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Processing of incongruous mental calculation problems: Evidence for an arithmetic N400 effect
Abstract
We investigated if incongruent solutions of simple multiplication problems would elicit similar event-related brain potentials as inappropriate words in sentences. In Experiment I, 12 subjects verified the appropriateness of solutions of multiplication problems or of final words in short sentences. Both incongruent solutions and incongruent words evoked a phasic negative shift between 300 and 500 ms having a similar topography. In Experiment II, we tested with another sample of 13 subjects if the amplitude of this arithmetic N400 effect was affected differently by different stimulus onset asynchronies (SOA = 200 and 500 ms) and by errors that were either table-related or table-unrelated to the preceding operands. Again, incorrect solutions elicited an arithmetic N400 effect whose amplitude depended on both the relatedness of the solution and the SOA. The ascending part of the N400 effect was always larger for unrelated than for related errors independently of the SOA, whereas the maximum of the N400 effect was larger for unrelated errors in case of a long SOA only. This pattern of effects was similar to that observed with semantic material varying lexical associations. These results suggest that arithmetic incongruencies are handled by the system in a manner functionally similar to that of semantic incongruencies.
... Event-related potentials (ERPs) have provided a window into the cognitive processes underlying multiplication verification in both monolinguals and bilinguals [4,6,14,15,[20][21][22][23][24][25]. ERPs are a measurement of the synchronized firing of cortical neurons with millisecond precision. ...
... When reading a sentence, for example, words that are expected based on preceding context will elicit greater activation in semantic memory, and in turn, smaller N400 amplitude than words that are not supported by context [35,37,38]. Under an N400 interpretation of the arithmetic effect, correct solutions are more facilitated in memory after reading the first two operands, and therefore elicit less N400 amplitude compared to incorrect solutions [23][24][25]. ...
... These studies with bilinguals address a broader body of literature that investigates the cognitive processes underlying multiplication verification in the adult brain. Niedeggen and colleagues were the first to report ERP measures from adults verifying simple multiplication problems [23,24]. In these studies, participants saw three consecutive Arabic numbers (digits) and judged if the third number was the correct product of the first two (e.g., 2 4 9). ...
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.
... Group differences were observed in the arithmetic N400 component, with children displaying a larger amplitude and longer latency with a greater spatial distribution than adults. There is general agreement that arithmetic facts are stored in semantic networks (Kutas and Hillyard, 1980), with N400 amplitude modulations attributed to the relatedness or memory representations associated with the problem and its possible solutions (Niedeggen et al., 1999). Thus, Prieto-Corona et al. (2010) concluded that children displayed greater cognitive effort in retrieving the solution from longterm memory than adults. ...
... Grand averaged ERPs showed positivity between 100 and 200 ms (P150 component), followed by a positivity between 200 and 400 ms (P300 component, Polich, 2007) on frontal regions and a negative wave between 300 and 500 ms on central parietal regions (arithmetic N400) (Niedeggen et al., 1999;Prieto-Corona et al., 2010;Zhou et al., 2011). We analyzed only the ERPs components with a more robust signal observed in both addition and subtraction regardless of group. ...
... We explored specific region of interest (ROIs) for each ERP component based on the topographical locations associated with these ERP components in previous literature (e.g., Niedeggen et al., 1999;Polich, 2007;Prieto-Corona et al., 2010;Zhou et al., 2011). For P150 and P300 components three ROIs were compared between weight groups: right frontal (sensors 3, 4, 117, 118, 122, 123, and 124), left frontal (sensors 19, 20, 23, 24, 27, 28, and 33), and fronto-central (sensors 5, 6, 10, 11, 12, 16, and 18); for the arithmetic N400 component we analyzed six anatomical regions: right central (sensors 87,93,103,104,105,110,and 111),left central (sensors 29,30,35,36,37,41,and 42),central (6,7,31,55,80,106,and Cz), right parietal (sensors 85, 86, 91, 92, 97, and 98), left parietal (sensors 47, 51, 52, 53, 59, and 60), centro-parietal (61, 62, 67, 72, 77, and 78) (see Figure 2). ...
Preadolescence is an important period for the consolidation of certain arithmetic facts, and the development of problem-solving strategies. Obese subjects seem to have poorer academic performance in math than their normal-weight peers, suggesting a negative effect of obesity on math skills in critical developmental periods. To test this hypothesis, event-related potentials (ERPs) were collected during a delayed-verification math task using simple addition and subtraction problems in obese [above 95th body mass index (BMI) percentile] and non-obese (between 5th and 90th BMI percentile) preteens with different levels of math skill; thirty-one with low math skills (14 obese, mean BMI = 26.40, 9.79 years old; 17 non-obese, BMI = 17.45, 9.76 years old) and thirty-one with high math skills (15 obese, BMI = 26.90, 9.60 years old; 16 non-obese, BMI = 17.13, 9.63 years old). No significant differences between weight groups were observed in task accuracy regardless of their mathematical skill level. For ERPs, electrophysiological differences were found only in the subtraction condition; participants with obesity showed an electrophysiologic pattern associated with a reduced ability to allocate attention resources regardless of their math skill level, these differences were characterized by longer P300 latency than their normal-weight peers. Moreover, the participants with obesity with high math skills displayed hypoactivity in left superior parietal lobule compared with their normal-weight peers. Additionally, obese preteens with low math skills displayed smaller arithmetic N400 amplitude than non-obese participants, reflecting difficulties in retrieving visual, semantic, and lexical information about numbers. We conclude that participants with obesity are less able than their normal-weight peers to deploy their attention regardless of their behavioral performance, which seems to have a greater effect on obese participants with low math skills because they also show problems in the retrieval of solutions from working memory, resulting in a delay in the development of mathematical skills.
... Generally, an N1 component can provide evidence for automatic and asemantic processing. Semantic processing of numerical information is thought to be reflected by the N400 ERP component (Niedeggen et al., 1999;Galfano et al., 2004;Szücs and Csépe, 2005;Paulsen and Neville, 2008;Szücs and Soltész, 2010;Pinhas et al., 2014). The N400 is a central negative component peaking at around 400 ms, generally known to be sensitive to semantic mismatch or unexpectedness (Kutas and Federmeier, 2011). ...
... It is important to note that the numerical N400 effect can be dissociated from earlier N2b effects of perceptual non-match: Increased negative amplitudes have been reported at central electrode sites around 300-400 ms for incorrect versus correct calculations in arithmetic verification (Niedeggen et al., 1999;Szücs and Soltész, 2010) as well as in implicit probe tasks (Galfano et al., 2009). In terms of polarity and topography, this numerical N400 effect is highly similar to the classical N400 effect, often considered to reflect Lexico-semantic processing (Szücs et al., 2007;Szücs and Soltész, 2010). ...
... Our finding of a more pronounced N400 for numerically non-identical than identical number pairs is in line with previous numerical cognition studies investigating the ERP correlates of semantic incongruencies (e.g., Niedeggen et al., 1999;Szücs et al., 2007: Szücs andSoltész, 2010;Pinhas et al., 2014). The finding of an N400 effect of numerical identity in the crossformat condition supports the hypothesis that number words and digits are only indirectly linked via their underlying numerical meaning, as proposed by semantic models of transcoding (e.g., Power and Dal Martello, 1990;McCloskey, 1992). ...
Converting visual-Arabic digits to auditory number words and vice versa is seemingly effortless for adults. However, it is still unclear whether this process takes place automatically and whether accessing the underlying magnitude representation is necessary during this process. In two event-related potential (ERP) experiments, adults were presented with identical (e.g., “one” and 1) or non-identical (e.g., “one” and 9) number pairs, either unimodally (two visual-Arabic digits) or cross-format (an auditory number word and a visual-Arabic digit). In Experiment 1 (N=17), active task demands required numerical judgments, whereas this was not the case in Experiment 2 (N=19). We found pronounced early ERP markers of numerical identity unimodally in both experiments. In the cross-format conditions, however, we only observed late neural correlates of identity and only if the task required semantic number processing (Experiment 1). These findings suggest that unimodal pairs of digits are automatically integrated, whereas cross-format integration of numerical information occurs more slowly and involves semantic access.
... Research using ERPs to study how arithmetic is processed has revealed robust brain responses to proposed solutions in both children and adults. This research has been dominated by studies that include adult populations Dickson and Federmeier, 2017;Jasinski and Coch, 2012;Jost et al., 2003;Martinez-Lincoln et al., 2015;Niedeggen et al., 1999;Núñez-Peña et al., 2006;Salillas and Wicha, 2012), with a smaller group of studies that have compared child and adult brain responses (Moore et al., 2014;Prieto-Corona et al., 2010;Xuan et al., 2007;Zhou et al., 2011). The methods used in these studies have varied, with some using verification tasks and others production, or different operations (addition vs multiplication, etc.). ...
... Seminal ERP studies with adults had similarly argued that arithmetic expressions elicit brain responses analogous to the N400 observed for words that vary in expectancy within a sentence context (Jost et al., 2003;Niedeggen et al., 1999). Initial research therefore implied that both children and adults construct meaning-level representations for simple multiplication problems. ...
... Critically, the timing of the N400 effects did not differ across tasks (390 ms for both), further supporting that both tasks elicited comparable N400 responses. Therefore, children appear to prepare meaning-level expectations in both tasks and respond to the solutions according to the semantic congruency of their continuation for each sequence of numbers (Jost et al., 2003;Niedeggen et al., 1999;Prieto-Corona et al., 2010). Like children, adults also exhibited an N400 effect in the word-picture task, with reduced N400 amplitude for contextually supported (match) trials. ...
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.
... В дальнейшем генерация компонента N400 была получена при самых разных исследованиях, включая обработку языка, объектов, лиц, действий и жестов, математическое распознавание, семантическую память и т.д. В частности, в 1999 г. был получен схожий с семантическим арифметический эффект N400 (N400 effect) [Niedeggen et al., 1999]. Авторы показали, что в случае появления неверных ответов, следующих за примерами умножения из однозначных чисел, возникает негативное отклонение в интервале от 300 до 500 мс, амплитуда пика которого больше в сравнении с амплитудой пика негативной волны на верные ответы. ...
... Для установки хлорсеребряных электродов была использована токопроводящая паста Ten 20 conductive, а также абразивная паста Nuprep для подготовки поверхности кожи перед установкой электрода, что обеспечивает низкое сопротивление контакта. Поскольку было показано, что эффект N400 максимально выражен в центро-париетальной области [Dehaene et al., 2003;Jost et al., 2004;Niedeggen et al., 1999], то регистрация вызванных потенциалов в нашем исследовании проводилась от следующих точек отведения: F z , C z , P z , С 3 , С 4 , P 3 , P 4 (в соответствии с системой 10-20 по H.H. Jasper, 1958). С целью контроля над движениями глаз выполнялась запись электроокулограммы (ЭОГ). ...
... По результатам первого этапа исследования было получено, что формирование эффекта N400 при неосознанном восприятии примеров на умножение в первом блоке первого этапа исследования не происходит. Во втором блоке с осознанным восприятием регистрируется арифметический эффект N400, что полностью соответствует данным, указанным в литературе [Jost et al., 2004;Niedeggen et al., 1999;Prieto-Corona et al., 2010]. В этих работах было показано, что арифметический эффект N400 был зарегистрирован в интервале от 250 мс до 500 мс и амплитуда арифметического компонента N400 была меньше на верные, чем на неверные ответы, что также подтверждается нашими данными. ...
The unconscious arithmetic calculations (single-digit multiplication) were studied. The masked
priming paradigm was applied. To test the possibility of unconscious arithmetic operations the
event related potentials method was used. The arithmetic N400 effect served as calculations correctness
criterion. The influence of training on the N400 component formation during stimuli unconscious
perception was revealed. The results of this study confirm the possibility of unconsciously
executing simple operations for multiplication. The N400 arithmetic effect can be used to study reflex
calculations at an unconscious level.
... In order to assess arithmetic processing during sleep, in the absence of overt behavior, we looked for neurophysiological correlates of mental arithmetic. In event-related potentials (ERPs), the presentation of incorrect arithmetic facts (e.g. 2 + 2 = 9) in comparison to correct ones (e.g. 2 + 2 = 4) elicits a succession of N400 and P600 waves, very similar to the ones elicited by semantic violations in sentences [32]. The N400 was indeed first described as an ERP response to words that violate the semantic context of the previous sentence, characterized by a central negativity elicited around 400 ms after an incongruent word [33] (e.g. ...
