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

Short-term number sense training recapitulates long-term neurodevelopmental changes from childhood to adolescence

Number sense is fundamental to the development of numerical problem-solving skills. In early childhood, children establish associations between non-symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non-symbolic and symbolic representations of quantity evolves with age, with increased dissociation across development. Consistent with this theory, recent research suggests that cross-format neural representational similarity (NRS) between non-symbolic and symbolic quantities is correlated with arithmetic fluency in children but not in adolescents. However, it is not known if short-term training (STT) can induce similar changes as long-term development. In this study, children aged 7-10 years underwent a theoretically motivated 4-week number sense training. Using multivariate neural pattern analysis, we investigated whether short-term learning could modify the relation between cross-format NRS and arithmetic skills. Our results revealed a significant correlation between cross-format NRS and arithmetic fluency in distributed brain regions, including the parietal and prefrontal cortices, prior to training. However, this association was no longer observed after training, and multivariate predictive models confirmed these findings. Our findings provide evidence that intensive STT during early childhood can promote behavioral improvements and neural plasticity that resemble and recapitulate long-term neurodevelopmental changes that occur from childhood to adolescence. More generally, our study contributes to our understanding of the malleability of number sense and highlights the potential for targeted interventions to shape neurodevelopmental trajectories in early childhood. RESEARCH HIGHLIGHTS: We tested the hypothesis that short-term number sense training induces the dissociation of symbolic numbers from non-symbolic representations of quantity in children. We leveraged a theoretically motivated intervention and multivariate pattern analysis to determine training-induced neurocognitive changes in the relation between number sense and arithmetic problem-solving skills. Neural representational similarity between non-symbolic and symbolic quantity representations was correlated with arithmetic skills before training but not after training. Short-term training recapitulates long-term neurodevelopmental changes associated with numerical problem-solving from childhood to adolescence.

Integrated number sense tutoring remediates aberrant neural representations in children with mathematical disabilities

Number sense is essential for early mathematical development but it is compromised in children with mathematical disabilities (MD). Here we investigate the impact of a personalized 4-week Integrated Number Sense (INS) tutoring program aimed at improving the connection between nonsymbolic (sets of objects) and symbolic (Arabic numerals) representations in children with MD. Utilizing neural pattern analysis, we found that INS tutoring not only improved cross-format mapping but also significantly boosted arithmetic fluency in children with MD. Critically, the tutoring normalized previously low levels of cross-format neural representations in these children to pre-tutoring levels observed in typically developing, especially in key brain regions associated with numerical cognition. Moreover, we identified distinct, 'inverted U-shaped' neurodevelopmental changes in the MD group, suggesting unique neural plasticity during mathematical skill development. Our findings highlight the effectiveness of targeted INS tutoring for remediating numerical deficits in MD, and offer a foundation for developing evidence-based educational interventions.

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network

Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.

The developmental relationship between nonsymbolic and symbolic fraction abilities

A fundamental research question in quantitative cognition concerns the developmental relationship between nonsymbolic and symbolic quantitative abilities. This study examined this developmental relationship in abilities to process nonsymbolic and symbolic fractions. There were 99 6th graders (M_age = 11.86 years), 101 10th graders (M_age = 15.71 years), and 102 undergraduate and graduate students (M_age = 21.97 years) participating in this study, and their nonsymbolic and symbolic fraction abilities were measured with nonsymbolic and symbolic fraction comparison tasks, respectively. Nonsymbolic and symbolic fraction abilities were significantly correlated in all age groups even after controlling for the ability to process nonsymbolic absolute quantity and general cognitive abilities, including working memory and inhibitory control. Moreover, the strength of nonsymbolic-symbolic correlations was higher in 6th graders than in 10th graders and adults. These findings suggest a weakened association between nonsymbolic and symbolic fraction abilities during development, and this developmental pattern may be related with participants' increasing proficiency in symbolic fractions.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Behavioral Studies Using Large-Scale Brain Networks – Methods and Validations

Mapping human behaviors to brain activity has become a key focus in modern cognitive neuroscience. As methods such as functional MRI (fMRI) advance cognitive scientists show an increasing interest in investigating neural activity in terms of functional connectivity and brain networks, rather than activation in a single brain region. Due to the noisy nature of neural activity, determining how behaviors are associated with specific neural signals is not well-established. Previous research has suggested graph theory techniques as a solution. Graph theory provides an opportunity to interpret human behaviors in terms of the topological organization of brain network architecture. Graph theory-based approaches, however, only scratch the surface of what neural connections relate to human behavior. Recently, the development of data-driven methods, e.g., machine learning and deep learning approaches, provide a new perspective to study the relationship between brain networks and human behaviors across the whole brain, expanding upon past literatures. In this review, we sought to revisit these data-driven approaches to facilitate our understanding of neural mechanisms and build models of human behaviors. We start with the popular graph theory approach and then discuss other data-driven approaches such as connectome-based predictive modeling, multivariate pattern analysis, network dynamic modeling, and deep learning techniques that quantify meaningful networks and connectivity related to cognition and behaviors. Importantly, for each topic, we discuss the pros and cons of the methods in addition to providing examples using our own data for each technique to describe how these methods can be applied to real-world neuroimaging data.