The association between working memory and mathematical problem solving: A three-level meta-analysis

Although working memory (WM) is an important factor in mathematical problem solving (MPS), it remains unclear how well WM relates to MPS. Thus, we aimed to determine this relationship by using a meta-analysis. We searched electronic databases for studies published between 2000 and 2020 and established operational criteria. We conducted Egger’s regression tests and created funnel plots to test for publication bias. Finally, a three-level meta-analytic model analysis of data from 130 studies involving 43,938 participants and 1,355 effect sizes revealed a moderate relationship between WM and MPS (r = 0.280, 95% CI = [0.263, 0.314]). Moreover, moderator analyses showed that: (1) dressed-up word problems were more strongly tied to WM than to intra-mathematical problems; (2) the central executive function showed the strongest relation with MPS, whereas the phonological loop had the weakest; (3) gender ratio had significant moderating effects; and (4) some of the above-mentioned significant moderating effects were unique after controlling for other factors. Implications for research and practice were also discussed.

The Relationship between Working Memory and Arithmetic in Primary School Children: A Meta-Analysis

Working memory (WM) plays a crucial role in the development of arithmetic ability. However, research findings related to which factors influence the relationship between WM and arithmetic skills are inconsistent. The present meta-analysis aimed to examine the links between WM and arithmetic in primary school children and investigate whether this is dependent on WM domains (i.e., verbal, visual, spatial), child age, arithmetic operation type, and arithmetic task type. A total of 11,224 participants with an age range of 6- to 12 years, from 55 independent samples were included in the meta-analysis. Analysis of 46 studies with 187 effect sizes revealed an overall significant and medium correlation between WM and arithmetic. Heterogeneity analyses indicated that verbal WM showed a stronger correlation with arithmetic than visuospatial WM, and that correlations between verbal WM and arithmetic declined with age, whereas correlations between spatial-sequential, and spatial-simultaneous WM and arithmetic remained stable throughout development. Addition and subtraction were more involved in verbal WM than multiplication and division. Moreover, mental and written arithmetic showed comparable correlations with WM in all domains. These findings suggest moderation effects of WM domains, age, and operation types in the WM-arithmetic relationship and highlight the significant role of verbal WM in arithmetic ability in primary school children.

The role of working memory updating, inhibition, fluid intelligence, and reading comprehension in explaining differences between consistent and inconsistent arithmetic word-problem-solving performance

Children's performance in arithmetic word problems (AWPs) predicts their academic success and their future employment and earnings in adulthood. Understanding the nature and difficulties of interpreting and solving AWPs is important for theoretical, educational, and social reasons. We investigated the relation between primary school children's performance in different types of AWPs and their basic cognitive abilities (reading comprehension, fluid intelligence, inhibition, and updating processes). The study involved 182 fourth- and fifth-graders. Participants were administered an AWP-solving task and other tasks assessing fluid intelligence, reading comprehension, inhibition, and updating. The AWP-solving task included comparison problems incorporating either the adverb more than or the adverb less than, which demand consistent or inconsistent operations of addition or subtraction. The results showed that consistent problems were easier than inconsistent problems. Efficiency in solving inconsistent problems is related to inhibition and updating. Moreover, our results seem to indicate that the consistency effect is related to updating processes' efficiency. Path analyses showed that reading comprehension was the most important predictor of AWP-solving accuracy. Moreover, both executive functions-updating and inhibition-had a distinct and significant effect on AWP accuracy. Fluid intelligence had both direct and indirect effects, mediated by reading comprehension, on the overall measure of AWP performance. These domain-general factors are important factors in explaining children's performance in solving consistent and inconsistent AWPs.

The contributions of working memory domains and processes to early mathematical knowledge between preschool and first grade

Working Memory (WM) plays a crucial role in supporting children's mathematical learning. However, there is no consensus on the relative contributions of different WM domains (i.e., verbal, visuo-spatial, and numerical-verbal) and processes (i.e., low-control and high-control) to mathematical performance, specifically before and after the onset of formal education. This cross-sectional study examined the relations between WM domains and processes and early mathematical knowledge, comparing a group of children in the second year of preschool (N = 66) to a group of first graders (N = 110). Results of multigroup path analysis showed that whereas visuo-spatial low-control WM significantly predicted early mathematical knowledge only among preschoolers, verbal low-control WM was a significant predictor only among first graders. Instead, the contribution of visuo-spatial high-control WM emerged as significant for both age groups, as well as that of numerical-verbal WM, although the latter to a greater extent among preschoolers. These findings provide new insights into the WM domains and processes most involved in early mathematical knowledge at different developmental stages, with potential implications for the implementation of age-appropriate training interventions targeting specific WM skills before and after the onset of formal education.