... "He took a paper and pencil to fly"). This N400 is typically followed, after both semantic and arithmetic violations, by a late centro-posterior positivity, termed the P600, which is thought to be related to cognitive control mechanisms and rule violation detection [32,[34][35][36][37]. It has often been compared to the P300 ERP event, considering that it follows the same spatial dynamic, increases in amplitude with the amount of violation, and is time-locked to the motor response (as the P300) while the N400 is stimulus-locked [35,37,38]. ...
... then a late positivity starting from 500 ms at the vertex and spreading to posterior areas (500-792 ms, p = 0.01, d = 0.63). Those activations were very similar to the arithmetic N400 and P600 effects reported in prior studies [32,34]. In MEG, the corresponding "N400" effect was characterized by strong bilateral activations in temporal-anterior areas (left cluster: 192-496 ms, p = 0.002, d = −1.17; ...
Can the sleeping brain develop predictions of future auditory stimuli? Past research demonstrated disrupted prediction capabilities during sleep in the context of novel, arbitrary auditory sequences, but the availability of over-learned knowledge already stored in long-term memory could still be preserved. We tested the sleeping brain capabilities to detect violations of simple arithmetic facts. Sleeping subjects were presented with spoken arithmetic facts such as “two plus two is nine” and brain responses to correct or incorrect results were recorded in electro and magneto-encephalography. Sleep responses were compared to both attentive and inattentive wakefulness. During attentive wakefulness, arithmetic violations elicited a succession of N400 and P600 effects, while no such activations could be recorded in sleep or in inattentive wakefulness. Still, small but significant effects remained in sleep, advocating for a preserved but partial accessibility to arithmetic facts stored in long-term memory and preserved predictions of low-level and already learned knowledge. Those effects were very different from residual activities seen in inattention, highlighting the differences of information processing between the sleeping and the inattentive brain.
... ERP arithmetic verification studies have observed amplitude differences around 400ms when the evoked potential of incongruous trials (e.g. 7 x 4 = 26) is compared to congruent ones (e.g. 7 x 4 = 28) (Niedeggen, Rösler, & Jost 1999;. In these studies, correct solutions elicit ERPs with higher amplitude positivity than incorrect solutions around 200-400ms. ...
... The mismatch condition, having significantly higher RT shows a clear trend of processing costs for incongruous information. This pattern is seen in similar arithmetic tasks when incongruous stimulus is processed Niedeggen, Rösler, & Jost, 1999). ...
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.
... In the field of simple arithmetic (e.g., problems with one-digit operands) it is widely assumed that the resolution of some problems (e.g., multiplications) necessarily implies semantic processing (i.e., the retrieval of arithmetic facts from memory, Campbell, 1995). Moreover, the N400 has been shown to be an index of the retrieval of arithmetic facts with onedigit multiplication problems (e.g., Niedeggen and Rösler, 1999;Prieto-Corona et al., 2010). In verification of multiplications tasks, the N400 is inversely proportional to the degree of relationship between the proposed result and the correct result (e.g., Niedeggen and Rösler, 1999). ...
... Moreover, the N400 has been shown to be an index of the retrieval of arithmetic facts with onedigit multiplication problems (e.g., Niedeggen and Rösler, 1999;Prieto-Corona et al., 2010). In verification of multiplications tasks, the N400 is inversely proportional to the degree of relationship between the proposed result and the correct result (e.g., Niedeggen and Rösler, 1999). The N400 would allow the dissociation between the use of memory retrieval and the use of procedural strategies to verify simple arithmetic problems. ...
There is current debate about the way adult individuals solve simple additions composed of one-digit operands. There are two opposing views. The first view assumes that people retrieve the result of additions from memory, whilst the second view states that individuals use automatized counting procedures. Our study aimed to dissociate between these two hypotheses. To this end, we analysed the type of problem effect when participants resolved simple additions by comparing additions with operands between 1 and 4 and control additions with at least one operand larger than 4. Brain-waves activity of a group of 30 adult individuals were recorded with 64 scalp electrodes mounted on an elastic cap, referenced against an electrode between Cz and CPz and re-referenced to an average reference offline. We considered two electrophysiological indexes, event-related potentials, ERPs, time-locked to the addition problems to distinguish between retrieval from memory and the use of procedures: A late positivity component (LP, 500-650 time window) over posterior regions associated to memory retrieval difficulty with higher LP positivity when participants resolve difficult vs. easy additions, and a negative component (N400, 250-450 ms time window) over fronto-central regions related to the use memory retrieval vs. procedures with more pronounced N400 amplitudes when the difficulty in the retrieval of semantic information increased. LP modulations were observed depending on the type of problem over posterior regions, P3 and Pz electrodes, whilst the N400 component was not affected. This pattern of results suggests that adult individuals use retrieval from memory to solve simple additions.
... Originally reported using semantic language paradigms in which the negative deflection was observed in the incongruent condition waveform relative to congruent [19], N400-like responses have since been demonstrated across numerous domains including language processing, semantic memory, and recognition memory. Sample experimental paradigms have included viewing of videos that lack meaning [24], incorrect solutions to math problems [25], unfamiliar versus familiar faces [26], and viewing incorrect action sequences [27]. Additionally, N400-like responses have also been shown to index world knowledge, as studies have demonstrated these responses using statements that violated factual information known to be true (e.g. ...
... The N400-like response to inconsistent or unexpected stimuli is believed to represent the brain's processing of incoming information within the context of an established knowledge schema [23,29]. This response has been demonstrated across a diverse range of experimental paradigms, with stimuli including incorrect solutions to math problems [25], nonsensical videos [24], and sentences with semantically incorrect words [22,52]. Although most studies have elicited the N400 response using semantic knowledge violations, a recent report by Hagoort et al suggested that the N400like response might also be elicited when a given stimulus is semantically correct but violates known world knowledge [28]. ...
Objective: The ability to orient with respect to the current context (e.g. current time or location) is crucial for daily functioning, and is used to measure overall cognitive health across many frontline clinical assessments. However, these tests are often hampered by their reliance on verbal probes (e.g. “What city are we in?”) in evaluating orientation. Objective, physiology-based measures of orientation processing are needed, but no such measures are currently in existence. We report the initial development of potential brainwave-based markers of orientation processing as characterized using electroencephlography (EEG) and magnetoencephalography (MEG).
Approach: An auditory stimulus sequence embedded with words corresponding to orientation-relevant (i.e. related to the ‘here and now’) and orientation-irrelevant (i.e. unrelated to the current context) conditions was used to elicit orientation processing responses. EEG/MEG data, in concert with clinical assessments, were collected from 29 healthy adults. Analysis at sensor and source levels identified and characterized neural signals related to orientation processing.
Results: Orientation-irrelevant stimuli elicited increased negative amplitude in EEG-derived event-related potential (ERP) waveforms during the 390-570ms window (p<0.05), with cortical activations across the left frontal, temporal, and parietal regions. These effects are consistent with the well-known N400 response to semantic incongruence. In contrast, ERP responses to orientation-relevant stimuli exhibited increased positive amplitude during the same interval (p<0.05), with activations across the bilateral temporal and parietal regions. Importantly, these differential responses were robust at the individual level, with machine-learning classification showing high accuracy (89%), sensitivity (0.88) and specificity (0.90).
Significance: This is the first demonstration of a neurotechnology platform that elicits, captures, and evaluates electrophysiological markers of orientation processing. We demonstrate neural responses to orientation stimuli that are validated across EEG and MEG modalities and robust at the individual level. The extraction of physiology-based markers through this technique may enable improved objective brain functional evaluation in clinical applications.
... ERP studies of arithmetic have typically measured two effects: the congruency effect, primarily observed in verification tasks during recordings of the brain response to a provided answer (e.g., Niedeggen, Rosler, & Jost, 1999), and the problem-size effect, observed during recordings of the brain response either to provided answers or after presentation of the operands (e.g., 7 Â 6) but prior to the answer itself ( Jost, Hennighausen, & R€ osler, 2004;Zhou et al., 2006). We focus here on the congruency effect, found in comparisons of brain responses for congruent solutions (correct answers) and incongruent solutions (incorrect answers), as this has been the primary effect measured in bilingual populations. ...
... The congruency effect is characterized by a more negative response to incorrect solutions (e.g., 7 Â 6 ¼ 36) compared with correct solutions (e.g., 7 Â 6 ¼ 42), with a maximum peak amplitude difference occurring about 350-400 ms after the presentation of the answer (Niedeggen et al., 1999). This arithmetic congruency effect has drawn comparisons to similar effects in other domains that study the processing of potentially meaningful items (e.g., language and object processing). ...
... Indeed, the retrieval strategy has been extensively studied by comparing ERPs elicited by true products to ERPs of false products. The rationale of comparing true and false products is that operands are assumed to automatically activate correct products of problems as well as immediate neighbors of correct products, in an arithmetic associative network (e.g., Ashcraft, 1992Ashcraft, , 1995 Campbell, 1995; Campbell & Oliphant, 1992; Lemaire et al., 1994 Lemaire et al., , 1996 Verguts & Fias, 2005 Niedeggen et al., 1999; Szücs & Csépe., 2004, 2005 Szücs & Soltész, 2010, average reference). N400 is also modulated by problem size, with maximal amplitude reached earlier for small relative to larger problems (Jost et al., 2004). ...
... Moreover, these modulations were found to be correlated with behavioral RIF. This component was assumed to reflect activation of cue-item associations (e.g., Niedeggen & Rösler, 1999). It was proposed that retrieval of practiced arithmetic facts elicited inhibition of other related facts to reduce retrieval competition (see also Bäuml et al., 2010). ...
Arithmetic strategies refer to the set of procedures used to solve arithmetic problems. Previous studies revealed that participants can solve arithmetic problems by using several arithmetic strategies. In this review, we discuss the added value of using electroencephalography (EEG) to investigate such strategies. Indeed, this technique enables to delineate different aspects of information processing, and can further our understanding of arithmetic strategies. The investigation of processes involved within arithmetic strategies with event-related potentials (ERPs) and frequency analyses allows to discover how participants solve different types of problems by enabling to distinguish arithmetic strategies on the bases of their electrophysiological signatures. Moreover, this technique is fruitful to investigate the time course of arithmetic strategy selection and execution. EEG can also help to investigate the role of general cognitive processes during execution of arithmetic strategies. Finally, EEG is also a powerful tool to specify how strategy use differs between groups of different skills or ages. Overall, by addressing these ends, EEG further our understanding of variations in participants’ arithmetic performance as a function of different characteristics, such as participants’ (e.g., age, skills), problems’ (e.g., problem or split size, rule violation), or situations’ (e.g., strategy execution on previous problems, correctness of proposed answers) characteristics.
... [39]), and the number 1 was arbitrarily excluded so that two groups of four numerals could be defined. This also corresponds with the numerals that have been used in many previous EEG studies ( [24]; as operands [4,5,[40][41][42]). The control conditions were designed to provide two relative measures of non-conceptual, physical differences across numeral groups: these groups did not differ in parity, each containing two even and two odd numbers. ...
The goal of measuring conceptual processing in numerical cognition is distanced by the possibility that neural responses to symbolic numerals are influenced by physical stimulus confounds. Here, we targeted conceptual responses to parity (even versus odd), using electroencephalogram (EEG) frequency-tagging with a symmetry/asymmetry design. Arabic numerals (2–9) were presented at 7.5 Hz in 50 s sequences; odd and even numbers were alternated to target differential, ‘asymmetry’ responses to parity at 3.75 Hz (7.5 Hz/2). Parity responses were probed with four different stimulus sets, increasing in intra-numeral stimulus variability, and with two control conditions composed of non-conceptual numeral alternations. Significant asymmetry responses were found over the occipitotemporal cortex to all conditions, even for the arbitrary controls. The large physical-differences control condition elicited the largest response in the stimulus set with the lowest variability (one font). Only in the stimulus set with the highest variability (20 drawn, coloured exemplars/numeral) did the response to parity surpass both control conditions. These findings show that physical differences across small sets of Arabic numerals can strongly influence, and even account for, automatic brain responses. However, carefully designed control conditions and highly variable stimulus sets may be used towards identifying truly conceptual neural responses.
