An event-related brain potential study of the arithmetic split effect

The involvement of the semantic neural network in rule identification of mathematical processing

The role of the visuospatial network in mathematical processing has been established, but the involvement of the semantic network in mathematical processing is still poorly understood. The current study utilized a number series completion paradigm with the event-related potential (ERP) technique to examine whether the semantic network supports mathematical processing and to find the corresponding spatiotemporal neural marker. In total, 32 right-handed undergraduate students were recruited and asked to complete the number series completion as well as the arithmetical computation task in which numbers were presented in sequence. The event-related potential and multi-voxel pattern analysis showed that the rule identification process involves more semantic processing when compared with the arithmetical computation processes, and it elicited higher amplitudes for the late negative component (LNC) in left frontal and temporal lobes. These results demonstrated that the semantic network supports the rule identification in mathematical processing, with the LNC acting as the neural marker.

Related consistent lures increase the judgment of multiplication facts: Evidence using event-related potential technique

Simple multiplication errors are primarily shown in whether the lures are related to the operands (relatedness, such as 3 × 4 = 15 vs. 17) or whether the same decades are shared with the correct answers (consistency, such as 3 × 4 = 16 vs. 21). This study used a delayed verification paradigm and event-related potential technique to investigate the effects of relatedness and consistency in simple multiplication mental arithmetic for 30 college students in an experiment of presenting probes in auditory channels. We found that, compared to the related inconsistent lures, the related consistent lures showed significantly faster reaction time and induced significantly large amplitudes of N400 and late positive component. The findings suggest that related consistent lures are less affected by the activation diffusion of the arithmetic problem, and the credibility of being perceived as the correct answer is less; the lures related to operands and sharing the same decades with the accurate results can promote the judgment of multiplication mental arithmetic, and the results support the Interacting Neighbors Model.

When multiplying is meaningful in memory: Electrophysiological signature of the problem size effect in children

Children are less fluent at verifying the answers to larger single-digit arithmetic problems compared with smaller ones. This problem size effect may reflect the structure of memory for arithmetic facts. In the current study, typically developing third to fifth graders judged the correctness of single-digit multiplication problems, presented as a sequence of three digits, that were either small (e.g., 4 3 12 vs. 4 3 16) or large (e.g., 8 7 56 vs. 8 7 64). We measured the N400, an index of access to semantic memory, along with accuracy and response time. The N400 was modulated by problem size only for correct solutions, with larger amplitude for large problems than for small problems. This suggests that only solutions that exist in memory (i.e., correct solutions) reflect a modulation of semantic access likely based on the relative frequency of encountering small versus large problems. The absence of an N400 problem size effect for incorrect solutions suggests that the behavioral problem size effects were not due to differences in initial access to memory but instead were due to a later stage of cognitive processing that was reflected in a post-N400 main effect of problem size. A second post-N400 main effect of correctness at occipital electrodes resembles the beginning of an adult-like brain response observed in prior studies. In sum, event-related brain potentials revealed different cognitive processes for correct and incorrect solutions. These results allude to a gradual transition to an adult-like brain response, from verifying multiplication problems using semantic memory to doing so using more automatic categorization.

Incongruity in fraction verification elicits N270 and P300 ERP effects

Understanding how the numerical magnitudes of fractions are accessed is a topic of major interest in numerical cognition and mathematics education. Only a few studies have investigated fraction processing using EEG methods. In the present study, 24 adult participants completed a fraction magnitude verification task while EEGs were recorded. Similar to other arithmetic verification tasks, behavioral results show increased response times to validate mismatching magnitudes compared to matching ones. ERP results show an early frontal N270 component to mismatching trials and a late parietal P300 component during matching trials. These ERP results highlight that participants treat matching fractions as targets and suggest that additional cognitive resources are needed to process mismatching targets. These results provide evidence that fractions processing shares a similar neurocognitive process as those observed during the processing of arithmetic operations and open the door to further explore fraction processing using ERP methods.

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.

Task relevance effect on number/shape conflict detection in the number-matching task: An ERP study

It is debatable whether the task relevance effect on a conflict occurs in the detection or in the inhibition underlying sequential matching. To explore this issue, three types of number pairs, identical (e.g., 12, 12), conserved (e.g., 12, ), and non-conserved (e.g., 12, 15) pairs, were displayed to be judged as perceptually (identical shape condition) or quantitatively (identical value condition) the same. Both error rates and RTs for the three types of number pairs showed different patterns to detect perceptual mismatch in the identical shape condition and number inequivalence in the identical value conditions. The event-related potential (ERP) results showed that increased N200 and N400 as well as decreased P300 were triggered by the conserved and non-conserved pairs in contrast to identical pairs in the identical shape condition and by the non-conserved pairs relative to the conserved and identical pairs in the identical value condition. These results showed that task-relevant mismatches were attended to and detected in both conditions. Therefore, for the task-relevance effect on a conflict, attention is selectively directed to task-relevant features rather than inhibiting task-irrelevant conflict.

