The purpose of this study is to identify consistencies across functional neuroimaging studies regarding common and unique brain regions/networks for individuals with reading difficulties (RD) and math difficulties (MD) compared to typically developing (TD) individuals. A systematic search of the literature, utilizing multiple databases, yielded 116 functional magnetic resonance imaging and positron emission tomography studies that met the criteria. Coordinates that directly compared TD with either RD or MD were entered into GingerALE (Brainmap.org). An activation likelihood estimate (ALE) meta-analysis was conducted to examine common and unique brain regions for RD and MD. Overall, more studies examined RD (n = 96) than MD (n = 20). Across studies, overactivation for reading and math occurred in the right insula and inferior frontal gyrus for atypically developing (AD) > TD comparisons, albeit in slightly different areas of these regions; however, inherent threshold variability across imaging studies could diminish overlying regions. For TD > AD comparisons, there were no similar or overlapping brain regions. Results indicate there were domain-specific differences for RD and MD; however, there were some similarities in the ancillary recruitment of executive functioning skills. Theoretical and practical implications for researchers and educators are discussed.

Language comprehension requires the rapid retrieval and integration of contextually appropriate concepts ("semantic cognition"). Current neurobiological models of semantic cognition are limited by the spatial and temporal restrictions of single-modality neuroimaging and lesion approaches. This is a major impediment given the rapid sequence of processing steps that have to be coordinated to accurately comprehend language. Through the use of fused functional magnetic resonance imaging and electroencephalography analysis in humans (n = 26 adults; 15 females), we elucidate a temporally and spatially specific neurobiological model for real-time semantic cognition. We find that semantic cognition in the context of language comprehension is supported by trade-offs between widespread neural networks over the course of milliseconds. Incorporation of spatial and temporal characteristics, as well as behavioral measures, provide convergent evidence for the following progression: a hippocampal/anterior temporal phonological semantic retrieval network (peaking at ∼300 ms after the sentence final word); a frontotemporal thematic semantic network (∼400 ms); a hippocampal memory update network (∼500 ms); an inferior frontal semantic syntactic reappraisal network (∼600 ms); and nodes of the default mode network associated with conceptual coherence (∼750 ms). Additionally, in typical adults, mediatory relationships among these networks are significantly predictive of language comprehension ability. These findings provide a conceptual and methodological framework for the examination of speech and language disorders, with additional implications for the characterization of cognitive processes and clinical populations in other cognitive domains.SIGNIFICANCE STATEMENT the present study identifies a real-time neurobiological model of the meaning processes required during language comprehension (i.e. "semantic cognition"). Using a novel application of fused magnetic resonance imaging and electroencephalography in humans, we found that semantic cognition during language comprehension is supported by a rapid progression of widespread neural networks related to meaning, meaning integration, memory, reappraisal, and conceptual cohesion. Relationships among these systems were predictive of individuals' language comprehension efficiency. Our findings are the first to use fused neuroimaging analysis to elucidate language processes. In so doing, this study provides a new conceptual and methodological framework in which to characterize language processes and guide the treatment of speech and language deficits/disorders.

A growing body of evidence suggests that in adults, there is a spatially consistent "inferior temporal numeral area" (ITNA) in the occipitotemporal cortex that appears to preferentially process Arabic digits relative to non-numerical symbols and objects. However, very little is known about why the ITNA is spatially segregated from regions that process other orthographic stimuli such as letters, and why it is spatially consistent across individuals. In the present study, we used diffusion-weighted imaging and functional magnetic resonance imaging to contrast structural and functional connectivity between left and right hemisphere ITNAs and a left hemisphere letter-preferring region. We found that the left ITNA had stronger structural and functional connectivity than the letter region to inferior parietal regions involved in numerical magnitude representation and arithmetic. Between hemispheres, the left ITNA showed stronger structural connectivity with the left inferior frontal gyrus (Broca's area), while the right ITNA showed stronger structural connectivity to the ipsilateral inferior parietal cortex and stronger functional coupling with the bilateral IPS. Based on their relative connectivity, our results suggest that the left ITNA may be more readily involved in mapping digits to verbal number representations, while the right ITNA may support the mapping of digits to quantity representations.

