Individual differences in children’s math performance have been associated with math anxiety, attention problems, working memory (WM), and reading skills, but the mechanisms by which these factors jointly contribute to children’s math achievement are unknown. Here, we use structural equation modeling to characterize the relation between these factors and their influence on non-verbal Numerical Operations (NO) and verbal Math Reasoning (MR) in 330 children (M=8.34years). Our findings indicate that WM plays a central role in both non-verbal NO and verbal MR, whereas math anxiety and reading comprehension have unique and more pronounced influences on MR, compared to NO. Our study elucidates how affective and cognitive factors distinctly influence non-verbal and verbal mathematical problem solving.

Early numerical proficiency lays the foundation for acquiring quantitative skills essential in today's technological society. Identification of cognitive and brain markers associated with long-term growth of children's basic numerical computation abilities is therefore of utmost importance. Previous attempts to relate brain structure and function to numerical competency have focused on behavioral measures from a single time point. Thus, little is known about the brain predictors of individual differences in growth trajectories of numerical abilities. Using a longitudinal design, with multimodal imaging and machine-learning algorithms, we investigated whether brain structure and intrinsic connectivity in early childhood are predictive of 6 year outcomes in numerical abilities spanning childhood and adolescence. Gray matter volume at age 8 in distributed brain regions, including the ventrotemporal occipital cortex (VTOC), the posterior parietal cortex, and the prefrontal cortex, predicted longitudinal gains in numerical, but not reading, abilities. Remarkably, intrinsic connectivity analysis revealed that the strength of functional coupling among these regions also predicted gains in numerical abilities, providing novel evidence for a network of brain regions that works in concert to promote numerical skill acquisition. VTOC connectivity with posterior parietal, anterior temporal, and dorsolateral prefrontal cortices emerged as the most extensive network predicting individual gains in numerical abilities. Crucially, behavioral measures of mathematics, IQ, working memory, and reading did not predict children's gains in numerical abilities. Our study identifies, for the first time, functional circuits in the human brain that scaffold the development of numerical skills, and highlights potential biomarkers for identifying children at risk for learning difficulties.SIGNIFICANCE STATEMENT:Children show substantial individual differences in math abilities and ease of math learning. Early numerical abilities provide the foundation for future academic and professional success in an increasingly technological society. Understanding the early identification of poor math skills has therefore taken on great significance. This work provides important new insights into brain structure and connectivity measures that can predict longitudinal growth of children's math skills over a 6 year period, and may eventually aid in the early identification of children who might benefit from targeted interventions.

Although behavioral difficulties are well documented in reading disabilities, little is known about the relationship between math ability and internalizing and externalizing behaviors. Here, we use standardized measures to investigate the relation among early math ability, math anxiety, and internalizing and externalizing behaviors in a group of 366 second and third graders. Math achievement was significantly correlated with attentional difficulties and social problems but not with internalizing symptoms. The relation between math achievement and externalizing behavioral problems was stronger in girls than in boys. Math achievement was not correlated with trait anxiety but was negatively correlated with math anxiety. Critically, math anxiety differed significantly between children classified as math learning disabled (MLD), low achieving (LA), and typically developing (TD), with math anxiety significantly higher in the MLD and LA groups compared to the TD group. Our findings suggest that, even in nonclinical samples, math difficulties at the earliest stages of formal math learning are associated with attentional difficulties and domain-specific anxiety. These findings underscore the need for further examination of the shared cognitive, neural, and genetic influences underlying problem solving and nonverbal learning difficulties and accompanying internalizing and externalizing behaviors.

Reading disability (RD) and math disability (MD) frequently co-occur, but the etiology of this comorbidity is not well understood. Groups with RD only (N = 241), MD only (N = 183), and RD + MD (N = 188) and a control group with neither disorder (N = 411) completed a battery of measures of internalizing and externalizing psychopathology, social and academic functioning, and 10 neuropsychological processes. Groups with RD only, MD only, and RD + MD were significantly impaired versus the control group on nearly all measures, and the group with RD + MD was more impaired than the groups with MD and RD alone on measures of internalizing psychopathology, academic functioning, and 7 of 10 neuropsychological constructs. Multiple regression analyses of the neuropsychological measures indicated that deficits in reading and math were associated with shared weaknesses in working memory, processing speed, and verbal comprehension. In contrast, reading difficulties were uniquely associated with weaknesses in phoneme awareness and naming speed, and math deficits were uniquely associated with weaknesses in set shifting. These results support multiple-deficit neuropsychological models of RD and MD and suggest that RD and MD are distinct but related disorders that co-occur because of shared neuropsychological weaknesses in working memory, processing speed, and verbal comprehension.

Math anxiety is a negative emotional reaction to situations involving mathematical problem solving. Math anxiety has a detrimental impact on an individual's long-term professional success, but its neurodevelopmental origins are unknown. In a functional MRI study on 7- to 9-year-old children, we showed that math anxiety was associated with hyperactivity in right amygdala regions that are important for processing negative emotions. In addition, we found that math anxiety was associated with reduced activity in posterior parietal and dorsolateral prefrontal cortex regions involved in mathematical reasoning. Multivariate classification analysis revealed distinct multivoxel activity patterns, which were independent of overall activation levels in the right amygdala. Furthermore, effective connectivity between the amygdala and ventromedial prefrontal cortex regions that regulate negative emotions was elevated in children with math anxiety. These effects were specific to math anxiety and unrelated to general anxiety, intelligence, working memory, or reading ability. Our study identified the neural correlates of math anxiety for the first time, and our findings have significant implications for its early identification and treatment.

