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.

Emergent math difficulties among English learners: can the odds be reduced?

Solving word problems in mathematics presents difficulties for many English learners (ELs), including those who use Spanish as a home language. In the early stage of learning to solve mathematics word problems, some children, including ELs, experience difficulties. By English status, EL refers to those children whose home language was Spanish while in the process of developing English at school. Math difficulties (MD) refers to those children with low normative mathematical problem-solving scores in both English and Spanish. The purpose of this study was to determine those measures that increase the odds of identifying EL children with emergent MD. Elementary school children (grades 1, 2, and 3) were administered a battery of math, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, working memory [WM]) in both Spanish (L1) and English (L2) in Year 1 and again one year later. Multilevel growth modeling compared MD children identified one year later who manifested MD to children who were average math achievers or poor math achievers across the two testing waves (year 1 and year 2). The results indicated that significant growth parameters (i.e., measures of estimation, WM) increased the odds of identifying emergent MD relative to children with Persistent math deficits and average achievers. The results were discussed in terms of a multidimensional model that taps domain-specific skills and general cognitive processes that increase the odds of identifying later math difficulties.

Cognitive and academic growth among emergent bilingual children at risk and not at risk for math difficulties.

One purpose of this study was to identify cognitive processes within the English (second language [L2]) and Spanish (first language [L1]) language systems that underlie growth in math problem solving among emergent bilingual (EB) children with and without math difficulties (MD). A second purpose was to determine those L1 cognitive processes that play an essential role in predicting math word-problem-solving difficulties. To this end, children (N = 275; children with MD = 90) 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. Three findings were important. First, multilevel logistic modeling suggested that the log-odds of identifying children with MD were best captured by the level of performance on measures of fluid intelligence, Spanish STM, and English WM. Second, the log-odds of identifying children with MD were uniquely related to growth on WM, computation, and number magnitude judgment measures. Finally, the level of performance on L1 measures of reading, calculation, and naming speed and inhibition facilitated the identification of children with MD. In contrast, growth on all Spanish measures, except vocabulary and estimation, increased the log-odds of identifying children with MD. In general, the results suggest that there are constraints or inefficiencies in cognitive processes within and across both language systems that underlie the development of EB children's MD. The results highlight the importance of the phonological and executive systems of WM as important predictors of EB children's math problem-solving difficulties.

Math problem-solving and cognition among emerging bilingual children at risk and not at risk for math difficulties.

Cognitive processes that underlie individual differences in mathematical problem-solution accuracy in elementary emerging bilingual children (English Learners) at risk and not at risk for math problem-solving difficulties (MD) were examined. A battery of tests was administered in both English and Spanish that assessed problem-solving, achievement, and cognitive processing in children in first (N = 155/MD N = 23), second (N = 129/MD N = 44) and third grades (N = 110/MD N = 39). The results were that (a) the executive component of working memory (WM) predicted MD status independent of measures of fluid intelligence, reading, calculation, knowledge of algorithms, processing speed, short-term memory, and inhibition, (b) low performance on Spanish measures of numeracy and executive component of WM were major predictors of the odds of being classified as MD and (c) bilingual proficiency primarily moderated English rather than Spanish measures of cognition. The results support the notion that the executive system of WM is an important predictor of emerging bilingual children's math problem-solving difficulties.

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

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.

Does the structure of working memory in EL children vary across age and two language systems?

This study examined the cross-sectional structure of working memory (WM) among elementary school English learners (ELs). A battery of WM tasks was administered in Spanish (L1) and English (L2) within five age groups (ages 6, 7, 8, 9, & 10). Confirmatory factor analysis showed a three-factor structure of WM emerged in both L1 and L2 administrations for each age group. The important findings, however, were: (1) the separation between the executive component and storage component (phonological loop) structure of WM increased as a function of age within both language systems, (2) the structure of WM supported a domain general phonological storage component and a domain general executive system across both language systems, and (3) the visual-spatial WM system shared minimal variance with the executive system. Taken together, the findings support Baddeley's multicomponent model (e.g., Baddeley & Logie, 1999. The multiple-component model. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 28-61). Cambridge: Cambridge University Press) as a good fit to the structure of WM in EL children's English and Spanish language system.

Math Difficulties and Working Memory Growth in English Language Learner Children: Does Bilingual Proficiency Play a Significant Role?

Purpose: The purpose of this study was to determine those components of working memory (WM) that play a significant role in predicting math growth in children who are English language learners (N = 157) with serious math difficulties (MD). Method: A battery of tests was administered in English and Spanish that assessed computation, reading, vocabulary, inhibition, and components of WM in Grade 1 children with follow-up testing in Grades 2 and 3. Results: The results indicated that growth in the executive component of WM was related to growth in math performance. Proficient bilingual children (proficient in both Spanish and English vocabulary) with MD outperformed less proficient bilingual children with MD on measures of math calculation, fluid intelligence, reading, and Spanish WM at Grade 3. Conclusion: Growth in the executive component of WM is significantly related to growth in math computation, and increased bilingual proficiency across testing waves yielded positive gains in both math and cognitive performance in children with MD.

