ERPs across arithmetic operations in a delayed answer verification task

Temporal-spatial deciphering mental subtraction in the human brain

Mental subtraction, involving numerical processing and operation, requires a complex interplay among several brain regions. Diverse studies have utilized scalp electroencephalograph, electrocorticogram, or functional magnetic resonance imaging to resolve the structure pattern and functional activity during subtraction operation. However, a high resolution of the spatial-temporal understanding of the neural mechanisms involved in mental subtraction is unavailable. Thus, this study obtained intracranial stereoelectroencephalography recordings from 20 patients with pharmacologically resistant epilepsy. Specifically, two sample-delayed mismatch paradigms of numeric comparison and subtracting results comparison were used to help reveal the time frame of mental subtraction. The brain sub-regions were chronologically screened using the stereoelectroencephalography recording for mental subtraction. The results indicated that the anterior cortex, containing the frontal, insular, and parahippocampous, worked for preparing for mental subtraction; moreover, the posterior cortex, such as parietal, occipital, limbic, and temporal regions, cooperated during subtraction. Especially, the gamma band activities in core regions within the parietal-cingulate-temporal cortices mediated the critical mental subtraction. Overall, this research is the first to describe the spatiotemporal activities underlying mental subtraction in the human brain. It provides a comprehensive insight into the cognitive control activity underlying mental arithmetic.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09937-z.

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.

Comparing Clinically Applicable Behavioral and Electrophysiological Measures of Speech Detection, Discrimination, and Comprehension

Effective communication requires good speech perception abilities. Speech perception can be assessed with behavioral and electrophysiological methods. Relating these two types of measures to each other can provide a basis for new clinical tests. In audiological practice, speech detection and discrimination are routinely assessed, whereas comprehension-related aspects are ignored. The current study compared behavioral and electrophysiological measures of speech detection, discrimination, and comprehension. Thirty young normal-hearing native Danish speakers participated. All measurements were carried out with digits and stationary speech-shaped noise as the stimuli. The behavioral measures included speech detection thresholds (SDTs), speech recognition thresholds (SRTs), and speech comprehension scores (i.e., response times). For the electrophysiological measures, multichannel electroencephalography (EEG) recordings were performed. N100 and P300 responses were evoked using an active auditory oddball paradigm. N400 and Late Positive Complex (LPC) responses were evoked using a paradigm based on congruent and incongruent digit triplets, with the digits presented either all acoustically or first visually (digits 1-2) and then acoustically (digit 3). While no correlations between the SDTs and SRTs and the N100 and P300 responses were found, the response times were correlated with the EEG responses to the congruent and incongruent triplets. Furthermore, significant differences between the response times (but not EEG responses) obtained with auditory and visual-then-auditory stimulus presentation were observed. This pattern of results could reflect a faster recall mechanism when the first two digits are presented visually rather than acoustically. The visual-then-auditory condition may facilitate the assessment of comprehension-related processes in hard-of-hearing individuals.

Bridging the environment and neurodevelopment for children's health: Associations between real-time air pollutant exposures and cognitive outcomes

Research suggests that children's exposure to pollutants may impact their neurocognitive development. While researchers have found associations between air pollutants and cognitive development, these associations remain underspecified. Further, these exposures occur in the context of the built environment and may be exacerbated by local social vulnerability; in this context, individuals may experience a suite of socioenvironmental stressors that lead to increased cumulative risk exposure. In this pilot study, we tested whether real-time-measured personal exposure to PM2.5 relates to children's executive function and mathematical skills, outcomes that may predict later mathematical performance, general academic performance and even employment outcomes. We recruited 30 families to participate in two rounds in Winter 2020 and Summer 2021. We collected children's demographic data, as well as data about their living environment. In each round, children carried a small device that collected real-time ambient air pollution data for 3 days; parents logged their children's activities each day. On the last day, children completed cognitive assessments indexing their working memory (n-back), inhibitory control (Go/No-Go), nonsymbolic math skills (dot comparison), and arithmetic skills (equation verification). Overall, 29 participants had pollutant readings from both rounds, and 21 had a full dataset. Nonparametric statistical analysis revealed no significant differences in ambient air pollution and cognitive performance over time, Spearman's rho correlation assessment found that PM2.5 was not significantly correlated with cognitive outcomes in R1 and R2. However, the correlations suggested that an increase in PM2.5 was associated with worse working memory, inhibitory control, nonsymbolic skills, and arithmetic skills, at least in R1. We used each participant's zip code-aggregated Social Vulnerability Index, which range from 0 to 1, with higher numbers indicating more social vulnerability. Wilcoxon Rank-Sum tests indicated that participants living in higher SVI zip codes (≥0.70; n = 15) were not significantly different from those living in lower SVI zip codes (<0.70; n = 14), in terms of their PM2.5 exposures and cognitive performance in each round. We also found that socioeconomic characteristics mattered, such that children whose parent (s) had at least a Master's degree or earned more than $100,000 a year had lower PM2.5 exposures than children in the other end.

