Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging meta-analysis

Parietal and hippocampal hyper-connectivity is associated with low math achievement in adolescence - A preliminary study

Mathematical cognition requires coordinated activity across multiple brain regions, leading to the emergence of resting-state functional connectivity as a method for studying the neural basis of differences in mathematical achievement. Hyper-connectivity of the intraparietal sulcus (IPS), a key locus of mathematical and numerical processing, has been associated with poor mathematical skills in childhood, whereas greater connectivity has been related to better performance in adulthood. No studies to date have considered its role in adolescence. Further, hippocampal connectivity can predict mathematical learning, yet no studies have considered its contributions to contemporaneous measures of math achievement. Here, we used seed-based resting-state fMRI analyses to examine IPS and hippocampal intrinsic functional connectivity relations to math achievement in a group of 31 adolescents (mean age = 16.42 years, range 15-17), whose math performance spanned the 1% to 99% percentile. After controlling for IQ, IPS connectivity was negatively related to math achievement, akin to findings in children. However, the specific temporo-occipital regions were more akin to the posterior loci implicated in adults. Hippocampal connectivity with frontal regions was also negatively correlated with concurrent math measures, which contrasts with results from learning studies. Finally, hyper-connectivity was not a global feature of low math performance, as math performance did not modulate connectivity of Heschl's gyrus, a control seed not involved in math cognition. Our results provide preliminary evidence that adolescence is a transitional stage in which patterns found in childhood and adulthood can be observed; most notably, hyper-connectivity continues to be related to low math ability into this period.

Automatic integration of numerical formats examined with frequency-tagged EEG

How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers (< 5) depicted in single (digits, dots, number words) or mixed notation (dots-digits, number words-dots, digits-number words), presented at 10 Hz. Periodically, a deviant stimulus (> 5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits-number words and number words-dots, but not for digits-dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats.

Neural representational similarity between symbolic and non-symbolic quantities predicts arithmetic skills in childhood but not adolescence

Mathematical knowledge is constructed hierarchically from basic understanding of quantities and the symbols that denote them. Discrimination of numerical quantity in both symbolic and non-symbolic formats has been linked to mathematical problem-solving abilities. However, little is known of the extent to which overlap in quantity representations between symbolic and non-symbolic formats is related to individual differences in numerical problem solving and whether this relation changes with different stages of development and skill acquisition. Here we investigate the association between neural representational similarity (NRS) across symbolic and non-symbolic quantity discrimination and arithmetic problem-solving skills in early and late developmental stages: elementary school children (ages 7-10 years) and adolescents and young adults (AYA, ages 14-21 years). In children, cross-format NRS in distributed brain regions, including parietal and frontal cortices and the hippocampus, was positively correlated with arithmetic skills. In contrast, no brain region showed a significant association between cross-format NRS and arithmetic skills in the AYA group. Our findings suggest that the relationship between symbolic-non-symbolic NRS and arithmetic skills depends on developmental stage. Taken together, our study provides evidence for both mapping and estrangement hypotheses in the context of numerical problem solving, albeit over different cognitive developmental stages.

The neural basis of number word processing in children and adults

The ability to map number words to their corresponding quantity representations is a gatekeeper for children's future math success (Spaepen et al., 2018). Without number word knowledge at school entry, children are at greater risk for developing math learning difficulties (Chu et al., 2019). In the present study, we used functional magnetic resonance imaging (fMRI) to examine the neural basis for processing the meaning of spoken number words and its developmental trajectory in 4- to 10-year-old children, and in adults. In a number word-quantity mapping paradigm, participants listened to number words while simultaneously viewing quantities that were congruent or incongruent to the number word they heard. Whole brain analyses revealed that adults showed a neural congruity effect with greater neural activation for incongruent relative to congruent trials in anterior cingulate cortex (ACC) and left intraparietal sulcus (LIPS). In contrast, children did not show a significant neural congruity effect. However, a region of interest analysis in the child sample demonstrated age-related increases in the neural congruity effect, specifically in the LIPS. The positive correlation between neural congruity in LIPS and age was stronger in children who were already attending school, suggesting that developmental changes in LIPS function are experience-dependent.

The relation between parietal GABA concentration and numerical skills

Several scientific, engineering, and medical advancements are based on breakthroughs made by people who excel in mathematics. Our current understanding of the underlying brain networks stems primarily from anatomical and functional investigations, but our knowledge of how neurotransmitters subserve numerical skills, the building block of mathematics, is scarce. Using 1H magnetic resonance spectroscopy (N = 54, 3T, semi-LASER sequence, TE = 32 ms, TR = 3.5 s), the study examined the relation between numerical skills and the brain's major inhibitory (GABA) and excitatory (glutamate) neurotransmitters. A negative association was found between the performance in a number sequences task and the resting concentration of GABA within the left intraparietal sulcus (IPS), a key region supporting numeracy. The relation between GABA in the IPS and number sequences was specific to (1) parietal but not frontal regions and to (2) GABA but not glutamate. It was additionally found that the resting functional connectivity of the left IPS and the left superior frontal gyrus was positively associated with number sequences performance. However, resting GABA concentration within the IPS explained number sequences performance above and beyond the resting frontoparietal connectivity measure. Our findings further motivate the study of inhibition mechanisms in the human brain and significantly contribute to our current understanding of numerical cognition's biological bases.

