Access to numerical information is dependent on the modality of stimulus presentation in mental addition: a combined ERP and behavioral study

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

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

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.

How numerical surface forms affect strategy execution in subtraction? Evidence from behavioral and ERP measures

In this study, to investigate the influence of numerical surface forms on strategy execution in subtraction and addition, 25 college students were required to perform a mental arithmetic task. Behavioral and electroencephalography responses were recorded to explore the stages of strategy execution. Arithmetic problems were presented within 11-20 by Arabic, Chinese and English numerals, respectively. The results showed that, compared with Arabic and Chinese numerals, participants had longer RTs under the condition of English numerals. English numerals induced stronger N100, P200 and P300 amplitudes, and longer latency in P200 and P300 amplitudes than in other conditions. These findings indicated that numerical surface forms affected the execution of mental arithmetic strategies, with Chinese and English numerals being processed deeper in the brain. Especially, the English digital word form occupied more psychological resources, and it was activated more in the frontal area and the parietal area, which would obviously hinder the processing of arithmetic information.

Neural Dissociations between Magnitude Processing of Fractions and Decimals

Fraction and decimal magnitude processing are crucial for mathematic achievement. Previous neuroimaging results showed that fraction and decimal processing activated both overlapping and distinct neural substrates, but temporal dissociations between fraction and decimal processing remained unknown. This event-related potential (ERP) study explored differences in neural activities between magnitude processing of fractions and decimals, by examining the notation effect (fraction vs. decimal) and distance effect (far vs. close) on early components of P1/N1, P2 and N2. Results showed that decimals elicited larger N1 and smaller P1 than fractions at the parietal region. Fractions demonstrated the significant distance effect on fronto-central P2 while decimals showed the distance effect on left anterior N2. ERP results reflect distinct processing of identification and semantic access stages between fractions and decimals. Identification is located at the visual-related region with enhanced perception acuity and identification efficiency for decimals. Semantic access activates the fronto-central region associated with elaborative magnitude manipulation for fractions, while semantic access reflects automatic phonological retrieval for decimals. Our findings disintegrate the magnitude processing of fractions and decimals from identification to magnitude processing. It reveals that temporal discrepancies between fraction and decimal magnitude processing appear as early as post-stimulus 100 ms.

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.

Implicit happy and fear experience contributes to computational estimation strategy execution: Behavioral and neurophysiological evidence

Previous study have explored the influence of explicit emotion priming on computational estimation strategy execution, but the corresponding influence of implicit emotion priming still remains unknown. The present study aimed to solve this problem. Participants were asked to complete two-digit multiplication computational estimation task, under different implicit emotion priming conditions (gender judgment task). In the two-digit multiplication computational estimation task, the computational estimation question was presented in the middle of the screen, meanwhile, two alternative answers were presented side by side at the bottom of the screen, participants were required to select which answer is correct, by using the down-up strategy (e.g., doing 30 × 50 = 1500 for 34 × 46). Behavioral results showed that the response speed under implicit happy and fear (vs. neutral and angry) priming conditions was quicker, and the accuracy under different priming conditions showed no significant difference. The ERP results showed that the influence of implicit emotion priming on computational estimation strategy execution consisted of two phases: in the first phase, the N1 amplitudes elicited by completing the multiplication computational estimation task were smaller under implicit fear (vs. angry) priming condition; in the second phase, the corresponding P2 amplitudes under implicit happy (vs. fear) priming condition were smaller. The present study indicated that implicit happy and fear experience contributed to complete computational estimation tasks, suggesting that implicit negative emotional (e.g., fear) experience was not always detrimental to computational estimation strategy execution.

Neural Correlate Differences in Number Sense Between Children With Low and Middle/High Socioeconomic Status

Although some cognitive studies provided reasons that children with low socioeconomic status (SES) showed poor mathematical achievements, there was no explicit evidence to directly explain the root of lagged performance in children with low SES. Therefore, the present study explored the differences in neural correlates in the process of symbolic magnitude comparison between children with different SESs by the event-related potentials (ERPs). A total of 16 second-graders from low-SES families and 16 from middle/high-SES families participated in this study. According to the results of anterior N1 (early attention) and P2 (extraction of numerical meaning) over the frontal region, the differences among children with different SESs were manifested as differences in general neural activities in terms of attention and top-down cognitive control. In the late stage of cognitive processing, there was no significant difference in the average amplitude of the late positive component (LPC) between children with different SES, indicating that low SES did not influence the information encoding and memory updating of numerical representation, which was responsible by the parietal lobe. The educational implications of this study are mentioned in the discussion.