The impact of working memory training on near and far transfer measures: Is it all about fluid intelligence?

This randomized control study investigates the effects of working memory (WM) training on near (similar WM memory tasks) and far (math problem-solving processes and accuracy tasks) transfer in children aged 7 to 11 years who vary in fluid intelligence. Participants were randomly assigned to either a control group or one of two WM training conditions (repeated practice vs. cued recall). ​When compared to the control condition, the results show that the cued recall condition yields higher post-test scores for the far transfer measures, whereas the repeated practice condition yields higher scores for the near transfer​ measures. However, these finding are qualified by significant treatment × fluid intelligence interactions. Thus, improvements in WM and related measures, as well as the positive transfer in learning outcomes, are moderated by fluid intelligence.

A meta-analysis on the relation between reading and working memory.

The purpose of this study was to determine the relation between reading and working memory (WM) in the context of 3 major theories: the domain-specificity theory (debate) of WM, the intrinsic cognitive load theory, and the dual process theory. A meta-analysis of 197 studies with 2026 effect sizes found a significant moderate correlation between reading and WM, r = .29, 95% CI [.27, .31]. Moderation analyses indicated that after controlling for publication type, bilingual status, domains of WM, and grade level, the relation between WM and reading was not affected by types of reading. The effects of WM domains were associated with grade level: before 4th grade, different domains of WM were related to reading to a similar degree, whereas verbal WM showed the strongest relations with reading at or beyond 4th grade. Further, the effect of WM on reading comprehension was partialed out when decoding and vocabulary were controlled for. Taken together, the findings are generally compatible with aspects of the domain-specificity theory of WM and the dual process theory, but, importantly, add a developmental component that is not currently reflected in models of the relation between reading and WM. The findings suggest that the domain-general central executive of WM is implicated in early reading acquisition, and verbal WM is more strongly implicated in later reading performance as readers gain more experience with reading. The implications of these findings for reading instruction and WM training are also discussed. (PsycINFO Database Record

A meta-analysis of self-monitoring on reading performance of K-12 students.

The published single-case design (SCD) research (N = 19 articles) on self-monitoring and reading performance was synthesized. The following inclusion criteria were used: (a) the study must have been peer-reviewed, (b) implemented an intervention targeting student self-monitoring of reading skills, (c) included data on at least 1 reading outcome, (d) included visual representation of the data, and (f) the study must have used an SCD to assess the topic of interest. A total of 67 participants, 45 males and 22 females, ranging in age from 7:8 -18:7 were included in the current meta-analysis. Ethnicity was reported for 42 students: 23 were Caucasian, 12 were African American, and 7 were Latino/Hispanic. Studies were compared with those meeting What Works Clearinghouse (WWC) standards and those not meeting standards. The Tau-U effect size (ES) method was the main calculation method used; however, Phi ES estimates are included for comparison purposes. Results indicated that self-monitoring had an overall significant large positive effect on the reading performance of K-12 students, Tau-U = 0.79, 95% confidence interval (CI) [0.64, 0.93], p < .0001. However, self-monitoring for studies that met WWC criteria yielded a larger overall positive ES, Tau-U = 0.93, 95% CI [0.79, 1.07], p < .0001. Although the current meta-analysis is limited to peer-reviewed SCD studies, the findings provide support for self-monitoring as an evidence-based reading intervention for students in Grades K-12. Furthermore, findings indicate that larger ES values were identified when consolidating studies based on WWC guidelines as compared with consolidating across all studies. (PsycINFO Database Record

Verbal and visual-spatial working memory: What develops over a life span?

This study investigates whether age-related changes in the structure of 5 complex working memory (WM) tasks (a) reflect a general or domain specific system, (b) follows a similar trajectory across different age spans, and (c) contribute domain general or domain specific resources to achievement measures. The study parsed the sample (N = 2,471) into 11 age groups (mean ages of 6, 7, 8, 9, 11, 13, 15, 18, 26, 41, and 66 years), and compared their performances on verbal and visuospatial WM measures. Three important findings emerged: (a) a confirmatory factor analysis and Schmid-Leiman transformation to a high-order model solution supported a domain general factor model for the total sample as well as separately for children and adults, (b) performance on visual-spatial WM tasks as a function of age decreased at a faster rate than verbal WM tasks, and (c) both verbal and visual-spatial WM measures in concert with each other uniquely predicted reading and math measures, suggesting that a domain general WM system contributed to performance on achievement measures. The results support the notion that (a) complex WM tasks function as a domain general system and (b) the factor structure for children and adults on complex WM tasks was highly similar, even though there was evidence of differentiation among verbal and visual-spatial WM measures at certain age groups. (PsycINFO Database Record

Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence?