BACKGROUND: Childhood adversity is associated with poorer health and lower academic achievement later in life. Poor math skills in particular place individuals at higher risk for physical and mental illness, unemployment, and incarceration, suggesting math achievement may be one explanatory mechanism linking adversity to later functioning. While it is well documented that children's adversity is associated with lower academic achievement, it is also plausible that adversity mothers experience across their lifetime may affect the child's academic achievement. OBJECTIVE: Determine whether adversity children directly experience and adversity mothers experience in their own childhood and/or adulthood is related to children's kindergarten math skills. PARTICIPANTS AND METHODS: 91 Mothers completed the Assessment of Parent and Child Adversity questionnaire, and their kindergartners completed the KeyMath-3 Diagnostic Assessment. RESULTS: Maternal childhood adversity, but not adulthood adversity, was negatively related to children's numeration (β = -0.27, 95% CI [-0.48, -0.05], p = .015) and addition/subtraction abilities in kindergarten (β = -0.25, 95% CI [-0.46, -0.04], p = .023). Maternal childhood maltreatment and other adversity were together related to their child's numeration only (R2 = 0.08, 95% CI [0.02, 0.23], p = .026). Prevalence of children's direct adversity was low and not related to their kindergarten math skills. CONCLUSIONS: Our findings suggest that adversity impacts children's math skills as early as kindergarten via the intergenerational transmission of maternal adversity. Mothers that experienced early-life adversity and their children may benefit from early intervention to level the playing field at school entry.

A critical goal of cognitive neuroscience is to predict behavior from neural structure and function, thereby providing crucial insights into who might benefit from clinical and/or educational interventions. Across development, the strength of functional connectivity among a distributed set of brain regions is associated with children's math skills. Therefore, in the present study we use connectome-based predictive modeling to investigate whether functional connectivity during numerical processing and at rest "predicts" children's math skills (N = 31, Mage = 9.21 years, 14 Female). Overall, we found that functional connectivity during symbolic number comparison and rest, but not during nonsymbolic number comparison, predicts children's math skills. Each task revealed a largely distinct set of predictive connections distributed across canonical brain networks and major brain lobes. Most of these predictive connections were negatively correlated with children's math skills so that weaker connectivity predicted better math skills. Notably, these predictive connections were largely nonoverlapping across task states, suggesting children's math abilities may depend on state-dependent patterns of network segregation and/or regional specialization. Furthermore, the current predictive modeling approach moves beyond brain-behavior correlations and toward building models of brain connectivity that may eventually aid in predicting future math skills.

The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children. However, whether this improvement continues for older students who are fluent with number symbols, and what cognitive factors relate to this improvement, is unknown. This study used a longitudinal sample of U.S. middle school students (n = 394) to examine whether symbolic number comparison performance changes over middle school (i.e. students aged 11-14), whether there are individual differences in students’ rate of change, and potential predictors of that change. Students completed measures of single-digit symbolic number comparison, nonsymbolic number comparison, executive function (EF), and mathematics competence in Grade 5 (M = 11.02 years; SD = 0.32), and double-digit symbolic number comparison in Grades 6-8. Results showed that, on average, students’ symbolic number comparison performance improved from Grades 6-8. Grade 5 Symbolic number comparison performance predicted Grade 8 symbolic number comparison and rate of change over Grades 6-8. Grade 5 nonsymbolic number comparison, EF, and mathematics competence predicted Grade 8 symbolic number comparison performance. Results suggest that numerical magnitude processing, executive functions, and mathematics competence are related to symbolic number processing well into middle school, and that students continue to refine their ability to process number symbols into adolescence.

PURPOSE: Diffusion-weighted imaging allows investigators to identify structural, microstructural, and connectivity-based differences between subjects, but variability due to session and scanner biases is a challenge. METHODS: to investigate DWI variability, we present MASiVar, a multisite data set consisting of 319 diffusion scans acquired at 3 T from b = 1000 to 3000 s/mm2 across 14 healthy adults, 83 healthy children (5 to 8 years), three sites, and four scanners as a publicly available, preprocessed, and de-identified data set. With the adult data, we demonstrate the capacity of MASiVar to simultaneously quantify the intrasession, intersession, interscanner, and intersubject variability of four common DWI processing approaches: (1) a tensor signal representation, (2) a multi-compartment neurite orientation dispersion and density model, (3) white-matter bundle segmentation, and (4) structural connectomics. Respectively, we evaluate region-wise fractional anisotropy, mean diffusivity, and principal eigenvector; region-wise CSF volume fraction, intracellular volume fraction, and orientation dispersion index; bundle-wise shape, volume, fractional anisotropy, and length; and whole connectome correlation and maximized modularity, global efficiency, and characteristic path length. RESULTS: We plot the variability in these measures at each level and find that it consistently increases with intrasession to intersession to interscanner to intersubject effects across all processing approaches and that sometimes interscanner variability can approach intersubject variability. CONCLUSIONS: This study demonstrates the potential of MASiVar to more globally investigate DWI variability across multiple levels and processing approaches simultaneously and suggests harmonization between scanners for multisite analyses should be considered before inference of group differences on subjects.

