What does EEG tell us about arithmetic strategies? A review

Mathematical problem solving is modulated by word priming

This study aimed to explore the influence of word priming on mathematical problem solving. In two experiments, participants were required to finish multiplication estimation tasks with a specified estimation strategy under different word priming conditions (Experiment 1: concrete words vs. Experiment 2: abstract words). The results showed that: (1) under the concrete word priming condition, in comparison to neutral, positive word priming improved accuracies (ACCs) when using a down-up strategy (e.g., doing 40 × 80 = 3200 for 43 × 78), while both positive and negative word priming reduced reaction time (RT); (2) under the abstract word priming condition, both positive and negative (vs. neutral) abstract word priming reduced RTs, while individuals' ACCs of completing the estimation task were not influenced by valence. The present study showed that whether concrete words or abstract words were adopted as experimental stimuli, participants' performance of completing mathematical problems was modulated by the valence of the priming word, which led us to develop a better understanding of how arithmetic performance is influenced by word processing.

EEG alpha and theta time-frequency structure during a written mathematical task

Since the first electroencephalogram (EEG) was obtained, there have been many possibilities to use it as a tool to access brain cognitive dynamics. Mathematical (Math) problem solving is one of the most important cortical processes, but it is still far from being well understood. EEG is an inexpensive and simple indirect measure of brain operation, but only recently has low-cost equipment (mobile EEG) allowed sophisticated analyses in non-clinical settings. The main purpose of this work is to study EEG activation during a Math task in a realistic environment, using mobile EEG. A matching pursuit (MP)-based signal analysis technique was employed, since MP properties render it a priori suitable to study induced EEG activity over long time sequences, when it is not tightly locked to a given stimulus. The study sample comprised sixty healthy volunteers. Unlike the majority of previous studies, subjects were studied in a sitting position with their eyes open. They completed a written Math task outside the EEG lab, wearing a mobile EEG device (EPOC+). Theta [4 Hz-7.5 Hz], alpha (7.5 Hz-13 Hz] and 0.5 Hz micro-bands in the [0.5 Hz-20 Hz] range were studied with a low-density stochastic MP dictionary. Over 1-min windows, ongoing EEG alpha and theta activity was decomposed into numerous MP atoms with median duration around 3 s, similar to the duration of induced, time-locked activity obtained with event-related (des)synchronization (ERS/ERD) studies. Relative to Rest, there was lower right-side and posterior MP alpha atom/min during Math, whereas MP theta atom/min was significantly higher on anteriorly located electrodes, especially on the left side. MP alpha findings were particularly significant on a narrow range around 10 Hz-10.5 Hz, consistent with FFT alpha peak findings from ERS/ERD studies. With a streamlined protocol, these results replicate previous findings of EEG alpha and theta activation obtained during Math tasks with different signal analysis techniques and in different time frames. The efficient application to real-world, noisy EEG data with a low-resolution stochastic MP dictionary shows that this technique is very encouraging. These results provide support for studies of mathematical cognition with mobile EEG and matching pursuit.

Detecting cognitive traits and occupational proficiency using EEG and statistical inference

Machine learning (ML) is widely used in classification tasks aimed at detecting various cognitive states or neurological diseases using noninvasive electroencephalogram (EEG) time series. However, successfully detecting specific cognitive skills in a healthy population, independent of subject, remains challenging. This study compared the subject-independent classification performance of three different pipelines: supervised and Riemann projections with logistic regression and handcrafted power spectral features with light gradient boosting machine (LightGBM). 128-channel EEGs were recorded from 26 healthy volunteers while they solved arithmetic, logical, and verbal tasks. The participants were divided into two groups based on their higher education and occupation: specialists in mathematics and humanities. The balanced accuracy of the education type was significantly above chance for all pipelines: 0.84-0.89, 0.85-0.88, and 0.86-0.88 for each type of task, respectively. All three pipelines allowed us to distinguish mathematical proficiency based on learning experience with different trade-offs between performance and explainability. Our results suggest that ML approaches could also be effective for recognizing individual cognitive traits using EEG.

