Growth in Math Computation among Monolingual and English Language Learners:Does the Executive System have a Role?

What mediates the relationship between growth in math problem-solving and working memory in English language learners?

“…Several studies have found that working memory (WM) is related to a large range of higher-order cognitive processes and academic skills within children's L1 (e.g., see Swanson & Alloway, 2012, for a review), and therefore these complex cognitive behaviors would be related to learning L2, especially in the area of math problem-solving. Further, there is accumulating evidence to suggest that WM plays a significant role in math performance for monolingual children (e.g., Cowan & Powell, 2014;De Smedt et al, 2009;Klesczewski et al, 2015;Peng et al, 2016;Swanson & Fung, 2016), as well as EB children's math performance whose L1 is Spanish (e.g., Harvey & Miller, 2017;Swanson et al, 2019aSwanson et al, , 2021Vukovic & Lesaux, 2013). Working memory is defined in this context as a limited capacity system of temporary stores that includes functions related to the preservation of information while simultaneously processing other information and attention control related to these functions (e.g., Baddeley, 2012).…”

“…An obvious precursor to successful mathematical problem-solving is computational knowledge. Children at risk for math difficulties and who also are EBs have been shown to yield poor performance on math computation measures (e.g., Swanson et al, 2019a; Vukovic & Lesaux, 2013). Mathematical computation (e.g., 2 + 2 = 4) reflects the student's use of algorithms and arithmetic to add, subtract, multiply, or divide whole numbers, decimals, or fractions.…”

Language Proficiency and the Relation to Word–Problem Performance in Emergent Bilingual Students with Mathematics Difficulties

“…Examinations of emergent bilinguals’ mathematics achievement data indicate that emergent bilingual students continue to perform disproportionately lower than their same‐aged, monolingual peers (Driver & Powell, 2017; Garcia & Cuéllar, 2006; Kong & Swanson, 2019; Swanson et al., 2019). Within the category of emergent bilinguals, some students experience persistent MD.…”

“…(2019) examined the specific role of comprehension skill on word‐problem accuracy. The authors noted that successful comprehension of word problems involves two important steps: problem integration and problem translation (Hegarty et al., 1995; Kintsch & Greeno, 1985; Lewis & Mayer, 1987; Mayer & Hegarty, 2012; Swanson et al., 2019). Problem integration involves a student's ability to read a problem, recognize the problem type, and use that information to construct a coherent representation (Bae et al., 2015).…”

“…Problem integration involves a student's ability to read a problem, recognize the problem type, and use that information to construct a coherent representation (Bae et al., 2015). However, this cannot be achieved without the ability to translate the embedded language of word problems into verbal representations (i.e., problem translation; Swanson et al., 2019). Problem translation , then, involves several cognitive processes as students must (a) “recode text or oral language into a phonological speech‐based code” (Swanson et al., 2019, p. 69); (b) connect prior contextual knowledge to the problem at hand; (c) link consecutive mathematical statements; (d) distinguish relevant from irrelevant information; and (e) determine appropriate problem‐solving procedures (Mayer & Hegarty, 2012; Swanson et al., 2019).…”