Linear and nonlinear profiles of weak behavioral and neural differentiation between numerical operations in children with math learning difficulties.

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.