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.

Examination of common and unique brain regions for atypical reading and math: a meta-analysis.

The purpose of this study is to identify consistencies across functional neuroimaging studies regarding common and unique brain regions/networks for individuals with reading difficulties (RD) and math difficulties (MD) compared to typically developing (TD) individuals. A systematic search of the literature, utilizing multiple databases, yielded 116 functional magnetic resonance imaging and positron emission tomography studies that met the criteria. Coordinates that directly compared TD with either RD or MD were entered into GingerALE (Brainmap.org). An activation likelihood estimate (ALE) meta-analysis was conducted to examine common and unique brain regions for RD and MD. Overall, more studies examined RD (n = 96) than MD (n = 20). Across studies, overactivation for reading and math occurred in the right insula and inferior frontal gyrus for atypically developing (AD) > TD comparisons, albeit in slightly different areas of these regions; however, inherent threshold variability across imaging studies could diminish overlying regions. For TD > AD comparisons, there were no similar or overlapping brain regions. Results indicate there were domain-specific differences for RD and MD; however, there were some similarities in the ancillary recruitment of executive functioning skills. Theoretical and practical implications for researchers and educators are discussed.

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.

The Cognitive Profile of Math Difficulties: A Meta-Analysis Based on Clinical Criteria.

Math difficulties (MD) manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD (n = 680) and a group without MD (n = 1565). Criteria according to DSM and ICD were applied to identify MD (percentile rank ≤ 16, age range 8-12 years, no comorbidities/low IQ). Effect sizes for 22 abilities were estimated and separated by their level and type of scoring (AC = accuracy, RT = response time). A cognitive profile of MD was identified, characterized by distinct weaknesses in: (a) computation (calculation [AC], fact retrieval [AC]), (b) number sense (quantity processing [AC], quantity-number linking [RT], numerical relations [AC]), and (c) visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that (a) effects are larger when dealing with numbers or number words than with quantities, (b) MD is not accompanied by any weakness in abilities typically assigned to reading, and (c) weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed.

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.

Piloting the Response to Intervention Model in the Canary Islands: Prevention of Reading and Math Learning Disabilities.

The main objective of this study was to examine the effectiveness of an intervention implemented by elementary school teachers within the context of the Response to Intervention (RtI) model. For this purpose, a Tier 2 or secondary intervention was implemented by Spanish-speaking teachers in grades K-3 after receiving training to implement RtI components with fidelity. A total of 1,923 at-risk students were assigned to treatment (in reading, n = 542; in math, n = 483) or control (in reading, n = 406; in math, n = 492). Teachers were provided with a support system that included two web-based training programs for reading (i.e., Letra program) and math (i.e., Primate program). Implementation fidelity was analyzed using direct observations and self-reports. All students were assessed three times during the academic year. A hierarchical linear growth modeling was conducted, and differences in the growth rate of reading and math performance were analyzed between at-risk students who have received the intervention and those who have not received it. Children at-risk in the intervention condition appeared to benefit more than at-risk children in the control condition. Moreover, findings indicate that the earlier the intervention, the greater the percentage of students who leave the situation of risk of learning difficulties in reading and math.

Co-occurrence of Reading Disabilities and Math Disabilities: A Meta-Analysis.

Despite the importance of identifying individuals with reading disabilities, existing operational definitions of reading disability do not result in reliable identification. A large part of the problem arises from measurement error when a cut-point is imposed on a continuous distribution, especially for low base-rate conditions. One way to reduce measurement error is to include additional predictors in reading disability models. The present study examined co-occurring math disability as a possible additional criterion for predicting reading disability. Meta-analysis was used to examine the probability of individuals with reading disability also having a comorbid math disability. Possible moderators including age, severity of disability, and language were examined. The main result was an average weighted odds ratio of 2.12, 95% confidence interval [1.76, 2.55], indicating that students with a math disability are just over two times more likely to also have a reading disability than those without a math disability. Implications of the results are discussed.

Do Chinese Children With Math Difficulties Have a Deficit in Executive Functioning?

Several studies have shown that Executive Functioning (EF) is a unique predictor of mathematics performance. However, whether or not children with mathematics difficulties (MD) experience deficits in EF remains unclear. Thus, the purpose of this study was to examine if Chinese children with MD experience deficits in EF. We assessed 23 children with MD (9 girls, mean age = 10.40 years), 30 children with reading difficulties and MD (RDMD; 12 girls, mean age = 10.82 years), and 31 typically-developing (TD) peers (16 girls, mean age = 10.41 years) on measures of inhibition (Color-Word Stroop, Inhibition), shifting of attention (Planned Connections, Rapid Alternating Stimuli), working memory (Digit Span Backwards, Listening Span), processing speed (Visual Matching, Planned Search), reading (Character Recognition, Sentence Verification), and mathematics (Addition and Subtraction Fluency, Math Standard Achievement Test). The results of MANOVA analyses showed first that the performance of the MD children in all EF tasks was worse than their TD peers. Second, with the exception of the shifting tasks in which the MD children performed better than the RDMD children, the performance of the two groups was similar in all measures of working memory and inhibition. Finally, covarying for the effects of processing speed eliminated almost all differences between the TD and MD groups (the only exception was Listening Span) as well as the differences between the MD and RDMD groups in shifting of attention. Taken together, our findings suggest that although Chinese children with MD (with or without comorbid reading difficulties) experience significant deficits in all EF skills, most of their deficits can be accounted by lower-level deficits in processing speed.

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.