Brain Active Areas Associated with a Mental Arithmetic Task: An eLORETA Study

The neural underpinnings of mental calculation, the fundamentals of arithmetic representations and processes, and the development of arithmetic abilities have been explored by researchers over the years. In the present work, we report a study that analyzes the brain-activated areas of a group of 35 healthy subjects (9 males, 26 females, mean age ± SD = 18.23 ± 2.20 years) who performed a serial subtraction arithmetic task. In contrast to most of the studies in the literature based on fMRI, we performed the brain active source reconstruction starting from EEG signals by means of the eLORETA method. In particular, the subjects were classified as bad counters or good counters, according to the results of the task, and the brain activity of the two groups was compared. The results were statistically significant only in the beta band, revealing that the left limbic lobe was found to be more active in people showing better performance. The limbic lobe is involved in visuospatial processing, memory, arithmetic fact retrieval, and emotions. However, the role of the limbic lobe in mental arithmetic has been barely explored, so these interesting findings could represent a starting point for future in-depth analyses. Since there is evidence in the literature that the motor system is affected by the execution of arithmetic tasks, a more extensive knowledge of the brain activation associated with arithmetic tasks could be exploited not only for the assessment of mathematical skills but also in the evaluation of motor impairments and, consequently, in rehabilitation for motor disorders.

Nonlinear and machine learning analyses on high-density EEG data of math experts and novices

Current trend in neurosciences is to use naturalistic stimuli, such as cinema, class-room biology or video gaming, aiming to understand the brain functions during ecologically valid conditions. Naturalistic stimuli recruit complex and overlapping cognitive, emotional and sensory brain processes. Brain oscillations form underlying mechanisms for such processes, and further, these processes can be modified by expertise. Human cortical functions are often analyzed with linear methods despite brain as a biological system is highly nonlinear. This study applies a relatively robust nonlinear method, Higuchi fractal dimension (HFD), to classify cortical functions of math experts and novices when they solve long and complex math demonstrations in an EEG laboratory. Brain imaging data, which is collected over a long time span during naturalistic stimuli, enables the application of data-driven analyses. Therefore, we also explore the neural signature of math expertise with machine learning algorithms. There is a need for novel methodologies in analyzing naturalistic data because formulation of theories of the brain functions in the real world based on reductionist and simplified study designs is both challenging and questionable. Data-driven intelligent approaches may be helpful in developing and testing new theories on complex brain functions. Our results clarify the different neural signature, analyzed by HFD, of math experts and novices during complex math and suggest machine learning as a promising data-driven approach to understand the brain processes in expertise and mathematical cognition.

Dynamic fluctuations in ascending heart-to-brain communication under mental stress

Dynamical information exchange between central and autonomic nervous systems, as referred to functional brain-heart interplay, occurs during emotional and physical arousal. It is well documented that physical and mental stress lead to sympathetic activation. Nevertheless, the role of autonomic inputs in nervous system-wise communication under mental stress is yet unknown. In this study, we estimated the causal and bidirectional neural modulations between electroencephalogram (EEG) oscillations and peripheral sympathetic and parasympathetic activities using a recently proposed computational framework for a functional brain-heart interplay assessment, namely the sympathovagal synthetic data generation model. Mental stress was elicited in 37 healthy volunteers by increasing their cognitive demands throughout three tasks associated with increased stress levels. Stress elicitation induced an increased variability in sympathovagal markers, as well as increased variability in the directional brain-heart interplay. The observed heart-to-brain interplay was primarily from sympathetic activity targeting a wide range of EEG oscillations, whereas variability in the efferent direction seemed mainly related to EEG oscillations in the γ band. These findings extend current knowledge on stress physiology, which mainly referred to top-down neural dynamics. Our results suggest that mental stress may not cause an increase in sympathetic activity exclusively as it initiates a dynamic fluctuation within brain-body networks including bidirectional interactions at a brain-heart level. We conclude that directional brain-heart interplay measurements may provide suitable biomarkers for a quantitative stress assessment and bodily feedback may modulate the perceived stress caused by increased cognitive demand.