Symbols Are Special: An fMRI Adaptation Study of Symbolic, Nonsymbolic, and Non-Numerical Magnitude Processing in the Human Brain

How are different formats of magnitudes represented in the human brain? We used functional magnetic resonance imaging adaptation to isolate representations of symbols, quantities, and physical size in 45 adults. Results indicate that the neural correlates supporting the passive processing of number symbols are largely dissociable from those supporting quantities and physical size, anatomically and representationally. Anatomically, passive processing of quantities and size correlate with activation in the right intraparietal sulcus, whereas symbolic number processing, compared with quantity processing, correlates with activation in the left inferior parietal lobule. Representationally, neural patterns of activation supporting symbols are dissimilar from neural activation patterns supporting quantity and size in the bilateral parietal lobes. These findings challenge the longstanding notion that the culturally acquired ability to conceptualize symbolic numbers is represented using entirely the same brain systems that support the evolutionarily ancient system used to process quantities. Moreover, these data reveal that regions that support numerical magnitude processing are also important for the processing of non-numerical magnitudes. This discovery compels future investigations of the neural consequences of acquiring knowledge of symbolic numbers.

Sulcation of the intraparietal sulcus is related to symbolic but not non-symbolic number skills

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The horizontal segment of intraparietal sulcus (HIPS) is one of the key functional regions for processing numbers.

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Sulcal morphology is a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning.

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The HIPS sulcal pattern explains part of the variance in participant’s symbolic number comparison and math fluency abilities.

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Participant’s non-symbolic number comparison abilities was not explained by HIPS sulcal pattern.

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This association between HIPS sulcal pattern and symbolic number abilities was stable from childhood to young adulthood.

Understanding the constraints, including biological ones, that may influence mathematical development is of great importance because math ability is a key predictor of career success, income and even psychological well-being. While research in developmental cognitive neuroscience of mathematics has extensively studied the key functional regions for processing numbers, particularly the horizontal segment of intraparietal sulcus (HIPS), few studies have investigated the effects of early cerebral constraints on later mathematical abilities. In this pre-registered study, we investigated whether variability of the sulcal pattern of the HIPS, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounts for individual difference in symbolic and non-symbolic number abilities. Seventy-seven typically developing school-aged children and 21 young adults participated in our study. We found that the HIPS sulcal pattern, (a) explains part of the variance in participant’s symbolic number comparison and math fluency abilities, and (b) that this association between HIPS sulcal pattern and symbolic number abilities was found to be stable from childhood to young adulthood. However, (c) we did not find an association between participant’s non-symbolic number abilities and HIPS sulcal morphology. Our findings suggest that early cerebral constraints may influence individual difference in math abilities, in addition to the well-established neuroplastic factors.

The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties

Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1-4) and a group with mathematical difficulties (study 2; N = 61, Grades 4-6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development.

Developmental dyscalculia: the progress of cognitive modeling in the field of numerical cognition deficits for children

The study of dyscalculia requires an analysis of the current developed hypotheses which describe the cognitive mechanisms involved in this neurodevelopmental disorder. The objective of our review is to determine any progress in modeling developmental dyscalculia. The first hypothesis suggests that dyscalculia is the consequence of a specific deficit level number on the precise number system and the approximate system. Then, the second hypothesis states that developmental dyscalculia is linked to a failure to process non-symbolic representations of numbers. On the other hand, the third suggests that dyscalculia is caused by a lack of access to numerical quantities from symbols. However, the last hypothesis asserts that developmental dyscalculia is linked to general deficits. All these hypotheses are compatible with recent neuroimaging results and raise new horizons for experimentation, which will allow the development of precise diagnostic tools and the improvement of intervention strategies and the remediation of developmental dyscalculia.

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.

Children With Dyscalculia Show Hippocampal Hyperactivity During Symbolic Number Perception

Dyscalculia is a learning disability affecting the acquisition of arithmetical skills in children with normal intelligence and age-appropriate education. Two hypotheses attempt to explain the main cause of dyscalculia. The first hypothesis suggests that a problem with the core mechanisms of perceiving (non-symbolic) quantities is the cause of dyscalculia (core deficit hypothesis), while the alternative hypothesis suggests that dyscalculics have problems only with the processing of numerical symbols (access deficit hypothesis). In the present study, the symbolic and non-symbolic numerosity processing of typically developing children and children with dyscalculia were examined with functional magnetic resonance imaging (fMRI). Control (n = 15, mean age: 11.26) and dyscalculia (n = 12, mean age: 11.25) groups were determined using a wide-scale screening process. Participants performed a quantity comparison paradigm in the fMRI with two number conditions (dot and symbol comparison) and two difficulty levels (0.5 and 0.7 ratio). The results showed that the bilateral intraparietal sulcus (IPS), left dorsolateral prefrontal cortex (DLPFC) and left fusiform gyrus (so-called “number form area”) were activated for number perception as well as bilateral occipital and supplementary motor areas. The task difficulty engaged bilateral insular cortex, anterior cingulate cortex, IPS, and DLPFC activation. The dyscalculia group showed more activation in the left orbitofrontal cortex, left medial prefrontal cortex, and right anterior cingulate cortex than the control group. The dyscalculia group showed left hippocampus activation specifically for the symbolic condition. Increased left hippocampal and left-lateralized frontal network activation suggest increased executive and memory-based compensation mechanisms during symbolic processing for dyscalculics. Overall, our findings support the access deficit hypothesis as a neural basis for dyscalculia.

Gray matter volume in left intraparietal sulcus predicts longitudinal gains in subtraction skill in elementary school

Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms.