Cognitive Dimensions of Learning in Children With Problems in Attention, Learning, and Memory

A data-driven, transdiagnostic approach was used to identify the cognitive dimensions linked with learning in a mixed group of 805 children aged 5 to 18 years recognised as having problems in attention, learning and memory by a health or education practitioner. Assessments included phonological processing, information processing speed, short-term and working memory, and executive functions, and attainments in word reading, spelling, and maths. Data reduction methods identified three dimensions of phonological processing, processing speed and executive function for the sample as a whole. This model was comparable for children with and without ADHD. The severity of learning difficulties in literacy was linked with phonological processing skills, and in maths with executive control. Associations between cognition and learning were similar across younger and older children and individuals with and without ADHD, although stronger links between learning-related problems and both executive skills and processing speed were observed in children with ADHD. The results establish clear domain-specific cognitive pathways to learning that distinguish individuals in the heterogeneous population of children struggling to learn.

Whether verbal and visuospatial working memory play different roles in pupil's mathematical abilities

BACKGROUND

Previous research showed a significant association between mathematics and working memory (WM). However, evidence regarding the different effects of verbal and visuospatial WM on mathematical abilities was very limited.

AIMS

The current research aims to explore the relationship between verbal and visuospatial WM with mathematical abilities, and how this relationship is moderated by age and math domains. We also wonder whether the results would change when we use several tests for each component and use a latent variable approach for more reliable measurement.

SAMPLE

131 first graders and 144 fifth graders from a primary school in Hangzhou, Zhejiang province, China, participated our research.

METHODS

All participants completed three verbal and three visuospatial WM tasks, mathematics tests, and fluid intelligence test. Hierarchical multiple regression analysis was used to examine the pattern of relations among these constructs.

RESULTS

The results of hierarchical multiple regression analysis showed that verbal WM significantly predicted mathematics achievement for fifth graders, while failed for first graders. However, visuospatial WM played a substantive role in both graders' mathematical performance. The different role of the two WM components also depend on various fields of mathematics.

CONCLUSION

Our results indicated the distinct influence of verbal and visuospatial WM on primary school students' mathematical abilities and highlighted the developmental and domain-specific effects of WM on mathematics.

Mapping components of verbal and visuospatial working memory to mathematical topics in seven- to fifteen-year-olds

BACKGROUND

Developmental research provides considerable evidence of a strong relationship between verbal and visuospatial working memory (WM) and mathematics ability across age groups. However, little is known about how components of WM (i.e., short-term storage, processing speed, the central executive) might relate to mathematics sub-categories and how these change as children develop.

AIMS

This study aimed to identify developmental changes in relationships between components of verbal and visuospatial WM and specific mathematics abilities.

SAMPLE

Children (n = 117) were recruited from four UK schools across three age groups (7-8 years; 9-10 years; and 14-15 years).

METHODS

Children's verbal and visuospatial short-term storage, processing speed, and central executive abilities were assessed. Age-based changes in the contributions from these abilities to performance on mathematics sub-categories were examined.

RESULTS

When WM was examined both as an amalgamation of its component parts, and individually, relationships with mathematics were more evident in younger children compared to the middle and older age groups. However, when unique variance was examined for each WM predictor (controlling for the other components), many of those relationships disappeared. Relationships with processing speed and the central executive were found to be more evident in the older age groups.

CONCLUSIONS

The WM-mathematics relationship changes dependent on age and mathematical sub-component. Overlap in individual WM abilities in younger children, compared to reliance on the central executive and processing speed in older children, suggests a set of fluid resources important in mathematics learning in younger children but separating out as children grow older.

Electroencephalography source localization analysis in epileptic children during a visual working-memory task

We localize the sources of brain activity of children with epilepsy based on electroencephalograph (EEG) recordings acquired during a visual discrimination working memory task. For the numerical solution of the inverse problem, with the aid of age-specific MRI scans processed from a publicly available database, we use and compare three regularization numerical methods, namely the standardized low resolution brain electromagnetic tomography (sLORETA), the weighted minimum norm estimation (wMNE) and the dynamic statistical parametric mapping (dSPM). We show that all three methods provide the same spatio-temporal patterns of differences between the groups of epileptic and control children. In particular, our analysis reveals statistically significant differences between the two groups in regions of the parietal cortex indicating that these may serve as "biomarkers" for diagnostic purposes and ultimately localized treatment.

