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Reasoning is the ability to formulate inferences or conclusions from available information. The two major types, deductive and inductive, are thought to rely on distinct cognitive mechanisms and recruit separate brain areas. Neuroimaging studies yield mixed results; some found the left inferior frontal gyrus (IFG) activations for deductive reasoning and the left dorsolateral prefrontal cortex (DLPFC) for inductive reasoning. This assumption was put to the test in the present study. In two double-blinded, sham-controlled experiments, high-definition transcranial direct current stimulation (HD-tDCS) was used to systematically explore the left IFG's and DLPFC's causal role in deductive and inductive reasoning. Participants with no formal training in logic judged deductive and inductive arguments before and after 10 minutes of anodal, cathodal, or sham tDCS of the left IFG (Experiment 1, n = 20) or left DLPFC (Experiment 2, n = 21). Left IFG anodal tDCS impairs reaction times (RTs) for easy categorical (p = < .001) and propositional (p = .025) deductive arguments and the accuracy for easy inductive propositional arguments (p = .003). Meanwhile, regardless of the active stimulation conditions, left DLPFC tDCS shortens RTs (anodal: p = < .001, cathodal: p = .014) and increases accuracy (anodal: p = .029, cathodal: p = .001) for difficult categorical inductive arguments, but decreases accuracy (anodal: p = .027, cathodal: p = < .001) for difficult propositional inductive arguments. The overall results showed a partial dissociation of the left frontal lobe areas subserving the two types of reasoning and argument difficulty-dependent stimulation effects. This study extends knowledge of the neural basis of reasoning and hopefully inspires interventions that could augment reasoning impairments associated with normal aging and brain lesions., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Fresnoza et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Determining if a sequence of numbers is ordered or not is one of the fundamental aspects of numerical processing linked to concurrent and future arithmetic skills. While some studies have explored the neural underpinnings of order processing using functional magnetic resonance imaging, our understanding of electrophysiological correlates is comparatively limited. To address this gap, we used a three-item symbolic numerical order verification task (with Arabic numerals from 1 to 9) to study event-related potentials (ERPs) in 73 adult participants in an exploratory approach. We presented three-item sequences and manipulated their order (ordered vs. unordered) as well as their inter-item numerical distance (one vs. two). Participants had to determine if a presented sequence was ordered or not. They also completed a speeded arithmetic fluency test, which measured their arithmetic skills. Our results revealed a significant mean amplitude difference in the grand average ERP waveform between ordered and unordered sequences in a time window of 500-750 ms at left anterior-frontal, left parietal, and central electrodes. We also identified distance-related amplitude differences for both ordered and unordered sequences. While unordered sequences showed an effect in the time window of 500-750 ms at electrode clusters around anterior-frontal and right-frontal regions, ordered sequences differed in an earlier time window (190-275 ms) in frontal and right parieto-occipital regions. Only the mean amplitude difference between ordered and unordered sequences showed an association with arithmetic fluency at the left anterior-frontal electrode. While the earlier time window for ordered sequences is consistent with a more automated and efficient processing of ordered sequential items, distance-related differences in unordered sequences occur later in time., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Brunner et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Transcranial alternating current stimulation (tACS) offers a unique method to temporarily manipulate the activity of the stimulated brain region in a frequency-dependent manner. However, it is not clear if repetitive modulation of ongoing oscillatory activity with tACS over multiple days can induce changes in grey matter resting-state functional connectivity and white matter structural integrity. The current study addresses this question by applying multiple-session theta band stimulation on the left dorsolateral prefrontal cortex (L-DLPFC) during arithmetic training. Fifty healthy participants (25 males and 25 females) were randomly assigned to the experimental and sham groups, half of the participants received individually adjusted theta band tACS, and half received sham stimulation. Resting-state functional magnetic resonance (rs-fMRI) and diffusion-weighted imaging (DWI) data were collected before and after 3 days of tACS-supported procedural learning training. Resting-state network analysis showed a significant increase in connectivity for the frontoparietal network (FPN) with the precuneus cortex. Seed-based analysis with a seed defined at the primary stimulation site showed an increase in connectivity with the precuneus cortex, posterior cingulate cortex (PCC), and lateral occipital cortex. There were no effects on the structural integrity of white matter tracts as measured by fractional anisotropy, and on behavioral measures. In conclusion, the study suggests that multi-session task-associated tACS can produce significant changes in resting-state functional connectivity; however, changes in functional connectivity do not necessarily translate to changes in white matter structure or behavioral performance., (© 2023. The Author(s).)

In contrast to traditional expertise domains like chess and music, very little is known about the cognitive mechanisms in broader, more education-oriented domains like mathematics. This is particularly true for the role of mathematical experts' knowledge for domain-specific information processing in memory as well as for domain-specific and domain-general creativity. In the present work, we compared 115 experts in mathematics with 109 gender, age, and educational level matched novices in their performance in (a) a newly developed mathematical memory task requiring encoding and recall of structured and unstructured information and (b) tasks drawing either on mathematical or on domain-general creativity. Consistent with other expertise domains, experts in mathematics (compared to novices) showed superior short-term memory capacity for complex domain-specific material when presented in a structured, meaningful way. Further, experts exhibited higher mathematical creativity than novices, but did not differ from them in their domain-general creativity. Both lines of findings demonstrate the importance of experts' knowledge base in processing domain-specific material and provide new insights into the characteristics of mathematical expertise., (© 2023. The Author(s).)