P300 amplitude and latency reflect arithmetic skill: An ERP study of the problem size effect

The effect of arithmetic problem size is widespread in behavior (e.g., slower responses to 8 × 7 than 2 × 2). Here, we measure event related potentials (ERPs) to determine how the problem size effect unfolds under different conditions. Adults judged the correctness of simple multiplication problems (2 × 4 = 8 versus 9) that varied in size and operand number format (written digits versus spoken number words). The P300, an ERP component associated with stimulus categorization, was measured from solution onset. P300 amplitude was greatest for small and correct solutions, as expected for easily categorized stimuli. Large incorrect solutions elicited a disproportionately reduced P300, an interaction not measurable in verification behavior. Additionally, ERP measures revealed effects of operand format preceding, but not following, solution onset. The significance of these findings for theories of mathematical cognition are addressed.

Electrophysiological markers of poor versus superior math abilities in healthy individuals

Interindividual differences in the numerical ability of healthy adults have been previously demonstrated, mainly with tasks involving mental number line or size representation. However, electrophysiological correlates of superior versus poor arithmetic ability (in the healthy population) have been scarcely investigated. We correlated electric potentials with math performance in 13 skilled and 13 poor calculators selected from a sample of 41 graduate students on the basis of their poor or superior math abilities assessed through a timed test. EEG was recorded from 128 channels while participants solved 352 arithmetical operations (additions, subtractions, multiplications, divisions) and decided whether the provided solution was correct or incorrect. Overall skilled individuals correctly solved a higher number of operations than poor calculators and had faster response times. Consistently, the latency of fronto-central P300 component of event-related potentials (ERPs) peaked earlier in the skilled than poor group. The P300 was larger in amplitude to correct than incorrect solutions, but just in the skilled group, with a tendency found in poor calculators. Spearman's ρ correlation coefficient analyses showed that the larger P300 response was to correct arithmetic solutions, the better the performance; conversely, the larger the P300 amplitude was to incorrect solutions, the worse the performance. The results suggest that poor calculators had a less clear representation of arithmetic solutions and difficulty in quickly accessing it. This study provides a standard method for directly investigating math abilities throughout ERP recordings that could be useful for assessing acalculia/dyscalculia in the clinical population (children, elderly, brain-damaged patients).

When 2 × 4 is meaningful: the N400 and P300 reveal operand format effects in multiplication verification

Arithmetic problems share many surface-level features with typical sentences. They assert information about the world, and readers can evaluate this information for sensibility by consulting their memories as the statement unfolds. When people encounter the solution to the problem 3 × 4, the brain elicits a robust ERP effect as a function of answer expectancy (12 being the expected completion; 15 being unexpected). Initially, this was labeled an N400 effect, implying that semantic memory had been accessed. Subsequent work suggested instead that the effect was driven by a target P300 to the correct solutions. The current study manipulates operand format to differentially promote access to language-based semantic representations of arithmetic. Operands were presented either as spoken number words or as sequential Arabic numerals. The critical solution was always an Arabic numeral. In Experiment 1, the correctness of solutions preceded by spoken operands modulated N400 amplitude, whereas solutions preceded by Arabic numerals elicited a P300 for correct problems. In Experiment 2, using only spoken operands, the delay between the second operand and the Arabic numeral solution was manipulated to determine if additional processing time would result in a P300. With a longer delay, an earlier N400 and no distinct P300 were observed. In brief, highly familiar digit operands promoted target detection, whereas spoken numbers promoted semantic level processing-even when solution format itself was held constant. This provides evidence that the brain can process arithmetic fact information at different levels of representational meaningfulness as a function of symbolic format.

Brain-mechanistic responses to varying difficulty levels of approximate solutions to arithmetic problems

Approximate strategies are crucial in daily human life. The studies on the “difficulty effect” seen in approximate complex arithmetic have long been neglected. Here, we aimed to explore the brain mechanisms related to this difficulty effect in the case of complex addition, using event-related potential-based methods. Following previous path-finding studies, we used the inequality paradigm and different split sizes to induce the use of two approximate strategies for different difficulty levels. By comparing dependent variables from the medium- and large-split conditions, we anticipated being able to dissociate the effects of task difficulty based on approximate strategy in electrical components. In the fronto−central region, early P2 (150–250 ms) and an N400-like wave (250–700 ms) were significantly different between different difficulty levels. Differences in P2 correlated with the difficulty of separation of the approximate strategy from the early physical stimulus discrimination process, which is dominant before 200 ms, and differences in the putative N400 correlated with different difficulties of approximate strategy execution. Moreover, this difference may be linked to speech processing. In addition, differences were found in the fronto-central region, which may reflect the regulatory role of this part of the cortex in approximate strategy execution when solving complex arithmetic problems.