Working memory growth predicts mathematical problem-solving growth among emergent bilingual children

An area of mathematics found to be difficult for emergent bilingual children whose first language (L1) is Spanish in the United States is solving mathematical word problems. The purpose of this study was to determine the relationship between growth in the executive component of working memory (WM) and growth in mathematical word-problem solving in children whose L1 is Spanish. Elementary school children (Grades 1, 2, and 3) were administered a battery of mathematical, vocabulary, reading, and cognitive measures (short-term memory [STM], inhibition, and WM) in both Spanish (L1) and English (second language [L2]) in Year 1 and again 1 year later. Multilevel growth modeling showed that growth in WM significantly predicted growth in L1 and L2 mathematical word-problem solving. Furthermore, the contributions of WM to mathematical word-problem-solving growth in both L1 and L2 were independent of language skills in vocabulary, reading, estimation, naming speed, inhibition, STM, and calculation. Overall, the results suggest that the mental activities that underlie WM play a significant role in predictions of L1 and L2 mathematical word-problem-solving accuracy.

Do the Processes Engaged During Mathematical Word-Problem Solving Differ Along the Distribution of Word-Problem Competence?

Conventional research methods for understanding sources of individual differences in word-problem solving (WPS) only permit estimation of average relations between component processes and outcomes. The purpose of the present study was instead to examine whether and if so how the component processes engaged in WPS differ along the spectrum of WPS performance. Second graders (N = 1,130) from 126 classrooms in 17 schools were assessed on component processes (reasoning, in-class attentive behavior, working memory, language comprehension, calculation fluency, word reading) and WPS. Multilevel, unconditional quantile multiple regression indicated that 3 component processes, calculation fluency, language comprehension, and working memory, are engaged in WPS differentially depending on students' overall word-problem skill. The role of calculation fluency and language comprehension was stronger with more competent word-problem solving ability. By contrast, the role of working memory was stronger with intermediate-level than for strong problem solving. Results deepen insight into the role of these processes in WPS and provide the basis for hypothesizing how instructional strategies may be differentiated depending on students' overall level of WPS competence.

Executive functions predict literacy and mathematics achievements: The unique contribution of cognitive flexibility in grades 2, 4, and 6

Research has shown that cognitive flexibility plays a critical role in students' learning and academic achievement. However, the unique contribution of cognitive flexibility to academic achievement across schooling is not fully understood. Thus, this study tested whether cognitive flexibility explained a significant amount of variance in academic achievement (i.e., literacy and mathematics outcomes) across Grades 2, 4, and 6, above and beyond fluid intelligence, inhibitory control, working memory, attention, and planning. The sample included 243 second graders, 284 fourth graders, and 203 sixth graders. For Grades 4 and 6, we found that better performance on the flexibility score was associated with better academic outcomes after controlling for fluid intelligence, attention, inhibitory control, working memory, and planning. This effect was not observed for Grade 2. Our findings showed that cognitive flexibility is a key component for school achievement, particularly for older students.

The Effect of Traumatic Brain Injury (TBI) on Cognitive Performance in a Sample of Active Duty U.S. Military Service Members

Introduction

Traumatic brain injury (TBI) is considered a signature injury from the fighting in Iraq and Afghanistan. Since the year 2000, over 370,000 U.S. active duty service members have been diagnosed with TBI. Although prior research has shown that even mild forms of TBI are associated with impaired cognitive performance, it is not clear which facets of cognition (computation, memory, reasoning, etc.) are impacted by injury.

Method

In the present study, we compared active duty military volunteers (n = 88) with and without TBI on six measures of cognition using the Automated Neuropsychological Assessment Metric software.

Results

Healthy volunteers exhibited significantly faster response times on the matching-to-sample, mathematical processing, and second round of simple reaction time tasks and had higher throughput scores on the mathematical processing and the second round of the simple reaction time tasks (P < 0.05).

Conclusion

In this population, cognitive impairments associated with TBI influenced performance requiring working memory and basic neural processing (speed/efficiency).

A Comparison of the Storage-Only Deficit and Joint Mechanism Deficit Hypotheses of the Verbal Working Memory Storage Capacity Limitation of Children With Developmental Language Disorder

Purpose The storage-only deficit and joint mechanism deficit hypotheses are 2 possible explanations of the verbal working memory (vWM) storage capacity limitation of school-age children with developmental language disorder (DLD). We assessed the merits of each hypothesis in a large group of children with DLD and a group of same-age typically developing (TD) children. Method Participants were 117 children with DLD and 117 propensity-matched TD children 7-11 years of age. Children completed tasks indexing vWM capacity, verbal short-term storage, sustained attention, attention switching, and lexical long-term memory (LTM). Results For the DLD group, all of the mechanisms jointly explained 26.5% of total variance. Storage accounted for the greatest portion (13.7%), followed by controlled attention (primarily sustained attention; 6.5%) and then lexical LTM (5.6%). For the TD group, all 3 mechanisms together explained 43.9% of total variance. Storage accounted for the most variance (19.6%), followed by lexical LTM (16.0%), sustained attention (5.4%), and attention switching (3.0%). There was a significant LTM × Group interaction, in which stronger LTM scores were associated with significantly higher vWM capacity scores for the TD group as compared to the DLD group. Conclusions Results support a joint mechanism deficit account of the vWM capacity limitation of children with DLD. Results provide substantively new insights into the underlying factors of the vWM capacity limitation in DLD. Supplemental Material https://doi.org/10.23641/asha.9932312.