PURPOSE: Diffusion weighted MRI imaging (DWI) is often subject to low signal-to-noise ratios (SNRs) and artifacts. Recent work has produced software tools that can correct individual problems, but these tools have not been combined with each other and with quality assurance (QA). A single integrated pipeline is proposed to perform DWI preprocessing with a spectrum of tools and produce an intuitive QA document. METHODS: the proposed pipeline, built around the FSL, MRTrix3, and ANTs software packages, performs DWI denoising; inter-scan intensity normalization; susceptibility-, eddy current-, and motion-induced artifact correction; and slice-wise signal drop-out imputation. To perform QA on the raw and preprocessed data and each preprocessing operation, the pipeline documents qualitative visualizations, quantitative plots, gradient verifications, and tensor goodness-of-fit and fractional anisotropy analyses. RESULTS: Raw DWI data were preprocessed and quality checked with the proposed pipeline and demonstrated improved SNRs; physiologic intensity ratios; corrected susceptibility-, eddy current-, and motion-induced artifacts; imputed signal-lost slices; and improved tensor fits. The pipeline identified incorrect gradient configurations and file-type conversion errors and was shown to be effective on externally available datasets. CONCLUSIONS: the proposed pipeline is a single integrated pipeline that combines established diffusion preprocessing tools from major MRI-focused software packages with intuitive QA.

Numerosity estimation performance (e.g. how accurate, consistent, or proportionally spaced (linear) numerosity-numeral mappings are) has previously been associated with math competence. However, the specific mechanisms that underlie such a relation is unknown. One possible mechanism is the mapping process between numerical sets and symbolic numbers (e.g. Arabic numerals). The current study examined two hypothesized mechanisms of numerosity-numeral mappings (item-based "associative" and holistic "structural" mapping) and their roles in the estimation-and-math relation. Specifically, mappings for small numbers (e.g. 1-10) are thought to be associative and resistant to calibration (e.g. feedback on accuracy of estimates), whereas holistic "structural" mapping for larger numbers (e.g. beyond 10) may be supported by flexibly aligning a numeral "response grid" (akin to a ruler) to an analog "mental number line" upon calibration. In 57 adults, we used pre- and post-calibration estimates to measure the range of continuous associative mappings among small numbers (e.g. a base range of associative mappings from 1 to 10), and obtained measures of math competence and delayed multiple-choice strategy reports. Consistent with previous research, uncalibrated estimation performance correlated with calculation competence, controlling for reading fluency and working memory. However, having a higher base range of associative mappings was not related to estimation performance or any math competence measures. Critically, discontinuity in calibration effects was typical at the individual level, which calls into question the nature of "holistic structural mapping". A parsimonious explanation to integrate previous and current findings is that estimation performance is likely optimized by dynamically constructing numerosity-numeral mappings through the use of multiple strategies from trial to trial.

Deficits in numerical magnitude perception characterize the mathematics learning disability developmental dyscalculia (DD), but recent studies suggest the relation stems from inhibitory control demands from incongruent visual cues in the nonsymbolic number comparison task. This study investigated the relation among magnitude perception during differing congruency conditions, executive function, and mathematics achievement measured longitudinally in children (n = 448) from ages 4 to 13. This relation was investigated across achievement groups and as it related to mathematics across the full range of achievement. Only performance on incongruent trials related to achievement. Findings indicate that executive function in a numerical context, beyond magnitude perception or executive function in a non-numerical context, relates to DD and mathematics across a wide range of achievement.

