What Mediates the Relationship Between Growth in Math Problem-Solving and Working Memory in English Language Learners?

This study explored the role of growth in the executive components of working memory (WM) on second language (L2) mathematical problem-solving in elementary school children who are emerging bilinguals whose first language (L1) is Spanish. To this end, children (N = 429) 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. Four important findings emerged: (a) growth in the executive of WM was significantly related to growth in L2 math problem-solving independent of growth in reading, vocabulary, fluid intelligence, inhibition, and rapid naming speed; (b) a Nonmath achievement/aptitude (i.e., reading, vocabulary) model provided a better fit to the data than domain-specific math and process models; (c) the relationship between WM and L2 math problem-solving was significantly mediated by L1 mathematical problem-solving and English vocabulary; and (d) the influence of WM on L2 math problem-solving was unidirectional. Taken together, this is the first comprehensive study of the link between growth in WM and growth in emerging bilingual children's mathematical problem-solving in 2 language systems. The results are discussed within the context of four models that assess the contribution of WM in predictions of later math problem-solving in emergent bilingual children. Educational Impact and Implications StatementEmerging bilingual children with Spanish as a first language have been found to score lower than English monolingual students on math measures because of the high demands placed on the processing of multiple pieces of information. Growth in the executive system of working memory has been isolated as playing a particularly robust role in English learners' mathematical problem-solving growth. This article determines those measures accessed from either the English or Spanish language system that play a key role in mediating the growth between working memory and mathematical problem-solving. Key mediators include measures specific (e.g., magnitude judgments) and not specific to math (vocabulary), but none of the mediators partials out the influence of working memory on problem-solving growth, suggesting working memory is an important instructional focus. In addition, the contribution of working memory was directional in predictions