Is planning related to dynamic testing outcomes? Investigating the potential for learning of gifted and average-ability children

This study investigated the potential of dynamic testing of geometric analogical reasoning in differentiating between the potential for learning of gifted and average-ability children (aged 9-10 years old). In doing so, it was analysed whether planning, a higher-order executive function, was related to outcomes of the dynamic test, and to instructional needs during training. Employing a pretest-training-post-test control group design, participants were split into four subgroups: gifted dynamic testing (n = 24), gifted control (n = 26), average-ability dynamic testing (n = 48) and average-ability control (n = 50). The results revealed that children who were dynamically tested progressed more in accuracy from pre-test to post-test than their peers who received practice opportunities only. Gifted children outperformed their average-ability peers in accuracy, but showed similar levels of improvement after training or practice only. Moreover, gifted children showed they needed fewer prompts during training than their average-ability peers. Planning was found to be related only to pre-test accuracy, and the number of prompts needed at the first training session, but not to post-test accuracy or the number of prompts needed at the second training session. In the discussion, educational implications of the findings were discussed.

How does mathematics anxiety impair mathematical abilities? Investigating the link between math anxiety, working memory, and number processing

In contemporary society, it is essential to have adequate mathematical skills. Being numerate has been linked to positive life outcomes and well-being in adults. It is also acknowledged that math anxiety (MA) hampers mathematical skills increasingly with age. Still, the mechanisms by which MA affect performance remain debated. Using structural equation modeling (SEM), we contrast the different ways in which MA has been suggested to interfere with math abilities. Our models indicate that MA may affect math performance through three pathways: (1) indirectly through working memory ability, giving support for the 'affective drop' hypothesis of MA's role in mathematical performance, (2) indirectly through symbolic number processing, corroborating the notion of domain-specific mechanisms pertaining to number, and (3) a direct effect of MA on math performance. Importantly, the pathways vary in terms of their relative strength depending on what type of mathematical problems are being solved. These findings shed light on the mechanisms by which MA may interfere with mathematical performance.

The Role of Approximate Number System in Different Mathematics Skills Across Grades

Although approximate number system (ANS) has been found to predict mathematics ability, it remains unclear if both aspects of ANS (symbolic and non-symbolic estimation) contribute equally well to mathematics performance and if their contribution varies as a function of the mathematics outcome and grade level. Thus, in this study, we examined the effects of both aspects of ANS on different mathematics skills across three grade levels. Three hundred eleven children (100 children from kindergarten, 107 children from Grade 2, and 104 children from Grade 4) from two kindergartens and three elementary schools in Shanghai, China, were assessed on measures of ANS (dot estimation and number line estimation), general cognitive ability (nonverbal intelligence, inhibition, and working memory), and mathematics abilities (numerical operations and mathematical problem solving in all grades, early mathematical skills in kindergarten, and calculation fluency in Grades 2 and 4). Results of hierarchical regression analyses showed that, in kindergarten, non-symbolic estimation predicted all mathematics skills even after controlling for age, gender, and general cognitive ability. In Grades 2 and 4, symbolic estimation accounted for unique variance in mathematical problem solving, but not in calculation fluency. Symbolic estimation also predicted numerical operations in Grade 4. Taken together, these findings suggest that in the early phases of mathematics development different aspects of ANS contribute to different mathematics skills.

Different Subcomponents of Executive Functioning Predict Different Growth Parameters in Mathematics: Evidence From a 4-Year Longitudinal Study With Chinese Children