A region in the posterior inferior temporal gyrus (pITG) is thought to be specialized for processing Arabic numerals, but fMRI studies that compared passive viewing of numerals to other character types (e.g. letters and novel characters) have not found evidence of numeral preference in the pITG. However, recent studies showed that the engagement of the pITG is modulated by attention and task contexts, suggesting that passive viewing paradigms may be ill-suited for examining numeral specialization in the pITG. It is possible, however, that even if the strengths of responses to different category types are similar, the distributed response patterns (i.e. neural representations) in a candidate numeral-preferring pITG region ("pITG-numerals") may reveal categorical distinctions, even during passive viewing. Using representational similarity analyses with three datasets that share the same task paradigm and stimulus sets (total N ​= ​88), we tested whether the neural representations of digits, letters, and novel characters in pITG-numerals were organized according to visual form and/or conceptual categories (e.g. familiar versus novel, numbers versus others). Small-scale frequentist and Bayesian meta-analyses of our dataset-specific findings revealed that the organization of neural representations in pITG-numerals is unlikely to be described by differences in abstract shape, but can be described by a categorical "digits versus letters" distinction, or even a "digits versus others" distinction (suggesting greater numeral sensitivity). Evidence of greater numeral sensitivity during passive viewing suggest that pITG-numerals is likely part of a neural pathway that has been developed for automatic processing of objects with potential numerical relevance. Given that numerals and letters do not differ categorically in terms of shape, categorical distinction in pITG-numerals during passive viewing must reflect ontogenetic differentiation of symbol set representations based on repeated usage of numbers and letters in differing task contexts.

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."

The influential triple-code model of number representation proposed that there are three distinct brain regions for three different numerical representations: verbal words, visual digits and abstract magnitudes. It was hypothesized that the region for visual digits, known as the number form area, would be in ventral occipitotemporal cortex (vOTC), near other visual category-specific regions, such as the visual word form area. However, neuroimaging investigations searching for a region that responds in a category-specific manner to the visual presentation of number symbols have yielded inconsistent results. Price & Ansari (Price, Ansari 2011 Neuroimage 57, 1205-1211) investigated whether any regions activated more in response to passively viewing digits in contrast with letters and visually similar nonsense symbols and identified a region in the left angular gyrus. By contrast, Grotheer et al. (Grotheer, Herrmann, Kovács 2016 J. Neurosci. 36, 88-97) found bilateral regions in vOTC which were more activated in response to digits than other stimuli categories while performing a one-back task. In the current study, we aimed to replicate the findings reported in Grotheer et al. with Price & Ansari's passive viewing task as this is the most stringent test of bottom-up, sensory-driven, category-specific perception. Moreover, we used the contrasts reported in both papers in order to test whether the discrepancy in findings could be attributed to the difference in analysis.

Humans tend to be inaccurate and inconsistent when estimating a large number of objects. Furthermore, we modify our estimates when feedback or a reference array is provided, indicating that the mappings between perceived numerosity and their corresponding numerals are largely malleable in response to calibration. However, there is great variability in response to calibration across individuals. Using uncalibrated and calibrated numerosity estimation conditions, the current study explored the factors underlying individual differences in the extent and nature of the malleability of numerosity estimation performance as a result of calibration in a sample of 71 undergraduate students. We found that individual differences in performance were reliable across conditions, and participants' responses to calibration varied greatly. Participants who were less consistent or had more proportionally spaced (i.e. linear) estimates before calibration tended to shift the distributions of their estimates to a greater extent. Higher calculation competence also predicted an increase in how linear participants' estimates were after calibration. Moreover, the effect of calibration was not continuous across numerosities within participants. This suggests that the mechanisms underlying numeral-numerosity mappings may be less systematic than previously thought and likely depend on cognitive mechanisms beyond representation of numerosities. Taken together, the mappings between numerosities and numerical symbols may not be stable and direct, but transient and mediated by task-related (e.g. strategic) mechanisms. Rather than estimation skills being foundational for math competence, math competence may also influence estimation skills. Therefore, numerosity estimation tasks are not a pure measure of number representations.

The dominant model of number processing suggests the existence of a Number Form Area (NFA) in the inferior temporal gyrus (ITG) that supports the processing of Arabic digits as visual symbols of number. However, studies have produced inconsistent evidence for the presence and laterality of digit-specific ITG activity. Furthermore, whether any such activity relates to mathematical competence is unknown. This study investigated these two issues using functional magnetic resonance imaging. Thirty-two adults performed digit and letter detection tasks and reading and mathematics tests. During digit detection, participants determined whether digits were present in a string of letters (e.g. AH3NR versus AHTNR). During letter detection, participants determined whether letters were present in a string of digits (e.g. 93R78 versus 93478). Results showed four clusters in frontal, occipital, and temporal regions for digit detection, including a left ITG cluster. Five clusters in frontal, parietal, occipital, and temporal regions were associated with letter detection, including a left ITG cluster. Digit and letter-related ITG clusters were spatially distinct; however, a direct contrast of digit and letter processing did not reveal greater activity in the left ITG for digit detection. Whole brain correlations showed greater digit-related activity in the right ITG for participants with higher calculation skills, but there was no correlation between letter activity and calculation skills. Together, our results suggest functional localization, but not specialization, for digits in the left ITG and provide the first evidence of a relationship between calculation skills and digit processing in the right ITG.

