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. Educational Impact and Implications Statement: Both phonological short-term memory (STM) and the executive component of working memory (WM) play a unique and significant developmental role in emergent bilingual children's mathematical word problem solving (WPS). The two components are not only structurally different, but they also contribute to distinct types of growth in mathematical problem solving. In addition, the verbal components of WM (phonological STM and executive WM) can contribute jointly (i.e., interact) in predictions of mathematical problem-solving growth within the second language system. The study also found there are significant benefits of L1 processing (Spanish in this case) in WM that contribute to the rate of growth in L2 (English in this case) WM and L2 mathematical WPS. These findings have implications for bilingual instruction aimed at strengthening L1 WM in terms of its impact on mathematical WPS in the child's developing second language. [ABSTRACT FROM AUTHOR]