Lack of improvement in multiplication is associated with reverting from verbal retrieval to numerical operations

Structural and transcriptional signatures of arithmetic abilities in children

Arithmetic ability is critical for daily life, academic achievement, career development, and future economic success. Individual differences in arithmetic skills among children and adolescents are related to variations in brain structures. Most existing studies have used hypothesis-driven region of interest analysis. To identify distributed brain regions related to arithmetic ability, we used data-driven cross-validated predictive models to analyze cross-sectional behavioral and structural MRI data in children and adolescents. The gray matter volume (GMV) of widespread brain regions reliably predicted arithmetic abilities measured by the Comprehensive Mathematical Abilities Test. Furthermore, we applied neuroimaging-transcriptome association analysis to explore transcriptional signatures associated with structural patterns of arithmetic ability. Structural patterns of arithmetic ability primarily correlated with transcriptional profiles enriched for genes involved in transmembrane transport and synaptic signaling. Our findings enhance our understanding of the neural and genetic mechanisms underlying children's arithmetic ability and offer a practical predictor for arithmetic skills during development.

Brain markers of subtraction and multiplication skills in childhood: task-based functional connectivity and individualized structural similarity

Arithmetic, a high-order cognitive ability, show marked individual difference over development. Despite recent advancements in neuroimaging techniques have enabled the identification of brain markers for individual differences in high-order cognitive abilities, it remains largely unknown about the brain markers for arithmetic. This study used a data-driven connectome-based prediction model to identify brain markers of arithmetic skills from arithmetic-state functional connectivity and individualized structural similarity in 132 children aged 8 to 15 years. We found that both subtraction-state functional connectivity and individualized SS successfully predicted subtraction and multiplication skills but multiplication-state functional connectivity failed to predict either skill. Among the four successful prediction models, most predictive connections were located in frontal-parietal, default-mode, and secondary visual networks. Further computational lesion analyses revealed the essential structural role of frontal-parietal network in predicting subtraction and the essential functional roles of secondary visual, language, and ventral multimodal networks in predicting multiplication. Finally, a few shared nodes but largely nonoverlapping functional and structural connections were found to predict subtraction and multiplication skills. Altogether, our findings provide new insights into the brain markers of arithmetic skills in children and highlight the importance of studying different connectivity modalities and different arithmetic domains to advance our understanding of children's arithmetic skills.

Positive math attitudes are associated with greater frontal activation among children from higher socio-economic status families

Math learning is explained by the interaction between cognitive, affective, and social factors. However, studies rarely investigate how these factors interact with one another to explain math performance. This study aims to fill this gap in the literature by using functional magnetic resonance imaging (fMRI) to understand the neurocognitive mechanisms underlying the interaction between parental socioeconomic status (SES) and children's math attitudes. To this aim, 57 children solved multiplication problems inside the scanner. We measured parental SES by creating two groups based on parents' occupations and measured children's math attitudes using a questionnaire. We ran a cluster-wise regression analysis examining the interaction between these two variables while controlling for the main effects of SES, math attitudes, and full IQ. The analysis revealed a cluster in the left inferior frontal gyrus (IFG), which was due to children with positive math attitudes from high socio-economic status families showing greater IFG activation when solving large multiplication problems as compared to their negative attitudes high SES peers, suggesting that they exhibited more retrieval effort to solve large multiplication problems. We discuss how this may be because they were the only ones who fully engaged in math opportunities provided by their environment.

Early Gray Matter Structural Covariance Predicts Longitudinal Gain in Arithmetic Ability in Children