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.

Reevaluating the Language of Learning Advantage in Bilingual Arithmetic: An ERP Study on Spoken Multiplication Verification

Many studies of bilingual arithmetic report better performance when verifying arithmetic facts in the language of learning (LA+) over the other language (LA−). This could be due to language-specific memory representations, processes established during learning, or to language and task factors not related to math. The current study builds on a small number of event-related potential (ERP) studies to test this question while controlling language proficiency and eliminating potential task confounds. Adults proficient in two languages verified single-digit multiplications presented as spoken number words in LA+ and LA−, separately. ERPs and correctness judgments were measured from solution onset. Equivalent P300 effects, with larger positive amplitude for correct than incorrect solutions, were observed in both languages (Experiment 1A), even when stimuli presentation rate was shortened to increase difficulty (Experiment 1B). This effect paralleled the arithmetic correctness effect for trials presented as all digits (e.g., 2 4 8 versus 2 4 10), reflecting efficient categorization of the solutions, and was distinct from an N400 generated in a word–picture matching task, reflecting meaning processing (Experiment 2). The findings reveal that the language effects on arithmetic are likely driven by language and task factors rather than differences in memory representation in each language.

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.

The dynamic monitoring and control mechanism in problem solving: Evidence from theta and alpha oscillations

Although both originality and value are considered necessary criteria to identify creative ideas, little is known about how original and valuable ideas are generated in the human brain. To reveal how people monitor and control ongoing processing in the pursuit of original and valuable ideas, high-density electroencephalography (EEG) was used to record electrophysiological signals when participants were performing chunk decomposition tasks via novel-appropriate, novel-inappropriate, ordinary-appropriate and ordinary-inappropriate pathways. The results showed that approximately 100 ms after the problem was presented, novel pathways showed increased theta synchronization in the frontal sites compared to ordinary pathways. Novel pathways were associated with increased alpha desynchronization over the entire brain scale. These theta and alpha oscillations likely indicated rapid monitoring and effective control of novel processing in thinking. In the latter stages of problem solving, particularly during the 2000-2600-ms intervals, increased theta synchronization with decreased alpha desynchronization was found between novel-inappropriate and novel-appropriate pathways, which likely indicated slow monitoring and less control of inappropriate processing in novel thinking. The findings demonstrated the dynamic monitoring and control mechanism in the pursuit of original and valuable ideas.

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.

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.

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.

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.

