutral, happy, and fear priming conditions, during which they were asked to regulate their emotional experience by using cognitive reappraisal or expressive suppression. Behavioral results showed that, under happy priming condition, cognitive reappraisal (but not expression suppression) contributed to improving individual's estimation speed. Additionally, under happy and fear priming conditions, cognitive reappraisal (vs. expression suppression) reduced individuals' emotional experience intensity. The arithmetic problem verification task-related ERP results showed that the P1 amplitudes elicited by using cognitive reappraisal (vs. freely view) were larger under happy and fear priming conditions, but the P1 amplitudes elicited by using expression suppression were larger only under happy condition. Meanwhile, the corresponding N170 amplitudes were smaller when using cognitive reappraisal and expression suppression (vs. freely view). Additionally, using cognitive reappraisal (vs. expression suppression) cost less cognitive resource (smaller LPC amplitudes). The present study indicated that both cognitive reappraisal and expression suppression contributed to improving individual's arithmetic performance, and the regulation effect of cognitive reappraisal was better than that of expression suppression.

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

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.

Emotional valence modulates arithmetic strategy execution in priming paradigm: an event-related potential study

Combined with the prime paradigm, the present study aimed to explore the influence of emotion (anger, fear, happiness, and neutral) on performing multiplication estimation. Participants were asked to complete a two-digit multiplication estimation task using the down-up strategy (e.g., doing 20 × 80 = 1600 for 24 × 79). Behavioral results showed that the reaction time for completing multiplication estimation tasks under happy conditions was shorter than for those under anger and fear, and it was shorter under neutral than under fearful conditions. The ERP results showed that about 100 ms after multiplication estimation task onset, multiplication estimation execution in the context of happiness (vs. neutral) elicited smaller P1 amplitudes; about 170 ms after multiplication estimation task onset, the N170 amplitudes elicited by multiplication estimation strategy execution under different emotional priming conditions showed no significant differences. The above results showed that the impact of emotion priming demonstrates the occurrence of a dynamic process when participants use a specified strategy to complete the multiplication estimation task. The present study revealed that emotional valence modulated arithmetic strategy execution, suggesting the role of different emotions should be fully considered in similar study.

Meaning to multiply: Electrophysiological evidence that children and adults treat multiplication facts differently

Multiplication tables are typically memorized verbally, with fluent retrieval leading to better performance in advanced math. Arithmetic development is characterized by strategy shifts from procedural operations to direct fact retrieval, which would not necessitate access to the facts' conceptual meaning. This study tested this hypothesis using a combination of event related brain potentials (ERP) and behavioral measures with 3rd-5th grade children and young adults. Participants verified the solutions to simple multiplication problems (2 × 3 = 6 or = 7) and the semantic fit of word-picture pairs, separately. Children showed an N400 effect to multiplication solutions with larger (more negative) amplitude for incorrect than correct solutions, reflecting meaning-level processing. A similar ERP response was observed in the word-picture verification task, with larger negative amplitude for word-picture pairs that were semantically mismatched compared to matched. In contrast, adults showed a P300 response for correct solutions, suggesting that they treated these solutions as potential targets in over-rehearsed mathematical expressions. This P300 response was specific to math fact processing, as the word-picture verification task elicited a classic N400 in adults. These ERP findings reveal an overlooked developmental transition that occurs after fifth grade, and speak to theories of arithmetic that have been based primarily on adult data.

Effect of Finger Gnosis on Young Chinese Children's Addition Skills

Evidence has revealed an association between finger gnosis and arithmetic skills in young Western children, however, it is unknown whether such an association can be generalized to Chinese children and what mechanism may underlie this relationship. This study examines whether finger gnosis is associated with addition skills in young Chinese children and, if so, what numerical skills could explain this correlation. A total of 102 Chinese children aged 5–6 years were asked to complete finger gnosis and addition tasks in Study 1. Results showed that finger gnosis was significantly associated with addition performance. However, no significant correlation was found between finger gnosis and the use of finger counting in solving addition problems. Moreover, girls’ finger gnosis was better than boys’, and children with musical training demonstrated better finger gnosis than those without. In Study 2, 16 children with high finger gnosis and 20 children with low finger gnosis were selected from the children in Study 1 and asked to perform enumeration, order judgment, number sense, and number line estimation. Children with high finger gnosis performed better in number line estimation than their counterparts with low finger gnosis. Moreover, the number line estimation fully mediated the relationship between finger gnosis and addition performance. Together, these studies provide evidence of a correlation between finger gnosis and addition skills. They also highlight the importance of number line estimation in bridging this association.

Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

Arithmetic difficulties in children with mild traumatic brain injury at the subacute stage of recovery

AIM

Arithmetic difficulties have been reported in children with mild traumatic brain injury (mTBI), but the electrophysiological abnormalities underlying these impairments remain unknown. We therefore used event-related potentials (ERPs) to investigate brain functioning during arithmetic in children in the subacute phase after mTBI.

METHOD

The participants comprised 16 children with mTBI at the subacute phase of recovery (10 males, mean age 10y 8mo; six females, mean age 10y 8mo) and 16 well-matched comparison children (11 males, mean age 10y 11mo; five females, mean age 10y 6mo). All children were asked to solve single-digit addition problems of small (sum ≤10) and large problem size (sum >10) and ERPs were simultaneously recorded.

RESULTS

Children with mTBI performed significantly less accurately (mean 81%) than comparison children (mean 91%) on the large (p=0.026) but not on the small problems (p=0.171). We observed no group differences in the early ERP components P1, N1, P2, and N2 (all p values ≥0.241), yet significant group differences (p=0.019) emerged for the late positivity component (LPC), which showed smaller mean amplitudes (mean 8.35μV) in mTBI patients than comparison children (mean 12.95μV).

INTERPRETATION

Immediately after the injury, arithmetic difficulties in children with mTBI are particularly pronounced on more complex arithmetical problems that are less automated. This is reflected in the ERP pattern, with decreased LPC but normal N2 and early ERP components.

The arithmetic problem size effect in children: an event-related potential study

This study used for the first time event-related potentials (ERPs) to examine the well-known arithmetic problem size effect in children. The electrophysiological correlates of this problem size effect have been well documented in adults, but such information in children is lacking. In the present study, 22 typically developing 12-year-olds were asked to solve single-digit addition problems of small (sum ≤ 10) and large problem size (sum > 10) and to speak the solution into a voice key while ERPs were recorded. Children displayed similar early and late components compared to previous adult studies on the problem size effect. There was no effect of problem size on the early components P1, N1, and P2. The peak amplitude of the N2 component showed more negative potentials on left and right anterior electrodes for large additions compared to small additions, which might reflect differences in attentional and working memory resources between large and small problems. The mean amplitude of the late positivity component which follows the N2, was significantly larger for large than for small additions at right parieto-occipital electrodes, in line with previous adult data. The ERPs of the problem size effect during arithmetic might be a useful neural marker for future studies on fact retrieval impairments in children with mathematical difficulties.

Eating breakfast enhances the efficiency of neural networks engaged during mental arithmetic in school-aged children

To determine the influence of a morning meal on complex mental functions in children (8-11 y), time-frequency analyses were applied to electroencephalographic (EEG) activity recorded while children solved simple addition problems after an overnight fast and again after having either eaten or skipped breakfast. Power of low frequency EEG activity [2 Hertz (Hz) bands in the 2-12 Hz range] was determined from recordings over frontal and parietal brain regions associated with mathematical thinking during mental calculation of correctly answered problems. Analyses were adjusted for background variables known to influence or reflect the development of mathematical skills, i.e., age and measures of math competence and math fluency. Relative to fed children, those who continued to fast showed greater power increases in upper theta (6-8 Hz) and both alpha bands (8-10 Hz; 10-12 Hz) across sites. Increased theta suggests greater demands on working memory. Increased alpha may facilitate task-essential activity by suppressing non-task-essential activity. Fasting children also had greater delta (2-4 Hz) and greater lower-theta (4-6 Hz) power in left frontal recordings-indicating a region-specific emphasis on both working memory for mental calculation (theta) and activation of processes that suppress interfering activity (delta). Fed children also showed a significant increase in correct responses while children who continued to fast did not. Taken together the findings suggest that neural network activity involved in processing numerical information is functionally enhanced and performance is improved in children who have eaten breakfast, whereas greater mental effort is required for this mathematical thinking in children who skip breakfast.