Language-switching costs arise when learners encode information in one language and subsequently recall that information in a different language. The assumed cognitive mechanism behind these costs is the principle of encoding specificity that implies language-dependent representations of information. The aim of our study was to test this mechanism and to gain insights into the impact of language-switching on subsequent learning. To this end, we used retrieval-based learning as a carrier-paradigm. In a 2×3-design, 117 participants learned mathematical concepts with a practice-test or a restudy opportunity (within-subjects factor). In addition, the sample was divided into three groups regarding language-switching (between-subjects factor): one group without switching, one switched for the final tests, and one switched between initial learning and subsequent learning. Results show the expected main effects: participants performed better for the items learned via retrieval-based learning (testing-effect) and worse in conditions with language-switching (language-switching-costs). Most importantly, we were able to find an interaction between learning condition and language-switching: retrieval-based learning suffers particularly from language-switching. Additionally, our results indicate that language switching before subsequent learning seems to be particularly detrimental. These results provide both validation for encoding specificity as mechanism underlying language-switching costs and new information on the impact of the time of language-switching that can be considered in educational designs such as "Content and Language Integrated Learning.", Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Wußing, Grabner, Sommer and Saalbach.)

Previous studies on intelligence have demonstrated that higher abilities are associated with lower brain activation, indicating a higher neural efficiency. In other words, more able individuals use fewer brain resources. However, it is unclear whether the neural efficiency phenomenon also appears for mathematical performance, which is influenced by both domain-general giftedness and domain-specific competencies. Therefore, this study examined the effects of general giftedness (G) and excellence in mathematics (EM) on performance and brain activation while solving learning-based mathematical tasks that required translation from graphical to symbolic representations of functions. Overall, 118 high school students (aged 16-18) participated in the present study and were divided according to G and EM using a 2 × 2 study design. Participants worked on a function task requiring translation between symbolic and graphical representations of functions. Analyses of the behavioral data revealed positive effects of both G and EM on the accuracy of solutions and an interaction effect of both factors on reaction times, reflecting a positive effect of EM only among the gifted individuals. EEG analyses focused on oscillatory activity in the theta and alpha frequency bands and showed a significant effect of EM in the upper alpha band (10-12 Hz) event-related desynchronization (ERD) for both graphical and symbolic representations. Specifically, higher (compared to lower) EM was associated with a larger alpha ERD, indicating a higher level of brain activity. This stands in contrast with the neural efficiency phenomenon. These findings suggest that the neural efficiency phenomenon cannot be generalized to higher-order mathematical demands in high-performing individuals. Several explanations for this limitation are offered., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Background: One frequent learning obstacle in mathematics is conceptual interference. However, the majority of research on conceptual interference has focused on science. In this functional magnetic resonance imaging (fMRI) study, we examined the conceptual interference effects in both mathematics and science and the moderating influence of mathematical expertise., Methods: Thirty adult mathematicians and 31 gender-, age-, and intelligence-matched non-mathematicians completed a speeded reasoning tasks with statements from mathematics and science. Statements were either congruent (true or false according to both scientifically and naïve theories) or incongruent (differed in their truth value)., Findings: Both groups exhibited more errors and a slower response time when evaluating incongruent compared to congruent statements in the science and mathematics task, but mathematicians were less affected by naïve theories. In mathematics, the left dorsolateral prefrontal cortex was activated when inhibiting naïve theories, while in science it was the dorsolateral and the ventrolateral prefrontal cortex bilaterally. Mathematical expertise did not moderate the conceptual interference effect at the neural level., Conclusion: This study demonstrates that naïve theories in mathematics are still present in mathematicians, even though they are less affected by them in performance than novices. In addition, the differential brain activation in the mathematics and science task indicates that the extent of inhibitory control processes to resolve conceptual interference depends on the quality of the involved concepts., Competing Interests: Declaration of Competing Interest We wish to confirm that there are no known conflicts of interest associated with this publication. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us., (Copyright © 2022 The Authors. Published by Elsevier GmbH.. All rights reserved.)

Low-intensity transcranial electrical stimulation (tES), including alternating or direct current stimulation, applies weak electrical stimulation to modulate the activity of brain circuits. Integration of tES with concurrent functional MRI (fMRI) allows for the mapping of neural activity during neuromodulation, supporting causal studies of both brain function and tES effects. Methodological aspects of tES-fMRI studies underpin the results, and reporting them in appropriate detail is required for reproducibility and interpretability. Despite the growing number of published reports, there are no consensus-based checklists for disclosing methodological details of concurrent tES-fMRI studies. The objective of this work was to develop a consensus-based checklist of reporting standards for concurrent tES-fMRI studies to support methodological rigor, transparency and reproducibility (ContES checklist). A two-phase Delphi consensus process was conducted by a steering committee (SC) of 13 members and 49 expert panelists through the International Network of the tES-fMRI Consortium. The process began with a circulation of a preliminary checklist of essential items and additional recommendations, developed by the SC on the basis of a systematic review of 57 concurrent tES-fMRI studies. Contributors were then invited to suggest revisions or additions to the initial checklist. After the revision phase, contributors rated the importance of the 17 essential items and 42 additional recommendations in the final checklist. The state of methodological transparency within the 57 reviewed concurrent tES-fMRI studies was then assessed by using the checklist. Experts refined the checklist through the revision and rating phases, leading to a checklist with three categories of essential items and additional recommendations: (i) technological factors, (ii) safety and noise tests and (iii) methodological factors. The level of reporting of checklist items varied among the 57 concurrent tES-fMRI papers, ranging from 24% to 76%. On average, 53% of checklist items were reported in a given article. In conclusion, use of the ContES checklist is expected to enhance the methodological reporting quality of future concurrent tES-fMRI studies and increase methodological transparency and reproducibility., (© 2022. © The Author(s).)

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of a fact-retrieval account postulate that these are also solved through fact retrieval, whereas proponents of a compacted-counting account propose that solving very small additions (with operands between 1 and 4) involves highly automatized and unconscious compacted counting. In the present electroencephalography (EEG) study, we put these two accounts to the test by comparing neurophysiological correlates of solving very small additions and multiplications. Forty adults worked on an arithmetic production task involving all (nontie) single-digit additions and multiplications. Afterward, participants completed trial-by-trial strategy self-reports. In our EEG analyses, we focused on induced activity (event-related synchronization/desynchronization, ERS/ERD) in three frequency bands (theta, lower alpha, upper alpha). Across all frequency bands, we found higher evidential strength for similar rather than different neurophysiological processes accompanying the solution of very small addition and multiplication problems. In the alpha bands, evidence for similarity was even stronger when operand-1-problems were excluded. In two additional analyses, we showed that ERS/ERD can differentiate between self-reported problem-solving strategies (retrieval vs. procedure) and between very small n × 1 and n + 1 problems, demonstrating its high sensitivity to cognitive processes in arithmetic. The present findings support a fact-retrieval account, suggesting that both very small additions and multiplications are solved through fact retrieval. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group., (© 2021. The Author(s).)