The development of math skills is a critical component of early education and a strong indicator of later school and economic success. Recent research utilizing population-normed, standardized measures of math achievement suggest that structural and functional integrity of parietal regions, especially the intraparietal sulcus, are closely related to the development of math skills. However, it is unknown how these findings relate to in-school math learning. The present study is the first to address this issue by investigating the relationship between regional differences in grey matter (GM) volume and performance in grade-level mathematics as measured by a state-wide, school-based test of math achievement (TCAP math) in children from 3rd to 8th grade. Results show that increased GM volume in the bilateral hippocampal formation and the right inferior frontal gyrus, regions associated with learning and memory, is associated with higher TCAP math scores. Secondary analyses revealed that GM volume in the left angular gyrus had a stronger relationship to TCAP math in grades 3-4 than in grades 5-8 while the relationship between GM volume in the left inferior frontal gyrus and TCAP math was stronger for grades 5-8. These results suggest that the neuroanatomical architecture related to in-school math achievement differs from that related to math achievement measured by standardized tests, and that the most related neural structures differ as a function of grade level. We suggest, therefore, that the use of school-relevant outcome measures is critical if neuroscience is to bridge the gap to education.

The present study investigates the relation between resting-state functional connectivity (rsFC) of cytoarchitectonically defined subdivisions of the parietal cortex at the end of 1st grade and arithmetic performance at the end of 2nd grade. Results revealed a dissociable pattern of relations between rsFC and arithmetic competence among subdivisions of intraparietal sulcus (IPS) and angular gyrus (AG). rsFC between right hemisphere IPS subdivisions and contralateral IPS subdivisions positively correlated with arithmetic competence. In contrast, rsFC between the left hIP1 and the right medial temporal lobe, and rsFC between the left AG and left superior frontal gyrus, were negatively correlated with arithmetic competence. These results suggest that strong inter-hemispheric IPS connectivity is important for math development, reflecting either neurocognitive mechanisms specific to arithmetic processing, domain-general mechanisms that are particularly relevant to arithmetic competence, or structural 'cortical maturity'. Stronger connectivity between IPS, and AG, subdivisions and frontal and temporal cortices, however, appears to be negatively associated with math development, possibly reflecting the ability to disengage suboptimal problem-solving strategies during mathematical processing, or to flexibly reorient task-based networks. Importantly, the reported results pertain even when controlling for reading, spatial attention, and working memory, suggesting that the observed rsFC-behavior relations are specific to arithmetic competence.

A growing body of research suggests that the processing of nonsymbolic (e.g. sets of dots) and symbolic (e.g. Arabic digits) numerical magnitudes serves as a foundation for the development of math competence. Performance on magnitude comparison tasks is thought to reflect the precision of a shared cognitive representation, as evidence by the presence of a numerical ratio effect for both formats. However, little is known regarding how visuo-perceptual processes are related to the numerical ratio effect, whether they are shared across numerical formats, and whether they relate to math competence independently of performance outcomes. The present study investigates these questions in a sample of typically developing adults. Our results reveal a pattern of associations between eye-movement measures, but not their ratio effects, across formats. This suggests that ratio-specific visuo-perceptual processing during magnitude processing is different across nonsymbolic and symbolic formats. Furthermore, eye movements are related to math performance only during symbolic comparison, supporting a growing body of literature suggesting symbolic number processing is more strongly related to math outcomes than nonsymbolic magnitude processing. Finally, eye-movement patterns, specifically fixation dwell time, continue to be negatively related to math performance after controlling for task performance (i.e. error rate and reaction time) and domain general cognitive abilities (IQ), suggesting that fluent visual processing of Arabic digits plays a unique and important role in linking symbolic number processing to formal math abilities.