Executive functioning (EF), an umbrella term used to represent cognitive skills engaged in goal-directed behaviors, has been found to be a unique predictor of mathematics performance. However, very few studies have examined how the three core EF subcomponents (inhibition, shifting, and working memory) predict the growth parameters (intercept and slope) in mathematics skills and even fewer studies have been conducted in a non-Western country. Thus, the purpose of this study was to examine how inhibition, shifting, and working memory predict the growth parameters in arithmetic accuracy and fluency in a group of Chinese children (n = 179) followed from Grade 2 (mean age = 97.89 months) to Grade 5 (mean age = 133.43 months). In Grade 2, children were assessed on measures of nonverbal IQ, number sense, speed of processing, inhibition, shifting, and working memory. In addition, in Grades 2–5, they were assessed on arithmetic accuracy and fluency. Results of structural equation modeling showed that nonverbal IQ, speed of processing, and number sense predicted the intercept in arithmetic accuracy, while working memory was the only EF subcomponent to predict the slope (rate of growth) in arithmetic accuracy. In turn, number sense, speed of processing, inhibition, and shifting were significant predictors of the intercept in arithmetic fluency. None of the EF subcomponents predicted the slope in arithmetic fluency. Our findings reinforce those of previous studies in North America and Europe showing that EF contributes to mathematics performance over and above other key predictors of mathematics, and suggest that different EF subcomponents may predict different growth parameters in mathematics.

Bivariate Developmental Relations between Calculations and Word Problems: A Latent Change Approach

The relation between 2 forms of mathematical cognition, calculations and word problems, was examined. Across grades 2-3, performance of 328 children (mean starting age 7.63 [SD=0.43]) was assessed 3 times. Comparison of a priori latent change score models indicated a dual change model, with consistently positive but slowing growth, described development in each domain better than a constant or proportional change model. The bivariate model including change models for both calculations and word problems indicated prior calculation performance and change were not predictors of subsequent word-problem change, and prior word-problem performance and change were not predictors of subsequent calculation change. Results were comparable for boys versus girls. The bivariate model, along with correlations among intercepts and slopes, suggest calculation and word-problem development are related, but through an external set of overlapping factors. Exploratory supplemental analyses corroborate findings and provide direction for future study.

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth “strategy selection”) in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

Can you spell dyslexia without SLI? Comparing the cognitive profiles of dyslexia and specific language impairment and their roles in learning

The aim of the present study is to explore whether those with Specific Language Impairment (SLI) and dyslexia display distinct or overlapping cognitive profiles with respect to learning outcomes. In particular, we were interested in two key cognitive skills associated with academic performance - working memory and IQ. We recruited three groups of children - those with SLI, those with dyslexia, and a control group. All children were given standardized tests of working memory, IQ (vocabulary and matrix), spelling, and math. The pattern of results suggests that both children with dyslexia and SLI are characterized with poorer verbal working memory and IQ compared to controls, but preserved nonverbal cognitive skills. It appears that that these two disorder groups cannot be distinguished by the severity of their cognitive deficits. However, there was a differential pattern with respect to learning outcomes, where the children with dyslexia rely more on visual skills in spelling, while those with SLI use their relative strengths in vocabulary. These findings can have important implications for how intervention is tailored in the classroom, as disorder-specific support could yield important gains in learning.

Mathematical learning disabilities and attention deficit and/or hyperactivity disorder: A study of the cognitive processes involved in arithmetic problem solving

BACKGROUND

The purpose of this study was to examine the contribution of cognitive functioning to arithmetic problem solving and to explore the cognitive profiles of children with attention deficit and/or hyperactivity disorder (ADHD) and with mathematical learning disabilities (MLD).

METHODS

The sample was made up of a total of 90 students of 4th, 5th, and 6th grade organized in three: ADHD (n=30), MLD (n=30) and typically achieving control (TA; n=30) group. Assessment was conducted in two sessions in which the PASS processes and arithmetic problem solving were evaluated.

RESULTS

The ADHD group's performance in planning and attention was worse than that of the control group. Children with MLD obtained poorer results than the control group in planning and simultaneous and successive processing. Executive processes predicted arithmetic problem solving in the ADHD group whereas simultaneous processing was the unique predictor in the MLD sample.

CONCLUSIONS

Children with ADHD and with MLD showed characteristic cognitive profiles. Groups' problem-solving performance can be predicted from their cognitive functioning.

Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school

The relative importance of visual-spatial and verbal working memory for mathematics performance and learning seems to vary with age, the novelty of the material, and the specific math domain that is investigated. In this study, the relations between verbal and visual-spatial working memory and performance in four math domains (i.e., addition, subtraction, multiplication, and division) at different ages during primary school are investigated. Children (N = 4337) from grades 2 through 6 participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed at the start, middle, and end of the school year using a speeded arithmetic test. Multilevel Multigroup Latent Growth Modeling was used to model individual differences in level and growth in math performance, and examine the predictive value of working memory per grade, while controlling for effects of classroom membership. The results showed that as grade level progressed, the predictive value of visual-spatial working memory for individual differences in level of mathematics performance waned, while the predictive value of verbal working memory increased. Working memory did not predict individual differences between children in their rate of performance growth throughout the school year. These findings are discussed in relation to three, not mutually exclusive, explanations for such age-related findings.