Over the last decades, interest in transcranial electrical stimulation (tES) has grown, as it might allow for causal investigations of the associations between cortical activity and cognition as well as to directly influence cognitive performance. The main objectives of the present work were to assess whether tES can enhance the acquisition and application of arithmetic abilities, and whether it enables a better assessment of underlying neurophysiological processes. To this end, the present, double-blind, sham-controlled study assessed the effects of six active stimulations (three tES protocols: anodal transcranial direct current stimulation (tDCS), alpha band transcranial alternating current stimulation (tACS), and theta band tACS; targeting the left dorsolateral prefrontal cortex or the left posterior parietal cortex) on the acquisition of an arithmetic procedure, arithmetic facts, and event-related synchronization/desynchronization (ERS/ERD) patterns. 137 healthy adults were randomly assigned to one of seven groups, each receiving one of the tES-protocols during learning. Results showed that frontal theta band tACS reduced the repetitions needed to learn novel facts and both, frontal and parietal theta band tACS accelerated the decrease in calculation times in fact learning problems. The beneficial effect of frontal theta band tACS may reflect enhanced executive functions, allowing for better control and inhibition processes and hence, a faster acquisition and integration of novel fact knowledge. However, there were no significant effects of the stimulations on procedural learning or ERS/ERD patterns. Overall, theta band tACS appears promising as a support for arithmetic fact training, but effects on procedural calculations and neurophysiological processes remain ambiguous., (Copyright © 2021 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

When students learn a scientific theory that conflicts with their earlier naïve theories, the newer and more correct knowledge does not always replace the older and more incorrect knowledge. Both may coexist in a learner's long-term memory. Using a new speeded reasoning task, Shtulman and Valcarcel (2012) showed that naïve theories interfere with retrieving scientific theories. Although mathematics learning is a central aim of schooling and a vital prerequisite for success in life, no study has tested whether Shtulman and Valcarcel's (2012) findings generalize to mathematical subdomains such as algebra, geometry, and probability. Additionally, it is unclear how the interference strength relates to domain-specific and domain-general competencies. We investigated these questions using the speeded reasoning task with new mathematical items in a sample of 62 university students. Solution rates and reaction times indicated interference between naïve and scientific mathematical theories. Additionally, interference strength was inversely related to mathematical achievement and unrelated to general inhibitory control. After controlling for general inhibitory control, mathematical achievement was still substantially related to interference strength. These findings indicate that interference strength reflects domain-specific achievement rather than domain-general inhibitory control., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training. Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems. Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals' low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge., (Copyright © 2021 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Scientific investigations have long emphasized the cortex's role in cognitive transfer and arithmetic abilities. To date, however, this assumption has not been thoroughly empirically investigated. Here we demonstrated that primitive mechanisms-lower visual channels-have a causal role in cognitive transfer of complex skills such as symbolic arithmetic. We found that exposing only one monocular channel to a visuospatial training resulted in a larger transfer effect in the trained monocular channel compared to the untrained monocular channel. Such cognitive transfer was found for both novel figural-spatial problems (near transfer) and novel subtraction problems (far transfer). Importantly, the benefits of the trained eye were not observed in old problems and in other tasks that did not involve visuospatial abilities (the Stroop task, a multiplication task). These results challenge the exclusive role of the cortex in cognitive transfer and complex arithmetic. In addition, the results suggest a new mechanism for the emergence of cognitive skills, that could be shared across different species.

Mathematical creativity is perceived as an increasingly important aspect of everyday life and, consequently, research has increased over the past decade. However, mathematical creativity has mainly been investigated in children and adolescents so far. Therefore, the first goal of the current study was to develop a mathematical creativity measure for adults (MathCrea) and to evaluate its reliability and construct validity in a sample of 100 adults. The second goal was to investigate how mathematical creativity is related to intelligence, mathematical competence, and general creativity. The MathCrea showed good reliability, and confirmatory factor analysis confirmed that the data fitted the assumed theoretical model, in which fluency, flexibility, and originality constitute first order factors and mathematical creativity a second order factor. Even though intelligence, mathematical competence, and general creativity were positively related to mathematical creativity, only numerical intelligence and general creativity predicted unique variance of mathematical creativity. Additional analyses separating quantitative and qualitative aspects of mathematical creativity revealed differential relationships to intelligence components and general creativity. This exploratory study provides first evidence that intelligence and general creativity are important predictors for mathematical creativity in adults, whereas mathematical competence seems to be not as important for mathematical creativity in adults as in children.

Non-invasive brain stimulation (NIBS) has been highlighted as a powerful tool to promote neuroplasticity, and an attractive approach to support cognitive remediation. Here we provide a systematic review of 26 papers using NIBS to ameliorate cognitive dysfunctions in three prevalent neurodevelopmental disorders: Attention-Deficit/Hyperactivity Disorder (ADHD), Developmental Dyslexia and Developmental Dyscalculia. An overview of the state of research shows a predominance of studies using repetitive transcranial magnetic stimulation (rTMS) and transcranial direct current stimulation (tDCS) techniques, and an unequal distribution among clinical conditions. Regarding the utility of NIBS, the results are promising but also ambiguous. Twenty-three papers reported beneficial effects, but many of these effects were found only once or were only partially replicated and some studies even reported detrimental effects. Furthermore, most studies differed in at least one core aspect, the NIBS applied, the questionnaires and cognitive tests conducted, or the age group investigated, and sample sizes were mostly small. Hence, further studies are needed to rigorously examine the potential of NIBS in the remediation of cognitive functions. Finally, we discuss potential caveats and future directions. We reason that if adequately addressing these challenges NIBS can be feasible, with potential benefits in treating neurodevelopmental disorders., Competing Interests: Conflicts of interest Roi Cohen Kadosh serves on the scientific advisory boards of Neuroelectrics Inc. and Innosphere Inc. Katya Rubia has received a grant from TAKEDA pharmaceuticals for another study. The other authors declare that there is no conflict of interest regarding the publication of this paper., (Copyright © 2021 Elsevier B.V. All rights reserved.)

