Electrophysiological correlates of symbolic numerical order processing.

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.

Mathematical expertise: the role of domain-specific knowledge for memory and creativity.

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.

Modulation of resting-state networks following repetitive transcranial alternating current stimulation of the dorsolateral prefrontal cortex.

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.

Interference between naïve and scientific theories in mathematics and science: An fMRI study comparing mathematicians and non-mathematicians.

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.

Fact retrieval or compacted counting in arithmetic-A neurophysiological investigation of two hypotheses.

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).

Revisiting the Role of Worries in Explaining the Link Between Test Anxiety and Test Performance.

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.

Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders.

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.

Theta Band Transcranial Alternating Current Stimulation Enhances Arithmetic Learning: A Systematic Comparison of Different Direct and Alternating Current Stimulations.

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.

Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years.

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

Developmental brain dynamics of numerical and arithmetic abilities.

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.

Interference between naïve and scientific theories occurs in mathematics and is related to mathematical achievement.

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.

Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study.

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.

Mathematical Creativity in Adults: Its Measurement and Its Relation to Intelligence, Mathematical Competence and General Creativity.

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.

Associations Between Individual Differences in Mathematical Competencies and Surface Anatomy of the Adult Brain.

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.

The semantic control network mediates the relationship between symbolic numerical order processing and arithmetic performance in children.

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.

A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI-adaptation study.

How are number symbols (e.g., Arabic digits) represented in the brain? Functional resonance imaging adaptation (fMRI-A) research has indicated that the intraparietal sulcus (IPS) exhibits a decrease in activation with the repeated presentation of the same number, that is followed by a rebound effect with the presentation of a new number. This rebound effect is modulated by the numerical ratio or difference between presented numbers. It has been suggested that this ratio-dependent rebound effect is reflective of a link between the symbolic numerical representation system and an approximate magnitude system. Experiment 1 used fMRI-A to investigate an alternative hypothesis: that the rebound effect observed in the IPS is related to the ordinal relationships between symbols (e.g., 3 comes before 4; C after B). In Experiment 1, adult participants exhibited the predicted distance-dependent parametric rebound effect bilaterally in the IPS for number symbols during a number adaptation task, however, the same effect was not found anywhere in the brain in response to letters. When numbers were contrasted with letters (numbers > letters), the left intraparietal lobule remained significant. Experiment 2 demonstrated that letter stimuli used in Experiment 1 generated a behavioral distance effect during an active ordinality task, despite the lack of a neural distance effect using fMRI-A. The current study does not support the hypothesis that general ordinal mechanisms underpin the neural parametric recovery effect in the IPS in response to number symbols. Additional research is needed to further our understanding of mechanisms underlying symbolic numerical representation in the brain.

Interference during the retrieval of arithmetic and lexico-semantic knowledge modulates similar brain regions: Evidence from functional magnetic resonance imaging (fMRI).

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.

The neural substrates of the problem size and interference effect in children's multiplication: An fMRI study.

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.

Automatic and intentional processing of numerical order and its relationship to arithmetic performance.

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.

Interference and problem size effect in multiplication fact solving: Individual differences in brain activations and arithmetic performance.

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.