**LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith‐Chant, B. L., Bisanz, J., Kamawar, D., & Penner‐Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child development, 81(6), 1753-1767.**

A model of the relations among cognitive precursors, early numeracy skill, and mathematical outcomes was tested for 182 children from 4.5 to 7.5 years of age. The model integrates research from neuroimaging, clinical populations, and normal development in children and adults. It includes 3 precursor pathways: quantitative, linguistic, and spatial attention. These pathways (a) contributed independently to early numeracy skills during preschool and kindergarten and (b) related differentially to performance on a variety of mathematical outcomes 2 years later. The success of the model in accounting for performance highlights the need to understand the fundamental underlying skills that contribute to diverse forms of mathematical competence.

**McCaskey, U., von Aster, M., Maurer, U., Martin, E., O’Gorman Tuura, R., & Kucian, K. (2018). Longitudinal brain development of numerical skills in typically developing children and children with developmental dyscalculia. Frontiers in human neuroscience, 11, 629.**

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deﬁcits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a ﬁrst attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8–11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deﬁcits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.

**Nelson, G., & Powell, S. R. (2017). A systematic review of longitudinal studies of mathematics difficulty. Journal of learning disabilities. **

**Abstract. **Some students may be diagnosed with a learning disability in mathematics or dyscalculia, whereas other students may demonstrate below-grade-level mathematics performance without a disability diagnosis. In the literature, researchers often identify students in both groups as experiencing *math difficulty*. To understand the performance of students with math difficulty, we examined 35 studies that reported longitudinal results of mathematics achievement (i.e., mathematics performance measured across at least a 12-month span). Our primary goal was to conduct a systematic review of these studies and to understand whether the growth of students with math difficulty was comparable or stagnant when compared with that of students without math difficulty. We also analyzed whether identification of math difficulty was predictive of mathematics achievement in later grades and whether a diagnosis of math difficulty was stable across grade levels. Results indicate that Results indicate that students with math difficulty demonstrate growth on mathematics measures, but this growth still leads to lower performance than that of students without math difficulty. Identification of math difficulty is strongly related to math performance in subsequent grades, and this diagnosis is often stable. Collectively, this literature indicates that students with math difficulty continue to struggle with mathematics in later grades.