The inverse relationship between test anxiety and test performance is commonly explained by test-anxious students' tendency to worry about a test and the consequences of failing. However, other cognitive facets of test anxiety have been identified that could account for this link, including interference by test-irrelevant thoughts and lack of confidence. In this study, we compare different facets of test anxiety in predicting test performance. Seven hundred thirty university students filled out the German Test Anxiety Inventory after completing a battery of standardized tests assessing general intelligence and mathematical competencies. Multiple regressions revealed that interference and lack of confidence but not worry or arousal explained unique variance in students' test performance. No evidence was found for a curvilinear relationship between arousal and performance. The present results call for revisiting the role of worries in explaining the test anxiety-performance link and can help educators to identify students who are especially at risk of underperforming on tests., Competing Interests: Conflict of InterestThe authors declare no competing interests., (© The Author(s) 2021.)

Behavioural and neuroimaging studies have recently demonstrated that symbolic numerical order processing (i.e., deciding whether numbers are in an increasing/decreasing sequence or not) and symbolic numerical magnitude processing (e.g., deciding which of two numerals is larger) engage different cognitive mechanisms and brain regions. Because of this dissociation, growing interest has emerged to better understand the neurocognitive mechanisms of symbolic numerical order processing and their relationship to individual differences in arithmetic performance. In the present functional imaging work, we further investigated this link in a group of thirty children (7.2-10.25 years) from elementary school, who completed a symbolic numerical order verification (are the numbers going up? e.g., 1-2-3) and a symbolic numerical magnitude comparison task (which is the larger number? e.g., 5-7) inside the scanner, as well as an arithmetic fluency test outside the scanner. Behavioural results demonstrated the unique role of numerical order to predict children's arithmetic skills and confirmed its mediating power to explain the association between numerical magnitude and arithmetic performance. Imaging results showed a significant association between numerical order and arithmetic in the intersection of the right inferior frontal gyrus and insula, as well as the posterior middle temporal gyrus. An age-dependent change in brain activity was found in the left intraparietal sulcus. These findings solidify the developmental importance of symbolic numerical order processing in children and provide new evidence that the semantic control network mediates the relationship with arithmetic performance., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

Previously conducted structural magnetic resonance imaging (MRI) studies on the neuroanatomical correlates of mathematical abilities and competencies have several methodological limitations. Besides small sample sizes, the majority of these studies have employed voxel-based morphometry (VBM)-a method that, although it is easy to implement, has some major drawbacks. Taking this into account, the current study is the first to investigate in a large sample of typically developed adults the associations between mathematical abilities and variations in brain surface structure by using surface-based morphometry (SBM). SBM is a method that also allows the investigation of brain morphometry by avoiding the pitfalls of VBM. Eighty-nine young adults were tested with a large battery of psychometric tests to measure mathematical competencies in four different areas: (1) simple arithmetic; (2) complex arithmetic; (3) higher-order mathematics; and (4) numerical intelligence. Also, we asked participants for their mathematics grades for their final school exams. Inside the MRI scanner, we collected high-resolution T1-weighted anatomical images from each subject. SBM analyses were performed with the computational anatomy toolbox (CAT12) and indices for cortical thickness, for cortical surface complexity, for gyrification, and sulcal depth were calculated. Further analyses revealed associations between: (1) the cortical surface complexity of the right superior temporal gyrus and numerical intelligence; (2) the depth of the right central sulcus and adults' ability to solve complex arithmetic problems; and (3) the depth of the left parieto-occipital sulcus and adults' higher-order mathematics competence. Interestingly, no relationships with previously reported brain regions were observed, thus, suggesting the importance of similar research to confirm the role of the brain regions found in this study., (Copyright © 2020 Heidekum, Vogel and Grabner.)

Arithmetic abilities are among the most important school-taught skills and form the basis for higher mathematical competencies. At the same time, their acquisition and application can be challenging. Hence, there is broad interest in methods to improve arithmetic abilities. One promising method is transcranial direct current stimulation (tDCS). In the present study, we compared two anodal tDCS protocols in their efficacy to improve arithmetic performance and working memory. In addition, we investigated stimulation-related electrophysiological changes. Three groups of participants solved arithmetic problems (additions and subtractions) and an n-back task before, during, and after receiving either frontal or parietal anodal tDCS (25 min; 1 mA) or sham stimulation. EEG was simultaneously recorded to assess stimulation effects on event-related (de-) synchronisation (ERS/ERD) in theta and alpha bands. Persons receiving frontal stimulation showed an acceleration of calculation speed in large subtractions from before to during and after stimulation. However, a comparable, but delayed (apparent only after stimulation) increase was also found in the sham stimulation group, while it was absent in the group receiving parietal stimulation. In additions and small subtractions as well as the working memory task, analyses showed no effects of stimulation. Results of ERS/ERD during large subtractions indicate changes in ERS/ERD patterns over time. In the left hemisphere there was a change from theta band ERD to ERS in all three groups, whereas a similar change in the right hemisphere was restricted to the sham group. Taken together, tDCS did not lead to a general improvement of arithmetic performance. However, results indicate that frontal stimulation accelerated training gains, while parietal stimulation halted them. The absence of general performance improvements, but acceleration of training effects might be a further indicator of the advantages of using tDCS as training or learning support over tDCS as a sole performance enhancer., (Copyright © 2020 Mosbacher, Brunner, Nitsche and Grabner.)