Predicting learning and achievement using GABA and glutamate concentrations in human development

Previous research has highlighted the role of glutamate and gamma-aminobutyric acid (GABA) in learning and plasticity. What is currently unknown is how this knowledge translates to real-life complex cognitive abilities that emerge slowly and how the link between these neurotransmitters and human learning and plasticity is shaped by development. While some have suggested a generic role of glutamate and GABA in learning and plasticity, others have hypothesized that their involvement shapes sensitive periods during development. Here we used a cross-sectional longitudinal design with 255 individuals (spanning primary school to university) to show that glutamate and GABA in the intraparietal sulcus explain unique variance both in current and future mathematical achievement (approximately 1.5 years). Furthermore, our findings reveal a dynamic and dissociable role of GABA and glutamate in predicting learning, which is reversed during development, and therefore provide novel implications for models of learning and plasticity during childhood and adulthood.

ADGRL3, FGF1 and DRD4: Linkage and Association with Working Memory and Perceptual Organization Candidate Endophenotypes in ADHD

Attention deficit hyperactivity disorder (ADHD) is a highly heritable neurobehavioral disorder that affects children worldwide, with detrimental long-term consequences in affected individuals. ADHD-affected patients display visual-motor and visuospatial abilities and skills that depart from those exhibited by non-affected individuals and struggle with perceptual organization, which might partially explain impulsive responses. Endophenotypes (quantifiable or dimensional constructs that are closely related to the root cause of the disease) might provide a more powerful and objective framework for dissecting the underlying neurobiology of ADHD than that of categories offered by the syndromic classification. In here, we explore the potential presence of the linkage and association of single-nucleotide polymorphisms (SNPs), harbored in genes implicated in the etiology of ADHD (ADGRL3, DRD4, and FGF1), with cognitive endophenotypes related to working memory and perceptual organization in 113 nuclear families. These families were ascertained from a geographical area of the Caribbean coast, in the north of Colombia, where the community is characterized by its ethnic diversity and differential gene pool. We found a significant association and linkage of markers ADGRL3-rs1565902, DRD4-rs916457 and FGF1-rs2282794 to neuropsychological tasks outlining working memory and perceptual organization such as performance in the digits forward and backward, arithmetic, similarities, the completion of figures and the assembly of objects. Our results provide strong support to understand ADHD as a combination of working memory and perceptual organization deficits and highlight the importance of the genetic background shaping the neurobiology, clinical complexity, and physiopathology of ADHD. Further, this study supplements new information regarding an ethnically diverse community with a vast African American contribution, where ADHD studies are scarce.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Numerosity representation in a deep convolutional neural network

Enumerating objects in the environment (i.e., “number sense”) is crucial for survival in many animal species, and foundational for the construction of more abstract and complex mathematical knowledge in humans. Perhaps surprisingly, deep convolutional neural networks (DCNNs) spontaneously emerge a similar number sense even without any explicit training for numerosity estimation. However, little is known about how the number sense emerges, and the extent to which it is comparable with human number sense. Here, we examined whether the numerosity underestimation effect, a phenomenon indicating that numerosity perception acts upon the perceptual number rather than the physical number, can be observed in DCNNs. In a typical DCNN, AlexNet, we found that number-selective units at late layers operated on the perceptual number, like humans do. More importantly, this perceptual number sense did not emerge abruptly, rather developed progressively along the hierarchy in the DCNN, shifting from the physical number sense at early layers to perceptual number sense at late layers. Our finding hence provides important implications for the neural implementation of number sense in the human brain and advocates future research to determine whether the representation of numerosity also develops gradually along the human visual stream from physical number to perceptual number.

Neural representation of prediction error signals in substance users

Abnormal decision making can result in detrimental outcomes of clinical importance, and decision making is strongly linked to neural prediction error signalling. Activation likelihood estimation (ALE) meta-analyses were used to examine the neural correlates of prediction error signals of individuals taking different types of substances and healthy controls with contrast and conjunction analyses. Twenty-eight studies were included in the meta-analysis, representing 424 substance users' individuals and 834 healthy control individuals. Robust brain activity associated with prediction error signals in substance users was found for the bilateral striatum and insula. Healthy control subjects also activated bilateral striatum, midbrain, right insula and right medial-inferior frontal gyrus. Compared with healthy controls, substance users showed blunted activity in the bilateral putamen, right medial-inferior frontal gyrus and insula. The current meta-analysis of cross-sectional findings investigated neural prediction error signals in substance users. PE abnormalities in substance users might be related to poor decision making. In conclusion, the present study helps identify the pathophysiological underpinnings of maladaptive decision making in substance users.

Automatic Processing of Numerosity in Human Neocortex Evidenced by Occipital and Parietal Neuromagnetic Responses

Humans and other animal species are endowed with the ability to sense, represent, and mentally manipulate the number of items in a set without needing to count them. One central hypothesis is that this ability relies on an automated functional system dedicated to numerosity, the perception of the discrete numerical magnitude of a set of items. This system has classically been associated with intraparietal regions, however accumulating evidence in favor of an early visual number sense calls into question the functional role of parietal regions in numerosity processing. Targeting specifically numerosity among other visual features in the earliest stages of processing requires high temporal and spatial resolution. We used frequency-tagged magnetoencephalography to investigate the early automatic processing of numerical magnitudes and measured the steady-state brain responses specifically evoked by numerical and other visual changes in the visual scene. The neuromagnetic responses showed implicit discrimination of numerosity, total occupied area, and convex hull. The source reconstruction corresponding to the implicit discrimination responses showed common and separate sources along the ventral and dorsal visual pathways. Occipital sources attested the perceptual salience of numerosity similarly to both other implicitly discriminable visual features. Crucially, we found parietal responses uniquely associated with numerosity discrimination, showing automatic processing of numerosity in the parietal cortex, even when not relevant to the task. Taken together, these results provide further insights into the functional roles of parietal and occipital regions in numerosity encoding along the visual hierarchy.

