Mathematical knowledge is constructed hierarchically during development from a basic understanding of addition and subtraction, two foundational and inter-related, but semantically distinct, numerical operations. Early in development, children show remarkable variability in their numerical problem-solving skills and difficulties in solving even simple addition and subtraction problems are a hallmark of math learning difficulties. Here, we use novel quantitative analyses to investigate whether less distinct representations are associated with poor problem-solving abilities in children during the early stages of math-skill acquisition. Crucially, we leverage dimensional and categorical analyses to identify linear and nonlinear neurobehavioral profiles of individual differences in math skills. Behaviorally, performance on the two different numerical operations was less differentiated in children with low math abilities, and lower problem-solving efficiency stemmed from weak evidence-accumulation during problem-solving. Children with low numerical abilities also showed less differentiated neural representations between addition and subtraction operations in multiple cortical areas, including the fusiform gyrus, intraparietal sulcus, anterior temporal cortex and insula. Furthermore, analysis of multi-regional neural representation patterns revealed significantly higher network similarity and aberrant integration of representations within a fusiform gyrus-intraparietal sulcus pathway important for manipulation of numerical quantity. These findings identify the lack of distinct neural representations as a novel neurobiological feature of individual differences in children's numerical problem-solving abilities, and an early developmental biomarker of low math skills. More generally, our approach combining dimensional and categorical analyses overcomes pitfalls associated with the use of arbitrary cutoffs for probing neurobehavioral profiles of individual differences in math abilities.

数学知识是在开发过程中从对加法和减法的基本理解分层构建的，这是两个基础且相互关联但语义不同的数值运算。在发展的早期，儿童在解决数字问题的能力方面表现出显着的差异，即使是简单的加法和减法问题也难以解决，这是数学学习困难的一个标志。在这里，我们使用新颖的定量分析来调查在数学技能习得的早期阶段，不太明显的表征是否与儿童解决问题的能力差有关。至关重要的是，我们利用维度和分类分析来识别数学技能个体差异的线性和非线性神经行为特征。在行为上，数学能力低的儿童在两种不同的数值运算上的表现差异较小，解决问题的效率较低是由于解决问题过程中证据积累不足。数字能力低的儿童在多个皮层区域（包括梭状回、顶叶沟、前颞叶皮层和岛叶）的加法和减法运算之间也表现出较少分化的神经表征。此外，对多区域神经表征模式的分析揭示了梭状回-顶内沟通路内表征的显着更高的网络相似性和异常整合，这对于数值操作很重要。这些发现将缺乏不同的神经表征确定为儿童数字问题解决能力个体差异的新神经生物学特征，以及低数学技能的早期发育生物标志物。更一般地说，我们结合维度和分类分析的方法克服了与使用任意截止值来探测数学能力个体差异的神经行为特征相关的缺陷。