... Event-related potential (ERP) studies have been useful in understanding the time course of arithmetic processing more generally and have found additional evidence that the arithmetic language bias is influenced by a bilingual's language history. Seminal studies measuring ERPs in monolinguals asked participants to verify the correctness of simple multiplication problems presented as sequential Arabic digits Niedeggen, Rösler, & Jost, 1999). ERPs time-locked to the presentation of proposed solutions revealed that correct problems elicited a less negative amplitude compared with incorrect problems. ...
In 2020, 21.5% of US preschoolers spoke a language other than English at home. These children transition into English‐speaking classrooms in different ways, often handling foundational concepts in two languages. Critically, some knowledge may be dependent on the language of learning. For instance, both bilingual children and adults typically prefer, and exhibit higher performance on arithmetic in the language in which they learned math (LA+) compared with their other language (LA−). The typical interpretation is that arithmetic facts are accessed from memory more efficiently or solely in LA+. However, recent research suggests that bilingual arithmetic is not restricted to one language in memory, and that language experience plays an important role in performance. Moreover, evidence suggests children and adults process arithmetic fundamentally differently. Thus, bilingual arithmetic memory may manifest differently across the life span. This review outlines evidence to date at the intersection between the brain basis of bilingualism, arithmetic processing, and development.
... In a study of children with specific disorders of mathematics performing an arithmetic verification task, an absence of both an N400 component (negative peak at around 400 ms after stimulus onset) and a late positive complex (LPC: positive-going waveform between 500 and 900 ms after stimulus onset) was found in comparison to control children [30]. In this task, the N400 component would be elicited with a greater amplitude for incongruent results of an arithmetic operation compared to congruent results; this difference in amplitudes is considered an arithmetic N400 effect [35]. Moreover, an LPC effect may be indicative of a re-evaluation process of the arithmetic operation [36,37]. ...
Children with learning disorders (LD children) often have heterogeneous cognitive impairments that affect their ability to learn and use basic academic skills. A proposed cause for this variability has been working memory (WM) capacity. Altered patterns of event-related potentials (ERPs) in these children have also been found in the N400 component associated with semantic priming. However, regarding the semantic priming effect in LD children, no distinction has been made for children with varying WM abilities. This study aims to explore the relationship of WM with the brain’s electrophysiological response that underlies semantic priming in LD children that performed a lexical decision task. A total of 40 children (8-10 years old) participated: 28 children with LD and 12 age-matched controls. The ERPs were recorded for each group and analyzed with permutation-based t-tests. The N400 effect was observed only in the control group, and both groups showed a late positive complex (LPC). Permutation-based regression analyses were performed for the results from the LD group using the WISC-IV indices (e.g., Verbal Comprehension and WM) as independent predictors of the ERPs. The Verbal Comprehension Index, but not the WM index, was a significant predictor of the N400 and LPC effects in LD children.
... Trials with response times below 200 ms were excluded, as these are not considered valid (e.g. Berger & Kiefer, 2021;Niedeggen et al., 1999;Whelan, 2008). Response time reflects the trimmed mean (excluding the outer 10% of the distribution) of the response duration of all correctly answered trials. ...
... ERP studies have also reported an arithmetic problem size effect in adults, which has been interpreted as a late positive component (Niedeggen, Rösler, & Jost, 1999;Núñez-Peña, 2008;Szucs & Csépe, 2005) or as a delayed P300 (Dickson & Wicha, 2019). Much less is known about the ERP correlates of the problem size effect in children, with no studies to date testing verification (Van Beek, Ghesquière, De Smedt, & Lagae, 2014. ...
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.
... Thus, most of the studies have assessed the math skills identifying the brain response of participants when they attend and recognize the correct response of math operation, standing on at the end of arithmetic processing. In these studies, there are two event-related potentials (ERPs) modulated by the level of math skills: the P300 is commonly linked with the attention process (Polich, 2007) and the arithmetic N400 amplitude, which has been related to the relatedness or interconnectedness of the involved memory representations associated with the problem and their possible results (Niedeggen et al., 1999;Prieto-Corona, 2010). Therefore, we suppose that overweight or obese preteens would show differences in these ERPs components compared with their normal-weight peers. ...
... Problematically, this differential processing of correct versus incorrect solutions in simple arithmetic verification tasks has been found to generate a Stroop-like interference effect during incorrect problems, which interferes with the ability to produce the correct solution as individuals have to engage aspects of inhibitory control to override the prepotent response [67,68]. Indeed, the arithmetic verification task used by Moore et al. ...
Background: Aerobic fitness relates to superior math achievement, but the underlying reasons remain unclear. This study tested how more efficient processing (efficiency hypothesis) or enhanced allocation of cognitive resources (resources hypothesis) underly fitness-related differences in arithmetic cognition in a sample of 138 college-aged adults.
Method: Participants completed an arithmetic task while pupillary measures were recorded prior to an aerobic fitness test.
Results: Higher aerobic fitness was associated with shorter reaction time for all problems and greater pupillary reactivity for problems requiring approximate and exact arithmetic.
Conclusions: Superior aerobic fitness relates to greater cognitive resources available to execute exact and approximate arithmetic faster. Fitness-related differences in math achievement may be driven by the cognitive resources underlying arithmetic strategy. These differences may extend beyond educational achievement and affect the motivation to engage in health behaviors based on quantitative information. Thus, improving cardiovascular fitness has the potential to also ameliorate health numeracy.
... In addition to the modulation of the ERPs of main interest, we observed a frontal negativity peaking around 480 msec after stimulus onset, the amplitude of which was inversely related to the distance between object and the observer. This negativity could be considered as the N400 potential, which likely reflects the brain's response to any type of meaningful stimulus (Kutas & Federmeier, 2000) in language, ( Johnson & Hamm, 2000;Kutas & Hillyard, 1980), pictorial stimuli (Hamm, Johnson, & Kirk, 2002), mathematics (Niedeggen, Rösler, & Jost, 1999), gestures ( Wu & Coulson, 2011), action-outcome relationships (Bach, Gunter, Knoblich, Prinz, & Friederici, 2009), and mismatches between objects and selected actions (Sitnikova, Kuperberg, & Holcomb, 2003). The frontal distribution of the N400 in this study is consistent with previous findings that showed that the action-related N400 has a more frontal focus compared to the language-related N400 (Amoruso et al., 2013). ...
Previous work suggests that perception of an object automatically facilitates actions related to object grasping and manipulation. Recently, the notion of automaticity has been challenged by behavioral studies suggesting that dangerous objects elicit aversive affordances that interfere with encoding of an object's motor properties; however, related EEG studies have provided little support for these claims. We sought EEG evidence that would support the operation of an inhibitory mechanism that interferes with the motor encoding of dangerous objects, and we investigated whether such mechanism would be modulated by the perceived distance of an object and the goal of a given task. EEGs were recorded by 24 participants who passively perceived dangerous and neutral objects in their peripersonal, boundary, or extrapersonal space and performed either a reachability judgment task or a categorization task. Our results showed that greater attention, reflected in the visual P1 potential, was drawn by dangerous and reachable objects. Crucially, a frontal N2 potential, associated with motor inhibition, was larger for dangerous objects only when participants performed a reachability judgment task. Furthermore, a larger parietal P3b potential for dangerous objects indicated the greater difficulty in linking a dangerous object to the appropriate response, especially when it was located in the participants' extrapersonal space. Taken together, our results show that perception of dangerous objects elicits aversive affordances in a task-dependent way and provides evidence for the operation of a neural mechanism that does not code affordances of dangerous objects automatically, but rather on the basis of contextual information.
... In contrast to the N300, the N400 during the processing of the final visual scene was unaffected by whether or not the two actors shared attention, but it was smaller when the two actors had previously communicated via mutual eye contact or via a pointing gesture. The N400 is typically enlarged in relation to semantic incongruities in verbal and non-verbal communication, and also in mathematics, action sequences and interpersonal coordination 25,32,[35][36][37] . It is believed to reflect the operation of a multimodal comprehension system that binds current contextual input with previous experiences in order to derive the meaning of any given stimulus 20,21,38 . ...
We investigated whether communicative cues help observers to make sense of human interaction. We recorded EEG from an observer monitoring two individuals who were occasionally communicating with each other via either mutual eye contact and/or pointing gestures, and then jointly attending to the same object or attending to different objects that were placed on a table in front of them. The analyses were focussed on the processing of the interaction outcome (i.e. presence or absence of joint attention) and showed that its interpretation is a two-stage process, as reflected in the N300 and the N400 potentials. The N300 amplitude was reduced when the two individuals shared their focus of attention, which indicates the operation of a cognitive process that involves the relatively fast identification and evaluation of actor–object relationships. On the other hand, the N400 was insensitive to the sharing or distribution of the two individuals’ attentional focus. Interestingly, the N400 was reduced when the interaction outcome was preceded either by mutual eye contact or by a perceived pointing gesture. This shows that observation of communication “opens up” the mind to a wider range of action possibilities and thereby helps to interpret unusual outcomes of social interactions.
... Further, the nature of the simple arithmetic verification task used by Moore and colleagues (2014) was such that all incorrect solutions would have required the use of exact calculation (i.e., the solutions were all within ± 1 of the correct solution, thus being too challenging to implement retrieval or approximation strategies), whereas all correct solutions would vary in strategy and be dependent upon arithmetic skill. Problematically, this differential processing of correct versus incorrect solutions in simple arithmetic verification tasks, has been found to produce a Stroop-like interference effect during incorrect problems, which interferes with the ability to produce the correct solution and individuals have to engage aspects of inhibitory control to override the prepotent response (Niedeggen et al., 1999;Zbrodoff & Logan, 2000). Indeed, the arithmetic verification task used by Moore et al. (2014) may have enabled higher fit children to more accurately detect correct and incorrect solutions as a function of reduced susceptibility to task interference (Buck et al., 2008;Kamijo & Takeda, 2009;Wang et al., 2019) independent of actual differences in strategy efficiency and selection during arithmetic cognition. ...
Background: Aerobic fitness relates to superior math achievement, but the underlying reasons remain unclear. This study tested how more efficient processing (efficiency hypothesis) or enhanced allocation of cognitive resources (resources hypothesis) underly fitness-related differences in arithmetic cognition in a sample of 138 college-aged adults.Method: Participants completed an arithmetic task while pupillary measures were recorded prior to an aerobic fitness test.Results: Higher aerobic fitness was associated with shorter reaction time for all problems and greater pupillary reactivity for problems requiring approximate and exact arithmetic.Conclusions: Superior aerobic fitness relates to greater cognitive resources available to execute exact and approximate arithmetic faster. Fitness-related differences in math achievement may be driven by the cognitive resources underlying arithmetic strategy. These differences may extend beyond educational achievement and affect the motivation to engage in health behaviors based on quantitative information. Thus, improving cardiovascular fitness has the potential to also ameliorate health numeracy.
... Specifically, the N400 activity would be generated by matching comparisons of se-mantic encodings of the stimuli with long-term representations. In the context of arithmetic tasks, N400-like effects have been reported in arithmetic facts incongruities (Galfano et al., 2004;Jost, Hennighausen and Rösler, 2004;Martinez-Lincoln et al., 2015;Niedeggen, Rösler and Jost 1999), with a noticeable functional similarity to the linguistic N400 (Kutas and Hillyard, 1980). Thus, instead of semantic representations, the N400-like in numerical tasks would reflect automatic activation of long-term arithmetic facts networks . ...
The objective of this thesis is the study of bilingual mathematics within the scientific field of Numerical Cognition. The approach to how bilingual people represent and access magnitude is currently a matter of growing interest that responds to the need to understand the role that language plays in the early acquisition of mathematics. This importance is usually reflected in the context of education, where learning arithmetic and bilingualism come together naturally. Given the importance in our society of both, math competence and early learning of a second language, research from a Cognitive Neuroscience perspective is necessary to better understand the bilingual brain.