Single-digit multiplications are mainly solved by memory retrieval. However, these problems are also prone to errors due to systematic interference (i.e., co-activation of interconnected but incorrect solutions). Semantic control processes are crucial to overcome this type of interference and to retrieve the correct information. Previous research suggests the importance of several brain regions such as the left inferior frontal cortex and the intraparietal sulcus (IPS) for semantic control. But, this evidence is mainly based on tasks measuring interference during the processing of lexico-semantic information (e.g., pictures or words). Here, we investigated whether semantic control during arithmetic problem solving (i.e., multiplication fact retrieval) draws upon similar or different brain mechanisms as in other semantic domains (i.e., lexico-semantic). The brain activity of 46 students was measured with fMRI while participants performed an operand-related-lure (OR) and a picture-word (PW) task. In the OR task participants had to verify the correctness of a given solution to a single-digit multiplication. Similarly, in the PW task, participants had to judge whether a presented word matches the concept displayed in a picture or not. Analyses showed that resolving interference in these two tasks modulates the activation of a widespread fronto-parietal network (e.g., left/right IFG, left insula lobe, left IPS). Importantly, conjunction analysis revealed a neural overlap in the left inferior frontal gyrus (IFG) pars triangularis and left IPS. Additional Bayesian analyses showed that regions that are thought to store lexico-semantic information (e.g., left middle temporal gyrus) did not show evidence for an arithmetic interference effect. Overall, our findings not only indicate that semantic control plays an important role in arithmetic problem solving but also that it is supported by common brain regions across semantic domains. Additionally, by conducting Bayesian analysis we confirmed the hypothesis that the semantic control network contributes differently to semantic tasks of various domains., (Copyright © 2019 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

The relative importance of different factors in the development of human skills has been extensively discussed. Research on expertise indicates that focused practice may be the sole determinant of skill, while intelligence researchers underline the relative importance of abilities at even the highest level of skill. There is indeed a large body of research that acknowledges the role of both factors in skill development and retention. It is, however, unknown how intelligence and practice come together to enable the acquisition and retention of complex skills across the life span. Instead of focusing on the 2 factors, intelligence and practice, in isolation, here we look at their interplay throughout development. In a longitudinal study that tracked chess players throughout their careers, we show that both intelligence and practice positively affect the acquisition and retention of chess skill. Importantly, the nonlinear interaction between the 2 factors revealed that more intelligent individuals benefited more from practice. With the same amount of practice, they acquired chess skill more quickly than less intelligent players, reached a higher peak performance, and arrested decline in older age. Our research demonstrates the futility of scrutinizing the relative importance of highly intertwined factors in human development., Competing Interests: The authors declare no conflict of interest.

Functional neuroimaging studies have revealed that, compared with novices, science experts show increased activation in dorsolateral and ventrolateral prefrontal brain areas associated with inhibitory control mechanisms when providing scientifically valid responses in tasks related to electricity and mechanics. However, no study thus far has explored the relationship between activation of the key brain regions involved in inhibitory control mechanisms, namely the ventrolateral prefrontal cortex (VLPC) and dorsolateral prefrontal cortex (DLPC), and individual differences in conceptual science competence, while controlling for scientific training. In the present study, 24 secondary school students (11 female participants, 13 male participants) were selected from a larger pool based on their performance on a conceptual science questionnaire and were divided into groups with low and high conceptual science competence. In an fMRI block design, participants had to verify the correctness (true or false) of congruent and incongruent statements. In congruent statements, both spontaneous and scientific conceptions about given natural phenomena lead to a scientifically appropriate judgment. However, in incongruent statements, commonly held spontaneous conceptions about natural phenomena lead to a scientifically inappropriate judgment. The interaction effect reveals that students with higher conceptual science competence display stronger activation of the left VLPC and DLPC in incongruent trials than in congruent trials. These findings show that activation of the VLPC and DLPC when reasoning in incongruent situations underlies individual differences in conceptual science competence, and suggests stronger recruitment of inhibitory control mechanisms in more competent individuals., (© 2019 Wiley Periodicals, Inc.)

Within children's multiplication fact retrieval, performance can be influenced by various effects, such as the well-known problem size effect (i.e., smaller problems are solved faster and more accurately) and the more recent interference effect (i.e., the quality of memory representations of problems depends on previously learned problems; the more similar a problem is to a previously learned one, the more proactive interference impacts on storing in long-term-memory). This interference effect has been observed in behavioral studies, and determines a substantial part of performance beyond problem size. Unlike the problem size effect, the neural basis of the interference effect in children has not been studied. To better understand the underpinning mechanisms behind children's arithmetic fact retrieval, we aimed to investigate the neural basis of both effects in typically developing children. Twenty-four healthy 9- to 10-year-olds took part in a behavioral and fMRI scanning session, during which multiplication items had to be solved. Data were analyzed by manipulating problem size and interference level in a 2 × 2 factorial design. Concurring with previous studies, our results reveal clear behavioral effects of problem size and interference, with larger and high interfering items being solved significantly slower. On the neural level, a clear problem size effect was observed in a fronto-parietal and temporal network. The interference effect, however, was not detected; no clear neural distinctions were observed between low and high interfering items., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Recent findings have demonstrated that numerical order processing (i.e., the application of knowledge that numbers are organized in a sequence) constitutes a unique and reliable predictor of arithmetic performance. The present work investigated two central questions to further our understanding of numerical order processing and its relationship to arithmetic. First, are numerical order sequences processed without conscious monitoring (i.e., automatically)? Second, are automatic and intentional ordinal processing differentially related to arithmetic performance? In the first experiment, adults completed a novel ordinal congruity task. Participants had to evaluate whether number triplets were arranged in a correct (e.g., ) physical order or not (e.g., ). Results of this experiment showed that participants were faster to decide that the physical size of ascending numbers was in-order when the physical and numerical values were congruent compared to when they were incongruent (i.e., congruency effect). In the second experiment, a new group of participants was asked to complete an ordinal congruity task, an ordinal verification task (i.e., are the number triplets in a correct order or not) and an arithmetic fluency test. Results of this experiment revealed that the automatic processing of ascending numerical order is influenced by the numerical distance of the numbers. Correlation analysis further showed that only reaction time measures of the intentional ordinal verification task were associated with arithmetic performance. While the findings of the present work suggest that ascending numerical order is processed automatically, the relationship between numerical order processing and arithmetic appears to be limited to the intentional manipulation of numbers. The present findings show that the mental engagement of verifying the order of numbers is a crucial factor for explaining the link between numerical order processing and arithmetic performance., (Copyright © 2018 Elsevier B.V. All rights reserved.)

Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation method that allows to directly modulate brain oscillations of a given frequency. Using this method, it was recently shown that increasing alpha (10Hz) oscillations improved creative ideation with figural material and that increasing gamma (40Hz) oscillations speeded up performance in a figural matrices intelligence task. The aim of the present study was to examine whether these findings generalize to verbal creativity and intelligence tasks. In addition, we explored whether the stimulation effects are moderated by individual differences in creative potential and intelligence. Twenty-two adults received 10Hz, 40Hz and sham tACS while they worked on a verbal creativity (alternate uses) task and a verbal intelligence (anagram) task. Analyses revealed that 10Hz stimulation had a marginally significant effect on ideational fluency in the alternate uses task, whereas originality was unaffected. The beneficial effect of stimulation on fluency tended to emerge mainly in the individuals with higher creative potential. In the verbal intelligence task, in contrast, 40Hz stimulation did neither impact on performance nor interacted with individual differences in intelligence. These findings provide first tentative evidence that enhancing alpha oscillations through tACS may improve creative thinking not only in the figural but also in the verbal domain. The previously reported beneficial effect of gamma tACS on figural intelligence, however, could not be observed in a verbal task. In sum, the present study further corroborates the causal link between alpha oscillations and creative thinking and suggests that tACS may be a promising tool to enhance cognitive processes., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

In the development of math ability, a large variability of performance in solving simple arithmetic problems is observed and has not found a compelling explanation yet. One robust effect in simple multiplication facts is the problem size effect, indicating better performance for small problems compared to large ones. Recently, behavioral studies brought to light another effect in multiplication facts, the interference effect. That is, high interfering problems (receiving more proactive interference from previously learned problems) are more difficult to retrieve than low interfering problems (in terms of physical feature overlap, namely the digits, De Visscher and Noël, 2014). At the behavioral level, the sensitivity to the interference effect is shown to explain individual differences in the performance of solving multiplications in children as well as in adults. The aim of the present study was to investigate the individual differences in multiplication ability in relation to the neural interference effect and the neural problem size effect. To that end, we used a paradigm developed by De Visscher, Berens, et al. (2015) that contrasts the interference effect and the problem size effect in a multiplication verification task, during functional magnetic resonance imaging (fMRI) acquisition. Forty-two healthy adults, who showed high variability in an arithmetic fluency test, participated in our fMRI study. In order to control for the general reasoning level, the IQ was taken into account in the individual differences analyses. Our findings revealed a neural interference effect linked to individual differences in multiplication in the left inferior frontal gyrus, while controlling for the IQ. This interference effect in the left inferior frontal gyrus showed a negative relation with individual differences in arithmetic fluency, indicating a higher interference effect for low performers compared to high performers. This region is suggested in the literature to be involved in resolution of proactive interference. Besides, no correlation between the neural problem size effect and multiplication performance was found. This study supports the idea that the interference due to similarities/overlap of physical traits (the digits) is crucial in memorizing arithmetic facts and in determining individual differences in arithmetic., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Researchers have recently started evaluating whether stimulating the brain noninvasively with a weak and painless electrical current (transcranial Electrical Stimulation, tES) enhances physiological and cognitive processes. Some studies found that tES has weak but positive effects on brain physiology, cognition, or assessment performance, which has attracted massive public interest. We present the first meta-analytic test of the hypothesis that tES in a learning phase is more effective than tES in an assessment phase. The meta-analysis included 246 effect sizes from studies on language or mathematical competence. The effect of tES was stronger when stimulation was administered during a learning phase (d=0.712) as compared to stimulation administered during test performance (d=0.207). The overall effect was stimulation-dosage specific and, as found in a previous meta-analysis, significant only for anodal stimulation and not for cathodal. The results provide evidence for the modulation of long-term synaptic plasticity by tES in the context of practically relevant learning tasks and highlight the need for more systematic evaluations of tES in educational settings., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

A growing body of evidence from functional Magnetic Resonance Imaging adaptation (fMRIa) has implicated the left intraparietal sulcus (IPS) as a crucial brain region representing the semantic of number symbols. However, it is currently unknown to what extent the left IPS brain activity can be generalized across modalities (e.g., Arabic digits and spoken number words) and how robust and reproducible numerical adaptation effects are. In two separate fMRIa experiments we habituated the brain response of 20 native English-speaking (Experiment 1) and 34 native German-speaking (Experiment 2) adults to Arabic digits or spoken number words. Consistent with previous findings, experiment 1 revealed numerical ratio dependent adaptation to Arabic numerals in the left IPS using both conventional and cortex-based alignment techniques. Experiment 2 revealed numerical ratio dependent signal recovery in the left IPS following adaptation to both Arabic numerals and spoken number words using both conventional and cortex-based alignment techniques. Together, these findings suggest that the left IPS is involved in symbolic number processing across modalities., (Copyright © 2017 Elsevier Inc. All rights reserved.)