Processing of multi-digit additions in high math-anxious individuals: psychophysiological evidence

We investigated the time course of neural processing of multi-digit additions in high- (HMA) and low-math anxious (LMA) individuals. Seventeen HMA and 17 LMA individuals were presented with two-digit additions and were asked to perform a verification task. Behavioral data showed that HMA individuals were slower and more error prone than their LMA peers, and that incorrect solutions were solved more slowly and less accurately than correct ones. Moreover, HMA individuals tended to need more time and commit more errors when having to verify incorrect solutions than correct ones. ERPs time-locked to the presentation of the addends (calculation phase) and to the presentation of the proposed solution (verification phase) were also analyzed. In both phases, a P2 component of larger amplitude was found for HMA individuals than for their LMA peers. Because the P2 component is considered to be a biomarker of the mobilization of attentional resources toward emotionally negative stimuli, these results suggest that HMA individuals may have invested more attentional resources both when processing the addends (calculation phase) and when they had to report whether the proposed solution was correct or not (verification phase), as compared to their LMA peers. Moreover, in the verification phase, LMA individuals showed a larger late positive component (LPC) for incorrect solutions at parietal electrodes than their HMA counterparts. The smaller LPC shown by HMA individuals when verifying incorrect solutions suggests that these solutions may have been appeared more plausible to them than to their LMA counterparts.

Arithmetic split effect in complex subtractions: an event-related potential study

This study explores the relationship between the split effect and the use of exact versus approximate strategies in complex-subtraction calculations. One-hundred and two-digit subtraction problems were presented, with half of them being small-split problems with answers ±2 or ±5 from 50 and the other half being large-split problems with answers ±10 or ±15 from 50. Participants were asked to indicate whether the answer was less than 50. The measures were speed and accuracy of task performance, and high temporal resolution event-related potentials. Behavioral data showed that participants had a longer time requirement and a lower accuracy in solving small-split problems than in solving large-split problems. Event-related potential data show that, comparatively, the small-split problems led to more-negative, more-lateralized waves as early as 250 ms at frontal, frontocentral, and central sites. Our results, which are in agreement with previous studies, suggest that the participants used exact strategies to solve small-split problems and approximate strategies to solve large-split problems when performing complex subtractions. These results further our understanding of the brain mechanisms underlying the relationship between small/large-split effects and exact/approximate strategies in this task domain.

Dissociation between arithmetic relatedness and distance effects is modulated by task properties: an ERP study comparing explicit vs. implicit arithmetic processing

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ERPs were recorded while performing number matching and arithmetic verification tasks.

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Access to the arithmetic facts lexicon is modulated by task properties.

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Arithmetic relatedness and distance effects are sensitive to task properties.

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Matching tasks involve semantic processes.

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Verification tasks involve semantic and detection of mismatch processes.

Event-related potential (ERP) studies have detected several characteristic consecutive amplitude modulations in both implicit and explicit mental arithmetic tasks. Implicit tasks typically focused on the arithmetic relatedness effect (in which performance is affected by semantic associations between numbers) while explicit tasks focused on the distance effect (in which performance is affected by the numerical difference of to-be-compared numbers). Both task types elicit morphologically similar ERP waves which were explained in functionally similar terms. However, to date, the relationship between these tasks has not been investigated explicitly and systematically. In order to fill this gap, here we examined whether ERP effects and their underlying cognitive processes in implicit and explicit mental arithmetic tasks differ from each other. The same group of participants performed both an implicit number-matching task (in which arithmetic knowledge is task-irrelevant) and an explicit arithmetic-verification task (in which arithmetic knowledge is task-relevant). 129-channel ERP data differed substantially between tasks. In the number-matching task, the arithmetic relatedness effect appeared as a negativity over left-frontal electrodes whereas the distance effect was more prominent over right centro-parietal electrodes. In the verification task, all probe types elicited similar N2b waves over right fronto-central electrodes and typical centro-parietal N400 effects over central electrodes. The distance effect appeared as an early-rising, long-lasting left parietal negativity. We suggest that ERP effects in the implicit task reflect access to semantic memory networks and to magnitude discrimination, respectively. In contrast, effects of expectation violation are more prominent in explicit tasks and may mask more delicate cognitive processes.

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.