The Monkey game: A computerized verbal working memory task for self-reliant administration in primary school children

In two studies, the psychometric properties of an online self-reliant verbal working memory task (the Monkey game) for primary school children (6-12 years of age) were examined. In Study 1, children (n = 5,203) from 31 primary schools participated. The participants completed computerized verbal and visual-spatial working memory tasks (i.e., the Monkey game and the Lion game) and a paper-and-pencil version of Raven's Standard Progressive Matrices. Reading comprehension and math achievement test scores were obtained from the schools. First, the internal consistency of the Monkey game was examined. Second, multilevel modeling was used to examine the effects of classroom membership. Multilevel multivariate regression analysis was used to examine the Monkey game's concurrent relationship with the Lion game and its predictive relationships with reading comprehension and math achievement. Also, age-related differences in performance were examined. In Study 2, the concurrent relationships between the Monkey game and two tester-led computerized working memory tasks were further examined (n = 140). Also, the 1- and 2-year stability of the Monkey game was investigated. The Monkey game showed excellent internal consistency, good concurrent relationships with the other working memory measures, and significant age differences in performance. Performance on the Monkey game was also predictive of subsequent reading comprehension and mathematics performance, even after controlling for individual differences in intelligence. Performance on the Monkey game was influenced by classroom membership. The Monkey game is a reliable and suitable instrument for the online computerized and self-reliant assessment of verbal working memory in primary school children.

Validity and reliability of an online visual-spatial working memory task for self-reliant administration in school-aged children

Working memory is an important predictor of academic performance, and of math performance in particular. Most working memory tasks depend on one-to-one administration by a testing assistant, which makes the use of such tasks in large-scale studies time-consuming and costly. Therefore, an online, self-reliant visual-spatial working memory task (the Lion game) was developed for primary school children (6-12 years of age). In two studies, the validity and reliability of the Lion game were investigated. The results from Study 1 (n = 442) indicated satisfactory six-week test-retest reliability, excellent internal consistency, and good concurrent and predictive validity. The results from Study 2 (n = 5,059) confirmed the results on the internal consistency and predictive validity of the Lion game. In addition, multilevel analysis revealed that classroom membership influenced Lion game scores. We concluded that the Lion game is a valid and reliable instrument for the online computerized and self-reliant measurement of visual-spatial working memory (i.e., updating).

Children with well controlled epilepsy possess different spatio-temporal patterns of causal network connectivity during a visual working memory task

Using spectral Granger causality (GC) we identified distinct spatio-temporal causal connectivity (CC) patterns in groups of control and epileptic children during the execution of a one-back matching visual discrimination working memory task. Differences between control and epileptic groups were determined for both GO and NOGO conditions. The analysis was performed on a set of 19-channel EEG cortical activity signals. We show that for the GO task, the highest brain activity in terms of the density of the CC networks is observed in α band for the control group while for the epileptic group the CC network seems disrupted as reflected by the small number of connections. For the NOGO task, the denser CC network was observed in θ band for the control group while widespread differences between the control and the epileptic group were located bilaterally at the left temporal-midline and parietal areas. In order to test the discriminative power of our analysis, we performed a pattern analysis approach based on fuzzy classification techniques. The performance of the classification scheme was evaluated using permutation tests. The analysis demonstrated that, on average, 87.6 % of the subjects were correctly classified in control and epileptic. Thus, our findings may provide a helpful insight on the mechanisms pertaining to the cognitive response of children with well controlled epilepsy and could potentially serve as "functional" biomarkers for early diagnosis.

Executive functioning predicts reading, mathematics, and theory of mind during the elementary years

The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years.

A Meta-Analysis of Working Memory Deficits in Children With Learning Difficulties: Is There a Difference Between Verbal Domain and Numerical Domain?

Children with learning difficulties suffer from working memory (WM) deficits. Yet the specificity of deficits associated with different types of learning difficulties remains unclear. Further research can contribute to our understanding of the nature of WM and the relationship between it and learning difficulties. The current meta-analysis synthesized research on verbal WM and numerical WM among children with reading difficulties (RD), children with mathematics difficulties (MD), and children with reading and mathematics difficulties (RDMD). A total of 29 studies subsuming 110 comparisons were included. Results showed that compared to typically developing children, all learning difficulty groups demonstrated deficits in verbal WM and numerical WM, with RDMD children showing the most severe WM deficits. MD children and RD children showed comparable verbal WM deficits, but MD children showed more severe numerical WM deficits than RD children. Neither severity of learning difficulties nor type of academic screening emerged as a moderator of WM deficit profiles. Although the findings indicate the domain-general nature of WM deficits in RD, MD, and RDMD children, the numerical WM deficits of children with MD and RDMD may reflect the domain-specific nature of WM deficits.

Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation

Number facts are commonly assumed to be verbally stored in an associative multiplication fact retrieval network. Prominent evidence for this assumption comes from so-called operand-related errors (e.g., 4 × 6 = 28). However, little is known about the development of this network in children and its relation to verbal and non-verbal memories. In a longitudinal design, we explored elementary school children from grades 3 and 4 in a multiplication verification task with the operand-related and -unrelated distractors. We examined the contribution of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory (WM). Children in grade 4 showed smaller reaction times in all conditions. However, there was no significant difference in errors between grades. Contribution of verbal and visuo-spatial WM also changed with grade. Multiplication correlated with verbal WM and performance in grade 3 but with visuo-spatial WM and performance in grade 4. We suggest that the relation to verbal WM in grade 3 indicates primary linguistic learning of and access to multiplication in grade 3 which is probably based on verbal repetition of the multiplication table heavily practiced in grades 2 and 3. However, the relation to visuo-spatial semantic WM in grade 4 suggests that there is a shift from verbal to visual and semantic learning in grade 4. This shifting may be induced because later in elementary school, multiplication problems are rather carried out via more written, i.e., visual tasks, which also involve executive functions. More generally, the current data indicates that mathematical development is not generally characterized by a steady progress in performance; rather verbal and non-verbal memory contributions of performance shift over time, probably due to different learning contents.

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners

The focus of the present study was enhancing word-problem and calculation achievement in ways that support pre-algebraic thinking among 2^nd-grade students at risk for mathematics difficulty. Intervention relied on a multi-tier support system (i.e., responsiveness-to-intervention or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation RTI, word-problem RTI, and business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word-problem outcomes; word-problem RTI enhanced proximal word-problem outcomes as well as performance on some calculation outcomes; and word-problem RTI provided a stronger route than calculation RTI to pre-algebraic knowledge.

Early numerical abilities and cognitive skills in kindergarten children

In this study, a unitary path analysis model was developed to investigate the relationship between cognitive variables (derived from published studies) and early numerical abilities in children attending the last year of kindergarten. We tested 100 children starting their last year of kindergarten on the following cognitive abilities: intelligence, phonological abilities, counting, verbal and visuospatial short-term memory and working memory, processing speed, and early numerical abilities. The same children were tested again on early numerical abilities at the end of the same year. The children's early numerical abilities at the beginning of the final year of kindergarten were found to be directly related to their verbal intelligence, phonological abilities, processing speed, and working memory and to be indirectly related to their nonverbal intelligence. Early numerical abilities at the end of the same year are directly related not only to early numerical abilities assessed at the beginning of the year but also to working memory and phonological abilities as well as have an indirect relationship with verbal and nonverbal intelligence. Overall, our results showed that both general and specific abilities are related to early mathematic learning in kindergarten-age children.

Cognitive and mathematical profiles for different forms of learning difficulties

The purpose of this study was to compare subgroups of students with various forms of learning difficulties (< 25th percentile) on cognitive and mathematics characteristics. Students with mathematics difficulty (MD, n = 105), reading difficulty (RD, n = 65), both (MDRD, n = 87), or neither (NoLD, n = 403) were evaluated on an array of cognitive measures (e.g., working memory and language) and on mathematics measures of foundational numerical competencies, computation, and problem solving. Results revealed expected level differences among groups in both domains: NoLD outperformed RD, and MD outperformed MDRD. Profile differences were noted among pairs of subgroups on cognitive measures. On mathematics measures, profile differences were noted between RD and other subgroups, but not between MD and MDRD subgroups. The most discriminating cognitive measures were processing speed and language; the most discriminating mathematics measures depended on the subgroups being compared. Results were further evaluated according to more severe (< 10th percentile) criteria for MD and RD, which generally affected level differences more than the profile patterns. Results have implications for understanding comorbid MD and RD and for conceptualizing core deficits in MD.

Is Word-Problem Solving a Form of Text Comprehension?

This study's hypotheses were that (a) word-problem (WP) solving is a form of text comprehension that involves language comprehension processes, working memory, and reasoning, but (b) WP solving differs from other forms of text comprehension by requiring WP-specific language comprehension as well as general language comprehension. At the start of the 2nd grade, children (n = 206; on average, 7 years, 6 months) were assessed on general language comprehension, working memory, nonlinguistic reasoning, processing speed (a control variable), and foundational skill (arithmetic for WPs; word reading for text comprehension). In spring, they were assessed on WP-specific language comprehension, WPs, and text comprehension. Path analytic mediation analysis indicated that effects of general language comprehension on text comprehension were entirely direct, whereas effects of general language comprehension on WPs were partially mediated by WP-specific language. By contrast, effects of working memory and reasoning operated in parallel ways for both outcomes.