... The amplitude of the negative component is greater at presentation of a wrong solution compared to a correct solution in solving various mathematical problems (multiplication, subtraction); this component has a frontal distribution and is similar to the mismatch negativity, emerging with a latency of approximately 270 ms [4]. A number of authors consider the negative component with a peak latency of approximately 400 ms as a specific "arithmetic" N400 [5][6][7], which is associated with the presentation of a non-congruent solution. The amplitude of the P300 component is higher at presentation of a correct answer, which is associated with the response to the target stimulus, while the late positive component, the amplitude of which is higher upon presentation of an incorrect answer, is correlated with a recheck of the solution in the conditions of comparing the presented answer with those obtained as result of own calculation. ...
... Thus, replicating the methodology from our previous study, we aimed to verify earlier findings from the direct contrast of expected and unexpected sequence endings within the N400 time frame [6]. These results were well in line with the established role of N400 as a modality-independent marker of representations in need of revision due to expectancy violations [15], as has been shown in paradigms involving memory [16], language [17][18], and arithmetic problems [19][20]. ...
While prediction errors have been established to instigate learning through model adaptation, recent studies have stressed the role of model-compliant events in predictive processing. Specifically, probabilistic information at critical points in time (so-called checkpoints) has been suggested to be sampled in order to evaluate the internal model, particularly in uncertain contexts. This way, initial model-based expectations are iteratively reaffirmed under uncertainty, even in the absence of prediction errors. Using electroencephalography (EEG), the present study aimed to investigate the interplay of such global uncertainty information and local adjustment cues prompting on-line adjustments of expectations. Within a stream of single digits, participants were to detect ordered sequences (i.e., 3-4-5-6-7) that had a regular length of five digits and were occasionally extended to seven digits. Over time, these extensions were either rare (low irreducible uncertainty) or frequent (high uncertainty) and could be unexpected or indicated by incidental colour cues. Accounting for cue information, an N400 component was revealed as the correlate of locally unexpected (vs expected) outcomes, reflecting effortful integration of incongruous information. As for model-compliant information, multivariate pattern decoding within the P3b time frame demonstrated effective exploitation of local (adjustment cues vs non-informative analogues) and global information (high vs low uncertainty regular endings) sampled from probabilistic events. Finally, superior fit of a global model (disregarding local adjustments) compared to a local model (including local adjustments) in a representational similarity analysis underscored the precedence of global reference frames in hierarchical predictive processing. Overall, results suggest that just like error-induced model adaptation, model evaluation is not limited to either local or global information. Following the hierarchical organisation of predictive processing, model evaluation too can occur at several levels of the processing hierarchy.
... Correct solutions (e.g., 2×4=8) elicit ERPs with more positive voltage than incorrect solutions (e.g., 2×4=9) around 200-400 ms after the onset of the solution. Given the presupposition that verification of these math facts would tap into semantic memory, initial reports of this ERP effect of arithmetic congruency interpreted the brain response as an N400 (Niedeggen, Rösler, & Jost, 1999). The N400 is an ERP component that is sensitive to semantic (meaning) level processing and is facilitated (more positive) for expected or repeated meaningful items (for review, see Kutas & Federmeier, 2000. ...
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.
... ERPs provide a continuous measure of brain activity. In turn, changes in brain activity can be measured in the period of time leading up to a behavioral response ( Dickson et al., 2018;Jost, Hennighausen, & Rösler, 2004;Martinez-Lincoln, Cortinas, & Wicha, 2015;Niedeggen, Rösler, & Jost, 1999;Prieto-Corona et al., 2010;Salillas & Wicha, 2012). Moreover, ERPs are a multidimensional measure of brain activity that can reveal both quantitative differences across conditions, as indexed by the amplitude or timing of a brain component, as well as qualitative differences in the type of brain response elicited, as indexed by the polarity or scalp distribution of the ERP. ...
... Aside from the aforementioned conceptual commonalities of CP and PE, one critical distinction remains, namely the mismatch signal that is intrinsic to prediction errors. N400 is elicited by a multitude of sensory events and its amplitude is known to scale with event surprise in language [18][19], recognition memory (reviewed in [20]), and arithmetic tasks [21][22], presumably marking modality-independent integration of incongruous information. More generally, N400 has been discussed as a modality-independent index of representations needing revision in light of expectancy violations (for review, see [11]). ...
While prediction errors (PE) have been established to drive learning through adaptation of internal models, the role of model-compliant events in predictive processing is less clear. Checkpoints (CP) were recently introduced as points in time where expected sensory input resolved ambiguity regarding the validity of the internal model. Conceivably, these events serve as on-line reference points for model evaluation, particularly in uncertain contexts. Evidence from fMRI has shown functional similarities of CP and PE to be independent of event-related surprise, raising the important question of how these event classes relate to one another. Consequently, the aim of the present study was to characterise the functional relationship of checkpoints and prediction errors in a serial pattern detection task using electroencephalography (EEG). Specifically, we first hypothesised a joint P3b component of both event classes to index recourse to the internal model (compared to non-informative standards, STD). Second, we assumed the mismatch signal of PE to be reflected in an N400 component when compared to CP. Event-related findings supported these hypotheses. We suggest that while model adaptation is instigated by prediction errors, checkpoints are similarly used for model evaluation. Intriguingly, behavioural subgroup analyses showed that the exploitation of potentially informative reference points may depend on initial cue learning: Strict reliance on cue-based predictions may result in less attentive processing of these reference points, thus impeding upregulation of response gain that would prompt flexible model adaptation. Overall, present results highlight the role of checkpoints as model-compliant, informative reference points and stimulate important research questions about their processing as function of learning und uncertainty.
... The operands were presented one after another and completed with either the correct or an incorrect solution. A comparable event-related brain potential (ERP) effect was elicited by incongruous solutions in simple multiplication problems (Niedeggen, Rösler, & Jost, 2007). Correct solutions elicited a large P300 response, while incorrect solutions evoked a negativity between 300 and 500 ms with a maximum over the centro-parietal scalp, followed by a late positive component which was interpreted as a "positive syntactic shift" or P600 (Hagoort, Brown, & Groothusen, 1993), also found in response to syntactic and musical violations (Osterhout, Holcomb, & Swinney, 1994;Patel, Gibson, Ratner, Besson, & Holcomb, 1998). ...
Inter‐individual 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 vs. 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 if 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 Rho 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).
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... These ERP effects have been interpreted in terms of category-specific access to lexical and semantic information, and are thus thought to reflect how conceptual knowledge is represented and which type of experiential information is being retrieved (Kiefer, 2001;but see Hauk, 2016). Furthermore, the N400 effect has been shown for incongruous vs. congruous arithmetic problems, which suggests that the processing of arithmetic and semantic anomalies relies on at least partly overlapping mechanisms Niedeggen, Rösler, & Jost, 1999; for a positive component involved in arithmetic processing in this time window see, e.g., Dehaene, 1996). ...
Embodied theories assign experience a crucial role in shaping conceptual representations. Supporting evidence comes mostly from studies on concrete concepts, where e.g., motor expertise facilitated action concept processing. This study examined experience-dependent effects on abstract concept processing. We asked participants with high and low mathematical expertise to perform a lexical decision task on mathematical and nonmathematical abstract words, while acquiring event-related potentials. Analyses revealed an interaction of expertise and word type on the amplitude of a fronto-central N400 and a centro-parietal late positive component (LPC). For mathematical words, we found a trend for a lower N400 and a significantly higher LPC amplitude in experts compared to nonexperts. No differences between groups were found for nonmathematical words. The results suggest that expertise affects the processing stages of semantic integration and memory retrieval specifically for expertise-related concepts. This study supports the generalization of experience-dependent conceptual processing mechanisms to the abstract domain.
... The audio/visual correspondence effect observed in Experiment 1, on the other hand, may be indicative of the activation of higher order evaluation processes. In fact, latency, polarity, and scalp distribution of this effect resemble those typically observed in ERPs elicited during the evaluation of semantically inconsistent words embedded in sentences (Kutas & Federmeier, 2011) and arithmetically incorrect results in single-digit operations (Galfano, Mazza, Angrilli, & Umiltà, 2004;Galfano, Penolazzi, Vervaeck, Angrilli, & Umiltà, 2009;Niedeggen, Rösler, & Jost, 1999). These ERPs emerge when participants are presented, for instance, with a numerical problem (e.g., 3 × 1 = ?) ...
Humans share with a variety of animal species the spontaneous ability to detect the numerical correspondence between limited quantities of visual objects and discrete auditory events. Here, we explored how such mental representation is generated in the visual modality by monitoring a parieto‐occipital ERP component, N2pc, whose amplitude covaries with the number of visual targets in explicit enumeration. Participants listened to an auditory sequence of one to three tones followed by a visual search display containing one to three targets. In Experiment 1, participants were asked to respond based on the numerical correspondence between tones and visual targets. In Experiment 2, participants were asked to ignore the tones and detect a target presence in the search display. The results of Experiment 1 showed an N2pc amplitude increase determined by the number of visual targets followed by a centroparietal ERP component modulated by the numerical correspondence between tones and visual targets. The results of Experiment 2 did not show an N2pc amplitude increase as a function of the number of visual targets. However, the numerical correspondence between tones and visual targets influenced N2pc amplitude. By comparing a subset of amplitude/latency parameters between Experiment 1 and 2, the present results suggest N2pc reflects two modes for representing the number of visual targets. One mode, susceptible to subjective control, relies on visual target segregation for exact target individuation, whereas a different mode, likely enabling spontaneous cross‐modal matching, relies on the extraction of rough information about number of targets from visual input.
... Some numerical cognition studies have made use of the N400 component, traditionally seen in linguistic semantically incongruent comparisons, to study numerical processing in arithmetic tasks (Niedeggen, Rösler, & Jost 1999;. These studies have seen a similar ERP component in numerically incongruous trials (e.g. 7 x 4 = 28 vs. 7 x 4 = 26) as in linguistic ones (e.g. ...
Fractions processing is a topic of major interest both in numerical cognition and mathematics education. The literature on the processing of common fractions has focused on whether fractions are compared by their magnitude or through their components. Only a few neuroimaging studies have looked at this question. The N400 component, traditionally seen in linguistic semantic congruency event-related-potential (ERPs) experimental designs, has been adapted to study arithmetic processing. Observing the N400, allows the study of how different arithmetic components affect overall processing. In this study, an N400 paradigm is used to investigate semantic congruency during a fraction magnitude comparison task (Match/Mismatch) in 24 adults. Behavioral results reveal interference by shared components across the compared fractions. EEG analysis results show an N400-like difference wave between Match and Mismatch conditions. Shared components modulate the latency of this N400 effect. These results show the N400 as a viable method for studying fractions.
... Note, however, that this positive wave appeared after the N400 component, the maximum of which is achieved over the anterior electrode sites. This anterior negativity is frequently interpreted as an indicator of a mismatch between the given answer and the preceding question or is thought to be connected to the involvement of working memory and attention resources (e.g., Niedeggen, Rosler & Jost, 1999). Additionally, both N400-like and P500-700 components appeared to be related to insight-based problem solving (e.g., Dietrich & Kanso, 2011). ...
This paper addresses the neuro-cognitive characterization of super mathematically gifted high school students. The research population consisted of three groups of students excelling in mathematics: super mathematically gifted (S-MG), generally gifted students who excel in school mathematics (G-EM), and students who excel in school mathematics but are not identified as being generally gifted (NG-EM). An Event Related Potentials (ERP) research methodology was employed to examine behavioral and electrophysiological measures associated with insight-based and learning-based problem solving. Forty-two male adolescents participated in the study. Analysis of the electrical potentials evoked when solving these two distinct types of problems revealed three types of neuro-efficiency effects, which highlight the different characteristics of electrical activity of super mathematically gifted students. These characteristics are predominantly task-dependent, emerge at different stages of the task and are reflected in different scalp topography.
... This N400 effect is a neurological response that has been thoroughly studied for over 30 years and can be used to identify semantic congruity since there is a larger amplitude deflection for incongruous stimuli over congruous ones (see [19], [20] for review). Although this ERP has predominantly been used in studying words, it can be found in many different modes such as actions in videos (reviewed in Sitnikova et al. [21]), math [22], [23], [24], hearing [25], [26] and semantic memory [18], [27]. ...