How negative emotions influence arithmetic performance: a comparison of young and older adults

We investigated the influence of negative emotions on arithmetic problem-solving performance and age-related differences therein. Participants were asked to verify complex multiplication problems that were either true (e.g., 4 × 26 = 104) or false (e.g., 5 × 41 = 201). Half the problems were five problems (e.g., 5 × 28 = 140) and half were non-five problems (e.g., 6 × 36 = 216). False five problems violated the five-rule, the parity-rule, both rules, or no rule. Problems were preceded by emotionally neutral or negative pictures. For true problems, emotions impaired performance while verifying non-five problems in young adults only and while verifying five problems in older adults only. For false five problems, negative emotions influenced young adults’ performance while verifying both-rule and no-rule violation problems but not when verifying parity-rule violation or five-rule violation problems. Negative emotions did not influence older adults’ performance whichever false five problems they solved. These findings suggest that negative emotions may change the mechanisms that participants use to solve arithmetic problems and that emotions influence young and older adults via different mechanisms.

Multiple functions of the angular gyrus at high temporal resolution

Here, the functions of the angular gyrus (AG) are evaluated in the light of current evidence from transcranial magnetic/electric stimulation (TMS/TES) and EEG/MEG studies. 65 TMS/TES and 52 EEG/MEG studies were examined in this review. TMS/TES literature points to a causal role in semantic processing, word and number processing, attention and visual search, self-guided movement, memory, and self-processing. EEG/MEG studies reported AG effects at latencies varying between 32 and 800 ms in a wide range of domains, with a high probability to detect an effect at 300-350 ms post-stimulus onset. A three-phase unifying model revolving around the process of sensemaking is then suggested: (1) early AG involvement in defining the current context, within the first 200 ms, with a bias toward the right hemisphere; (2) attention re-orientation and retrieval of relevant information within 200-500 ms; and (3) cross-modal integration at late latencies with a bias toward the left hemisphere. This sensemaking process can favour accuracy (e.g. for word and number processing) or plausibility (e.g. for comprehension and social cognition). Such functions of the AG depend on the status of other connected regions. The much-debated semantic role is also discussed as follows: (1) there is a strong TMS/TES evidence for a causal semantic role, (2) current EEG/MEG evidence is however weak, but (3) the existing arguments against a semantic role for the AG are not strong. Some outstanding questions for future research are proposed. This review recognizes that cracking the role(s) of the AG in cognition is possible only when its exact contributions within the default mode network are teased apart.

Estimation Strategy Utilization Is Modulated by Implicit Emotion Regulation: Evidence from Behavioral and Event-Related Potentials Studies

A large number of studies have studied the influence of emotional experience on an individual's estimation performance, but the influence of implicit emotion regulation is still unknown. Participants were asked to complete the following tasks in order: idiom matching task, multiplication computational estimation task (MCE task), gender judgment task (GJ task), and emotional experience intensity assessment task. The words matching task was adopted to achieve the purpose of implicit emotion regulation (implicit reappraisal and implicit suppression). Behavioral results showed that implicit reappraisal and implicit suppression equally contributed to improving an individual's estimation speed (but not ACC (accuracy)). The MCE task related ERP (event-related potential) results showed that the influence of implicit emotion regulation on estimation consisted of two phases. In the first phase (encoding phase), implicit reappraisal both enhanced (larger P1 amplitudes) and weakened (smaller N170 amplitudes) an individual's encoding sensitivity, while implicit suppression enhanced an individual's encoding sensitivity (larger P1 amplitudes). In the second phase (estimation strategies retrieval phase), implicit reappraisal (but not implicit suppression) cost more attention resources (larger LPC2 and LPC3 amplitudes). The present study suggested that both implicit reappraisal and implicit suppression contributed to improving an individual's estimation performance, and the regulation effect of implicit suppression (vs. implicit reappraisal) was better.