Previous neuroimaging studies on arithmetic development have mainly focused on functional activation or functional connectivity between brain regions. It remains largely unknown how brain structures support arithmetic development. The present study investigated whether early gray matter structural covariance contributes to later gain in arithmetic ability in children. We used a public longitudinal sample comprising 63 typically developing children. The participants received structural magnetic resonance imaging scanning when they were 11 years old and were tested with a multiplication task at 11 years old (time 1) and 13 years old (time 2), respectively. Mean gray matter volumes were extracted from eight brain regions of interest to anchor salience network (SN), frontal-parietal network (FPN), motor network (MN), and default mode network (DMN) at time 1. We found that longitudinal gain in arithmetic ability was associated with stronger structural covariance of the SN seed with frontal and parietal regions and stronger structural covariance of the FPN seed with insula, but weaker structural covariance of the FPN seed with motor and temporal regions, weaker structural covariance of the MN seed with frontal and motor regions, and weaker structural covariance of the DMN seed with temporal region. However, we did not detect correlation between longitudinal gain in arithmetic ability and behavioral measure or regional gray matter volume at time 1. Our study provides novel evidence for a specific contribution of gray matter structural covariance to longitudinal gain in arithmetic ability in childhood.

Temporal cortex activation explains children's improvement in math attitudes

Math attitudes are related to achievement, yet we do not know how the brain supports changes in math attitudes. 51 children (54.9% female, 45.1% male; 37.3% White, 33.3% Black, 11.8% Latino, 5.9% Asian, 11.8% Other) solved a multiplication task inside the scanner when they were approximately 11 (time 1; T1) and 13 (time 2; T2) years old (i.e., mean age). Results revealed clusters in the left middle to superior temporal gyri at T1 associated with math attitudes at T1 and with their longitudinal improvement. However, changes in attitudes were not associated with brain changes over time. These findings suggest that relying on the storage of arithmetic facts, involved in memory retrieval, explains the development of positive math attitudes.

The longitudinal development of large-scale functional brain networks for arithmetic ability from childhood to adolescence

Arithmetic ability is an important high-level cognitive function that requires interaction among multiple brain regions. Previous studies on arithmetic development have focused on task-induced activation in isolated brain regions or functional connectivity among particular seed regions. However, it remains largely unknown whether and how functional connectivity among large-scale brain modules contributes to arithmetic development. In the present study, we used a longitudinal sample of task-based functional magnetic resonance imaging (fMRI) data comprising 63 typically developing children, with two testing points being about two years apart. With graph theory, we examined the longitudinal development of large-scale brain modules for a multiplication task in younger (mean age 9.88 at time 1) and older children (mean age 12.34 at time 1), respectively. The results showed that the default-mode (DMN) and frontal-parietal networks (FPN) became increasingly segregated over time. Specifically, intra-connectivity within the DMN and FPN increased significantly with age, and inter-connectivity between the DMN and visual network decreased significantly with age. Such developmental changes were mainly observed in the younger children, but not in the older children. Moreover, the change in network segregation of the DMN was positively correlated with longitudinal gain in arithmetic performance in the younger children, and individual difference in network segregation of the FPN was positively correlated with arithmetic performance at time 2 in the older children. Taken together, the present results highlight the development of the functional architecture in large-scale brain networks from childhood to adolescence, which may provide insights into potential neural mechanisms underlying arithmetic development.

Neurocognitive mechanisms explaining the role of math attitudes in predicting children's improvement in multiplication skill

Enhancing student's math achievement is a significant educational challenge. Numerous studies have shown that math attitudes can predict improvement in math performance, but no study has yet revealed the underlying neurocognitive mechanisms explaining this effect. To answer this question, 50 children underwent functional magnetic resonance imaging (fMRI) when they were 11 (time 1; T1) and 13 (time 2; T2) years old. Children solved a rhyming judgment and a single-digit multiplication task inside the scanner at T1. The rhyming task was used to independently define a verbal region of interest in the left inferior frontal gyrus (IFG). We focused on this region because of previous evidence showing math attitudes-related effects in the left IFG for children with low math skill (Demir-Lira et al., 2019). Children completed standardized testing of math attitudes at T1 and of multiplication skill both at T1 and T2. We performed a cluster-wise regression analysis to investigate the interaction between math attitudes and improvement in multiplication skill over time while controlling for the main effects of these variables, intelligence, and accuracy on the task. This analysis revealed a significant interaction in the left IFG, which was due to improvers with positive math attitudes showing enhanced activation. Our result suggests that IFG activation, possibly reflecting effort invested in retrieving multiplication facts, is one of the possible neurocognitive mechanism by which children with positive math attitudes improve in multiplication skill. Our finding suggests that teachers and parents can help children do better in math by promoting positive math attitudes.