The aim of this study was to investigate in an EEG
experiment the reaction time of the participants deciding on the
semantic congruency of sentences with subsequent pictures of
symbolic or iconic hand gestures. More specifically, we investigated
the reaction time employed by the participants to determine
the semantic congruence of sentences and gesture pictures which
are semantically related in different ways. In one case the gesture
conveys the same content as the sentence, in the second case it
provides additional content to the sentence. The hypothesis that
we wanted to test was that the reaction time would be shorter
in the latter case than in the former since preceding corpusbased
studies have indicated that speech and gestures conveying
the same information are more temporally synchronous than
speech and gestures which convey complementary information.
Therefore, we expect that it will be harder to process semantic
congruency for gestures which usually are synchronous to speech
if they follow the sentences they are related to than in the case
where gestures provide additional information. Our study confirms
the hypothesis showing that not only was the participants
reaction time shorter in the case of gestures which provided
additional information to sentences, but also that the accuracy in
the semantic congruency task was higher.
The N400 component of the event-related potential (ERP) is the most widely used brain signal in research on semantic processing. It has been discovered now more than 30 years ago, in 1980, as a larger negativity for semantically incongruent sentence continuations such as “I take my coffee with cream and dog” (as compared to congruent continuations such as “sugar”). The N400 has meanwhile been shown to be modulated by a very wide variety of lexical and semantic variables and has taught us a lot about how meaning is processed in language and beyond. This chapter reviews the literature on the N400 component including its relationship to the subsequent P600 component and discusses implications for the neurocognition of semantic processing.Key wordsN400P600Semantic processingMeaningLanguage
Neural processing of numerical concepts may be measured in humans automatically, without a related numerical task. However, the extent to which neural responses to symbolic numbers are due to physical stimulus confounds independently of conceptual representations remains unknown. Here, we targeted conceptual responses to parity (even vs. odd), using an electroencephalographic (EEG) frequency-tagging approach with a symmetry/asymmetry paradigm. Fifty second sequences of Arabic numerals (2-9) were presented at 7.5 Hz; odd and even numbers were alternated, so that differential responses to parity would be captured at 3.75 Hz (7.5 Hz/2). Parity responses were probed with four different stimulus sets, increasing in intra-numeral stimulus variability. Moreover, two control conditions were tested for each stimulus set, comprised of non-conceptual numeral alternations (strong control, for small inter-group physical differences: 2,3,6,7 vs. 4,5,8 and 9; weak control, for large physical differences: 2,4,5,7 vs. 3,6,8,9). Significant asymmetrical responses at 3.75 Hz were found over the occipitotemporal cortex to all conditions, thus even for arbitrary numeral groups. The weak control condition elicited the largest response in the stimulus set with the lowest level of variability (1 font). Only in the stimulus set with the highest level of variability (20 hand-drawn, colored exemplars per numeral) did the response to parity surpass both control conditions. These findings show that physical differences across small sets of Arabic numerals can strongly influence, and even account for, automatic brain responses. However, carefully designed control conditions and highly variable stimulus sets may be used towards identifying truly conceptual neural responses.
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.
Fact retrieval deficits have been documented in children with mathematical learning disabilities. We assessed the retrieval of arithmetic facts in neurotypical 9-to-10-year-old children with different mathematical achievement levels using event-related potential methods while performing an arithmetic verification task (addition, subtraction, and multiplication). Forty-eight participants were divided into High (H), Average (A), and Low (L) mathematics performance according to their scores on The Wide Range Achievement Test 4 (WRAT4). Children determined whether appearing digits matched or not the correct solution of the preceding problem. L group showed a lower number of correct responses, prolonged reaction times, and poorer performance on working memory (WM) tasks. P300 component showed significantly higher amplitudes for correct solutions in H, while N270 showed higher amplitudes for incorrect solutions. L children showed difficulty in recovering arithmetic facts and poorly modulated N270 and P300 components, probably reflecting WM processing problems affecting the construction and retrieval of numerical information. ARTICLE HISTORY
As relational integration performance can be used to predict reasoning ability, the present study aimed to provide electrophysiological evidence for numerical inductive reasoning. Number series with two levels of relational complexity were utilized, including simple and hierarchical problems (such as “15–16‐17” versus “15–16‐18”). Two tasks were adopted: a relational integration task that required to determine whether the numerical relations were changed across numbers; a number series task that required to determine whether a hidden rule was acquired (Experiment 1) or to predict the subsequent number (Experiment 2), whose phases were divided as rule searching, rule discovery, and rule following. The event‐related potential (ERP) results of both experiments indicated that, in contrast to simple problems, hierarchical problems triggered enhanced N400 and late negative component (LNC), reflecting numerical fact retrieval, and generalizing novel hypotheses about the hidden rules by integrating adjacent numerical relations, respectively; relational integration showed similar N400 and LNC activation patterns to rule discovery (Experiment 1) or rule searching (Experiment 2). Additionally, the N400 and LNC elicited by relational integration showed strong positive correlations and even were able to predict the ones triggered by rule discovery (Experiment 1) or rule searching (Experiment 2). Therefore, the results supported the role of relational integration in numerical inductive reasoning and thereby in intelligence. In the first report to use identical numerical series to compare numerical inductive reasoning to relational integration, we observed that the N400 and LNC effects on relational integration not only exhibited similar patterns to those on rule acquisition but were also positively correlated with and able to predict rule acquisition. This supports the role of relational integration in intelligence.
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.
Our ability to calculate implies more than the sole retrieval of the correct solution. Essential processes for simple calculation are related to the spreading of activation through arithmetic memory networks. There is behavioral and electrophysiological evidence for these mechanisms. Their brain location is, however, still uncertain. Here, we measured magnetoencephalographic brain activity during the verification of simple multiplication problems. Following the operands, the solutions to verify could be preactivated correct solutions, preactivated table-related incorrect solutions, or unrelated incorrect solutions. Brain source estimation, based on these event-related fields, revealed 3 main brain networks involved in simple calculation: 1) bilateral inferior frontal areas mainly activated in response to correct, matching solutions; 2) a left-lateralized frontoparietal network activated in response to incorrect table-related solutions; and (3) a strikingly similar frontoparietal network in the opposite hemisphere activated in response to unrelated solutions. Directional functional connectivity analyses revealed a bidirectional causal loop between left parietal and frontal areas for table-related solutions, with frontal areas explaining the resolution of arithmetic competition behaviorally. Hence, this study isolated at least 3 neurofunctional networks orchestrated between hemispheres during calculation.
Numerical Cognition: The Basics provides an understanding of the neural and cognitive mechanisms that enable us to perceive, process, and memorize numerical information. Starting from basic numerical competencies that humans share with other species, the book explores the mental coding of numbers and their neural representation. It explains the strategies of mental calculation, their pitfalls and their development, as well as the developmental steps children make while learning about numbers. The book gradually builds our understanding of the underlying mental processes of numeracy and concludes with an insightful examination of the diagnosis, etiology and treatment of dyscalculia. Written in an accessible manner, the book summarizes and critically evaluates the major psychological explanations for various empirical phenomena in numerical cognition. Containing a wealth of student-friendly features including end of chapter summaries, informative figures, further reading lists, and links to relevant websites, Numerical Cognition: The Basics is an essential starting point for anybody new to the field.
Aim of this study was to investigate the association between finger and number representation in a task in which students had to perform arithmetic calculations and decide whether the provided solution was correct or incorrect, while a pair of task-irrelevant hands gesturally expressed the same or a different number. In particular we aimed at investigating whether irrelevant finger-counting might interfere with arithmetic computing, thus showing the existence of a strict neural association between the two processes. 20 volunteers took part to the investigation and EEG/ERPs were recorded from 128 scalp sites. P300 amplitude was greater to correct than incorrect solutions. Accuracy was higher when there was no conflict between the two sets of information A numerical error-related negativity (nERN) was elicited by incorrect solutions, and also by correct solutions when the finger-counting was incongruent. Source analysis applied to the incongruent minus congruent difference showed that when finger-counting was incorrect nERN mostly derived from medial and superior prefrontal cortex activity (supporting action monitoring and suppression). Conversely, when finger-counting indicated the correct solution brain activation included occipital areas, somatosensory regions and visuomotor mirror areas, inferior and superior temporal cortex, reflecting attentional orienting toward the hands. In both cases, the left angular gyrus (BA39) was found active during conjoined digit/number processing, suggesting a strict neural association between finger and digit processing. The present findings help explaining why a lesion in the left parietal cortex may simultaneously lead to finger apraxia and acalculia (Gertsmann syndrome).
In this mini-review, I use event-related potential (ERP) studies to test the minimalist program (MP) prediction that organisms with the faculty of language cognitively process languagelike systems in a qualitatively distinct manner. I first discuss “languagelike” as a technical term defined by recursion criteria. From this definition and using a generative perspective, I show that certain domains of math and music can be considered languagelike. These domains are then used as case studies to test whether or not different languagelike systems are cognitively processed in a similar manner. This is done by investigating the elicitation of common language-related ERPs (namely, the left-anterior negativity (LAN), N400, and P600) in these languagelike systems. I show that these systems do indeed elicit the same language-related ERPs, supporting the claim that different languagelike systems are processed similarly. I then discuss discrepancies between these systems, as exemplified by the P3, and I provide plausible accounts for interpreting those results. I ultimately conclude that present data on the LAN, N400, and P600 disprove language-specificity but that languagelike-specificity remains plausible, and as yet there is no reason to reject MP’s prediction that languagelike systems are processed in a qualitatively distinct way.
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.
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.
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.
This study aimed at exploring the time course of processes underlying the associative confusion effect. We also evaluated the consequences of selecting arithmetic facts to resolve addition problems. We gathered electrophysiological evidence when participants performed a verification task. Simple addition problems were presented in blocks of two trials and participants decided whether they were correct or not. The N400-like component was considered an index of semantic access (i.e., the retrieval of arithmetic facts), and the P200 component was used to determine the difficulty associated with encoding after the answer to an addition problem. When an addition problem was incorrect but the result presented to the participant was that of multiplying the operands (e.g., 2 + 4 = 8), N400-like amplitude was reduced relative to an unrelated condition (e.g., 2 + 4 = 10). This finding suggested that the coactivation of addition and multiplication facts took place. Furthermore, the P200 amplitude was more positive when participants answered to addition problems whose result was that of multiplying the operands of the previous trial (e.g., 2 + 6 = 8). This suggests that irrelevant results were inhibited and it was difficult to encode them later.
Delineating the neurobiology of language comprehension calls for an understanding of when and how (and not just where) inputs make contact with semantic memory (semantic access) to yield meaning. We examine this temporally extended function through the lens of event-related brain potentials (ERPs) measured to linguistic in comparison with nonlinguistic inputs, both in isolation and in larger language contexts. Extant data suggest remarkable consistency in the time course and nature of processing across input types: 150 ms for basic level (face, object, string) categorization and 150 ms more for perceptual grouping and generating a structured representation of individual items, followed by semantic access starting at about 300 ms. However, the presence of context information allows information to be activated in advance and creates expectancies at all levels of analysis that permit semantically yoked effects from the earliest levels of sensory processing and beyond.
La musicothérapie n’est pas une thérapeutique nouvelle, et les évidences quant à ses bienfaits ne sont plus à démontrer. Cependant, si plusieurs auteurs en font mention, très peu d’entre eux expliquent « pourquoi » et « comment » la musicothérapie permet à la personne autiste, le passage d’une parole que nous qualifions d’a signifiante à un discours nouveau et chargé de sens. C’est ce que tente d’expliquer cette thèse de doctorat, et ce, grâce à de nombreux aller-retour entre clinique et concepts psychanalytiques (lacaniens en particulier).