EEG based functional brain networks analysis in dyslexic children during arithmetic task

Developmental Dyslexia is a neuro-developmental disorder that often refers to a phonological processing deficit regardless of average IQ. The present study investigated the distinct functional changes in brain networks of dyslexic children during arithmetic task performance using an electroencephalogram. Fifteen dyslexic children and fifteen normally developing children (NDC) were recruited and performed an arithmetic task. Brain functional network measures such as node strength, clustering coefficient, characteristic pathlength and small-world were calculated using graph theory methods for both groups. Task performance showed significantly less performance accuracy in dyslexics against NDC. The neural findings showed increased connectivity in the delta band and reduced connectivity in theta, alpha, and beta band at temporoparietal, and prefrontal regions in dyslexic group while performing the task. The node strengths were found to be significantly high in delta band (T3, O1, F8 regions) and low in theta (T5, P3, Pz regions), beta (Pz) and gamma band (T4 and prefrontal regions) during the task in dyslexics compared to the NDC. The clustering coefficient was found to be significantly low in the dyslexic group (theta and alpha band) and characteristic pathlength was found to be significantly high in the dyslexic group (theta and alpha band) compared to the NDC group while performing task. In conclusion, the present study shows evidence for poor fact-retrieval mechanism and altered network topology in dyslexic brain networks during arithmetic task performance.

Predicting Math Ability Using Working Memory, Number Sense, and Neurophysiology in Children and Adults

Previous work has shown relations between domain-general processes, domain-specific processes, and mathematical ability. However, the underlying neurophysiological effects of mathematical ability are less clear. Recent evidence highlighted the potential role of beta oscillations in mathematical ability. Here we investigate whether domain-general (working memory) and domain-specific (number sense) processes mediate the relation between resting-state beta oscillations and mathematical ability, and how this may differ as a function of development (children vs. adults). We compared a traditional analysis method normally used in EEG studies with a more recently developed parameterization method that separates periodic from aperiodic activity. Regardless of methods chosen, we found no support for mediation of working memory and number sense, neither for children nor for adults. However, we found subtle differences between the methods. Additionally, we showed that the traditional EEG analysis method conflates periodic activity with aperiodic activity; in addition, the latter is strongly related to mathematical ability and this relation differs between children and adults. At the cognitive level, our findings do not support previous suggestions of a mediation of working memory and number sense. At the neurophysiological level our findings suggest that aperiodic, rather than periodic, activity is linked to mathematical ability as a function of development.

Different Language Modalities Yet Similar Cognitive Processes in Arithmetic Fact Retrieval

Does experience with signed language impact the neurocognitive processes recruited by adults solving arithmetic problems? We used event-related potentials (ERPs) to identify the components that are modulated by operation type and problem size in Deaf American Sign Language (ASL) native signers and in hearing English-speaking participants. Participants were presented with single-digit subtraction and multiplication problems in a delayed verification task. Problem size was manipulated in small and large problems with an additional extra-large subtraction condition to equate the overall magnitude of large multiplication problems. Results show comparable behavioral results and similar ERP dissociations across groups. First, an early operation type effect is observed around 200 ms post-problem onset, suggesting that both groups have a similar attentional differentiation for processing subtraction and multiplication problems. Second, for the posterior-occipital component between 240 ms and 300 ms, subtraction problems show a similar modulation with problem size in both groups, suggesting that only subtraction problems recruit quantity-related processes. Control analyses exclude possible perceptual and cross-operation magnitude-related effects. These results are the first evidence that the two operation types rely on distinct cognitive processes within the ASL native signing population and that they are equivalent to those observed in the English-speaking population.

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.

Magnetoencephalography reveals differences in brain activations for fast and slow responses to simple multiplications

Despite decades of studies, it is still an open question on how and where simple multiplications are solved by the brain. This fragmented picture is mostly related to the different tasks employed. While in neuropsychological studies patients are asked to perform and report simple oral calculations, neuroimaging and neurophysiological studies often use verification tasks, in which the result is shown, and the participant must verify the correctness. This MEG study aims to unify the sources of evidence, investigating how brain activation unfolds in time using a single-digit multiplication production task. We compared the participants' brain activity-focusing on the parietal lobes-based on response efficiency, dividing their responses in fast and slow. Results showed higher activation for fast, as compared to slow, responses in the left angular gyrus starting after the first operand, and in the right supramarginal gyrus only after the second operand. A whole-brain analysis showed that fast responses had higher activation in the right dorsolateral prefrontal cortex. We show a timing difference of both hemispheres during simple multiplications. Results suggest that while the left parietal lobe may allow an initial retrieval of several possible solutions, the right one may be engaged later, helping to identify the solution based on magnitude checking.