The influence of the location of ordered symbols on the ordinal position effect: The involvement of the task performed

Since the ordinal position effect was identified, several studies have investigated its mechanism in various contexts; however, how the space location of ordinal symbols influences this effect remains unclear. Thus, the present study explored Chinese words representing the day before yesterday, yesterday, tomorrow, and the day after tomorrow as ordinal symbols to investigate how the stimulus space location influences the ordinal position effect across different task contexts. We randomly and equally presented days on the left or right location of a display and asked participants to perform a stimulus space location, a stimulus colour and a stimulus order classification task in three consecutive experiments, respectively. The results revealed that the spatial stimulus-response compatibility effect and Simon effect prevailed in the stimulus space location and colour classification task. Conversely, the ordinal position effect prevailed in the stimulus order classification task. These results suggested that (1) the spatial stimulus-response compatibility effect (or Simon effect) and the ordinal position effect cannot appear simultaneously in some experimental contexts and that (2) the task context predicted which of these effects prevailed. From these results, we conclude that the ordinal symbols could be coded depending on multiple reference frames, including spatial and non-spatial reference frame, and the use of the reference frame was mediated by the task context.

Working memory predictors of written mathematics in 7- to 8-year-old children

There is extensive evidence for the involvement of working memory in mathematical attainment. This study aims to identify the relative contributions of verbal, spatial-simultaneous, and spatial-sequential working memory measures in written mathematics. Year 3 children (7-8 years of age, n = 214) in the United Kingdom were administered a battery of working memory tasks alongside a standardised test of mathematics. Confirmatory factor analyses and variance partitioning were then performed on the data to identify the unique variance accounted for by verbal, spatial-simultaneous, and spatial-sequential measures. Results revealed the largest individual contribution was that of verbal working memory, followed by spatial-simultaneous factors. This suggests the components of working memory underpinning mathematical performance at this age are those concerning verbal-numeric and spatial-simultaneous working memory. Implications for educators and further research are discussed.

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.

The Mechanism of the Ordinal Position Effect: Stability Across Sense Modalities and the Hands Crossed Context

The ordinal position effect posits that items positioned earlier in an ordinal sequence are responded to faster with the left key than the right key, and items positioned later in an ordinal sequence are responded to faster with the right key than the left key. Although the mechanism of the ordinal position effect has been investigated in many studies, it is unclear whether the ordinal position effect can extend to the auditory modality and the hands crossed context. Therefore, the present study employed days as the order information to investigate this question. Days were visually or acoustically displayed on a screen in random order, and participants were instructed to judge whether the probe day they perceived was before or after the current day (days-relevant task) or to identify the color or voice of the probe day they perceived (days-irrelevant task). The results indicate the following: (a) The days before the current day were responded to faster with the left key than the right key, and the days after the current day were responded to faster with the right key than the left key, both when the days-relevant task and the days-irrelevant task were performed, regardless of the sense modality. (b) The ordinal position effect for judgments of days was also obtained in the auditory modality even when the hands were crossed. These results indicate that the ordinal position effect can extend to the auditory modality and the hands crossed context, similar to the spatial-numerical association of response codes effect of numbers.

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.

Distinct neural mechanisms for reading Arabic vs. verbal numbers: An ERP study

In this electroencephalogram/event-related potential (EEG/ERP) study, 16 volunteers were asked to compare the numerical equality of 360 pairs of multidigit numbers presented in Arabic or verbal format. Behavioural data showed faster and more accurate responses for digit targets, with a right hand/left hemisphere advantage only for verbal numerals. Occipito-temporal N1, peaking at approximately 180 ms, was strongly left-lateralized during verbal number processing and bilateral during digit processing. A LORETA (low-resolution electromagnetic tomography) source reconstruction performed at the N1 latency stage (155-185 ms) revealed greater brain activation during coding of Arabic than of verbal stimuli. Digit perceptual coding was associated with the activation of the right angular gyrus (rAG), the left fusiform gyrus (FG,BA37), and left and right superior and medial frontal areas. N1 sources for verbal numerals included the left FG (BA37), the precuneus (BA31), the parahippocampal area and a small right prefrontal activation. In addition, verbal numerals elicited a late frontocentral negativity, possibly reflecting stimulus unfamiliarity or complexity. Overall, the data suggest distinct mechanisms for number reading through ciphers (digits) or words. Information about quantity was accessed earlier and more accurately if numbers were in a nonlinguistic code. Indeed, it can be speculated that numerosity processing would involve circuits originally involved in processing space (i.e., rAG/rIPS).