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.

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.

Neural representations of phonology in temporal cortex scaffold longitudinal reading gains in 5- to 7-year-old children

The objective of this study was to investigate whether phonological processes measured through brain activation are crucial for the development of reading skill (i.e. scaffolding hypothesis) and/or whether learning to read words fine-tunes phonology in the brain (i.e. refinement hypothesis). We specifically looked at how different grain sizes in two brain regions implicated in phonological processing played a role in this bidirectional relation. According to the dual-stream model of speech processing and previous empirical studies, the posterior superior temporal gyrus (STG) appears to be a perceptual region associated with phonological representations, whereas the dorsal inferior frontal gyrus (IFG) appears to be an articulatory region that accesses phonological representations in STG during more difficult tasks. 36 children completed a reading test outside the scanner and an auditory phonological task which included both small (i.e. onset) and large (i.e. rhyme) grain size conditions inside the scanner when they were 5.5-6.5 years old (Time 1) and once again approximately 1.5 years later (Time 2). To study the scaffolding hypothesis, a regression analysis was carried out by entering brain activation in either STG or IFG for either small (onset > perceptual) or large (rhyme > perceptual) grain size phonological processing at T1 as the predictors and reading skill at T2 as the dependent measure, with several covariates of no interest included. To study the refinement hypothesis, the regression analysis included reading skill at T1 as the predictor and brain activation in either STG or IFG for either small or large grain size phonological processing at T2 as the dependent measures, with several covariates of no interest included. We found that only posterior STG, regardless of grain size, was predictive of reading gains. Parallel models with only behavioral accuracy were not significant. Taken together, our results suggest that the representational quality of phonology in temporal cortex is crucial for reading development. Moreover, our study provides neural evidence supporting the scaffolding hypothesis, suggesting that brain measures of phonology could be helpful in early identification of reading difficulties.

Temporo-frontal activation during phonological processing predicts gains in arithmetic facts in young children

Behavioral studies have shown discrepant results regarding the role of phonology in predicting math gains. The objective of this study was to use fMRI to study the role of activation during a rhyming judgment task in predicting behavioral gains on math fluency, multiplication, and subtraction skill. We focused within the left middle/superior temporal gyrus and left inferior frontal gyrus, brain areas associated with the storage of phonological representations and with their access, respectively. We ran multiple regression analyses to determine whether activation predicted gains in the three math measures, separately for younger (i.e. 10 years old) and older (i.e 12 years old) children. Results showed that activation in both temporal and frontal cortex only predicted gains in fluency and multiplication skill, and only for younger children. This study suggests that both temporal and frontal cortex activation during phonological processing are important in predicting gains in math tasks that involve the retrieval of facts that are stored as phonological codes in memory. Moreover, these results were specific to younger children, suggesting that phonology is most important in the early stages of math development. When the math task involved subtractions, which relies on quantity representations, phonological processes were not important in driving gains.

A longitudinal neuroimaging dataset on arithmetic processing in school children

We describe functional and structural data acquired using a 3T scanner in a sample of 132 typically developing children, who were scanned when they were approximately 11 years old (i.e. Time 1). Sixty-three of them were scanned again approximately 2 years later (i.e. Time 2). Children performed four tasks inside the scanner: two arithmetic tasks and two localizer tasks. The arithmetic tasks were a single-digit multiplication and a single-digit subtraction task. The localizer tasks, a written rhyming judgment task and a numerosity judgment task, were used to independently identify verbal and quantity brain areas, respectively. Additionally, we provide data on behavioral performance on the tasks inside the scanner, participants' scores on standardized tests, including reading and math skill, and a developmental history questionnaire completed by parents. This dataset could be useful to answer questions regarding the neural bases of the development of math in children and its relation to individual differences in skill. The data, entitled "Brain Correlates of Math Development", are freely available from OpenNeuro (https://openneuro.org).