Monitoring the Cortical Activity of Children and Adults during Cognitive Task Completion

In this paper, we used an EEG system to monitor and analyze the cortical activity of children and adults at a sensor level during cognitive tasks in the form of a Schulte table. This complex cognitive task simultaneously involves several cognitive processes and systems: visual search, working memory, and mental arithmetic. We revealed that adults found numbers on average two times faster than children in the beginning. However, this difference diminished at the end of table completion to 1.8 times. In children, the EEG analysis revealed high parietal alpha-band power at the end of the task. This indicates the shift from procedural strategy to less demanding fact-retrieval. In adults, the frontal beta-band power increased at the end of the task. It reflects enhanced reliance on the top-down mechanisms, cognitive control, or attentional modulation rather than a change in arithmetic strategy. Finally, the alpha-band power of adults exceeded one of the children in the left hemisphere, providing potential evidence for the fact-retrieval strategy. Since the completion of the Schulte table involves a whole set of elementary cognitive functions, the obtained results were essential for developing passive brain-computer interfaces for monitoring and adjusting a human state in the process of learning and solving cognitive tasks of various types.

When the time is right: Temporal dynamics of brain activity in healthy aging and dementia

Brain activity and communications are complex phenomena that dynamically unfold over time. However, in contrast with the large number of studies reporting neuroanatomical differences in activation relative to young adults, changes of temporal dynamics of neural activity during normal and pathological aging have been grossly understudied and are still poorly known. Here, we synthesize the current state of knowledge from MEG and EEG studies that aimed at specifying the effects of healthy and pathological aging on local and network dynamics, and discuss the clinical and theoretical implications of these findings. We argue that considering the temporal dynamics of brain activations and networks could provide a better understanding of changes associated with healthy aging, and the progression of neurodegenerative disease. Recent research has also begun to shed light on the association of these dynamics with other imaging modalities and with individual differences in cognitive performance. These insights hold great potential for driving new theoretical frameworks and development of biomarkers to aid in identifying and treating age-related cognitive changes.

Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study

Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training. Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems. Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals' low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge.

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.

Differences in event-related potential (ERP) responses to small tie, non-tie and 1-problems in addition and multiplication

Using ERP, we investigated the cause of the tie advantage according to which problems with repeated operands are solved faster and more accurately than non-tie problems. We found no differences in early or N400 ERP components between problems, suggesting that tie problems are not encoded faster or suffer from less interference than non-tie problems. However, a lesser negative amplitude of the N2 component was found for tie than non-tie problems. This suggests more working-memory and attentional resource requirements for non-tie problems and therefore more frequent use of retrieval for tie than non-tie problems. The possible peculiarity of problems involving a 1 was also investigated. We showed less negative N2 amplitudes for these problems than for other non-tie problems, suggesting less working-memory resources for 1-problems than other non-tie problems. This could be explained either by higher reliance on memory retrieval for 1-problems than non-1 problems or by the application of non-arithmetical rules for 1-problems.

Validity of the Polar V800 Monitor for Assessing Heart Rate Variability in Elderly Adults under Mental Stress and Dual Task Conditions

Background: Aging may result in autonomic nervous dysfunction. Heart rate variability (HRV) is a non-invasive method to measure autonomic nervous activities. Many studies have shown that HRV contributes to the risk assessment of diseases. A Polar V800 heart rate monitor is a wearable device that measures R-R intervals, but has only been validated in younger adults under limited testing conditions. There is no validation of the V800 under mental stress or in dual task testing conditions. Therefore, this study investigated the validity of the Polar V800 heart rate monitor for assessing R-R intervals and evaluated if there were differences on HRV parameters under different situations in community-dwelling elderly adults. Methods: Forty community-dwelling elderly adults were recruited. Heart rates were recorded via electrocardiogram (ECG) and the V800 under sitting, during an arithmetic test, during a naming test, a self-selected walking velocity test (SSWV), and dual tasks (SSWV performing mental arithmetic test and SSWV performing naming test). Indices of time and frequency domains of HRV were calculated afterwards. The intra-class correlation coefficient (ICC) analysis and effect size were calculated to examine the concurrent validity between the V800 and the ECG. Results: All HRV indices from the V800 were highly correlated with the ECG under all tested conditions (ICC = 0.995–1.000, p < 0.001) and the effect size of bias was small (<0.1). Conclusion: Overall, the V800 has good validity on the assessment of HRV in community-dwelling elderly adults during sitting, mental arithmetic test, naming test, SSWV, and dual tasks.

