Mathematical Problem Solving in Emergent Bilingual Children: Is Growth Related to the Navigation between Two Working Memory Systems?

This cohort-sequential study explored the working memory (WM) structures that underlie growth in mathematical word problem solving (WPS) performance in elementary school emergent bilingual children whose first language (L1) is Spanish. To this end, children (N = 429) in Grades 1, 2, and 3 in southwest U.S. school districts at Wave 1 were administered a battery of cognitive (short-term memory [STM], WM, rapid naming, inhibition), domain-general nonmath (reading, vocabulary, and fluid intelligence) and domain-specific math measures (arithmetic computation, estimation, and magnitude judgment) in both Spanish (L1) and English (L2). These same measures were administered 1 and 2 years later. Four important findings emerged: (a) A three-factor structure (phonological STM, visual-spatial WM, and executive WM) captured the data across three testing waves within and across both language systems; (b) growth in phonological STM and executive WM uniquely predicted WPS growth, but these two WM structures interacted within the English language system; (c) Spanish verbal WM (phonological STM, executive WM) enhanced the magnitude of predictions of English verbal WM on English WPS; and (d) growth in language-specific phonological STM and executive WM predicted cross-sectional and within-child changes in WPS independent of growth in other domain-specific and domain-general academic areas. Taken together, the results suggest that language-specific age-related phonological STM growth and executive WM growth rates underlie Spanish and English math word problem-solving performance. The results extend the contribution of development models as a function of WM structures across two language systems as they apply to complex math performance.