Frontal Cortex Supports the Early Structuring of Multiple Solution Steps in Symbolic Problem-solving

problem-solving relies on a sequence of cognitive steps involving phases of task encoding, the structuring of solution steps, and their execution. On the neural level, metabolic neuroimaging studies have associated a frontal-parietal network with various aspects of executive control during numerical and nonnumerical problem-solving. We used EEG-MEG to assess whether frontal cortex contributes specifically to the early structuring of multiple solution steps. Basic multiplication ("3 × 4" vs. "3 × 24") was compared with an arithmetic sequence rule ("first add the two digits, then multiply the sum with the smaller digit") on two complexity levels. This allowed dissociating demands of early solution step structuring from early task encoding demands. Structuring demands were high for conditions that required multiple steps, that is, complex multiplication and the two arithmetic sequence conditions, but low for easy multiplication that mostly relied on direct memory retrieval. Increased right frontal activation in time windows between 300 and 450 msec was observed only for conditions that required multiple solution steps. General task encoding demands, operationalized by problem size (one-digit vs. two-digit numbers), did not predict these early frontal effects. In contrast, parietal effects occurred as a function of problem size irrespectively of structuring demands in early phases of task encoding between 100 and 300 msec. We here propose that frontal cortex subserves domain-general processes of problem-solving, such as the structuring of multiple solution steps, whereas parietal cortex supports number-specific early encoding processes that vary as a function of problem size.

Arithmetic Memory Is Modality Specific

In regards to numerical cognition and working memory, it is an open question as to whether numbers are stored into and retrieved from a central abstract representation or from separate notation-specific representations. This study seeks to help answer this by utilizing the numeral modality effect (NME) in three experiments to explore how numbers are processed by the human brain. The participants were presented with numbers (1–9) as either Arabic digits or written number words (Arabic digits and dot matrices in Experiment 2) at the first (S1) and second (S2) stimuli. The participant’s task was to add the first two stimuli together and verify whether the answer (S3), presented simultaneously with S2, was correct. We hypothesized that if reaction time (RT) at S2/S3 depends on the modality of S1 then numbers are retrieved from modality specific memory stores. Indeed, RT depended on the modality of S1 whenever S2 was an Arabic digit which argues against the concept of numbers being stored and retrieved from a central, abstract representation.

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.

Conceptual Integration of Arithmetic Operations With Real-World Knowledge: Evidence From Event-Related Potentials

Research on language processing has shown that the disruption of conceptual integration gives rise to specific patterns of event-related brain potentials (ERPs)-N400 and P600 effects. Here, we report similar ERP effects when adults performed cross-domain conceptual integration of analogous semantic and mathematical relations. In a problem-solving task, when participants generated labeled answers to semantically aligned and misaligned arithmetic problems (e.g., 6 roses + 2 tulips = ? vs. 6 roses + 2 vases = ?), the second object label in misaligned problems yielded an N400 effect for addition (but not division) problems. In a verification task, when participants judged arithmetically correct but semantically misaligned problem sentences to be "unacceptable," the second object label in misaligned sentences elicited a P600 effect. Thus, depending on task constraints, misaligned problems can show either of two ERP signatures of conceptual disruption. These results show that well-educated adults can integrate mathematical and semantic relations on the rapid timescale of within-domain ERP effects by a process akin to analogical mapping.

Neural adaptation to non-symbolic number and visual shape: an electrophysiological study

Several studies assumed that the analysis of numerical information happens in a fast and automatic manner in the human brain. Utilizing the high temporal resolution of electroencephalography (EEG) in a passive oddball adaptation paradigm, we compared event-related brain potentials (ERPs) evoked by unattended shape changes and unattended numerosity changes. We controlled visual stimulus properties in a stringent manner. Unattended changes in shape elicited significant, gradual adaptation effects in the range of early visual components, indicating the fast and automatic processing of shapes. Changes in numerosity did not elicit significant changes in these early ERP components. The lack of early number-specific effects was qualified by a significant interaction between Shape and Number conditions. Number change elicited gradual ERP effects only on late ERP components. We conclude that numerosity is a higher-level property assembled from naturally correlating perceptual cues and hence, it is identified later in the cognitive processing stream.

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.

