ABSTRACT This cohort-sequential study explored the components of working memory that underlie math calculation in elementary school children who are monolingual (English) or English language learners (ELLs) whose first language is Spanish. To this end, children (N = 789) in grades 1, 2, and 3 at wave 1 were administered a battery of math, vocabulary, reading and cognitive (short-term memory [STM], working memory [WM], rapid naming, and inhibition) measures. The battery of tests was administered again one year and two years later to the same participants. Three important findings emerged. First, along with naming speed, the results suggest that growth in the executive component of WM was significantly related to growth in calculation performance. Second, performance on measures of reading, fluid intelligence, naming speed and executive processes in wave 1 were significantly related to wave 3 math calculation performance. Finally, the full latent growth model showed that monolingual and ELL children were statistically comparable in computation at wave 3. Thus, strong support was found for the notion that the executive component of WM was related to math computation but weak support for the notion ELL children experienced a math achievement gap.

中文翻译：

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单语和英语学习者数学计算的增长：执行系统有作用吗？

摘要 这项队列序列研究探讨了作为母语为西班牙语的单语（英语）或英语学习者 (ELL) 的小学生数学计算基础的工作记忆成分。为此，第 1 波 1、2 和 3 年级的儿童（N = 789）接受了一系列数学、词汇、阅读和认知（短期记忆 [STM]、工作记忆 [WM]、快速命名） , 和抑制) 措施。一年和两年后对同一参与者再次进行了一系列测试。出现了三个重要的发现。首先，除了命名速度外，结果表明 WM 执行组件的增长与计算性能的增长显着相关。第二，在阅读、流体智力、第 1 波中的命名速度和执行过程与第 3 波数学计算性能显着相关。最后，完整的潜在增长模型表明，单语和 ELL 儿童在第 3 波的计算上具有统计可比性。 因此，WM 的执行成分与数学计算相关的观点得到了强有力的支持，但对 ELL 儿童的观点的支持较弱经历了数学成绩差距。