The mathematical word problem-solving performance gap between children with and without math difficulties: does working memory mediate and/or moderate treatment effects?

This study determined the extent to which working memory (WM) played a moderating and/or mediating role in word-problem-solving (WPS) instructional outcomes between children with and without math difficulties (MD). A randomized pretest-posttest control group study investigated the effects of 8-week strategy instruction in one of four treatment conditions on WPS accuracy of third graders with MD (N = 136) when compared to children with (N = 28) and without MD (N = 43). Comparisons were made of three strategy conditions that included overt cues (e.g. underlining key sentences, filling in diagrams), another treatment condition that removed the overt cues (material-only), and two control conditions (children with and without MD). Four important findings emerged. First, posttest WM significantly predicted posttest WPS, computation, and schema accuracy independent of pretest and treatment conditions. Second, posttest WM mediated posttest WPS treatment outcomes when the control conditions included children without MD. Third, strategy conditions that included overt cues (e.g. crossing out irrelevant sentences) decreased WM demands compared to the Materials-Only condition (without overt cues) for children with MD. Finally, incremental attention allocation training within treatment conditions improved posttest WM in children with MD but not posttest WPS. Results indicated that WPS differences between children with and without MD across treatment conditions were mediated by posttest WM performance.

The relation of bilingual cognitive skills to the second language writing performance of primary grade students.

The purposes of the current study were to examine the effects of cognitive and reading skills (i.e., working memory [WM], oral language development [OLD], and reading skills) on second language (L2) writing performance as well as the changes in these relationships across different grades among Spanish-speaking children learning English. A battery of measures assessing English and Spanish WM, OLD, reading skills, and English writing were administered to 494 English learners in Grades 1 to 3. Path analysis was conducted for each grade separately in both English and Spanish models. The findings indicated that the relationships between English writing performance and English cognitive and reading skills became stronger as the grades increased. However, the relationships between English writing and the Spanish cognitive and reading determinants were mixed, indicating a statistically significant relationship with Spanish WM and reading skills for Grade 2 and 3 students but not with OLD across all grades. Implications for L2 writing development are discussed.

Effects of Professional Development on English Learners' Problem Solving.

Teacher preparation for problem-solving instruction is essential to meeting the math needs of English learners (ELs) with math learning disabilities (MLD) in U.S. public schools. In investigating this instruction with Hispanic ELs with MLD, this study focused on how professional development supported one special educator's implementation of effective practices for both academic language and problem-solving instruction. The professional development prepared the teacher for instructional and cooperative learning phases that faded prompting as students achieved independence in applying the problem-solving strategy. A multiple-baseline design was used to assess nine third-grade Hispanic ELs with MLD. As compared with the baseline phase, instructional scaffolding increased word problem solving for all the participants. All students' level of probe performance was maintained during follow-up sessions. The results suggest the intervention facilitated improved math problem-solving performance.

Does Growth in the Executive System of Working Memory Underlie Growth in Literacy for Bilingual Children With and Without Reading Disabilities?

This cohort-sequential study explored the components of working memory (WM) that underlie second language (L2) reading growth in 450 children at risk and not at risk for reading disabilities (RD) whose first language is Spanish. English language learners designated as balanced and nonbalanced bilinguals with and without risk for RD in Grades 1, 2, and 3 at Wave 1 were administered a battery of cognitive (short-term memory, WM, naming speed, and inhibition), vocabulary, and reading measures in Spanish and English. These same measures were administered 1 and 2 years later. Two important findings occurred: First, growth in the WM executive component was significantly related to growth in English word identification and passage comprehension when competing measures (phonological processing, naming speed, inhibition, and fluid intelligence) were entered into the multilevel growth model. Second, children defined as at risk for RD in Wave 1 had lower intercepts than children not at risk at Wave 3 across several measures of cognition, language, and achievement. However, except on measures of the executive component of WM, no significant group differences in linear growth emerged. These findings suggest that growth in L2 reading was tied to growth in the executive system of WM.

Growth in literacy, cognition, and working memory in English language learners.

This cohort sequential study explored the components of working memory that underlie English reading and language acquisition in elementary school children whose first language is Spanish. To this end, children (N=410) in Grades 1, 2, and 3 at Wave 1 were administered a battery of cognitive (short-term memory [STM], working memory [WM], rapid naming, phonological processing, and random letter and number generation), vocabulary, and reading measures in both Spanish and English. These same measures were administered 1 and 2 years later. The results showed that (a) a three-factor structure (phonological STM, visual-spatial WM, and verbal WM) captured the data within both language systems, (b) growth in both the executive and STM storage components was uniquely related to growth in second language (L2) reading and language acquisition, and (c) the contribution of growth in the executive component of WM to growth in L2 processing was independent of growth in storage, phonological knowledge, inhibition, and rapid naming speed. The results suggested that growth in the phonological storage system does not supersede growth of the executive component of WM as a major contributor to growth in children's L2 reading and language.

Cognitive Strategies, Working Memory, and Growth in Word Problem Solving in Children With Math Difficulties.

This study investigated the role of strategy instruction and working memory capacity (WMC) on word problem solving accuracy in children with (n = 100) and without (n = 92) math difficulties (MD). Within classrooms, children in Grades 2 and 3 were randomly assigned to one of four treatment conditions: verbal-only strategies (e.g., underlining question sentence), verbal + visual strategies, visual-only strategies (e.g., correctly placing numbers in diagrams), or untreated control. Strategy interventions included 20 sessions in both Year 1 and Year 2. The intent-to-treat as well as the "as-treated" analyses showed that treatment effects were significantly moderated by WMC. In general, treatment outcomes were higher when WMC was set to a high rather than low level. When set to a relatively high WMC level, children with MD performed significantly better under visual-only strategy conditions and children without MD performed better under verbal + visual conditions when compared to control conditions.