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One important factor that hampers children's learning of mathematics is math anxiety (MA). Still, the mechanisms by which MA affects performance remain debated. The current study investigated the relationship between MA, basic number processing abilities (i.e., cardinality and ordinality processing), and executive functions in school children enrolled in grades 4-7 (N = 127). Children were divided into a high math anxiety group (N = 29) and a low math anxiety group (N = 31) based on the lowest quartile and the highest quartile. Using a series of analyses of variances, we find that highly math-anxious students do not perform worse on cardinality processing tasks (i.e., digit comparison and non-symbolic number sense), but that they perform worse on numerical and non-numerical ordinality processing tasks. We demonstrate that children with high MA show poorer performance on a specific aspect of executive functions-shifting ability. Our models indicate that shifting ability is tied to performance on both the numerical and non-numerical ordinality processing tasks. A central factor seems to be the involvement of executive processes during ordinality judgements, and executive functions may constitute the driving force behind these delays in numerical competence in math-anxious children.

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Symbolic numbers contain information about their relative numerical cardinal magnitude (e.g., 2 < 3) and ordinal placement in the count-list (e.g., 1, 2, 3). Previous research has primarily investigated magnitude discrimination skills and their predictive capacity for math achievement, whereas numerical ordering has been less systematically explored. At approximately 10-12 years of age, numerical order processing skills have been observed to surpass cardinal magnitude discrimination skills as the key predictor of arithmetic ability. The neurocognitive mechanisms underlying this shift remain unclear. To this end, we investigated children's (ages 10-12) neural correlates of numerical order and magnitude discrimination, as well as task-based functional connectomes and their predictive capacity for numeracy-related behavioral outcomes. Results indicated that number discrimination uniquely relied on bilateral temporoparietal correlates, whereas order processing recruited the bilateral IPS, cerebellum, and left premotor cortex. Connectome-based models were not cross-predictive for numerical order and magnitude, suggesting two dissociable mechanisms jointly supported by visuospatial working memory. Neural correlates of learning and memory were predictive of age and arithmetic ability, only for the ordinal task-connectome, indicating that the numerical order mechanism may undergo a developmental shift, dissociating it from mechanisms supporting cardinal number processing.

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BACKGROUND: Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is still limited. AIMS: First, to identify key cognitive abilities contributing to children's development of early arithmetic skills. Second, to examine the extent to which early arithmetic performance and early arithmetic development rely on different or similar constellations of domain-specific number abilities and domain-general cognitive abilities. SAMPLE: In all, 134 Swedish children (Mage = 6 years and 4 months, SD = 3 months, 74 boys) participated in this study. METHOD: Verbal and non-verbal logical reasoning, non-symbolic number comparison, counting knowledge, spatial processing, verbal working memory and arithmetic were assessed. Twelve months later, arithmetic skills were reassessed. A latent change score model was computed to determine whether any of the abilities accounted for variations in arithmetic development. RESULTS: Arithmetic performance was supported by counting knowledge, verbal and non-verbal logical reasoning and spatial processing. Arithmetic skill development was only supported by spatial processing. CONCLUSIONS: Results show that young children's early arithmetic performance and arithmetic development are supported by different cognitive processes. The findings regarding performance supported Fuchs et al.'s model (Dev Psychol, 46, 2010b, 1731) but the developmental findings did not. The developmental findings align partially to Geary et al.'s (J Educ Psychol, 109, 2017, 680) hypothesis stating that young children's early arithmetic development is more dependent on general cognitive abilities than number abilities.

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Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., "two"), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

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This study investigated the neural correlates of the so-called affect heuristic, which refers to the phenomenon whereby individuals tend to rely on affective states rather than rational deliberation of utility and probabilities during judgments of risk and utility of a given event or scenario. The study sought to explore whether there are shared regional activations during both judgments of relative risk and relative benefit of various scenarios, thus being a potential candidate of the affect heuristic. Using functional magnetic resonance imaging, we developed a novel risk perception task, based on a preexisting behavioral task assessing the affect heuristic. A whole-brain voxel-wise analysis of a sample of participants (n = 42) during the risk and benefit conditions revealed overlapping clusters in the left insula, left inferior frontal gyrus, and left medial frontal gyrus across conditions. Extraction of parameter estimates of these clusters revealed that activity of these regions during both tasks was inversely correlated with a behavioral measure assessing the inclination to use the affect heuristic. More activity in these areas during risk judgments reflect individuals' ability to disregard momentary affective impulses. The insula may be involved in integrating viscero-somatosensory information and forming a representation of the current emotional state of the body, whereas activity in the left inferior frontal gyrus and medial frontal gyrus indicates that executive processes may be involved in inhibiting the impulse of making judgments in favor of deliberate risk evaluations.

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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.

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To date, few studies have tried to pinpoint the mechanisms supporting children's skills in science. This study investigated to what extent logical reasoning, spatial processing, and working memory, tapped at age 9-10 years, are predictive of physics skills at age 12-13 years. The study used a sample of 81 children (37 girls). Measures of arithmetic calculation and reading comprehension were also included in the study. The multiple regression model accounted for 24% of the variation in physics achievement. The model showed that spatial processing (4.6%) and verbal working memory (4.5%) accounted for a similar amount of unique variance, while logical reasoning accounted for 5.7% variance. The measures of arithmetic calculation and reading comprehension did not account for any unique variance. Nine percent of the accounted variance was shared variance. The results demonstrate that physics is a multivariate discipline that draws upon numerous cognitive resources. Logical reasoning ability is a key component in order for children to learn about abstract physics facts, concepts, theories, and applying complex scientific methods. Spatial processing is important as it may sub-serve the assembly of diverse sources of visual-spatial information into a spatial-schematic image. The working memory system provides a flexible and efficient mental workspace that can supervise, coordinate, and execute processes involved in physics problem-solving.

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What are the underlying neurocognitive mechanisms that give rise to mathematical competence? This study investigated the relationship between tests of mathematical ability completed outside the scanner and resting-state functional connectivity (FC) of cytoarchitectonically defined subdivisions of the parietal cortex in adults. These parietal areas are also involved in executive functions (EFs). Therefore, it remains unclear whether there are unique networks for mathematical processing. We investigate the neural networks for mathematical cognition and three measures of EF using resting-state fMRI data collected from 51 healthy adults. Using 10 ROIs in seed to whole-brain voxel-wise analyses, the results showed that arithmetical ability was correlated with FC between the right anterior intraparietal sulcus (hIP1) and the left supramarginal gyrus and between the right posterior intraparietal sulcus (hIP3) and the left middle frontal gyrus and the right premotor cortex. The connection between the posterior portion of the left angular gyrus and the left inferior frontal gyrus was also correlated with mathematical ability. Covariates of EF eliminated connectivity patterns with nodes in inferior frontal gyrus, angular gyrus, and middle frontal gyrus, suggesting neural overlap. Controlling for EF, we found unique connections correlated with mathematical ability between the right hIP1 and the left supramarginal gyrus and between hIP3 bilaterally to premotor cortex bilaterally. This is partly in line with the "mapping hypothesis" of numerical cognition in which the right intraparietal sulcus subserves nonsymbolic number processing and connects to the left parietal cortex, responsible for calculation procedures. We show that FC within this circuitry is a significant predictor of math ability in adulthood.

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The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N = 46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.

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