Electrical cortical stimulation can impair production of the alphabet without impairing counting

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Counting is used in Electrical Stimulation Mapping (ESM), often as a language screen.

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We report a case where ESM reliably disrupted production of letters, but not numbers.

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Counting is not an accurate screen of all language functions in ESM.

Neurosurgery has the potential to cure patients with drug-resistant focal epilepsy, but carries the risk of permanent language impairment when surgery involves the dominant hemisphere of the brain. This risk can be estimated and minimized using electrical stimulation mapping (ESM), which uses cognitive and linguistic tasks during cortical ESM to differentiate “eloquent” and “resectable” areas in the brain. One such task, counting, is often used to screen and characterize language during ESM in patients whose language abilities are limited. Here we report a patient with drug-resistant epilepsy arising from the language-dominant hemisphere using fMRI. Our patient experienced loss of the ability to recite or write the alphabet, but not to count, during ESM of the dominant left posterior superior temporal gyrus. This selective impairment extended to both spoken and written production. We suggest the need for caution when using counting as a sole means to screen language function and as a method of testing low functioning patients using ESM.

Neurodevelopmental differences in child and adult number processing: An fMRI-based validation of the triple code model

The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children's and 44 healthy adults' recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.

The neural differences of arithmetic verification performance depend on math skill: Evidence from event-related potential

AIM

Math skill is a basic need for an individual, as a career prospect. However, little is known about early brain processes of arithmetic between individuals with different math skill. Therefore, we questioned the modulation of the amplitude of an early negative component by math skill level in an arithmetic verification paradigm using event-related potential (ERP).

METHODS

Thirty-six right-handed participants were assigned in two groups of high- and low-performing students. Their electroencephalogram was recorded while they completed an arithmetic verification task. Simple arithmetic operands were made by random digits from 1 to 9. Addition and subtraction operations were equally used in correct and incorrect responses. The accuracy scores, reaction times, and peak amplitude of the negativity in 200-400 ms time window were analyzed.

RESULTS

The high-performing group showed significantly higher response speeds, and they were more accurate than the low-performing group. The group × region interaction effect was significant. The high-performing group showed a significantly greater negativity, particularly in parietal region, while the low-performing group showed a significantly deeper negativity in frontal and prefrontal region. In the low-performing group, there were significant peak amplitude differences between the anterior and posterior areas. However, such differences were not detected in the high-performing group.

CONCLUSION

Students with different mathematical performance showed distinct patterns in early processing of arithmetic verification, as reflected by differences in negativity at 200-400 ms at anterior and posterior. This suggests that ERPs could be used to differentiate math mastery at neural level which is beneficial in educational and clinical contexts.

Neurofunctional plasticity in fraction learning: An fMRI training study

BACKGROUND

Fractions are known to be difficult for children and adults. Behavioral studies suggest that magnitude processing of fractions can be improved via number line estimation (NLE) trainings, but little is known about the neural correlates of fraction learning.

METHOD

To examine the neuro-cognitive foundations of fraction learning, behavioral performance and neural correlates were measured before and after a five-day NLE training.

RESULTS

In all evaluation tasks behavioral performance increased after training. We observed a fronto-parietal network associated with number magnitude processing to be recruited in all tasks as indicated by a numerical distance effect. For symbolic fractions, the distance effect on intraparietal activation was only observed after training.

CONCLUSION

The absence of a distance effect of symbolic fractions before the training could indicate an initially less automatic access to their overall magnitude. NLE training facilitates processing of overall fraction magnitude as indicated by the distance effect in neural activation.

What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior

There is an emerging consensus that spatial thinking plays a fundamental role in how people conceive, express, and perform mathematics. However, the underlying nature of this relationship remains elusive. Questions remain as to how, why, and under what conditions spatial skills and mathematics are linked. This review paper addresses this gap. Through a review and synthesis of research in psychology, neuroscience, and education, we examine plausible mechanistic accounts for the oft-reported close, and potentially causal, relations between spatial and mathematical thought. More specifically, this review targets candidate mechanisms that link spatial visualization skills and basic numerical competencies. The four explanatory accounts we describe and critique include the: (1) Spatial representation of numbers account, (2) shared neural processing account, (3) spatial modelling account, and (4) working memory account. We propose that these mechanisms do not operate in isolation from one another, but in concert with one another to give rise to spatial-numerical associations. Moving from the theoretical to the practical, we end our review by considering the extent to which spatial visualization abilities are malleable and transferrable to numerical reasoning. Ultimately, this paper aims to provide a more coherent and mechanistic account of spatial-numerical relations in the hope that this information may (1) afford new insights into the uniquely human ability to learn, perform, and invent abstract mathematics, and (2) on a more practical level, prove useful in the assessment and design of effective mathematics curricula and intervention moving forward.