Although the detrimental effects of math anxiety in adults are well understood, few studies have examined how it affects younger children who are beginning to learn math in a formal academic setting. Here, we examine the relationship between math anxiety and math achievement in second and third graders. In response to the need for a grade-appropriate measure of assessing math anxiety in this group we first describe the development of Scale for Early Mathematics Anxiety (SEMA), a new measure for assessing math anxiety in second and third graders that is based on the Math Anxiety Rating Scale. We demonstrate the construct validity and reliability of the SEMA and use it to characterize the effect of math anxiety on standardized measures of math abilities, as assessed using the Mathematical Reasoning and Numerical Operations subtests of the Wechsler Individual Achievement Test (WIAT-II). Math achievement, as measured by the WIAT-II Math Composite score, was significantly and negatively correlated with SEMA but not with trait anxiety scores. Additional analyses showed that SEMA scores were strongly correlated with Mathematical Reasoning scores, which involves more complex verbal problem solving. SEMA scores were weakly correlated with Numerical Operations which assesses basic computation skills, suggesting that math anxiety has a pronounced effect on more demanding calculations. We also found that math anxiety has an equally detrimental impact on math achievement regardless of whether children have an anxiety related to numbers or to the situational and social experience of doing math. Critically, these effects were unrelated to trait anxiety, providing the first evidence that the specific effects of math anxiety can be detected in the earliest stages of formal math learning in school. Our findings provide new insights into the developmental origins of math anxiety, and further underscore the need to remediate math anxiety and its deleterious effects on math achievement in young children.

Although lesion studies over the past several decades have focused on functional dissociations in posterior parietal cortex (PPC) during arithmetic, no consistent view has emerged of its differential involvement in addition, subtraction, multiplication, and division. To circumvent problems with poor anatomical localization, we examined functional overlap and dissociations in cytoarchitectonically defined subdivisions of the intraparietal sulcus (IPS), superior parietal lobule (SPL) and angular gyrus (AG), across these four operations. Compared to a number identification control task, all operations except addition, showed a consistent profile of left posterior IPS activation and deactivation in the right posterior AG. Multiplication and subtraction differed significantly in right, but not left, IPS and AG activity, challenging the view that the left AG differentially subserves retrieval during multiplication. Although addition and multiplication both rely on retrieval, multiplication evoked significantly greater activation in right posterior IPS, as well as the prefrontal cortex, lingual and fusiform gyri, demonstrating that addition and multiplication engage different brain processes. Comparison of PPC responses to the two pairs of inverse operations: division versus multiplication and subtraction versus addition revealed greater activation of left lateral SPL during division, suggesting that processing inverse relations is operation specific. Our findings demonstrate that individual IPS, SPL and AG subdivisions are differentially modulated by the four arithmetic operations and they point to significant functional heterogeneity and individual differences in activation and deactivation within the PPC. Critically, these effects are related to retrieval, calculation and inversion, the three key cognitive processes that are differentially engaged by arithmetic operations. Our findings point to distribute representation of these processes in the human PPC and also help explain why lesion and previous imaging studies have yielded inconsistent findings.

The contribution of the three core components of working memory (WM) to the development of mathematical skills in young children is poorly understood. The relation between specific WM components and Numerical Operations, which emphasize computation and fact retrieval, and Mathematical Reasoning, which emphasizes verbal problem solving abilities in 48 2nd and 50 3rd graders was assessed using standardized WM and mathematical achievement measures. For 2nd graders, the central executive and phonological components predicted Mathematical Reasoning skills; whereas the visuo-spatial component predicted both Mathematical Reasoning and Numerical Operations skills in 3rd graders. This pattern suggests that the central executive and phonological loop facilitate performance during early stages of mathematical learning whereas visuo-spatial representations play an increasingly important role during later stages. We propose that these changes reflect a shift from prefrontal to parietal cortical functions during mathematical skill acquisition. Implications for learning and individual differences are discussed.

Although children's use of a variety of strategies to solve arithmetic problems has been well documented, there is no agreed on standardized and validated method for assessing this mix. We examined the convergent validity of typically achieving (TA, N= 39) and low achieving (LA, N = 20) second and third grade children's strategy choices in simple addition using three different methods: child self-report, observer-report, and response time (RT). The high concordance between child and observer reports (Kappa =.948) in both groups suggests that the participants were aware of, and could accurately report, the strategies they used. The Receiver-Operator Characteristic (ROC) analysis showed that RT accurately differentiated between retrieval and counting (AUC = 82%). The specificity and sensitivity of the ROC profiles were significantly greater for the TA group than for LA group, even though the groups did not differ in the overall strategy mix. Our findings suggest that ROC analysis is more sensitive to group differences in the mechanisms governing strategy choice than observation or child report. Children's use of retrieval strategies as well as accuracy during both retrieval and counting trials were all related to the central executive, but not the phonological and visuospatial sketchpad, component of working memory. We discuss the implication of these findings for early mathematical learning.