During the course of divergent thinking (DT), the number of generated ideas decreases while the originality of ideas increases. This phenomenon is labeled as serial order effect in DT. The present study investigated whether different executive processes (i.e., updating, shifting, and inhibition) specifically contribute to the serial order effect in DT. Participants' executive functions were measured by corresponding experimental tasks outside of the EEG lab. They were required to generate original uses of conventional objects (alternative uses task) during EEG recording. The behavioral results revealed that the originality of ideas was higher in later stage of DT (i.e., Epoch 2) than in its earlier stage (i.e., Epoch 1) for higher-shifting individuals, but showed no difference between two epochs for lower-shifting individuals. The EEG results revealed that lower-inhibition individuals showed stronger upper alpha (10-13Hz) synchronization in left frontal areas during Epoch 1 compared to during Epoch 2. For higher-inhibition individuals, no changes in upper alpha activity from Epoch 1 to Epoch 2 were found. These findings indicated that shifting and inhibition contributed to create a serial order effect in DT, perhaps because individuals suppress interference from obvious ideas and switch to new idea categories during DT, thus more original ideas appear as time passes by., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Background: A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks., Methods: We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition., Results: We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand., Conclusions: The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area., (Copyright © 2016 Elsevier Inc. All rights reserved.)

The present study aimed to explore the neural correlates underlying the effects of idea evaluation on idea generation in creative thinking. Participants were required to generate original uses of conventional objects (alternative uses task) during EEG recording. A reflection task (mentally evaluating the generated ideas) or a distraction task (object characteristics task) was inserted into the course of idea generation. Behavioral results revealed that participants generated ideas with higher originality after evaluating the generated ideas than after performing the distraction task. The EEG results revealed that idea evaluation was accompanied with upper alpha (10-13 Hz) synchronization, most prominent at frontal cortical sites. Moreover, upper alpha activity in frontal cortices during idea generation was enhanced after idea evaluation. These findings indicate that idea evaluation may elicit a state of heightened internal attention or top-down activity that facilitates efficient retrieval and integration of internal memory representations., (Copyright © 2016 Elsevier Inc. All rights reserved.)

The successful acquisition of arithmetic skills is an essential step in the development of mathematical competencies and has been associated with neural activity in the left posterior parietal cortex (PPC). It is unclear, however, whether this brain region plays a causal role in arithmetic skill acquisition and whether arithmetic learning can be modulated by means of non-invasive brain stimulation of this key region. In the present study we addressed these questions by applying transcranial direct current stimulation (tDCS) over the left PPC during a short-term training that simulates the typical path of arithmetic skill acquisition (specifically the transition from effortful procedural to memory-based problem-solving strategies). Sixty participants received either anodal, cathodal or sham tDCS while practising complex multiplication and subtraction problems. The stability of the stimulation-induced learning effects was assessed in a follow-up test 24 h after the training. Learning progress was modulated by tDCS. Cathodal tDCS (compared with sham) decreased learning rates during training and resulted in poorer performance which lasted over 24 h after stimulation. Anodal tDCS showed an operation-specific improvement for subtraction learning. Our findings extend previous studies by demonstrating that the left PPC is causally involved in arithmetic learning (and not only in arithmetic performance) and that even a short-term tDCS application can modulate the success of arithmetic knowledge acquisition. Moreover, our finding of operation-specific anodal stimulation effects suggests that the enhancing effects of tDCS on learning can selectively affect just one of several cognitive processes mediated by the stimulated area., (© 2015 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.)

The problem size effect is a well-established finding in arithmetic problem solving and is characterized by worse performance in problems with larger compared to smaller operand size. Solving small and large arithmetic problems has also been shown to involve different cognitive processes and distinct electroencephalography (EEG) oscillations over the left posterior parietal cortex (LPPC). In this study, we aimed to provide further evidence for these dissociations by using transcranial direct current stimulation (tDCS). Participants underwent anodal (30min, 1.5 mA, LPPC) and sham tDCS. After the stimulation, we recorded their neural activity using EEG while the participants solved small and large arithmetic problems. We found that the tDCS effects on performance and oscillatory activity critically depended on the problem size. While anodal tDCS improved response latencies in large arithmetic problems, it decreased solution rates in small arithmetic problems. Likewise, the lower-alpha desynchronization in large problems increased, whereas the theta synchronization in small problems decreased. These findings reveal that the LPPC is differentially involved in solving small and large arithmetic problems and demonstrate that the effects of brain stimulation strikingly differ depending on the involved neuro-cognitive processes.

The ability to accurately process numerical magnitudes and solve mental arithmetic is of highest importance for schooling and professional career. Although impairments in these domains in disorders such as developmental dyscalculia (DD) are highly detrimental, remediation is still sparse. In recent years, transcranial brain stimulation methods such as transcranial Direct Current Stimulation (tDCS) have been suggested as a treatment for various neurologic and neuropsychiatric disorders. The posterior parietal cortex (PPC) is known to be crucially involved in numerical magnitude processing and mental arithmetic. In this study, we evaluated whether tDCS has a beneficial effect on numerical magnitude processing and mental arithmetic. Due to the unclear lateralization, we stimulated the left, right as well as both hemispheres simultaneously in two experiments. We found that left anodal tDCS significantly enhanced performance in a number comparison and a subtraction task, while bilateral and right anodal tDCS did not induce any improvements compared to sham. Our findings demonstrate that the left PPC is causally involved in numerical magnitude processing and mental arithmetic. Furthermore, we show that these cognitive functions can be enhanced by means of tDCS. These findings encourage to further investigate the beneficial effect of tDCS in the domain of mathematics in healthy and impaired humans.

While the left angular gyrus (lAG) has been repeatedly implicated in mental arithmetic, its precise functional role has not been established. On the one hand, it has been speculated that the lAG is involved in task-specific processes. On the other hand, the observation of relative deactivation during arithmetic has led to the contention that differential lAG activation reflects task-unrelated difficulty effects associated with the default mode network (DMN). Using functional magnetic resonance imaging, we investigated the neural correlates of the associative confusion effect that allowed us to dissociate effects of task difficulty and task-related arithmetic processes on lAG activation. The associative confusion effect is characterized by poorer performance while verifying addition and multiplication equations whose solutions are associated with the other operation (confusion equations: e.g., "9 × 6 = 15") compared with solutions unrelated to both operations (non-confusion equations: e.g., "9 × 6 = 52"). Comparing these two conditions revealed higher activation of the anterior lAG (areas PGa, PFm, and PF) and the left dorsolateral prefrontal cortex for the confusion problems. This effect displayed only slight anatomical overlap with the well-established reverse problem-size effect (small minus large problems) and task-related deactivation in the parietal cortex. The finding of greater lAG activity (less deactivation) in the more difficult task condition is inconsistent with the hypothesis that lAG activation during mental arithmetic reflects task difficulty related modulations of the DMN. Instead, the present findings provide further support for the symbol-referent mapping hypothesis, suggesting that the lAG mediates the automatic mapping of arithmetic problems onto solutions stored in memory., (Copyright © 2011 Wiley Periodicals, Inc.)