Simple additions: Dissociation between retrieval and counting with electrophysiological indexes

There is current debate about the way adult individuals solve simple additions composed of one-digit operands. There are two opposing views. The first view assumes that people retrieve the result of additions from memory, whilst the second view states that individuals use automatized counting procedures. Our study aimed to dissociate between these two hypotheses. To this end, we analysed the type of problem effect when participants resolved simple additions by comparing additions with operands between 1 and 4 and control additions with at least one operand larger than 4. Brain-waves activity of a group of 30 adult individuals were recorded with 64 scalp electrodes mounted on an elastic cap, referenced against an electrode between Cz and CPz and re-referenced to an average reference offline. We considered two electrophysiological indexes, event-related potentials, ERPs, time-locked to the addition problems to distinguish between retrieval from memory and the use of procedures: A late positivity component (LP, 500-650 time window) over posterior regions associated to memory retrieval difficulty with higher LP positivity when participants resolve difficult vs. easy additions, and a negative component (N400, 250-450 ms time window) over fronto-central regions related to the use memory retrieval vs. procedures with more pronounced N400 amplitudes when the difficulty in the retrieval of semantic information increased. LP modulations were observed depending on the type of problem over posterior regions, P3 and Pz electrodes, whilst the N400 component was not affected. This pattern of results suggests that adult individuals use retrieval from memory to solve simple additions.

Age-related differences in the structural and effective connectivity of cognitive control: a combined fMRI and DTI study of mental arithmetic

Cognitive changes with aging are highly variable across individuals. This study investigated whether cognitive control performance might depend on preservation of structural and effective connectivity in older individuals. Specifically, we tested inhibition following working memory (WM) updating and maintenance. We analyzed diffusion tensor imaging and functional magnetic resonance imaging data in thirty-four young adults and thirty-four older adults, who performed an arithmetic verification task during functional magnetic resonance imaging. Results revealed larger arithmetic interference in older adults relative to young adults after WM updating, whereas both groups showed similar interference after WM maintenance. In both groups, arithmetic interference was associated with larger activations and stronger effective connectivity among bilateral anterior cingulate, bilateral inferior frontal gyrus, and left angular gyrus, with larger activations of frontal regions in older adults than in younger adults. In older adults, preservation of frontoparietal structural microstructure, especially involving the inferior frontaloccipital fasciculus, was associated with reduced interference, and stronger task-related effective connectivity. These results highlight how both structural and functional changes in the cognitive control network contribute to individual variability in performance during aging.

Individual Differences in Math Ability Determine Neurocognitive Processing of Arithmetic Complexity: A Combined fNIRS-EEG Study

Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.

Oscillatory EEG Changes During Arithmetic Learning in Children

Most studies have investigated brain activation changes after the course of arithmetic learning, and the question remains whether these changes are detectable during the course of learning, i.e., before memory consolidation. Twenty-four fifth graders solved multiplication problems while ongoing electroencephalography (EEG) was recorded. The arithmetic training revealed reduced errors together with a power increase in theta (4-7 Hz) but not in lower alpha (8-10 Hz) or upper alpha (10-13 Hz) bands. We conclude that increases in theta power subserved a shift from slow, procedural strategies to more efficient, automated procedural and retrieval strategies, which led to more efficient performance.