Game-based learning environments affect frontal brain activity

Inclusion of game elements in learning environments to increase motivation and learning outcome is becoming increasingly popular. However, underlying mechanisms of game-based learning have not been studied sufficiently yet. In the present study, we investigated effects of game-based learning environments on a neurofunctional level. In particular, 59 healthy adults completed a game-based version (including game elements such as a narrative and virtual incentives) as well as a non-game-based version of a number line estimation task, to improve fractional knowledge, while their brain activity was monitored using near-infrared spectroscopy. Behavioral performance was comparable across the two versions, although there was a tendency that less errors were made in the game-based version. However, subjective user experience differed significantly between versions. Participants rated the game-based version as more attractive, novel, and stimulating but less efficient than the non-game-based version. Additionally, positive affect was reported to be higher while engaging in the game-based as compared to the non-game-based task version. Corroborating these user reports, we identified increased brain activation in areas associated with emotion and reward processing while playing the game-based version, which might be driven by rewarding elements of the game-based version. Moreover, frontal areas associated with attention were also more activated in the game-based version of the task. Hence, we observed converging evidence on a user experience and neurofunctional level indicating that the game-based version was more rewarding as well as emotionally and attentionally engaging. These results underscore the potential of game-based learning environments to promote more efficient learning by means of attention and reward up-tuning.

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

One of the most critical skills behind consumer's behavior is the ability to assess whether a price after a discount is a real bargain. Yet, the neural underpinnings and cognitive mechanisms associated with such a skill are largely unknown. While there is general agreement that the posterior parietal cortex (PPC) on the left is critical for mental calculations, and there is also recent repetitive transcranial magnetic stimulation (rTMS) evidence pointing to the supramarginal gyrus (SMG) of the right PPC as crucial for consumer-like arithmetic (e.g., multi-digit mental addition or subtraction), it is still unknown whether SMG is involved in calculations of sale prices. Here, we show that the neural mechanisms underlying discount arithmetic characteristic for shopping are different from complex addition or subtraction, with discount calculations engaging left SMG more. We obtained these outcomes by remodeling our laboratory to resemble a shop and asking participants to calculate prices after discounts (e.g., $8.80-25 or $4.80-75%), while stimulating left and right SMG with neuronavigated rTMS. Our results indicate that such complex shopping calculations as establishing the price after a discount involve SMG asymmetrically, whereas simpler calculations such as price addition do not. These findings have some consequences for neural models of mathematical cognition and shed some preliminary light on potential consumer's behavior in natural settings.

Network topology of symbolic and nonsymbolic number comparison

Studies of brain activity during number processing suggest symbolic and nonsymbolic numerical stimuli (e.g., Arabic digits and dot arrays) engage both shared and distinct neural mechanisms. However, the extent to which number format influences large-scale functional network organization is unknown. In this study, using 7 Tesla MRI, we adopted a network neuroscience approach to characterize the whole-brain functional architecture supporting symbolic and nonsymbolic number comparison in 33 adults. Results showed the degree of global modularity was similar for both formats. The symbolic format, however, elicited stronger community membership among auditory regions, whereas for nonsymbolic, stronger membership was observed within and between cingulo-opercular/salience network and basal ganglia communities. The right posterior inferior temporal gyrus, left intraparietal sulcus, and two regions in the right ventromedial occipital cortex demonstrated robust differences between formats in terms of their community membership, supporting prior findings that these areas are differentially engaged based on number format. Furthermore, a unified fronto-parietal/dorsal attention community in the nonsymbolic condition was fractionated into two components in the symbolic condition. Taken together, these results reveal a pattern of overlapping and distinct network architectures for symbolic and nonsymbolic number processing.

Shared Numerosity Representations Across Formats and Tasks Revealed with 7 Tesla fMRI: Decoding, Generalization, and Individual Differences in Behavior

Debate continues on whether encoding of symbolic number is grounded in nonsymbolic numerical magnitudes. Nevertheless, fluency of perceiving both number formats, and translating between them, predicts math skills across the life span. Therefore, this study asked if numbers share cortical activation patterns across formats and tasks, and whether neural response to number predicts math-related behaviors. We analyzed patterns of neural activation using 7 Tesla functional magnetic resonance imaging in a sample of 39 healthy adults. Discrimination was successful between numerosities 2, 4, 6, and 8 dots and generalized to activation patterns of the same numerosities represented as Arabic digits in the bilateral parietal lobes and left inferior frontal gyrus (IFG) (and vice versa). This indicates that numerosity-specific neural resources are shared between formats. Generalization was also successful across tasks where participants either identified or compared numerosities in bilateral parietal lobes and IFG. Individual differences in decoding did not relate to performance on a number comparison task completed outside of the scanner, but generalization between formats and across tasks negatively related to math achievement in the parietal lobes. Together, these findings suggest that individual differences in representational specificity within format and task contexts relate to mathematical expertise.

Persistent Differences in Brain Structure in Developmental Dyscalculia: A Longitudinal Morphometry Study

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex. Furthermore, dyscalculics show white matter differences for instance in the inferior (ILF) and superior longitudinal fasciculus (SLF). However, the longitudinal development of these structural differences is unknown. Therefore, our goal was to investigate the developmental trajectory of gray and white matter in children with and without DD. In this longitudinal study, neuropsychological measures and T1-weighted structural images were collected twice with an interval of 4 years from 13 children with DD (8.2-10.4 years) and 10 typically developing (TD) children (8.0-10.4 years). Voxel-wise estimation of gray and white matter volumes was assessed using voxel-based morphometry for longitudinal data. The present findings reveal for the first time that DD children show persistently reduced gray and white matter volumes over development. Reduced gray matter was found in the bilateral inferior parietal lobes including the IPS, supramarginal gyri, left precuneus, cuneus, right superior occipital gyrus, bilateral inferior and middle temporal gyri, and insula. White matter volumes were reduced in the bilateral ILF and SLF, inferior fronto-occipital fasciculus (IFOF), corticospinal tracts, and right anterior thalamic radiation (ATR). Behaviorally, children with DD performed significantly worse in various numerical tasks at baseline and follow-up, corroborating persistent deficits in number processing. The present results are in line with the literature showing that children with DD have reduced gray and white matter volumes in the numerical network. Our study further sheds light on the trajectory of brain development, revealing that these known structural differences in the long association fibers and the adjacent regions of the temporal- and frontoparietal cortex persist in dyscalculic children from childhood into adolescence. In conclusion, our results underscore that DD is a persistent learning disorder accompanied by deficits in number processing and reduced gray and white matter volumes in number related brain areas.