Toward a mental arithmetic process in risky choices

Mainstream theories about decision-making under risk suggest that risky decisions are made by choosing the option that offers the highest mathematical expectation. The present event-related potentials (ERPs) study investigated the neurocognitive mechanisms underlying risky choice by contrasting a preferential choice task with an expected value choice task. The ERP data revealed that (1) the computational difficulty, which would be expected to influence a compensatory process, affected the slow wave only when participants were forced to choose the option with the highest expectation; and that (2) the difference in the minimum outcome dimension between two options, which would be expected to be influential in a heuristic process, affected the P300 and slow wave when participants were asked to choose the preferred option. Our findings provide neural evidence that preferential choice is not based on an expectation computation and thus raised the question of whether expectation theories can provide an adequate description of individual risky decisions.

An ERP study of the processing of common and decimal fractions: how different they are

This study explored event-related potential (ERP) correlates of common fractions (1/5) and decimal fractions (0.2). Thirteen subjects performed a numerical magnitude matching task under two conditions. In the common fraction condition, a nonsymbolic fraction was asked to be judged whether its magnitude matched the magnitude of a common fraction; in the decimal fraction condition, a nonsymbolic fraction was asked to be matched with a decimal fraction. Behavioral results showed significant main effects of condition and numerical distance, but no significant interaction of condition and numerical distance. Electrophysiological data showed that when nonsymbolic fractions were compared to common fractions, they displayed larger N1 and P3 amplitudes than when they were compared to decimal fractions. This finding suggested that the visual identification for nonsymbolic fractions was different under the two conditions, which was not due to perceptual differences but to task demands. For symbolic fractions, the condition effect was observed in the N1 and P3 components, revealing stimulus-specific visual identification processing. The effect of numerical distance as an index of numerical magnitude representation was observed in the P2, N3 and P3 components under the two conditions. However, the topography of the distance effect was different under the two conditions, suggesting stimulus specific semantic processing of common fractions and decimal fractions.

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.

Is order the defining feature of magnitude representation? An ERP study on learning numerical magnitude and spatial order of artificial symbols

Using an artificial-number learning paradigm and the ERP technique, the present study investigated neural mechanisms involved in the learning of magnitude and spatial order. 54 college students were divided into 2 groups matched in age, gender, and school major. One group was asked to learn the associations between magnitude (dot patterns) and the meaningless Gibson symbols, and the other group learned the associations between spatial order (horizontal positions on the screen) and the same set of symbols. Results revealed differentiated neural mechanisms underlying the learning processes of symbolic magnitude and spatial order. Compared to magnitude learning, spatial-order learning showed a later and reversed distance effect. Furthermore, an analysis of the order-priming effect showed that order was not inherent to the learning of magnitude. Results of this study showed a dissociation between magnitude and order, which supports the numerosity code hypothesis of mental representations of magnitude.

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.

The Influence of verbalization on the pattern of cortical activation during mental arithmetic

Background

The aim of the present functional magnetic resonance imaging (fMRI) study at 3 T was to investigate the influence of the verbal-visual cognitive style on cerebral activation patterns during mental arithmetic. In the domain of arithmetic, a visual style might for example mean to visualize numbers and (intermediate) results, and a verbal style might mean, that numbers and (intermediate) results are verbally repeated. In this study, we investigated, first, whether verbalizers show activations in areas for language processing, and whether visualizers show activations in areas for visual processing during mental arithmetic. Some researchers have proposed that the left and right intraparietal sulcus (IPS), and the left angular gyrus (AG), two areas involved in number processing, show some domain or modality specificity. That is, verbal for the left AG, and visual for the left and right IPS. We investigated, second, whether the activation in these areas implied in number processing depended on an individual's cognitive style.

Methods

42 young healthy adults participated in the fMRI study. The study comprised two functional sessions. In the first session, subtraction and multiplication problems were presented in an event-related design, and in the second functional session, multiplications were presented in two formats, as Arabic numerals and as written number words, in an event-related design. The individual's habitual use of visualization and verbalization during mental arithmetic was assessed by a short self-report assessment.

Results

We observed in both functional sessions that the use of verbalization predicts activation in brain areas associated with language (supramarginal gyrus) and auditory processing (Heschl's gyrus, Rolandic operculum). However, we found no modulation of activation in the left AG as a function of verbalization.

Conclusions

Our results confirm that strong verbalizers use mental speech as a form of mental imagination more strongly than weak verbalizers. Moreover, our results suggest that the left AG has no specific affinity to the verbal domain and subserves number processing in a modality-general way.

