Event-related brain potentials uncover activation dynamics in the lexicon of multiplication facts

Cross-Format Integration of Auditory Number Words and Visual-Arabic Digits: An ERP Study

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.

Neurofunctional Components of Simple Calculation: A Magnetoencephalography Study

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.

Simple additions: Dissociation between retrieval and counting with electrophysiological indexes

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

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

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

N2pc reflects two modes for coding the number of visual targets

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.

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

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

Fact learning in complex arithmetic-the role of the angular gyrus revisited

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.

Asymmetric activation spreading in the multiplication associative network due to asymmetric overlap between numerosities semantic representations?

Simple multiplication facts are thought to be organised in a network structure in which problems and solutions are associated. Converging evidence suggests that the ability for solving symbolic arithmetic problems is based on an approximate number system (ANS). Most theoretical stances concerning the metric underlying the ANS converge on the assumption that the representational overlap between two adjacent numbers increases as the numerical magnitude of the numbers increases. Given a number N, the overlap between N and N+1 is larger than the overlap between N and N-1. Here, we test whether this asymmetric overlap influences the activation spreading within the multiplication associative network (MAN). When verifying simple multiplication problems such as 8×4 participants were slower in rejecting false but related outcomes that were larger than the actual outcome (e.g., 8×4=36) than rejecting smaller related outcomes (e.g., 8×4=28), despite comparable numerical distance from the correct result (here: 4). This effect was absent for outcomes which are not part of either operands table (e.g., 8×4=35). These results suggest that the metric of the ANS influences the activation spreading within the MAN, further substantiating the notion that symbolic arithmetic is grounded in the ANS.

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

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

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

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Arithmetic relatedness and distance effects are sensitive to task properties.

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Matching tasks involve semantic processes.

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Verification tasks involve semantic and detection of mismatch processes.

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

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

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

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

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

Single pulse TMS induced disruption to right and left parietal cortex on addition and multiplication

Whether or not mathematical operations are dependent on verbal codes in left hemisphere areas - particularly the left intraparietal sulcus - remains an issue of intense debate. Using single pulse transcranial magnetic stimulation directed at horizontal and ventral regions of the left and right intraparietal sulcus, we examined disruption to reaction times in simple addition and multiplication. Results indicate that these two operations differ in the pattern of lateralization across time for the two areas studied. These show that computational efficiency is not specifically dependent on left hemisphere regions and, in particular, that efficiency in multiplication is dependent on the ventral region of the intraparietal sulcus in the right hemisphere considered to be critical for motion representation and automatization.

Spatial congruency between stimulus presentation and response key arrangements in arithmetic fact retrieval

It is known that number and space representations are connected to one another in numerical and arithmetic abilities. Numbers are represented using the metaphor of a mental number line, oriented along horizontal and vertical space. This number line also seems to be linked to mental arithmetic, which is based partly on arithmetic fact retrieval. It seems that number representation and mental arithmetic are linked together. The present study tested the effect of spatial contextual congruency between stimulus presentation and response key arrangements in arithmetic fact retrieval, using number-matching and addition verification tasks. For both tasks in Experiment 1, a contextual congruency effect was present horizontally (i.e., horizontal presentation of stimuli and horizontal response key alignments) but not vertically (i.e., vertical presentation of stimuli but horizontal response key alignments). In Experiment 2, both tasks showed a contextual congruency effect for both spatial conditions. Experiment 1 showed that the interference and distance effects were found in the horizontal condition, probably because of the spatial congruency between stimulus presentation and response key arrangements. This spatial congruency could be related to the activation of the horizontal number line. Experiment 2 showed similar interference and distance effects for both spatial conditions, suggesting that the congruency between stimulus presentation and response alignment could facilitate the retrieval of arithmetic facts. This facilitation could be related to the activation of both horizontal and vertical number lines. The results are discussed in light of the possible role of a mental number line in arithmetic fact retrieval.

Arithmetic mismatch negativity and numerical magnitude processing in number matching

Background

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

Results

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

Conclusions

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

Neurophysiological markers of retrieval-induced forgetting in multiplication fact retrieval

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