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

There is debate in the literature regarding how single-digit arithmetic fluency is achieved over development. While the Fact-retrieval hypothesis suggests that with practice, children shift from quantity-based procedures to verbally retrieving arithmetic problems from long-term memory, the Schema-based hypothesis claims that problems are solved through quantity-based procedures and that practice leads to these procedures becoming more automatic. To test these hypotheses, a sample of 46 typically developing children underwent functional magnetic resonance imaging (fMRI) when they were 11 years old (time 1), and 2 years later (time 2). We independently defined regions of interest (ROIs) involved in verbal and quantity processing using rhyming and numerosity judgment localizer tasks, respectively. The verbal ROIs consisted of left middle/superior temporal gyri (MTG/STG) and left inferior frontal gyrus (IFG), whereas the quantity ROIs consisted of bilateral inferior/superior parietal lobules (IPL/SPL) and bilateral middle frontal gyri (MFG)/right IFG. Participants also solved a single-digit subtraction task in the scanner. We defined the extent to which children relied on verbal vs. quantity mechanisms by selecting the 100 voxels showing maximal activation at time 1 from each ROI, separately for small and large subtractions. We studied the brain mechanisms at time 1 that predicted gains in subtraction fluency and how these mechanisms changed over time with improvement. When looking at brain activation at time 1, we found that improvers showed a larger neural problem size effect in bilateral parietal cortex, whereas no effects were found in verbal regions. Results also revealed that children who showed improvement in behavioral fluency for large subtraction problems showed decreased activation over time for large subtractions in both parietal and frontal regions implicated in quantity, whereas non-improvers maintained similar levels of activation. All children, regardless of improvement, showed decreased activation over time for large subtraction problems in verbal regions. The greater parietal problem size effect at time 1 and the reduction in activation over time for the improvers in parietal and frontal regions implicated in quantity processing is consistent with the Schema-based hypothesis arguing for more automatic procedures with increasing skill. The lack of a problem size effect at time 1 and the overall decrease in verbal regions, regardless of improvement, is inconsistent with the Fact-retrieval hypothesis.

Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison

Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.

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.

Neural representations of transitive relations predict current and future math calculation skills in children

A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T₁), children (n = 31) processed transitive relations in an MRI scanner. Math skills were measured at T₁ and again 1.5 years later (T₂). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T₁ and T₂. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

Developmental alterations of the numerical processing networks in the brain

Neuroimaging studies revealed that number perception is mainly located in parietal cortex. Although controversial, it was suggested that number is processed in the frontal lobe in childhood and in the parietal cortex in adulthood. The purpose of this study is to investigate developmental differences in the neural correlates of number representation with fMRI. Sixteen healthy young adults (age:21.69 ± 0.79) and 15 healthy children (age:11.87 ± 0.52) performed a numerosity comparison paradigm which consists of two numerical conditions with two difficulty levels. Adults showed broad parietal cortex activation, as well as activation in the inferior parietal lobes, dorsolateral and medial prefrontal cortex, anterior and posterior cingulate cortex, and peristriate cortex (PC) during number processing. Children showed activations in the intraparietal sulcus and PC. Group differences were observed in the posterior insula, fusiform gyrus, and PC whose coordinates correspond to the number form area (NFA). Region of interest analysis was performed for these clusters to get the time series of hemodynamic responses which were estimated with a finite impulse response function. In contrast to the prominent frontoparietal shift theory, no age-related differences were observed in the frontoparietal regions. Overall, the presented study suggests developmental changes in the brain's number processing revolving around the NFA.

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.

Canine sense of quantity: evidence for numerical ratio-dependent activation in parietotemporal cortex

The approximate number system (ANS), which supports the rapid estimation of quantity, emerges early in human development and is widespread across species. Neural evidence from both human and non-human primates suggests the parietal cortex as a primary locus of numerical estimation, but it is unclear whether the numerical competencies observed across non-primate species are subserved by similar neural mechanisms. Moreover, because studies with non-human animals typically involve extensive training, little is known about the spontaneous numerical capacities of non-human animals. To address these questions, we examined the neural underpinnings of number perception using awake canine functional magnetic resonance imaging. Dogs passively viewed dot arrays that varied in ratio and, critically, received no task-relevant training or exposure prior to testing. We found evidence of ratio-dependent activation, which is a key feature of the ANS, in canine parietotemporal cortex in the majority of dogs tested. This finding is suggestive of a neural mechanism for quantity perception that has been conserved across mammalian evolution.

