Cognitive and academic growth among emergent bilingual children at risk and not at risk for math difficulties.

One purpose of this study was to identify cognitive processes within the English (second language [L2]) and Spanish (first language [L1]) language systems that underlie growth in math problem solving among emergent bilingual (EB) children with and without math difficulties (MD). A second purpose was to determine those L1 cognitive processes that play an essential role in predicting math word-problem-solving difficulties. To this end, children (N = 275; children with MD = 90) in Grades 1, 2, and 3 at Wave 1 were administered a battery of math, reading, vocabulary, and cognitive (short-term memory [STM], working memory [WM], rapid naming, and inhibition) measures. The battery of tests was administered again 1 year and 2 years later to the same participants. Three findings were important. First, multilevel logistic modeling suggested that the log-odds of identifying children with MD were best captured by the level of performance on measures of fluid intelligence, Spanish STM, and English WM. Second, the log-odds of identifying children with MD were uniquely related to growth on WM, computation, and number magnitude judgment measures. Finally, the level of performance on L1 measures of reading, calculation, and naming speed and inhibition facilitated the identification of children with MD. In contrast, growth on all Spanish measures, except vocabulary and estimation, increased the log-odds of identifying children with MD. In general, the results suggest that there are constraints or inefficiencies in cognitive processes within and across both language systems that underlie the development of EB children's MD. The results highlight the importance of the phonological and executive systems of WM as important predictors of EB children's math problem-solving difficulties.