Nonsymbolic numerical comparison task performance (whereby a participant judges which of two groups of objects is numerically larger) is thought to index the efficiency of neural systems supporting numerical magnitude perception, and performance on such tasks has been related to individual differences in math competency. However, a growing body of research suggests task performance is heavily influenced by visual parameters of the stimuli (e.g. surface area and dot size of object sets) such that the correlation with math is driven by performance on trials in which number is incongruent with visual cues. Almost nothing is currently known about whether the neural correlates of nonsymbolic magnitude comparison are also affected by visual congruency. To investigate this issue, we used functional magnetic resonance imaging (fMRI) to analyze neural activity during a nonsymbolic comparison task as a function of visual congruency in a sample of typically developing high school students (n = 36). Further, we investigated the relation to math competency as measured by the preliminary scholastic aptitude test (PSAT) in 10th grade. Our results indicate that neural activity was modulated by the ratio of the dot sets being compared in brain regions previously shown to exhibit an effect of ratio (i.e. left anterior cingulate, left precentral gyrus, left intraparietal sulcus, and right superior parietal lobe) when calculated from the average of congruent and incongruent trials, as it is in most studies, and that the effect of ratio within those regions did not differ as a function of congruency condition. However, there were significant differences in other regions in overall task-related activation, as opposed to the neural ratio effect, when congruent and incongruent conditions were contrasted at the whole-brain level. Math competency negatively correlated with ratio-dependent neural response in the left insula across congruency conditions and showed distinct correlations when split across conditions. There was a positive correlation between math competency in the right supramarginal gyrus during congruent trials and a negative correlation in the left angular gyrus during incongruent trials. Together, these findings support the idea that performance on the nonsymbolic comparison task relates to math competency and ratio-dependent neural activity does not differ by congruency condition. With regards to math competency, congruent and incongruent trials showed distinct relations between math competency and individual differences in ratio-dependent neural activity.

Recent studies report a putative "number form area" (NFA) in the inferior temporal gyrus (ITG) suggested to be specialized for Arabic numeral processing. However, a number of earlier studies report no such NFA. The reasons for such discrepancies across studies are unclear. To examine evidence for a convergent NFA across studies, we conducted two activation likelihood estimation meta-analyses on 31 and a subset of 20 neuroimaging studies that have contrasted digits with other meaningful symbols. Results suggest the potential existence of an NFA in the right ITG, in addition to a 'symbolic number processing network' comprising bilateral parietal regions, and right-lateralized superior and inferior frontal regions. Critically, convergent localization for the NFA was only evident when contrasts were appropriately controlled for task demands, and does not appear to depend on employing methods designed to overcome fMRI signal dropout in the ITG. Importantly, only five studies had foci within the identified ITG NFA cluster boundary, indicating that more empirical evidence is necessary to determine the true functional specialization and regional specificity of the putative NFA.

This study investigated the relation between symbolic and nonsymbolic magnitude processing abilities with 2 standardized measures of math competence (WRAT Arithmetic and KeyMath Numeration) in 150 3rd-grade children (mean age 9.01 years). Participants compared sets of dots and pairs of Arabic digits with numerosities 1-9 for relative numerical magnitude. In line with previous studies, performance on both symbolic and nonsymbolic magnitude processing was related to math ability. Performance metrics combining reaction and accuracy, as well as weber fractions, were entered into mediation models with standardized math test scores. Results showed that symbolic magnitude processing ability fully mediates the relation between nonsymbolic magnitude processing and math ability, regardless of the performance metric or standardized test.

Mathematical and numerical competence is a critical foundation for individual success in modern society yet the neurobiological sources of individual differences in math competence are poorly understood. Neuroimaging research over the last decade suggests that neural mechanisms in the parietal lobe, particularly the intraparietal sulcus (IPS) are structurally aberrant in individuals with mathematical learning disabilities. However, whether those same brain regions underlie individual differences in math performance across the full range of math abilities is unknown. Furthermore, previous studies have been exclusively cross-sectional, making it unclear whether variations in the structure of the IPS are caused by or consequences of the development of math skills. The present study investigates the relation between grey matter volume across the whole brain and math competence longitudinally in a representative sample of 50 elementary school children. Results show that grey matter volume in the left IPS at the end of 1st grade relates to math competence a year later at the end of 2nd grade. Grey matter volume in this region did not change over that year, and was still correlated with math competence at the end of 2nd grade. These findings support the hypothesis that the IPS and its associated functions represent a critical foundation for the acquisition of mathematical competence.

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1-6. In grades 1-2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing.

Developmental dyscalculia (DD) is a learning disorder affecting the acquisition of school level arithmetic skills present in approximately 3-6% of the population. At the behavioral level DD is characterized by poor retrieval of arithmetic facts from memory, the use of immature calculation procedures and counting strategies, and the atypical representation and processing of numerical magnitude. At the neural level emerging evidence suggests DD is associated with atypical structure and function in brain regions associated with the representation of numerical magnitude. The current state of knowledge points to a core deficit in numerical magnitude representation in DD, but further work is required to elucidate causal mechanisms underlying the disorder.