Arithmetic in the adult deaf signing brain

We have previously shown that deaf signers recruit partially different brain regions during simple arithmetic compared to a group of hearing non-signers, despite similar performance. Specifically, hearing individuals show more widespread activation in brain areas that have been related to the verbal system of numerical processing, i.e., the left angular and inferior frontal gyrus, whereas deaf individuals engaged brain areas that have been related to the quantity system of numerical processing, i.e., the right horizontal intraparietal sulcus. This indicates that compared to hearing non-signers, deaf signers can successfully make use of processes located in partially different brain areas during simple arithmetic. In this study, which is a conceptual replication and extension of the above-presented study, the main aim is to understand similarities and differences in neural correlates supporting arithmetic in deaf compared to hearing individuals. The primary objective is to investigate the role of the right horizontal intraparietal gyrus, the left inferior frontal gyrus, the hippocampus, and the left angular gyrus during simple and difficult arithmetic and how these regions are connected to each other. A second objective is to explore what other brain regions support arithmetic in deaf signers. Up to 34 adult deaf signers and the same amount of hearing non-signers will be enrolled in an functional magnetic resonance imaging study that will include simple and difficult subtraction and multiplication. Brain imaging data will be analyzed using whole-brain analysis, region of interest analysis and connectivity analysis. This is the first study to investigate neural underpinnings of arithmetic of different difficulties in deaf individuals.

Numerical cognition: A meta-analysis of neuroimaging, transcranial magnetic stimulation and brain-damaged patients studies

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We review neuroimaging, TMS, and patients studies on numerical cognition.

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We focused on the predictions derived from the Triple Code Model (TCM).

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Our findings generally agree with TCM predictions.

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Our results open avenues for the study of the neural bases of numerical cognition.

This article offers the first comprehensive review examining the neurocognitive bases of numerical cognition from neuroimaging, Transcranial Magnetic Stimulation (TMS) and brain-damaged patients studies. We focused on the predictions derived from the Triple Code Model (TCM), particularly the assumption that the representation of numerical quantities rests on a single format-independent representation (i.e., the analogical code) involving both intraparietal sulci (IPS). To do so, we conducted a meta-analysis based on 28 neuroimaging, 12 TMS and 12 brain-damaged patients studies, including arithmetic and magnitude tasks in symbolic and non-symbolic formats. Our findings generally agree with the TCM predictions indicating that both IPS are engaged in all tasks. Nonetheless, the results of brain-damaged patients studies conflicted with neuroimaging and TMS studies, suggesting a right hemisphere lateralization for non-symbolic formats. Our findings also led us to discuss the involvement of brain regions other than IPS in the processing of the analogical code as well as the neural substrate of other codes underlying numerical cognition (i.e., the auditory-verbal code).

Regional specificity of cathodal transcranial direct current stimulation (tDCS) effects on spatial-numerical associations: Comparison of four stimulation sites

Based on a theory of impulsive and reflective human behavior, we test the effects of transcranial direct current stimulation (tDCS) targeting either prefrontal or parietal cortex in either hemisphere. In a confirmatory registered report, cathodal tDCS is administered to conceptually reproduce tDCS modulations of implicit spatial-numerical associations, numerical distance effects, and response inhibition. Those cognitive operations are hypothesized to draw on left prefrontal, parietal, and right prefrontal activations, respectively, thereby susceptible to inhibitory, cathodal tDCS across those regions. Vice versa, the mutual regional and behavioral specificity of tDCS effects on these behavioral indices is examined and expected to produce double dissociations. In a mixed within-subjects (baseline, during tDCS, post-tDCS) and between-subjects (target electrode: left/right prefrontal cortex/posterior parietal cortex, or sham tDCS) design, we collect (a) confirmatory data on the robustness of cathodal tDCS effects on three behavioral effects and (b) differential data on the specificity of regional targets in male and female human participants. Results will provide crucial tests of theories of cortical organization implied by implicit associations and explicit regulation, which can direct future brain stimulation studies.

Symbol grounding of number words in the subitization range

In three experiments, we explored whether number words are grounded in a nonsymbolic representation of numerosity. We used a sentence-picture verification task, where participants are required to check whether the concept given in a sentence corresponds to the subsequently presented object. We concurrently manipulated numerical congruency by orthogonally varying the number word attached to the concept and the quantity of objects. The number words and numerosities varied from one to four in Experiment 1 and from six to nine in Experiment 2. In Experiment 3, we employed number words six and eight with the constraint that, in the incongruent condition, a constant number-to-numerosity ratio of 2:1 was used. In Experiment 1, we found that participants were faster and more efficient when concept-object matches were accompanied by numerical congruency relative to incongruency. On the other hand, no such difference was observed in Experiments 2 and 3 for numbers falling outside of the subitization range. The results are consistent with the hypothesis that number words from one to four are grounded in a nonsymbolic representation of the size of small sets.

Challenging the neurobiological link between number sense and symbolic numerical abilities

A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.

A Transcranial Stimulation Intervention to Support Flow State Induction

Background: Flow states are considered a positive, subjective experience during an optimal balance between skills and task demands. Previously, experimentally induced flow experiences have relied solely on adaptive tasks. Objective: To investigate whether cathodal transcranial direct current stimulation (tDCS) over the left dorsolateral prefrontal cortex (DLPFC) area and anodal tDCS over the right parietal cortex area during video game play will promote an increased experience of flow states. Methods: Two studies had participants play Tetris or first-person shooter (FPS) video games while receiving either real tDCS or sham stimulation. Tetris recruited 21 untrained players who infrequently played video games while the 11 FPS participants played FPS frequently. Flow experience was assessed before and after stimulation. Results: Compared to sham stimulation, real stimulation increased flow experience for both untrained Tetris and trained FPS players. Improved performance effects were only seen with untrained groups. Conclusion: Cathodal and anodal tDCS over the left DLPFC and right parietal areas, respectively may encourage flow experiences in complex real-life motor tasks that occur during sports, games, and everyday life.