Hemispheric asymmetries in processing numerical meaning in arithmetic

Hemispheric asymmetries in arithmetic have been hypothesized based on neuropsychological, developmental, and neuroimaging work. However, it has been challenging to separate asymmetries related to arithmetic specifically, from those associated general cognitive or linguistic processes. Here we attempt to experimentally isolate the processing of numerical meaning in arithmetic problems from language and memory retrieval by employing novel non-symbolic addition problems, where participants estimated the sum of two dot arrays and judged whether a probe dot array was the correct sum of the first two arrays. Furthermore, we experimentally manipulated which hemisphere receive the probe array first using a visual half-field paradigm while recording event-related potentials (ERP). We find that neural sensitivity to numerical meaning in arithmetic arises under left but not right visual field presentation during early and middle portions of the late positive complex (LPC, 400-800 ms). Furthermore, we find that subsequent accuracy for judgements of whether the probe is the correct sum is better under right visual field presentation than left, suggesting a left hemisphere advantage for integrating information for categorization or decision making related to arithmetic. Finally, neural signatures of operational momentum, or differential sensitivity to whether the probe was greater or less than the sum, occurred at a later portion of the LPC (800-1000 ms) and regardless of visual field of presentation, suggesting a temporal and functional dissociation between magnitude and ordinal processing in arithmetic. Together these results provide novel evidence for differences in timing and hemispheric lateralization for several cognitive processes involved in arithmetic thinking.

Bilingual children access multiplication facts from semantic memory equivalently across languages: Evidence from the N400

Typically, bilinguals learn multiplication facts in only one instruction language. Consequently, these facts may be represented and/or accessed as language-specific memories, requiring a qualitatively different retrieval process in their other language. Indeed, behavioral studies reveal that bilinguals verify arithmetic facts faster and better in the language of learning. Here, event-related potentials (ERPs) were used as a window into the neurocognitive processes underlying this language bias in children. ERPs were recorded while bilingual children verified the correctness of multiplication solutions. Operands were presented as spoken number words in Spanish and English, separately. Although a language bias was revealed in behavior, both languages elicited the same ERP correctness effect, an N400, reflecting similar cognitive processes in both languages. This suggests that the source of the behavioral difference is not at the level of semantic access. Our findings highlight the flexibility of the bilingual brain, especially when both languages are learned early.

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.

Neuroplasticity, bilingualism, and mental mathematics: A behavior-MEG study

Bilingual experience alters brain structure and enhances certain cognitive functions. Bilingualism can also affect mathematical processing. Reduced accuracy is commonly reported when arithmetic problems are presented in bilinguals' second (L2) vs. first (L1) language. We used MEG brain imaging during mental addition to characterize spatiotemporal dynamics during mental addition in bilingual adults. Numbers were presented auditorally and sequentially in bilinguals' L1 and L2, and brain and behavioral data were collected simultaneously. Behaviorally, bilinguals showed lower accuracy for two-digit addition in L2 compared to L1. Brain data showed stronger response magnitude in L2 versus L1 prior to calculation, especially when two-digit numbers were involved. Brain and behavioral data were significantly correlated. Taken together, our results suggest that differences between languages emerge prior to mathematical calculation, with implications for the role of language in mathematics.

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.

Do we access meaning when we name Arabic digits? Electrophysiological evidence

In this study, we evaluated whether the naming of Arabic digits required access to semantic information. Participants named pictures and Arabic digits blocked by category or intermixed with exemplars of other categories while behavioural and electrophysiological measures were gathered. Pictures were named slower and Arabic digits faster in the blocked context relative to the mixed context. Around 350-450 ms after the presentation of pictures and Arabic digits, brain waves were more positive in anterior regions and more negative in posterior regions when the blocked context was compared with the mixed context. The pattern of electrophysiological results suggests that pictures and Arabic digits are both processed semantically and they are subject to repetition effects during the naming task.

The Influence of Gain and Loss on Arithmetic Performance

Gain and loss modulation of different aspects of executive functions (EF) has been studied under changing conditions. However, the nature of this effect varies in different EF tasks, as both gain and loss were found to improve performance in specific EF tasks while hindering performance in others. The current study examines the influence of gain and loss stimuli on arithmetic performance. Since arithmetic processes have been found to rely heavily on EF, the current study addresses the question of "whether" and "in what direction" those stimuli might affect arithmetic performance. In three experiments, participants preformed an arithmetic equation judgment task, while gain and loss conditions were added in each trial in the form of a line drawn face representing either monetary gain, loss, or neither. In Experiment 1, the arithmetic task included carry and non-carry equations representing different arithmetic complexity levels. In Experiment 2, two and three addend equations were used, and in Experiment 3, the proportions of correct and incorrect equations differed. Results of all experiments demonstrated faster RT in the arithmetic task after gain stimuli when compared to the loss stimuli. Our results further extend our understanding regarding the nature of the relationship between gain and loss situations and arithmetic performance and further emphasize the conditions under which arithmetic performance can be improved or hindered.