How are numerical and non-numerical magnitudes processed in the brain? Brain imaging research, primarily using comparison paradigms (i.e. judging which of two magnitudes is larger), has provided strong evidence demonstrating that the intraparietal sulcus (IPS) is a key region for processing both numerical (e.g. Arabic numerals, arrays of dots) and non-numerical magnitudes (e.g. height, brightness). These studies have suggested that there is both activation overlap and segregation in the brain regions involved in processing different dimensions of magnitude. In the present functional Magnetic Resonance Imaging (fMRI) study, we extended this line of investigation by probing the brain mechanisms underlying the mapping of numerical (Arabic numerals) and non-numerical magnitudes (brightness levels) onto a number line. Consistent with previous studies the present results revealed that number and brightness estimation was associated with overlapping activation within right lateralized areas of the posterior IPS. In addition, the contrast between number and brightness estimation revealed that bilateral anterior regions of the IPS are specifically involved in the process of estimating the position of symbolic numbers onto a number line. Furthermore, we found a significant influence of landmark reference points (0, 50 and 100) on brain activation in the right IPS for number estimation only. No regions were found to be specifically associated with brightness estimation. The results of this study reveal that the estimation of both numerical and non-numerical magnitude are associated with the engagement of a right lateralized magnitude system, but that symbolic number estimation is associated with additional engagement of bilateral regions of the anterior IPS., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

There has been a long tradition of research on mathematics education showing that children and adults use different strategies to solve arithmetic problems. Neurophysiological studies have recently begun to investigate the brain correlates of these strategies. The existing body of data, however, reflect static end points of the learning process and do not provide information on how brain activity changes in response to training or intervention. In this study, we explicitly address this issue by training participants in using fact retrieval strategies. We also investigate whether brain activity related to arithmetic fact learning is domain-specific or whether this generalizes to other learning materials, such as the solution of figural-spatial problems. Twenty adult students were trained on sets of two-digit multiplication problems and figural-spatial problems. After the training, they were presented with the trained and untrained problems while their brain activity was recorded by means of electroencephalography (EEG). In both problem types, the training resulted in accuracies over 90% and significant decreases in solution times. Analyses of the oscillatory EEG data also revealed training effects across both problem types. Specifically, we observed training-related activity increases in the theta band (3-6 Hz) and decreases in the lower alpha band (8-10 Hz), especially over parietooccipital and parietal brain regions. These results provide the first evidence that a short-term fact retrieval training results in significant changes in oscillatory EEG activity. These findings further corroborate the role of the theta band in the retrieval of semantic information from memory and suggest that theta activity is sensitive to fact retrieval not only in mental arithmetic but also in other domains.

In this study, we presented sentences either ending with high or low probability cloze words or semantically incongruent words to investigate the influence of L2 proficiency on electrophysiological correlates of semantic processing in bilinguals. Event-related potentials (ERPs) as well as the oscillatory dynamics of the EEG signal, specifically, frequency power changes expressed as event-related (de)synchronization (ERD/S), were analyzed. Replicating earlier results, we found an N400 on semantically incongruent words, as well as on low cloze probability words. For the bilinguals investigated in the present study, N400 latency in the low cloze probability condition was found to be modulated by L2 proficiency, indicating that L2 proficiency in our sample might have influenced the speed of semantic integration. Relative Theta power increased for all three word conditions, but no influence of proficiency was observed. Different from the ERP results, we found a stronger increase in theta power for low cloze probability words than for incongruent and high cloze probability words, especially over temporo-parietal brain areas. The spatial distribution of the theta ERD/S results also differed from the N400 topography. Whereas the N400 showed a typical topography with a maximum over temporo-posterior electrode positions, the theta ERD/S topography was maximal for high and low cloze probability words over left central-posterior electrode positions. These findings show that the ERP and ERD/S results are sensitive to semantic processing. The different pattern of the ERD/S results compared to the ERP results, functionally and with regard to topography, suggests that the ERD/S reflects a different aspect or stage of semantic processing, possibly the successful conceptualization of a sentence.

The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams) is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus (AG) activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left AG activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left AG activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance.

Behavioral research has shown that arithmetic problems (e.g., 6+2=) are solved with various strategies, which can be inferred from the size of the presented problems or from trial-by-trial verbal strategy reports. The validity of these verbal strategy reports, however, has been repeatedly questioned. In the present electroencephalography study, we compared the association of both approaches with the oscillatory brain responses during arithmetic problem solving. Nineteen adults solved small and large addition and subtraction problems and indicated the applied strategy (fact retrieval vs. procedure use) on a trial-by-trial basis by means of verbal strategy reports. Analysis of event-related (de-)synchronization (ERS/ERD) in theta and alpha frequencies revealed a general convergence of verbal strategy reports and the problem size approach, with fact retrieval being accompanied by higher left-hemispheric theta ERS, and procedural strategies being reflected in higher widespread ERD in the lower alpha band and bilateral parietooccipital ERD in the upper alpha band. A direct comparison of the neurophysiological data from both approaches suggests a higher sensitivity of verbal strategy reports to problem solving strategies applied in mental arithmetic, particularly for large problems. Taken together, the current data provide the first neurophysiological evidence for the validity of verbal strategy reports., (Copyright © 2011 Elsevier B.V. All rights reserved.)