Arithmetic word problems describing discrete quantities: E.E.G evidence for the construction of a situation model

In this research, university students were asked to solve arithmetic word problems constructed either with discrete quantities, such as apples or marbles, or continuous quantities such as meters of rope or grams of sand. An analysis of their brain activity showed different alpha levels between the two types of problems with, in particular, a lower alpha power in the parieto-occipital area for problems describing discrete quantities. This suggests that processing discrete quantities during problem solving prompts more mental imagery than processing continuous quantities. These results are difficult to reconcile with the schema theory, according to which arithmetic problem solving depends on the activation of ready-made mental frames stored in long-term memory and triggered by the mathematical expression used in the texts. Within the schema framework, the nature of the objects described in the text should be quickly abstracted during problem solving because it cannot impact the semantic structure of the problem. On the contrary, our results support the situation model theory, which places greater emphasis on the problem context in order to account for individuals' behaviour. On a more methodological point of view, this study constitutes the first attempt to infer the characteristics of individual's mental representations of arithmetic text problems from EEG recordings. This opens the door for the application of brain activity measures in the field of arithmetic word problem.

Spatio-temporal patterns of cognitive control revealed with simultaneous electroencephalography and functional magnetic resonance imaging

Optimal performance depends in part on the ability to inhibit the automatic processing of irrelevant information and also on the adjusting the level of control from one trial to the next. In this study, we investigated the spatio-temporal neural correlates of cognitive control using simultaneous functional magnetic resonance imaging and electroencephalography, while 22 participants (10 women) performed a numerical Stroop task. We investigated the spatial and temporal dynamic of the conflict adaptation effects (i.e., reduced interference on items that follow an incongruent stimulus compared to after a congruent stimulus). Joint independent component analysis linked the N200 component to activation of anterior cingulate cortex (ACC) and the conflict slow potential to widespread activations within the fronto-parietal executive control network. Connectivity analyses with psychophysiological interactions and dynamic causal modeling demonstrated coordinated engagement of the cognitive control network after the processing of an incongruent item, and this was correlated with better behavioral performance. Our results combined high spatial and temporal resolution to propose the following network of conflict adaptation effect and specify the time course of activation within this model: first, the anterior insula and inferior frontal gyrus are activated when incongruence is detected. These regions then signal the need for higher control to the ACC, which in turn activates the fronto-parietal executive control network to improve the performance on the next trial.

The neural correlates of mental arithmetic in adolescents: a longitudinal fNIRS study

BACKGROUND

Arithmetic processing in adults is known to rely on a frontal-parietal network. However, neurocognitive research focusing on the neural and behavioral correlates of arithmetic development has been scarce, even though the acquisition of arithmetic skills is accompanied by changes within the fronto-parietal network of the developing brain. Furthermore, experimental procedures are typically adjusted to constraints of functional magnetic resonance imaging, which may not reflect natural settings in which children and adolescents actually perform arithmetic. Therefore, we investigated the longitudinal neurocognitive development of processes involved in performing the four basic arithmetic operations in 19 adolescents. By using functional near-infrared spectroscopy, we were able to use an ecologically valid task, i.e., a written production paradigm.

RESULTS

A common pattern of activation in the bilateral fronto-parietal network for arithmetic processing was found for all basic arithmetic operations. Moreover, evidence was obtained for decreasing activation during subtraction over the course of 1 year in middle and inferior frontal gyri, and increased activation during addition and multiplication in angular and middle temporal gyri. In the self-paced block design, parietal activation in multiplication and left angular and temporal activation in addition were observed to be higher for simple than for complex blocks, reflecting an inverse effect of arithmetic complexity.

CONCLUSIONS

In general, the findings suggest that the brain network for arithmetic processing is already established in 12-14 year-old adolescents, but still undergoes developmental changes.

The neural correlates of arithmetic difficulty depend on mathematical ability: evidence from combined fNIRS and ERP

Mathematical abilities are essential for an individual, as they predict career prospects among many other abilities. However, little is known about whether neural correlates of arithmetic problem difficulty differ between individuals with high and low math ability. For instance, the difficulty of two-digit addition and subtraction increases whenever a carry or borrow operation is required. Therefore, we systematically investigated the spatial and temporal neural correlates of the carry and borrow effects for high and low performers in a written production paradigm using combined functional near-infrared spectroscopy (fNIRS) and event-related potential (ERP) measurements. Effects of arithmetic difficulty interacted with an individual's math ability. High performers showed increased frontal activation especially in the left inferior frontal gyrus associated with the carry and borrow effects, whereas low performers did not. Furthermore, high and low performers even differed in their early processing of the borrow effect, as reflected by differences in slow waves at 1000-1500 ms at frontal sites. We conclude that the processing of arithmetic difficulty relies on an individual's mathematical ability, and suggest that individual differences should be taken into account when investigating mental arithmetic in an ecologically valid assessment.