This article presents a computational theory of retrieval of simple addition and multiplication facts (e.g. 9 x 6 = ?; 3 + 4 = ?). According to the network-interference model, a presented problem activates memory representations for a large number of related number facts, with strength of activation of specific facts determined by featural and magnitude similarity to the presented problem. Nonnative frequencies of confusion errors (e.g. 9 x 6 = 36) were u,sed to quantify similarity factors. Problem nodes continuously receive similarity-based excitatory input during retrieval and compete by way of mutual inhibition until one node reaches a critical activation threshold and triggers a response. The model demonstrates that similarity-based interference, in addition to accounting for many features of eJTors, also provides accurate prediction of variability in speed of correct retrieval among problems. The model also accounts for subtle features of inter-trial err.or priming, as well as changes in the rates and types of errors observed as a function of elapsed retrieval time. Most educated adults can quickly and accurately produce the answers to a large number of simple arithmetic problems (e.g. 4 + 2 = ?, 6 x 6 = ?). This knowledge of basic number facts is usually characterised as "simple arithmetic", but experimental analysis has uncovered many subtle phenomena reflecting a complex system of interacting memory representations and retrieval processes. Understanding these memory processes is important both because of the status of simple mental arithmetic as a fundamental intellectual skill and because simple arithmetic provides a unique opportunity to study elementary memory processes in a highly constrained domain. The article presents a revision of the network-inJeiference model of number-fact retrieval described by Campbell and Oliphant (1992). The model constitutes a detailed theory of the memory codes Requests for reprints should be sent to Jamie Campbell,
In two experiments, event-related brain potentials (ERPs) and cued-recall performance measures were used to examine the consequences of semantic congruity and repetition on the processing of words in sentences. A set of sentences, half of which ended with words that rendered them semantically incongruous, was repeated either once (eg, Experiment 1) or twice (e.g., Experiment 2). After each block of sentences, subjects were given all of the sentences and asked to recall the missing final words.
Repetition benefited the recall of both congruous and incongruous endings and reduced the amplitude and shortened the duration of the N400 component of the ERP more for (1) incongruous than congruous words, (2) open class than closed class words, and (3) low-frequency than high-frequency open class words. For incongruous sentence terminations, repetition increased the amplitude of a broad positive component subsequent to the N400.
Assuming additive factors logic and a traditional view of the lexicon, our N400 results indicate that in addition to their singular effects, semantic congruiry, repetition, and word frequency converge to influence a common stage of lexical processing. Within a parallel distributed processing framework, our results argue for substantial temporal and spatial overlap in the activation of codes subserving word recognition so as to yield the observed interactions of repetition with semantic congruity, lexical class, and word frequency effects.
The N400 component of the human event-related brain potential appears to be related to violations of semantic expectancy during language comprehension. The present experiment investigated whether the N400 is related specifically to activity in a language system or is an index of a conceptual system that is accessed by both pictures and words. Sentences were visually presented one word at a time with the last word being replaced in one condition by a line drawing representing the same concept (eg, the word "socks" was replaced by a picture of socks). The N400 recorded in the Pictures Condition was found to be identical to the N400 generated by words in terms of amplitude, scalp distribution, and latency. These results suggest that the N400 is an index of activity in a conceptual memory that is accessed by both pictures and words.
Abstract Slow, DC-like event-related brain potentials (ERPs) were recorded from the scalp of 30 healthy young adults to test the hypothesis that distinct cortical areas are activated when different types of information are retrieved from long-term memory. Three groups of 10 subjects each were first trained with associations between either pictures and spatial positions (spatial condition), pictures and color patches (color condition), or nouns and nouns (verbal condition). All three experimental conditions were completely analogous with respect to the established associative structure, the learning procedure, the performance criterion, and the retrieval test that followed 1 day after learning. Slow event-related brain potentials being recorded during retrieval had a significantly distinct topography. The maximum of a DC-like negative wave was found in the verbal condition over the left frontal, in the spatial condition over the parietal, and in the color condition over the right occipital to temporal cortex. These results are consistent with the idea that memory representations are either "down-loaded" into or directly reactivated within those cortical processing modules in which the same material was handled during perception. Response times, on the other hand, revealed no difference between the three retrieval conditions. In each case RT increased monotonically, if more items had to be scanned. Thus, while the ERPs suggest the involvement of different cortical processors during memory search the response times suggest that a sequentially operating scanning mechanism applies to all of them.
The objective of the present study was to delineate brain-electrical correlates of semantic and syntactic integration processes during language comprehension. Twenty-eight subjects were engaged in a lexical decision task. The target item (a legal word or a pseudo word) was always preceded by a prime consisting of a sentence fragment that provided a particular context. With respect to the prime a word target could be either a correct completion, a violation of a semantic selection restriction, or a violation of a syntactic subcategorization rule. An N400-like wave was elicited by both types of deviations. Syntactic anomalies evoked a negative shift predominantly over the anterior scalp with a preponderance over the left hemisphere, while semantic anomalies were accompanied by a much more widespread negativity with the maximum over posterior temporal areas. The amplitude of the semantic vie lation effect was found to be related to the strength of the priming constraints. The topographic difference is consistent with the idea that syntactic and semantic aspects of comprehension are handled by different neural subsystems.
A model of P300 amplitude is proposed that reduces the many hypothetical constructs invoked to explain variations in P300 amplitude to three dimensions: 1) Subjective Probahility, 2) Stimulus Meaning, and 3) Information Transmission. Evidence is presented to support the assertion that variables on the subjective prwbability and stimulus meaning dimensions have independent and additive contributions to overall P300 amplitude. The amplitude contributions of both of these dimensions, however, are modulated by a multiplicative relation with the proportion of transmitted stimulus information. Within each dimension, the fundamental experimental variables and their interrelations are specified. An example is presented to show how, by using an additive factors method, the respective amplitude effects of the probability and stimulus meaning dimensions can be separated. Supporting data are presented to show that the proposed model provides a reasonable and testable framework in which to conceptualize P300 results. DESCRIPTORS: Event-related potentials, P300. The prospect of having an electrophysio logical index of cognitive operations has led many re- searchers to explore the nature of the P300 com- ponent of the event-related brain potential (ERP). Since its discovery by Sutton and his colleagues (Sutton, Braren, Zubin, & John, 1965; Sutton, Tuet- ing, Zubin, & John, 1967), studies have demon- strated that P300 amplitude and latency can be used as indices of the nature and timing of a subject's cognitive response to a stimulus.' As a result of
Prior to each target letter string presented visually to 120 university students in a speeded word–nonword classification task, either {bird, body, building,} or {xxx} appeared as a priming event. Five types of word-prime/word-target trials were used: bird-robin, bird-arm, body-door, body-sparrow, and body-heart. The stimulus onset asynchrony (SOA) between prime and target letter string varied between 250 and 2,000 msec. At 2,000-msec SOA, reaction times (RTs) on bird-robin type trials were faster than on xxx-prime trials (facilitation), whereas RTs on bird-arm type trials were slower than on xxx-prime (inhibition). As SOA decreased, the facilitation effect on bird-robin trials remained constant, but the inhibition effect on bird-arm decreased until, at 250-msec SOA, there was no inhibition. For Shift conditions at 2,000-msec SOA, facilitation was obtained on body-door type trials and inhibition was obtained on body-sparrow type. These effects decreased as SOA decreased until there was no facilitation or inhibition. On body-heart type trials, there was an inhibition effect at 2,000 msec SOA, which decreased as SOA decreased until, at 250-msec SOA, it became a facilitation effect. Results support the theory of M. I. Posner and S. R. Snyder (1975) that postulated 2 distinct components of attention: a fast automatic inhibitionless spreading-activation process and a slow limited-capacity conscious-attention mechanism. (27 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Collected response time (RT) and error data on multiplication problems up to 9 × 9 from 86 Ss in Grades 2–5 and from 60 undergraduate and graduate students. Results show that most errors involved correct products to other problems and that a developmental trend emerged in which the specific errors made by children mirrored adult errors by Grade 5. The error patterns indicate that an associative network evolves in which problem operands become linked to specific sets of candidate answers. Retrieval is governed by a process that activates candidates, and accessibility of correct answers is impeded by competing associations: At all skill levels, both problem-error rates and product-error rates (i.e., how often a problem's correct product occurs as an incorrect response to other problems) contributed to predicting correct problem RT in multiple regression analyses. These interference variables yielded higher correlations than did structural variables (e.g., the numerical size of problem operands), the latter having provided the basis for previous models of arithmetic memory. A network-interference account is proposed that explains the slow course of acquisition and differential problem difficulty in terms of interference by false associations. (French abstract) (37 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Evaluated 40 undergraduates' performance on a simple mental multiplication task and the adequacy of several different models of mental addition as extended to multiplication. Exps I and II revealed that the performance of multiplication resembles simple mental addition, showing similar effects of problem size and of split (the numerical difference between a stated and correct answer). Exp III included a special manipulation of "confusion products," incorrect answers that were multiples of one of the problem's digits. Consistent with the assumption of interrelated network storage, confusion products slowed RT significantly, even when the problem was presented 600 msec in advance of the answer. Results are discussed in terms of a network-retrieval approach to mental arithmetic, the commonalities between addition and multiplication, and rule- vs retrieval-based performance. (26 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Error priming in simple multiplication refers to the finding that retrieval of a product via one problem can increase the probability that the product is stated on a later trial as an error response to another problem. To analyze the magnitude and time course of the error-priming effect, the observed frequencies with which errors matched previously generated answers at different lags were compared with chance frequencies based on the binomial distribution. The time interval between successive problems (4.5 s vs 7.5 s) and the intertrial activity (filled vs. unfilled) were varied. Surprisingly, the probability that an error matched the answer from the immediately preceding trial (lag of one) was significantly below chance in three of the four experimental conditions and at chance in the filled 7.5-s condition. Error matching probabilities two or three times greater than chance were obtained at an interval of about 30 s, and matches declined to chance thereafter. The results suggest that counteracting inhibitory and excitatory processes determine the magnitude of the error-priming effect over time. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Current models of mental arithmetic disagree on whether the same mental representation is activated by numbers in different forms (single-format assumption). Two experiments examined if the response times in arithmetic fact retrieval from arabic digits, number words, or dice are independent of the graphical representation of the numbers. S. Sternberg's (1969) additive factors method was used to analyze which response time interactions are compatible with the single-format assumption. In accord with the assumption, additive effects of form and operation were found in Experiment 1. In contrast, Experiment 2 showed additive effects only when an operand was held in memory, but a strong Form X Operation interaction otherwise. The authors discuss how phonological interference and form-specific retrieval could produce these interactions and how the single-format assumption can be extended to handle the findings. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This study is concerned with slowly varying, long-duration brain event-related potential (ERP) components, referred to as Slow Wave activity. Slow Wave activity can be observed in the epoch following P3b, suggesting that it reflects further processing invoked by increased task demands, beyond the processing that underlies P3b. The present experiment was designed to distinguish Slow Wave activity related to specific types of task demands which arise during difficult perceptual (pattern recognition) and conceptual (arithmetic) mental operations.
Three late ERP components that respond differentially in amplitude to manipulation of perceptual and conceptual difficulty were identified: 1) A P3b, with a topography focused about Pz, evidently related to the subjective categorization of easy and difficult conceptual operations, that increased when the subjective low-probability operation was performed; 2) A longer latency, centroparietal positive Slow Wave that increased directly with perceptual difficulty but was not affected by conceptual difficulty; 3) A very long latency negative Slow Wave, broadly distributed over centroposterior scalp, that increased directly with conceptual difficulty while its onset was delayed when perceptual difficulty increased.
Analysis of errors in simple multiplication has shown that answers retrieved on previous trials are initially inhibited (negative
error priming) but later are promoted as errors to subsequent problems (positive error priming). Two experiments investigated
whether error priming is associated either with problem-specific retrieval processes or with representations of answers that
can be manipulated independently of problems. In Experiment 1, answers were primed by visually presenting products for 200
msec prior to problems. Correct-answer primes facilitated retrieval, related-incorrect primes interfered with retrieval more
than unrelated primes, and both effects were greater for more difficult problems. Primes affected only the trial on which
they were presented, however, whereas both negative and positive error priming from previous problems were observed across
trials. In Experiment 2, subjects named and retrieved multiplication products on alternating trials. Just-named products were
inhibited as errors to the following multiplication problem (i.e., negative error priming), but, compared to positive priming
from previous retrieved products, positive error priming from previously named numbers was weak. The results indicate that
positive error priming is due mainly to an encoding or retrieval bias produced by previous problems, whereas negative error
priming entails suppression, or de-selection, of answer representations.