The purpose of this study was to assess whether the differential effects of working memory (WM) components (the central executive, phonological loop, and visual-spatial sketchpad) on math word problem-solving accuracy in children (N = 413, ages 6-10) are completely mediated by reading, calculation, and fluid intelligence. The results indicated that all three WM components predicted word problem solving in the nonmediated model, but only the storage component of WM yielded a significant direct path to word problem-solving accuracy in the fully mediated model. Fluid intelligence was found to moderate the relationship between WM and word problem solving, whereas reading, calculation, and related skills (naming speed, domain-specific knowledge) completely mediated the influence of the executive system on problem-solving accuracy. Our results are consistent with findings suggesting that storage eliminates the predictive contribution of executive WM to various measures Colom, Rebollo, Abad, & Shih (Memory & Cognition, 34: 158-171, 2006). The findings suggest that the storage component of WM, rather than the executive component, has a direct path to higher-order processing in children.

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.

Cognitive strategy interventions improve word problem solving and working memory in children with math disabilities.

This study investigated the role of strategy instruction and working memory capacity (WMC) on problem solving solution accuracy in children with and without math disabilities (MD). Children in grade 3 (N = 204) with and without MD subdivided into high and low WMC were randomly assigned to 1 of 4 conditions: verbal strategies (e.g., underlining question sentence), visual strategies (e.g., correctly placing numbers in diagrams), verbal + visual strategies, and an untreated control. The dependent measures for training were problem solving accuracy and two working memory transfer measures (operation span and visual-spatial span). Three major findings emerged: (1) strategy instruction facilitated solution accuracy but the effects of strategy instruction were moderated by WMC, (2) some strategies yielded higher post-test scores than others, but these findings were qualified as to whether children were at risk for MD, and (3) strategy training on problem solving measures facilitated transfer to working memory measures. The main findings were that children with MD, but high WM spans, were more likely to benefit from strategy conditions on target and transfer measures than children with lower WMC. The results suggest that WMC moderates the influence of cognitive strategies on both the targeted and non-targeted measures.

Reading disabilities in children: A selective meta-analysis of the cognitive literature.

This article synthesizes literature that compares the academic, cognitive, and behavioral performance of children with and without reading disabilities (RD). Forty-eight studies met the criteria for the meta-analysis, yielding 735 effect sizes (ESs) with an overall weighted ES of 0.98. Small to high ESs in favor of children without RD emerged on measures of cognition (rapid naming [ES = 0.89], phonological awareness [ES = 1.00], verbal working memory [ES = 0.79], short-term memory [ES = 0.56], visual-spatial memory [ES = 0.48], and executive processing [ES = 0.67]), academic achievement (pseudoword reading [ES = 1.85], math [ES = 1.20], vocabulary [ES = 0.83], spelling [ES = 1.25], and writing [ES = 1.20]), and behavior skills (ES = 0.80). Hierarchical linear modeling indicated that specific cognitive process measures (verbal working memory, visual-spatial memory, executive processing, and short-term memory) and intelligence measures (general and verbal intelligence) significantly moderated overall group effect size differences. Overall, the results supported the assumption that cognitive deficits in children with RD are persistent.

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.

Growth in working memory and inhibition predicts literacy in English language learners: a cross-sectional and longitudinal study.

The purpose of this study was to determine whether cross-sectional and growth effects in second language (L2) literacy are related to the executive component of working memory (WM) and whether inhibition may underlie the links between WM and reading in children whose first language (L1) is Spanish. Elementary school children (grades 1, 2 and 3) were administered a battery of cognitive [WM, short-term memory (STM), random generation, rapid naming, phonological processing], vocabulary and reading measures in both Spanish (L1) and English (L2) in Year 1 and again one year later. The regression analyses showed that L2 growth in WM significantly predicted growth in L2 reading skills even when inhibition was controlled. Further, the contributions of WM to reading growth in both L1 and L2 reading were independent of cross-language skills in phonological processing, STM, oral language and naming speed. Overall, the results suggest the mental activities that underlie WM and inhibition in predictions of L2 literacy reflect independent executive processes.

A longitudinal study of neuropsychological functioning and academic achievement in children with and without signs of attention-deficit/hyperactivity disorder.

OBJECTIVE: Attention-deficit/hyperactivity disorder (ADHD) in childhood is associated with poor academic functioning. Deficits in academic functioning have proven to be less responsive to intervention than behavioral deficits in this population, yet the causes of this academic underperformance are not well understood. The purpose of this study is to examine the relationship between ADHD and academic performance in elementary-aged children in a developmental context. To do this, we study important cognitive variables and academic achievement over a three-year timeframe. METHOD: Based on teacher ratings of ADHD, children were divided into a high symptom group (n = 17) and a low symptom group (n = 34). A thorough battery of cognitive and academic tests was administered at Time 1 and again 2 years later. Cognitive measures focused specifically on working memory and response inhibition. RESULTS: RESULTS indicate that children who have high levels of ADHD signs differ from their low-sign peers in academic achievement and in several cognitive domains. Differences in cognitive functioning show a developmental trend consistent with earlier developmental delays in response inhibition and later delays in working memory. Working memory appears to be particularly important in several academic domains. Importantly, in a longitudinal model, working memory was more predictive of math achievement for students demonstrating signs of ADHD than for those who did not. CONCLUSION: The relationship between these cognitive variables and academic functioning are explicated in the domains of reading, math, and problem solving.