The language of arithmetic across the hemispheres: An event-related potential investigation

Arithmetic expressions, like verbal sentences, incrementally lead readers to anticipate potential appropriate completions. Existing work in the language domain has helped us understand how the two hemispheres differently participate in and contribute to the cognitive process of sentence reading, but comparatively little work has been done with mathematical equation processing. In this study, we address this gap by examining the ERP response to provided answers to simple multiplication problems, which varied both in levels of correctness (given an equation context) and in visual field of presentation (joint attention in central presentation, or biased processing to the left or right hemisphere through contralateral visual field presentation). When answers were presented to any of the visual fields (hemispheres), there was an effect of correctness prior to the traditional N400 timewindow, which we interpret as a P300 in response to a detected target item (the correct answer). In addition to this response, equation answers also elicited a late positive complex (LPC) for incorrect answers. Notably, this LPC effect was most prominent in the left visual field (right hemisphere), and it was also sensitive to the confusability of the wrong answer - incorrect answers that were closely related to the correct answer elicited a smaller LPC. This suggests a special, prolonged role for the right hemisphere during answer evaluation.

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.

The influence of cardiorespiratory fitness on strategic, behavioral, and electrophysiological indices of arithmetic cognition in preadolescent children

The current study investigated the influence of cardiorespiratory fitness on arithmetic cognition in forty 9-10 year old children. Measures included a standardized mathematics achievement test to assess conceptual and computational knowledge, self-reported strategy selection, and an experimental arithmetic verification task (including small and large addition problems), which afforded the measurement of event-related brain potentials (ERPs). No differences in math achievement were observed as a function of fitness level, but all children performed better on math concepts relative to math computation. Higher fit children reported using retrieval more often to solve large arithmetic problems, relative to lower fit children. During the arithmetic verification task, higher fit children exhibited superior performance for large problems, as evidenced by greater d' scores, while all children exhibited decreased accuracy and longer reaction time for large relative to small problems, and incorrect relative to correct solutions. On the electrophysiological level, modulations of early (P1, N170) and late ERP components (P3, N400) were observed as a function of problem size and solution correctness. Higher fit children exhibited selective modulations for N170, P3, and N400 amplitude relative to lower fit children, suggesting that fitness influences symbolic encoding, attentional resource allocation and semantic processing during arithmetic tasks. The current study contributes to the fitness-cognition literature by demonstrating that the benefits of cardiorespiratory fitness extend to arithmetic cognition, which has important implications for the educational environment and the context of learning.

Brain systems involved in arithmetic with positive versus negative numbers

Positive number arithmetic is based on combining and separating sets of items, with systematic differences in brain activity in specific regions depending on operation. In contrast, arithmetic with negative numbers involves manipulating abstract values worth less than zero, possibly involving different operation-activity relationships in these regions. Use of procedural arithmetic knowledge, including transformative rules like "minus a negative is plus a positive," may also differ by operand sign. Here, we examined whether the activity evoked in negative number arithmetic was similar to that seen in positive problems, using region of interest analyses (ROIs) to examine a specific set of brain regions. Negative-operand problems demonstrated a positive-like effect of operation in the inferior parietal lobule with more activity for subtraction than addition, as well as increased activity across operation. Interestingly, while positive-operand problems demonstrated the expected addition > subtraction activity difference in the angular gyrus, negative problems showed a reversed effect, with relatively more activity for subtraction than addition. Negative subtraction problems may be understood after translation to addition via rule, thereby invoking more addition-like activity. Whole-brain analyses showed increased right caudate activity for negative-operand problems across operation, indicating a possible overall increase in usage of procedural rules. Arithmetic with negative numbers may thus shows some operation-activity relationships similar to positive numbers, but may also be affected by strategy. This study examines the flexibility of the mental number system by exploring to what degree the processing of an applied usage of a difficult, abstract mathematical concept is similar to that for positive numbers.