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 association between arithmetic and basic numerical processing depends on arithmetic problem size and not chronological age

The intraparietal sulcus (IPS) is thought to be an important region for basic number processing (e.g. symbol-quantity associations) and arithmetic (e.g. addition). Evidence for shared circuitry within the IPS is largely based on comparisons across studies, and little research has investigated number processing and arithmetic in the same individuals. It is also unclear how the neural overlap between number processing and arithmetic is influenced by age and arithmetic problem difficulty. This study investigated these unresolved questions by examining basic number processing (symbol-quantity matching) and arithmetic (addition) networks in 26 adults and 42 children. Number processing and arithmetic elicited overlapping activity in the IPS in children and adults, however, the overlap was influenced by arithmetic problem size (i.e. which modulated the need to use procedural strategies). The IPS was recruited for number processing, and for arithmetic problems more likely to be solved using procedural strategies. We also found that the overlap between number processing and small-problem addition in children was comparable to the overlap between number processing and large-problem addition in adults. This finding suggests that the association between number processing and arithmetic in the IPS is related to the cognitive operation being performed rather than age.

Anticipation of difficult tasks: neural correlates of negative emotions and emotion regulation

BACKGROUND

Difficult cognitive tasks are often associated with negative feelings. This can be already the case for the mere anticipation of having to do a difficult task. For the case of difficult math tasks, it was recently suggested that such a negative emotional response may be exclusive to highly math-anxious individuals. However, it is also conceivable that negative emotional responses simply reflect that math is perceived as difficult. Here we investigated whether non-math-anxious individuals also experience negative emotional responses when anticipating to do difficult math tasks.

METHODS

We compared brain activation following the presentation of a numerical cue indicating either difficult or easy upcoming proportion magnitude comparison tasks.

RESULTS

Comparable to previous results for highly math-anxious individuals we observed a network associated with negative emotions to be activated in non-math-anxious individuals when facing cues indicating a difficult upcoming task. Importantly, however, math anxiety scores did not predict the neural response. Furthermore, we observed activation in areas associated with processes of cognitive control areas such as anterior cingulate cortex, which were suggested to play a key role in emotion regulation.

CONCLUSION

Activation in the emotion processing network was observed when anticipating an upcoming difficult (math) task. However, this activation was not predicted by individual' degree of math anxiety. Therefore, we suggest that negative emotional responses to difficult math tasks might be a rather common reaction not specific to math-anxious individuals. Whether or not this initial negative response impairs math performance, however, might depend on the ability to regulate those emotions effectively.

Processing symbolic and non-symbolic proportions: Domain-specific numerical and domain-general processes in intraparietal cortex

Previous studies on the processing of fractions and proportions focused mainly on the processing of their overall magnitude information in the intraparietal sulcus (IPS). However, the IPS is also associated with domain-general cognitive functions beyond processing overall magnitude, which may nevertheless be involved in operating on magnitude information of proportions. To pursue this issue, the present study aimed at investigating whether there is a shared neural correlate for proportion processing in the intraparietal cortex beyond overall magnitude processing and how part-whole relations are processed on the neural level. Across four presentation formats (i.e., fractions, decimals, dot patterns, and pie charts) we observed a shared neural substrate in bilateral inferior parietal cortex, slightly anterior and inferior to IPS areas recently found for overall magnitude proportion processing. Nevertheless, when evaluating the neural correlates of part-whole processing (i.e., contrasting fractions, dot patterns, and pie charts vs. decimals), we found wide-spread activation in fronto-parietal brain areas. These results indicate involvement of domain-general cognitive processes in part-whole processing beyond processing the overall magnitude of proportions. The dissociation between proportions involving part-whole relations and decimals was further substantiated by a representational similarity analysis, which revealed common neural processing for fractions, pie charts, and dot patterns, possibly representing their bipartite part-whole structure. In contrast, decimals seemed to be processed differently on the neural level, possibly reflecting missing processes of actual proportion calculation in decimals.

Attention to number: The convergence of numerical magnitude processing, attention, and mathematics in the inferior frontal gyrus

Research indicates that the neurocognitive system representing nonsymbolic numerical magnitudes is foundational for the development of mathematical competence. However, recent studies found that the most common task used to measure numerical acuity, the nonsymbolic number comparison task, is heavily influenced by non-numerical visual parameters of stimuli that increase executive function demands. Further, this influence may be a confound invalidating theoretical accounts of the relation between number comparison performance and mathematical competence. Instead of acuity, the relation may depend on one's ability to attend to numerical information in the face of competing, non-numerical cues. The current study investigated this issue by measuring neural activity associated with numerical magnitude processing acuity, domain-general attention, and selective attention to number via functional magnetic resonance imaging while children 8-11 years old completed a nonsymbolic number comparison task and a flanker task. Results showed that activation in the right inferior frontal gyrus during incongruent versus congruent trials of the comparison task, our construct for attention to number, predicted mathematics achievement after controlling for verbal IQ, flanker accuracy rate, and the neural congruency effect from the flanker task. In contrast, activity in frontal and parietal regions responding to differences in difficulty of numerical comparisons, our construct for numerical magnitude processing acuity, did not correlate with achievement. Together, these findings suggest a need to reframe existing models of the relation between number processing and math competence to include the interaction between attention and use of numerical information, or in other words "attention to number."