An ERP study of simple addition: the semantics and syntax of arithmetic operation sign

The aim of the current study was to examine brain activity of adult regular calculators while processing addition sums with different types of answers. The task was a verification task, the incorrect answers were divided into two types: one was comprised of three numbers that do not belong to any additive triplet (such as 2, 4, 7) and it was always near the correct result (± 1); the other was a number which is related to the two numbers which appear in the stimulus but belongs to an incorrect competing triplet of numbers and it was always in a greater distance from the correct answer. Differences were found between the different types of answers in the behavioral reaction time with longest reaction time for the competing triplet and the shortest reaction time for the correct answer. In addition, differences in the latency and amplitude of the N170, N270, N400 and P600 components were found among the different types of answers. It can be concluded from these results that the effect of the interference of the competing triplets is greater than the split effect (distance effect), and that there is a different time zone for coding the numbers and coding of other more general syntactic-semantic arithmetic signs.

Mathematical anxiety effects on simple arithmetic processing efficiency: an event-related potential study

This study uses event-related brain potentials to investigate the difficulties that high math anxious individuals face when processing dramatically incorrect solutions to simple arithmetical problems. To this end, thirteen high math-anxious (HMA) and thirteen low math-anxious (LMA) individuals were presented with simple addition problems in a verification task. The proposed solution could be correct, incorrect but very close to the correct one (small-split), or dramatically incorrect (large-split). The two groups did not differ in mathematical ability or trait anxiety. We reproduced previous results for flawed scores suggesting HMA difficulties in processing large-split solutions. Moreover, large-split solutions elicited a late positive component (P600/P3b) which was more enhanced and delayed in the HMA group. Our study proposes that the pattern of flawed scores found by previous studies (and that we replicate) has to do with HMA individuals'difficulties in inhibiting an extended processing of irrelevant information (large-split solutions).

The N3 is sensitive to odd-even congruency information in arithmetic fact retrieval

This study investigated the behavioral and electrophysiological effects elicited by adults' simple addition verification when false answers agree or disagree with the odd-even status of the correct sum (parity congruency vs. parity incongruency), while they are near or far from correct (small vs. large splits). Event-related brain potentials were recorded from 18 students using a first-answer-then-problem paradigm. The results showed that odd-even congruency had a significant effect on the N3 latency with a small, but not a large split. Specifically, odd-even congruent answers with a small split elicited an N3 with a longer latency. Analyses of RT similarly indicated a bigger parity-congruency effect with small-split answers compared with large-split answers. This pattern parallels the corresponding effects on N3 and confirms that the N3 is sensitive to odd-even information in arithmetic fact retrieval and that there are clear links between the event-related brain potential pattern and behavioral effects.

Shared structural and temporal integration resources for music and arithmetic processing

While previous research has investigated the relationship either between language and music processing or between language and arithmetic processing, the present study investigated the relationship between music and arithmetic processing. Rule-governed number series, with the final number being a correct or incorrect series ending, were visually presented in synchrony with musical sequences, with the final chord functioning as the expected tonic or the less-expected subdominant chord (i.e., tonal function manipulation). Participants were asked to judge the correctness of the final number as quickly and accurately as possible. The results revealed an interaction between the processing of series ending and the processing of the task-irrelevant chords' tonal function, thus suggesting that music and arithmetic processing share cognitive resources. These findings are discussed in terms of general temporal and structural integration resources for linguistic and non-linguistic rule-governed sequences.

Processing false solutions in additions: differences between high- and lower-skilled arithmetic problem-solvers

This paper focuses on the capacity to solve numerical incongruities in high- and lower-skilled arithmetic problem-solvers by investigating event-related brain potentials elicited by incorrect solutions to additions. Fifteen high-skill and fifteen low-skill individuals were presented with simple addition problems in a verification task. The proposed solution was manipulated by presenting correct solutions and incorrect solutions very close to the correct ones. Incorrect solutions elicited a negative component followed by a late positive component (LPC/P3b), whose amplitude was smaller for the low-skill group than for the high-skill group. Because the LPC/P3b amplitude has been taken as an indicator of the plausibility of the stimulus, this result suggests that incorrect solutions close to the correct ones appear more plausible to low-skilled individuals than to their high-skilled counterparts. This result is interpreted in terms of differences in the strength of association between problems and potential solutions depending on arithmetical skill.

Simple mental arithmetic is not so simple: an ERP study of the split and odd-even effects in mental arithmetic

This study aimed to investigate the effects of split size (small vs. large splits) and odd-even congruency (parity congruency vs. parity incongruency) of answers on arithmetical equation processing. Event-related potentials were recorded from 18 students in a first-answer-then-equation presentation mode. The ERP results showed that the odd-even congruency had a significant effect on the late positive wave in the small, but not the large split, with a late positive slow wave elicited by the small-split and the odd-even congruent conditions. This result suggests that the split effect has priority over parity congruency when both split and parity are at play simultaneously. Specifically, in non-retrieval arithmetic verification tasks, parity is modulated in cases where a direct judgment cannot be reached simply by depending on the split information.