Working memory training in college students with ADHD or LD

OBJECTIVE

The objective of this study was to determine the feasibility and effectiveness of working memory (WM) training in college students with ADHD or learning disabilities (LD).

METHOD

A total of 62 students (21 males, 41 females) were randomized to a 5-week intensive WM training program or a wait-list control group. Participants were evaluated before treatment, 3 weeks after completion, and at 2-month follow-up. The criterion measures were standardized tests of auditory-verbal and visual-spatial WM. Near transfer measures included other cognitive tasks; far transfer measures included academic tasks and behavioral rating scales.

RESULTS

Intent-to-treat analysis revealed that participants receiving WM training showed significantly greater improvements on the criterion WM measures and self-reported fewer ADHD symptoms and cognitive failures. The follow-up assessment indicated that gains in WM were maintained, as were improvements in cognitive failures.

CONCLUSION

Computerized WM training is a feasible and possibly viable approach for enhancing WM in college students with ADHD or LD.

Development and Evaluation of an Online, Multicomponent Working Memory Battery

Research has demonstrated strong connections among working memory (WM), higher-level cognition, and academic achievement. Despite the importance of WM, currently available WM tests have practical limitations and lack comprehensive coverage of multiple WM components. The Working Memory Battery (WOMBAT) includes nine subtests measuring multiple content domains and processing demands, in accordance with contemporary WM theoretical frameworks. The current study evaluated the WOMBAT factor structure and identified misfitting items using confirmatory factor analysis and Rasch modeling with scores from 125 adolescents and 177 adults ( N = 302). Overall, results indicated the WOMBAT measures separate Verbal, Static Visual-Spatial, and Dynamic Visual-Spatial dimensions, and that more than 98% of items contribute to measurement of those dimensions. This provides support for the theoretical organization of WM into three distinct content domains in the WOMBAT. Misfitting items were identified using infit and outfit indices for further review to improve reliability and stability. Results also demonstrated adequate person separation and Rasch person reliability and item reliability. Test–retest reliability and internal consistency coefficients suggest adequate reliability for early-stage research, but further refinement is needed before the WOMBAT can be used for individual decision making. Implications for future test development and research on the WM construct are provided.

Early number knowledge and cognitive ability affect early arithmetic ability

Previous literature suggests that early number knowledge is important for the development of arithmetic calculation ability. The domain-general ability of verbal working memory also has an impact on arithmetic ability. This longitudinal study tested the impact of early number knowledge and verbal working memory on the arithmetic calculation ability of children in preschool (N=315) and then later in Grade 1 using structural equation modeling. Three models were used to test hypotheses drawn from previous literature. The current study demonstrates that both early number knowledge and the domain-general ability of verbal working memory affect preschool and Grade 1 arithmetic ability. Early number knowledge had a direct impact on the growth of arithmetic ability, whereas verbal working memory had only an indirect effect via number knowledge and preschool arithmetic ability. These results fit well with von Aster and Shalev's developmental model of numerical cognition (Developmental Medicine & Child Neurology, 2007, Vol. 49, pp. 868-873) and highlight the importance of considering arithmetic ability as independent from early number knowledge. Results also emphasize the importance of training early number knowledge before school entry to promote the development of arithmetic ability.

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement

Domain-general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense.

Working memory, worry, and algebraic ability

Math anxiety (MA)-working memory (WM) relationships have typically been examined in the context of arithmetic problem solving, and little research has examined the relationship in other math domains (e.g., algebra). Moreover, researchers have tended to examine MA/worry separate from math problem solving activities and have used general WM tasks rather than domain-relevant WM measures. Furthermore, it seems to have been assumed that MA affects all areas of math. It is possible, however, that MA is restricted to particular math domains. To examine these issues, the current research assessed claims about the impact on algebraic problem solving of differences in WM and algebraic worry. A sample of 80 14-year-old female students completed algebraic worry, algebraic WM, algebraic problem solving, nonverbal IQ, and general math ability tasks. Latent profile analysis of worry and WM measures identified four performance profiles (subgroups) that differed in worry level and WM capacity. Consistent with expectations, subgroup membership was associated with algebraic problem solving performance: high WM/low worry>moderate WM/low worry=moderate WM/high worry>low WM/high worry. Findings are discussed in terms of the conceptual relationship between emotion and cognition in mathematics and implications for the MA-WM-performance relationship.