Mathematical skills are of critical importance, both academically and in everyday life. Neuroimaging research has primarily focused on the relationship between mathematical skills and functional brain activity. Comparatively few studies have examined which white matter regions support mathematical abilities. The current study uses diffusion tensor imaging (DTI) to test whether individual differences in white matter predict performance on the math subtest of the Preliminary Scholastic Aptitude Test (PSAT). Grades 10 and 11 PSAT scores were obtained from 30 young adults (ages 17-18) with wide-ranging math achievement levels. Tract based spatial statistics was used to examine the correlation between PSAT math scores, fractional anisotropy (FA), radial diffusivity (RD) and axial diffusivity (AD). FA in left parietal white matter was positively correlated with math PSAT scores (specifically in the left superior longitudinal fasciculus, left superior corona radiata, and left corticospinal tract) after controlling for chronological age and same grade PSAT critical reading scores. Furthermore, RD, but not AD, was correlated with PSAT math scores in these white matter microstructures. The negative correlation with RD further suggests that participants with higher PSAT math scores have greater white matter integrity in this region. Individual differences in FA and RD may reflect variability in experience dependent plasticity over the course of learning and development. These results are the first to demonstrate that individual differences in white matter are associated with mathematical abilities on a nationally administered scholastic aptitude measure.

Do individual differences in the brain mechanisms for arithmetic underlie variability in high school mathematical competence? Using functional magnetic resonance imaging, we correlated brain responses to single digit calculation with standard scores on the Preliminary Scholastic Aptitude Test (PSAT) math subtest in high school seniors. PSAT math scores, while controlling for PSAT Critical Reading scores, correlated positively with calculation activation in the left supramarginal gyrus and bilateral anterior cingulate cortex, brain regions known to be engaged during arithmetic fact retrieval. At the same time, greater activation in the right intraparietal sulcus during calculation, a region established to be involved in numerical quantity processing, was related to lower PSAT math scores. These data reveal that the relative engagement of brain mechanisms associated with procedural versus memory-based calculation of single-digit arithmetic problems is related to high school level mathematical competence, highlighting the fundamental role that mental arithmetic fluency plays in the acquisition of higher-level mathematical competence.

The numerical ratio effect (NRE) and the Weber fraction (w) are common metrics of the precision of the approximate numbers sense (ANS), a cognitive mechanism suggested to play a role in the development of numerical and arithmetic skills. The task most commonly used to measure the precision of the ANS is the numerical comparison task. Multiple variants of this task have been employed yet it is currently unclear how these affect metrics of ANS acuity, and how these relate to arithmetic achievement. The present study investigates the reliability, validity and relationship to standardized measures of arithmetic fluency of the NRE and w elicited by three variants of the nonsymbolic number comparison task. Results reveal that the strengths of the NRE and w differ between task variants. Moreover, the reliability and validity of the reaction time NRE and the w were generally significant across task variants, although reliability was stronger for w. None of the task variants revealed a correlation between ANS metrics and arithmetic fluency in adults. These results reveal important consistencies across nonsymbolic number comparison tasks, indicating a shared cognitive foundation. However, the relationship between ANS acuity and arithmetic performance remains unclear.

The neural foundations of arithmetic learning are not well understood. While behavioral studies have revealed relationships between symbolic number processing and individual differences in children's arithmetic performance, the neurocognitive mechanisms that bind symbolic number processing and arithmetic are unknown. The current fMRI study investigated the relationship between children's brain activation during symbolic number comparison (Arabic digits) and individual differences in arithmetic fluency. A significant correlation was found between the numerical ratio effect on reaction times and accuracy and children's arithmetic scores. Furthermore, children with a stronger neural ratio effect in the left intraparietal sulcus (IPS) during symbolic number processing exhibited higher arithmetic scores. Previous research has demonstrated that activation of the IPS during numerical magnitude processing increases over the course of development, and that the left IPS plays an important role in symbolic number processing. The present findings extend this knowledge to show that children with more mature response modulation of the IPS during symbolic number processing exhibit higher arithmetic competence. These results suggest that the left IPS is a key neural substrate for the relationship between the relative of precision of the representation of numerical magnitude and school-level arithmetic competence.