The time course of symbolic number adaptation: oscillatory EEG activity and event-related potential analysis

Several functional magnetic resonance imaging (fMRI) studies have used neural adaptation paradigms to detect anatomical locations of brain activity related to number processing. However, currently not much is known about the temporal structure of number adaptation. In the present study, we used electroencephalography (EEG) to elucidate the time course of neural events in symbolic number adaptation. The numerical distance of deviants relative to standards was manipulated. In order to avoid perceptual confounds, all levels of deviants consisted of perceptually identical stimuli. Multiple successive numerical distance effects were detected in event-related potentials (ERPs). Analysis of oscillatory activity further showed at least two distinct stages of neural processes involved in the automatic analysis of numerical magnitude, with the earlier effect emerging at around 200ms and the later effect appearing at around 400ms. The findings support for the hypothesis that numerical magnitude processing involves a succession of cognitive events.

Arithmetic mismatch negativity and numerical magnitude processing in number matching

Background

This study examined the relationship of the arithmetic mismatch negativity (AMN) and the semantic evaluation of numerical magnitude. The first question was whether the AMN was sensitive to the incongruity in numerical information per se, or rather, to the violation of strategic expectations. The second question was whether the numerical distance effect could appear independently of the AMN. Event-related potentials (ERPs) were recorded while participants decided whether two digits were matching or non-matching in terms of physical similarity.

Results

The AMN was enhanced in matching trials presented infrequently relative to non-matching trials presented frequently. The numerical distance effect was found over posterior sites during a 92 ms long interval (236-328 ms) but appeared independently of the AMN.

Conclusions

It was not the incongruity in numerical information per se, but rather, the violation of strategic expectations that elicited the AMN. The numerical distance effect might only temporally coincide with the AMN and did not form an inherent part of it.

Neurophysiological markers of retrieval-induced forgetting in multiplication fact retrieval

Event-related potential (ERP) counterparts of practice effects in multiplication fact retrieval were examined. Participants performed a multiplication verification task after having practiced a specific problem set. Practice was either active (retrieval of solutions to multiplication problems) or passive (reexposure to the same operands plus the correct result). Behavioral data showed retrieval-induced facilitation for practiced items and retrieval-induced forgetting for related, unpracticed items, irrespective of practice type. ERPs revealed that, for the active practice group, forgetting was reflected in a reduced N100 component time-locked to result onset. Irrespective of practice type, forgetting was also reflected in a reduced result-locked P350 component, whereas facilitation was associated with an increased amplitude of the same component. These results suggest that beneficial and detrimental effects of practice may be mediated by partially distinct processes.

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

The present study examined developmental differences in event-related potentials between second graders and adults in arithmetic. Consistent with previous literature in adults, multiplication for both children and adults produced a greater left anterior negativity from 400 to 900 msec, whereas addition produced a greater right posterior negativity from 400 to 900 msec. Adults showed larger left anterior negativities in the time window suggesting that adults rely more than children on a verbal processing system for solving these problems. Children showed larger right posterior negativities in the time window suggesting that they rely more on quantitative manipulation for solving these problems.

Beyond format-specificity: Is analogue magnitude really the core abstract feature of the cultural number representation?

The issue of abstractness raises two distinct questions. First, is there a format-independent magnitude representation? Second, does analogue magnitude really play a crucial role in the development of human mathematics? We suggest that neither developmental nor cultural studies support this notion. The field needs to redefine the properties of the core number representation as used in human arithmetic.

Numerical abstractness and elementary arithmetic

Like number representation, basic arithmetic seems to be a natural candidate for abstract instantiation in the brain. To investigate this, researchers have examined effects of numeral format on elementary arithmetic (e.g., 4+5 vs. four+five). Different numeral formats often recruit distinct processes for arithmetic, reinforcing the conclusion that number processing is not necessarily abstracted away from numeral format.

Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm

In the numerical Stroop paradigm (NSP) participants compare simultaneously presented Arabic digits based on either their numerical or on their physical size dimension. Responses are faster when the numerical and size dimensions are congruent with each other (facilitation), and responses are slower when the numerical and size dimensions are incongruent with each other (interference). We aimed to find out whether facilitation and interference appears during the course of perceptual or response processing. To this end, facilitation and interference effects in the amplitude of event-related brain potentials (ERPs) were examined. The onset of motor preparation was determined by monitoring the lateralized readiness potential. In numerical comparison one facilitation effect was related to perceptual processing at the level of the magnitude representation. A second facilitation effect and interference effects appeared during response processing. In size comparison facilitation and interference appeared exclusively during response processing. In both tasks, ERP interference effects were probably related to contextual analysis and to the conflict monitoring and selection for action activity of the anterior cingulate cortex. The results demonstrate that facilitation and interference effects in the NSP appear during multiple stages of processing, and that they are related to different cognitive processes. Therefore these effects should be clearly separated in studies of the NSP. A model of the processes involved in the NSP is provided and implications for studies of the NSP are drawn.