Reduction but no shift in brain activation after arithmetic learning in children: A simultaneous fNIRS-EEG study

Neurocognitive studies of arithmetic learning in adults have revealed decreasing brain activation in the fronto-parietal network, along with increasing activation of specific cortical and subcortical areas during learning. Both changes are associated with a shift from procedural to retrieval strategies for problem-solving. Here we address the critical, open question of whether similar neurocognitive changes are also evident in children. In this study, 20 typically developing children were trained to solve simple and complex multiplication problems. The one-session and two-week training effects were monitored using simultaneous functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). FNIRS measurement after one session of training on complex multiplication problems revealed decreased activation at the left angular gyrus (AG), right superior parietal lobule, and right intraparietal sulcus. Two weeks of training led to decreased activation at the left AG and right middle frontal gyrus. For both simple and complex problems, we observed increased alpha power in EEG measurements as children worked on trained versus untrained problems. In line with previous multiplication training studies in adults, reduced activation within the fronto-parietal network was observed after training. Contrary to adults, we found that strategy shifts via arithmetic learning were not contingent on the activation of the left AG in children.

Functional localization and effective connectivity of cortical theta and alpha oscillatory activity during an attention task

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sLORETA analyses performed on 14 healthy adults at rest and during an arithmetic task.

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Theta and alpha directed connectivity revealed ACC and left IPL as hubs during task.

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Information flow between left IFG and STG suggested a feedback loop.

Objectives

The aim of this paper is to investigate cortical electric neuronal activity as an indicator of brain function, in a mental arithmetic task that requires sustained attention, as compared to the resting state condition. The two questions of interest are the cortical localization of different oscillatory activities, and the directional effective flow of oscillatory activity between regions of interest, in the task condition compared to resting state. In particular, theta and alpha activity are of interest here, due to their important role in attention processing.

Methods

We adapted mental arithmetic as an attention ask in this study. Eyes closed 61-channel EEG was recorded in 14 participants during resting and in a mental arithmetic task (“serial sevens subtraction”). Functional localization and connectivity analyses were based on cortical signals of electric neuronal activity estimated with sLORETA (standardized low resolution electromagnetic tomography). Functional localization was based on the comparison of the cortical distributions of the generators of oscillatory activity between task and resting conditions. Assessment of effective connectivity was based on the iCoh (isolated effective coherence) method, which provides an appropriate frequency decomposition of the directional flow of oscillatory activity between brain regions. Nine regions of interest comprising nodes from the dorsal and ventral attention networks were selected for the connectivity analysis.

Results

Cortical spectral density distribution comparing task minus rest showed significant activity increase in medial prefrontal areas and decreased activity in left parietal lobe for the theta band, and decreased activity in parietal-occipital regions for the alpha1 band. At a global level, connections among right hemispheric nodes were predominantly decreased during the task condition, while connections among left hemispheric nodes were predominantly increased. At more detailed level, decreased flow from right inferior frontal gyrus to anterior cingulate cortex for theta, and low and high alpha oscillations, and increased feedback (bidirectional flow) between left superior temporal gyrus and left inferior frontal gyrus, were observed during the arithmetic task.

Conclusions

Task related medial prefrontal increase in theta oscillations possibly corresponds to frontal midline theta, while parietal decreased alpha1 activity indicates the active role of this region in the numerical task. Task related decrease of intracortical right hemispheric connectivity support the notion that these nodes need to disengage from one another in order to not interfere with the ongoing numerical processing. The bidirectional feedback between left frontal-temporal-parietal regions in the arithmetic task is very likely to be related to attention network working memory function.

Significance

The methods of analysis and the results presented here will hopefully contribute to clarify the roles of the different EEG oscillations during sustained attention, both in terms of their functional localization and in terms of how they integrate brain function by supporting information flow between different cortical regions. The methodology presented here might be clinically relevant in evaluating abnormal attention function.

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth “strategy selection”) in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.