Arabic digits are one of the most ubiquitous symbol sets in the world. While there have been many investigations into the neural processing of the semantic information digits represent (e.g. through numerical comparison tasks), little is known about the neural mechanisms which support the processing of digits as visual symbols. To characterise the component neurocognitive mechanisms which underlie numerical cognition, it is essential to understand the processing of digits as a visual category, independent of numerical magnitude processing. The 'Triple Code Model' (Dehaene, 1992; Dehaene and Cohen, 1995) posits an asemantic visual code for processing Arabic digits in the ventral visual stream, yet there is currently little empirical evidence in support of this code. This outstanding question was addressed in the current functional Magnetic Resonance (fMRI) study by contrasting brain responses during the passive viewing of digits versus letters and novel symbols at short (50 ms) and long (500 ms) presentation times. The results of this study reveal increased activation for familiar symbols (digits and letters) relative to unfamiliar symbols (scrambled digits and letters) at long presentation durations in the left dorsal Angular gyrus (dAG). Furthermore, increased activation for Arabic digits was observed in the left ventral Angular gyrus (vAG) in comparison to letters, scrambled digits and scrambled letters at long presentation durations, but no digit specific activation in any region at short presentation durations. These results suggest an absence of a digit specific 'Visual Number Form Area' (VNFA) in the ventral visual cortex, and provide evidence for the role of the left ventral AG during the processing of digits in the absence of any explicit processing demands. We conclude that Arabic digit processing depends specifically on the left AG rather than a ventral visual stream VNFA.

Numbers are everywhere in modern life. Looking out a window, one might see both symbolic numbers, like the numerals on a thermometer, and nonsymbolic quantities, such as the number of chickadees at a bird feeder. Although differences between symbolic and nonsymbolic numbers appear very salient, most research on numerical cognition has focused on similarities rather than differences between numerical stimulus formats. Thus, little is known about differences in the processing of symbolic and nonsymbolic numerical magnitudes. A recent computational model proposed that symbolic and nonsymbolic quantities undergo distinct encoding processes which then converge on a common neural representation of numerical magnitude (Verguts, T. Fias, W. 2004. Representation of number in animals and humans: a neural model. J. Cogn. Neurosci. 16 (9), 1493-1504.). Moreover, this model predicted that discrete brain regions underlie these encoding processes. Using functional magnetic resonance imaging, the present study tested the predictions of this model by examining the functional neuroanatomy of symbolic and nonsymbolic number processing. Nineteen adults compared the relative numerical magnitude of symbolic and nonsymbolic stimuli. An initial conjunction analysis revealed the right inferior parietal lobule to be significantly active in both symbolic and nonsymbolic numerical comparison. A contrast of the activation associated with symbolic and nonsymbolic stimuli revealed that both the left angular and superior temporal gyri were more activated for symbolic compared to nonsymbolic numerical magnitude judgments. The reverse comparison (nonsymbolic>symbolic) revealed several regions including the right posterior superior parietal lobe. These results reveal both format-general and format-specific processing of numerical stimuli in the brain. The potential roles of these regions in symbolic and nonsymbolic numerical processing are discussed.

The aim of this study was to identify regional structural differences in the brains of native speakers of a tonal language (Chinese) compared to nontonal (European) language speakers. Our expectation was that there would be differences in regions implicated in pitch perception and production. We therefore compared structural brain images in three groups of participants: 31 who were native Chinese speakers; 7 who were native English speakers who had learnt Chinese in adulthood; and 21 European multilinguals who did not speak Chinese. The results identified two brain regions in the vicinity of the right anterior temporal lobe and the left insula where speakers of Chinese had significantly greater gray and white matter density compared with those who did not speak Chinese. Importantly, the effects were found in both native Chinese speakers and European subjects who learnt Chinese as a non-native language, illustrating that they were language related and not ethnicity effects. On the basis of prior studies, we suggest that the locations of these gray and white matter changes in speakers of a tonal language are consistent with a role in linking the pitch of words to their meaning.

Developmental dyscalculia (DD) is a specific learning disability affecting the acquisition of school-level mathematical abilities in the context of otherwise normal academic achievement, with prevalence estimates in the order of 3-6%. Behavioural studies show deficits in elementary numerical processing among individuals with pure DD, indicating that deficits in higher-level mathematical skills may stem from impaired representation and processing of basic numerical magnitude. Adult neuropsychological and neuroimaging research points to the intraparietal sulcus as a key region for the representation and processing of numerical magnitude. This raises the possibility of a parietal dysfunction as a root cause of DD. We show that, in children with pure DD, the right intraparietal sulcus is not modulated in response to numerical processing demands to the same degree as in typically developing children. This finding provides the first direct evidence for a specific impairment of parietal magnitude systems in DD during non-symbolic numerosity processing.