Three explanations of adults’ mental addition performance, a counting-based model, a direct-access model with a backup counting
procedure, and a network retrieval model, were tested. Whereas important predictions of the two counting models were not upheld,
reaction times (RTs) to simple addition problems were consistent with the network retrieval model. RT both increased with
problem size and was progressively attenuated to false stimuli as the split (numerical difference between the false and correct
sums increased. For large problems, the extreme level of split (13) yielded an RT advantage for false over true problems,
suggestive of a global evaluation process operating in parallel with retrieval. RTs to the more complex addition problems
in Experiment 2 exhibited a similar pattern of significance and, in regression analyses, demonstrated that complex addition
(e.g., 14+12=26) involves retrieval of the simple addition components (4+2=6). The network retrieval/decision model is discussed
in terms of its fit to the present data, and predictions concerning priming facilitation and inhibition are specified. The
similarities between mental arithmetic results and the areas of semantic memory and mental comparisons indicate both the usefulness
of the network approach to mental arithmetic and the usefulness of mental arithmetic to cognitive psychology.
Positron emission tomography was used to examine the cerebral networks underlying number comparison and multiplication in eight normal volunteers. Cerebral blood flow was measured within anatomical regions of interest defined in each subject using magnetic resonance imaging. Three conditions were used: rest with eyes closed, mental multiplication of pairs of arabic digits and larger-smaller comparison of the same pairs. Both multiplication and comparison activated the left and right lateral occipital cortices, the left precentral gyrus, and the supplementary motor area. Beyond these common activations, multiplication activated also the left and right inferior parietal gyri, the left fusiform and lingual gyri, and the right cuneus. Relative to comparison, multiplication also yielded superior activity in the left lenticular nucleus and in Brodmann's area 8, and induced a hemispheric asymmetry in the activation of the precentral and inferior frontal gyri. Conversely, relative to multiplication, comparison yielded superior activity in the right superior temporal gyrus, the left and right middle temporal gyri, the right superior frontal gyrus, and the right inferior frontal gyrus. These results underline the role of bilateral inferior parietal regions in number processing and suggest that multiplication and comparison may rest on partially distinct networks.
The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.
Presents a spreading-activation theory of human semantic processing,
which can be applied to a wide range of recent experimental results.
The theory is based on M. R. Quillian's (1967) theory of semantic
memory search and semantic preparation, or priming. In conjunction
with this, several misconceptions concerning Quillian's theory are
discussed. A number of additional assumptions are proposed for his
theory to apply it to recent experiments. The present paper shows
how the extended theory can account for results of several production
experiments by E. F. Loftus, J. F. Juola and R. C. Atkinson's (1971)
multiple-category experiment, C. Conrad's (1972) sentence-verification
experiments, and several categorization experiments on the effect
of semantic relatedness and typicality by K. J. Holyoak and A. L.
Glass (1975), L. J. Rips et al (1973), and E. Rosch (1973). The paper
also provides a critique of the Rips et al model for categorization
judgments.
This paper describes a uniform method for calculating the interpolation of scalp EEG potential distibution, the current source density (CSD), the cortical potential distribution (cortical mapping) and the CSD ot the cortical potential distribution. It will be shown that interpolation and deblurring methods such as CSD or cortical mapping are not independent of the inverse problem in potential theory. Not only the resolution but also the accuracy of these techniques, especially those of deblurring, depend greatly on the spatial sampling rate (i.e., the number of elechades). Using examples from simulated and real (64 channels) data it can be shown that the application of more than 100 EEG channels is not only favourable but necessary to guarantee a reasonable accuracy in the calculations of CSD or cortical mapping. Likewise, it can be shown that using more than 250 electrodes does not improve the resolution.
In separate studies of arithmetic and mental rotation, similar posterior negative slow waves have been found. This similarity was surprising given the difference in cognitive processing required by these tasks. Furthermore, delayed responses were employed in these studies, so that it was not possible to determine the extent to which the slow wave activity was too late to be associated with processing that was specific to performance of the tasks. This experiment was intended to clarify the task-specific and non-specific nature of the slow wave activity. Subjects performed either an arithmetic or mental rotation task at two levels of difficulty on a random, trial-to-trial basis and gave an immediate response. There were a number of late posterior negativities, each with a different timing and topography, which were sensitive to type of task and/or task difficulty. Some components were associated with early task processing that was synchronized to the stimulus while others, revealed by response-synchronized averaging, were associated with later stages of task processing. There also was post-task activity that was sensitive to the difficulty level of the prior operations. In both tasks, there was a pre-frontal positive wave that persisted over most of the pre-response epoch, evidently related to a process that was active throughout the task. There also was centro-frontal phasic negativity, with a large peak at 380 msec in mental rotation, and a smaller, longer latency peak in arithmetic, apparently related to the complexity of the stimulus. Thus we conclude that arithmetic and mental rotation each elicit task-specific slow wave activity.
Many intelligent strategy choices may be accomplished through relatively low-level cognitive processes. This article describes a detailed model of how such "mindless" processes might lead to intelligent choices of strategies in one common situation: that in which people need to choose between stating a retrieved answer and using a backup strategy. Several experiments testing the model's applicability to children's single-digit multiplication are reported. These include tests of predictions about when different strategies are used and how early experience shapes later performance. Then, the sufficiency of the model to generate both performance at any one time and changes in performance over time is tested through the medium of a running computer simulation of children's multiplication. The simulation acquires a considerable amount of multiplication knowledge, and its learning and performance parallel those of children in a number of ways. Finally, several implications of the model for understanding cognitive self-regulation and cognitive development are discussed.
Paivio's (1986) dual code theory was tested in 5 experiments with a new paradigm for the FAN effect that enforced genuine memory recall. Subjects had to learn associations between concepts and mediators. The FAN of the concepts in relation to the mediators was varied systematically. Response times (RT) were measured while subjects had to decide whether 2 concepts were linked to each other or not by a common mediator. In Experiment 1 the concepts and mediators were words, whereas in the other experiments the concepts were line drawings. Colors served as mediators in Experiment 2 and spatial locations served as mediators in Experiments 3, 4, and 5. All of the experiments were equivalent with respect to the FAN, the learning procedure, and the retrieval test. In all of the experiments, RT proved to be a linear function of the FAN. These results suggested that the same dynamics hold for all types of information stored in long-term memory.
Event-related potential (ERP) and cued-recall performance were used to investigate the influence of (a) context, (b) repeating a word's meaning to word repetition priming, and (c) repetition on the ERP difference related to memory (Dm). Sentences ended with either nonhomographs or homographs. For nonhomographs, either the sentence context, the final word, both, or neither were repeated. Homographs were repeated in their original context or in new sentences that biased the same or an alternative meaning. Large repetition effects were found for all words repeated in their original contexts; in contrast, changing contexts led to no repetition effects whether the meaning of the repeated words was preserved or not. These results favor an episodic contribution to word repetition priming and suggest a common process for Dm and repetition.
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This paper will examine the components of potentials evoked by checkerboard reversal. The components will be defined in terms of latency and scalp location, and we will show changes of components as a function of retinal stimulus site. A considerable problem in conventional evoked potential assessment is the different potential waveshapes which are recorded from different electrode sites on the head (see Fig. 1). In addition, waveshapes at given electrode sites may change when a different reference is used. An example is shown in Fig. 1 where a set of simultaneously recorded evoked potential data from forty-seven electrodes is illustrated as waveforms using two different reference points, the mean of the ears or an anterior midline electrode (Fig. 1A and B). Of course, any one of the forty-seven channels could have been used as a reference, creating an immense number of different waveshapes out of the same data set.
Words with a single spelling and pronunciation but at least two distinct meanings (homographs) were used to terminate sentences of moderate contextual constraint. Following each sentence, a target was presented which was either (1) related to the contextually biased meaning of the homograph, (2) related to the unbiased meaning, or (3) unrelated to either meaning. Across subjects, the stimulus onset asynchrony (SOA) between homograph and target was either short (200 ms) or long (700 ms). The naming latencies recorded in Experiment 1 revealed priming for both contextually appropriate and inappropriate related targets at the short SOA but for only the contextually appropriate targets at the long SOA. The event-related potentials elicited by these same stimuli in Experiment 2 showed a similar pattern of priming at the long SOA. At the short SOA, however, the priming effect for contextually inappropriate targets had a later onset than that for contextually appropriate targets. We interpret these data as indicating that both meanings of ambiguous words are not activated at the same time. The late priming effect for contextually inappropriate targets is discussed in tems of backward priming.
Measuring reaction times (RTs) using the additive-factors method provides information about the sequence of processing stages in a cognitive task. Here, I describe how the simultaneous recording of event-related potentials (ERPs) in the same task can provide complementary information that cannot be obtained using RTs alone. Most notably, ERP data can reveal the absolute activation time and the coarse brain localization of processing stages. RTs and ERPs can also be used to cross-validate a serial-stage model. These notions were applied to a study of the temporal unfolding of brain activations in a number comparison task. ERPs were recorded from 64 scalp electrodes while normal subjects classified numbers as larger or smaller than 5. Specific scalp signatures and timing data were obtained for stages of word and digit identification, magnitude comparison, response programming, and error capture and correction. The observed localizations were compatible with previous neuropsychological and brain imaging data and provided new insights into the cerebral lateralization and timing of number processing.
Abstract The N400 is an endogenous event-related brain potential (ERP) that is sensitive to semantic processes during language comprehension. The general question we address in this paper is which aspects of the comprehension process are manifest in the N400. The focus is on the sensitivity of the N400 to the automatic process of lexical access, or to the controlled process of lexical integration. The former process is the reflex-like and effortless behavior of computing a form representation of the linguistic signal, and of mapping this representation onto corresponding entries in the mental lexicon. The latter process concerns the integration of a spoken or written word into a higher-order meaning representation of the context within which it occurs. ERPs and reaction times (RTs) were acquired to target words preceded by semantically related and unrelated prime words. The semantic relationship between a prime and its target has been shown to modulate the amplitude of the N400 to the target. This modulation can arise from lexical access processes, reflecting the automatic spread of activation between words related in meaning in the mental lexicon. Alternatively, the N400 effect can arise from lexical integration processes, reflecting the relative ease of meaning integration between the prime and the target. To assess the impact of automatic lexical access processes on the N400, we compared the effect of masked and unmasked presentations of a prime on the N400 to a following target. Masking prevents perceptual identification, and as such it is claimed to rule out effects from controlled processes. It therefore enables a stringent test of the possible impact of automatic lexical access processes on the N400. The RT study showed a significant semantic priming effect under both unmasked and masked presentations of the prime. The result for masked priming reflects the effect of automatic spreading of activation during the lexical access process. The ERP study showed a significant N400 effect for the unmasked presentation condition, but no such effect for the masked presentation condition. This indicates that the N400 is not a manifestation of lexical access processes, but reflects aspects of semantic integration processes.
Long-latency components of event-related brain potentials (ERPs) recorded from subjects reading meaningful text are sensitive to semantic relationships among the major lexical items of sentences. In particular, the N400 components are enlarged to words that are semantically unrelated to or incongruous with the context provided by preceding items in a sentence. The present experiment was aimed at finding out whether this inverse relationship between N400 amplitude and semantic association would extend to situations where words were presented in isolated pairs, using a design that dissociated changes in N400 from confounding ERP waves elicited by active decision making. KRP's were recorded to 320 word pairs presented to eleven subjects. Each pair of words was followed by a letter, and subjects made a differential response according to whether or not the letter had been present in either of the words. After the ERP recording session, subjects rated the degree of semantic association between the words in each pair. ERP averages were formed on the basis of the subjects' ratings and on the basis of normative, a priori categories. For both types of averages the N400 amplitude was found to be a sensitive index of semantic association, even though the association was incidental to the subject's assigned task. These findings suggest the utility of the N400 measure in studies of semantic priming and as a probe of the automaticity of contextual influences in language processing.
In this chapter we give an overview of some of the studies in our laboratory in which event-related brain potentials (ERPs) have been recorded in tasks involving the repetition of stimuli such as words, nonwords, and pictures, and outline our current interpretation of the findings that have emerged. A major aim of this work has been to determine the conditions under which ERPs are sensitive to stimulus repetition when it is incidental to the experimental task, and hence when no discriminative response is required on the basis of whether an item is repeated or unrepeated.
Describes a unified experimental approach to the study of the mind based on experiments in the time course of human information processing. New studies on the role of intensity in information processing, on vigilance, and on orienting and detecting are presented. A historical introduction to mental chronometry together with an integration of performance and physiological techniques for its study are provided. (15 p ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991: Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook of aging and cognition, Erlbaum, Hillsdale, NJ, 1992, pp. 315-372] suggest that consciously controlled processes are more dependent on frontal lobe function than are automatic processes. It is appropriate, therefore to determine whether transitions in the locus of primary brain activity occur with practice on mental calculation. In this experiment, we examine the relationship between characteristics of event-related brain potentials (ERPs) and mental arithmetic. Single-digit mental multiplication problems varying in difficulty (problem size) were used, and subjects were trained on these problems for four sessions. Problem-size and practice effects were reliably found in behavioral measures (RT). The ERP was characterized by a pronounced late positivity after task presentation followed by a slow wave, and a negativity during response indication. These components responded differentially to the practice and problem-size manipulations. Practice mainly affected topography of the amplitude of positivity and offset latency of slow wave, and problem-size mainly offset latency of slow wave and pre-response negativity. Fronto-central positivity diminished from session to session, and the focus of positivity centered finally at centro-parietal regions.(ABSTRACT TRUNCATED AT 250 WORDS)
This article discusses cognitive neuropsychological research on acquired dyscalculia (i.e., impaired numerical processing resulting from brain damage), surveying issues of current interest, and illustrating the ways in which analyses of acquired deficits can contribute to an understanding of normal processing. I first review the logic whereby inferences concerning normal cognition are drawn from patterns of impaired performance. I then consider research exploring the general functional architecture of the cognitive numerical processing mechanisms, and finally turn to studies aimed at probing the internal structure and functioning of individual processing components.
This paper provides a tutorial introduction to numerical cognition, with a review of essential findings and current points of debate. A tacit hypothesis in cognitive arithmetic is that numerical abilities derive from human linguistic competence. One aim of this special issue is to confront this hypothesis with current knowledge of number representations in animals, infants, normal and gifted adults, and brain-lesioned patients. First, the historical evolution of number notations is presented, together with the mental processes for calculating and transcoding from one notation to another. While these domains are well described by formal symbol-processing models, this paper argues that such is not the case for two other domains of numerical competence: quantification and approximation. The evidence for counting, subitizing and numerosity estimation in infants, children, adults and animals is critically examined. Data are also presented which suggest a specialization for processing approximate numerical quantities in animals and humans. A synthesis of these findings is proposed in the form of a triple-code model, which assumes that numbers are mentally manipulated in an arabic, verbal or analogical magnitude code depending on the requested mental operation. Only the analogical magnitude representation seems available to animals and preverbal infants.
In this article, we present data from two brain-damaged patients with calculation impairments in support of claims about the cognitive mechanisms underlying simple arithmetic performance. We first present a model of the functional architecture of the cognitive calculation system based on previous research. We then elaborate this architecture through detailed examination of the patterns of spared and impaired performance of the two patients. From the patients' performance we make the following theoretical claims: that some arithmetic facts are stored in the form of individual fact representations (e.g., 9 x 4 = 36), whereas other facts are stored in the form of a general rule (e.g., 0 x N = 0); that arithmetic fact retrieval is mediated by abstract internal representations that are independent of the form in which problems are presented or responses are given; that arithmetic facts and calculation procedures are functionally independent; and that calculation algorithms may include special-case procedures that function to increase the speed or efficiency of problem solving. We conclude with a discussion of several more general issues relevant to the reported research.
Ruchkin, Johnson, Mahaffey, and Sutton (1988) presented evidence for a frontal positive/posterior negative late slow wave (SW) which they found to be functionally related to conceptual load, i.e., the difficulty of mental calculation problems increased both the positive and negative parts of it. In the present study we replicated the paradigm of Ruchkin et al. with some modifications, and we also found that this late SW pattern is actually due to a superimposition of two slow potentials. Our results suggest that one potential (positive at frontopolar scalp) is related to the mental operation of division. However, the other potential (negative over posterior scalp) is not related to the computational task itself but to the expectation of stimuli that follow the task. In addition, we found that memorizing a digit seems to be associated with a positive slow wave over posterior scalp. Altogether, our data suggest that load imposed on working memory is associated with positive slow waves which show a task specific topography—mental division is associated with a pSW at Fpz, remembering with a pSW at Pz/Oz. On the other hand, the state of stimulus and task anticipation is associated with negative slow waves. The latter reach their amplitude maximum over posterior scalp, if visually presented information is anticipated.
Our study demonstrates how functionally distinct slow waves can be disentangled by a systematic manipulation of events which either precede or follow the slow wave activity. Moreover, it shows that recording epochs must be of considerable length, if the functional significance of slow waves is the objective of research.
Event-related potentials (ERPs) were recorded from one midline and three pairs of lateral electrodes while subjects determined whether pairs of sequentially presented pictures were semantically associated. The ERPs evoked by the second picture of each pair differed as a consequence of whether it was associated with its predecessor, such that ERPs to nonassociated pictures were more negative-going than those to associated items. These differences resulted from the modulation of two ERP components, one frontally distributed and centered on an N300 deflection, the other distributed more widely over the scalp and encompassing an N450 deflection. The modulation of N450 is interpreted as further evidence that the "N400" ERP component is sensitive to semantic relationships between nonverbal stimuli. The earlier N300 effects, which do not appear to occur when ERPs are evoked by semantically primed and unprimed words, could suggest that the semantic processing of pictorial stimuli involves neural systems different from those associated with the semantic processing of words.
Analysis of variance (ANOVA) interactions involving electrode location are often used to assess the statistical significance of differences between event-related potential (ERP) scalp distributions for different experimental conditions, subject groups, or ERP components. However, there is a fundamental incompatibility between the additive model upon which ANOVAs are based and the multiplicative effect on ERP voltages produced by differences in source strength. Using potential distributions generated by dipole sources in spherical volume conductor models, we demonstrate that highly significant interactions involving electrode location can be obtained between scalp distributions with identical shapes generated by the same source. Therefore, such interactions cannot be used as unambiguous indications of shape differences between distributions and hence of differences in source configuration. This ambiguity can be circumvented by scaling the data to eliminate overall amplitude differences between experimental conditions before an ANOVA is performed. Such analyses retain sensitivity to genuine differences in distributional shape, but do not confuse amplitude and shape differences.
The neuroelectric activity of the human brain that accompanies linguistic processing can be studied through recordings of event-related potentials (e.r.p. components) from the scalp. The e.r.ps triggered by verbal stimuli have been related to several different aspects of language processing. For example, the N400 component, peaking around 400 ms post-stimulus, appears to be a sensitive indicator of the semantic relationship between a word and the context in which it occurs. Words that complete sentences in a nonsensical fashion elicit much larger N400 waves than do semantically appropriate words or non-semantic irregularities in a text. In the present study, e.r.ps were recorded in response to words that completed meaningful sentences. The amplitude of the N400 component of the e.r.p. was found to be an inverse function of the subject's expectancy for the terminal word as measured by its 'Cloze probability'. In addition, unexpected words that were semantically related to highly expected words elicited lower N400 amplitudes. These findings suggest N400 may reflect processes of semantic priming or activation.
A single case study of a patient with a selective impairment of arithmetical calculation is reported. DRC became severely acalculic after sustaining a left parietal intra-cerebral haematoma. His numeracy skills were documented as fully as possible. It was found that his knowledge of the significance of individual numbers and his concept of quantity appeared to be intact, but simple addition, subtraction and multiplication were all performed laboriously and inaccurately and his performance was inconsistent from trial to trial. Further it was shown that it was his knowledge of arithmetical facts not his knowledge of arithmetical operations which was impaired. The findings are discussed in relation to models of arithmetical calculation and it is concluded that for DRC there was a deficit in accessing one category of verbal semantic knowledge systems, namely arithmetical facts.
In a sentence reading task, words that occurred out of context were associated with specific types of event-related brain
potentials. Words that were physically aberrant (larger than normal) elecited a late positive series of potentials, whereas
semantically inappropriate words elicited a late negative wave (N400). The N400 wave may be an electrophysiological sign of
the "reprocessing" of semantically anomalous information.
This paper presents a model describing the temporal and neurotopological structure of syntactic processes during comprehension. It postulates three distinct phases of language comprehension, two of which are primarily syntactic in nature. During the first phase the parser assigns the initial syntactic structure on the basis of word category information. These early structural processes are assumed to be subserved by the anterior parts of the left hemisphere, as event-related brain potentials show this area to be maximally activated when phrase structure violations are processed and as circumscribed lesions in this area lead to an impairment of the on-line structural assignment. During the second phase lexical-semantic and verb-argument structure information is processed. This phase is neurophysiologically manifest in a negative component in the event-related brain potential around 400 ms after stimulus onset which is distributed over the left and right temporo-parietal areas when lexical-semantic information is processed and over left anterior areas when verb-argument structure information is processed. During the third phase the parser tries to map the initial syntactic structure onto the available lexical-semantic and verb-argument structure information. In case of an unsuccessful match between the two types of information reanalyses may become necessary. These processes of structural reanalysis are correlated with a centroparietally distributed late positive component in the event-related brain potential.(ABSTRACT TRUNCATED AT 250 WORDS)
Semantic priming effects (behavioral and electrophysiological) were compared in the visual and auditory modalities across three stimulus onset asynchronies (SOAs; 0, 200, and 800 ms). When both prime and target were presented in the visual modality (the prime just to the left of a fixation point and the target to the right), there were N400 priming effects present across the three SOAs. However, the N400 in the 0-ms SOA condition extended longer in time (800 vs. 500 ms) than in the other SOAs. When both the prime and target were presented in the auditory modality (the prime to the right ear and the target to the left), the largest priming effects were found for the 800-ms SOA. Moreover, there was a relatively early priming effect present in the 0- and 800-ms SOA conditions but not in the 200-ms condition. The results are discussed in terms of modality differences in the time course of word comprehension processes.
When subjects read an semantically unexpected word, the brain electrical activity shows a negative deflection at about 400 msec in comparison with the response to an expected word. In order to study the brain systems related to this effect we mapped it with a dense (64-channel) electrode array and two reference-independent measures, one estimating the average potential gradients and the other radial current density. With these measures, the event-related brain potential (ERP) begins at about 70 msec with the P1, reflecting bilateral current sources over occipitoparietal areas. A strongly left-lateralized N1 then follows, peaking at about 180 msec, accompanied by an anterior positivity, the P2. A separate posterior positive pattern then emerges that seems to repeat the topography of the P1. Next, at about 350 msec, the ERP for the congruous word develops a P300 or LPC, characterized by a diffuse positivity over the superior surface of the head and several negativities over inferior regions. This superior source/inferior sink pattern of the LPC is greater over the left hemisphere. In contrast, the ERP for the incongruous word in this interval displays the N400 as a period in which topographic features are absent. At about 400 msec the ERP for the incongruous word begins to develop an LPC, which then remains relatively symmetric over the two hemispheres.
Current theories of numerical cognition differ in assumptions about the componential architecture of number processing and about the extent of notation-specific processes. To investigate these issues, 64 adult subjects were tested on simple addition and multiplication problems presented in Arabic digit or English number-word format. Overall, response times and error rates were much higher with the word format, but more importantly, presentation format interacted with arithmetic operation and problem size. Operation errors (2 + 4 = 8), operand-naming errors (2 + 8 = 8), and operand-intrusion errors (9 x 6 = 36) were each characterized by a different format x operation interaction, and analysis of inter-trial error priming showed selective interference from preceding trials as a function of number format. These types of format-specific retrieval interference and operation-specific effects of format are problematic for models that hypothesize notation-independent memory processes for arithmetic. Furthermore, analyses of operand-naming errors, operand-intrusion errors, and other operand-priming effects, revealed strong interactions of number reading and number-fact retrieval processes; processes that are typically posited to be functionally independent. The results suggest a complex encoding architecture that incorporates notation-dependent activation of addition and multiplication facts, as well as interpenetration of number reading and number-fact retrieval processes.
Event-related potentials and lan-guage comprehension Coles ~Eds.!, Elec-trophysiology of mind: Event-related brain potentials and cognition ~pp
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Osterhout, L., & Holcomb, P. H. ~1995!. Event-related potentials and lan-guage comprehension. In: M. D. Rugg & M. G. H. Coles ~Eds.!, Elec-trophysiology of mind: Event-related brain potentials and cognition ~pp.171–215!. Oxford, UK: Oxford University Press.