Working memory and mathematical cognitive development: limitations of limited-capacity resource models

Influence of Gestational Age and Working Memory on Math Skills in Children Aged 8 to 9 Years

OBJECTIVE

Prematurity affects children's functioning in domains such as cognitive skills and math skills. However, there is limited research examining math skills as gestational age (GA) increases weekly. We aimed at determining, in a population-based cohort of children aged 8 to 9 years, the association between the GA spectrum and math skills and working memory's (WM's) role in this relationship.

METHODS

Children aged 8 to 9 years in 2014 (n = 1761), from 44 primary schools in a metropolitan city, were recruited through the Memory Maestros study in 2012. GA was measured using the parent report. Math skills were measured using the Wide Range Achievement Test 4 math computation subtest (mean, 100; SD, 15), and WM was measured using 2 subtests of the Automated Working Memory Assessment. The method of analysis was multivariate linear regression, with adjustment for both WM measures and social risk indicators as potential confounders.

RESULTS

A total of 1168 children (66%) had analyzable data. Compared with children of ≤34-week gestation, there was a mean difference increase of 0.48 in math standard scores per weekly increase in GA (95% confidence interval, 0.11-0.85%; p = 0.01). This equates to a difference of 6.29 (0.42 SD) standard math scores between the ≤34- and ≥42-week group. The relationship was independent of WM.

CONCLUSION

Weekly increases in GA beyond 34 weeks are associated with higher mathematics achievement scores for children aged 8 to 9 years, independent of the child's WM. This assists with identification of individuals at risk of poorer math skills.

Math anxiety and developmental dyscalculia: A study on working memory processes

INTRODUCTION

Although many children encounter difficulties in arithmetic, the underlying cognitive and emotive factors are still not fully understood. This study examined verbal and visuospatial short-term memory (STM) and working memory (WM) performance in children with developmental dyscalculia (DD) and high mathematics anxiety (MA) compared with typically developing (TD) children.

METHOD

Groups were matched on reading comprehension performance and IQ as well as on general anxiety. We aimed to test whether children with DD and MA were differently impaired in verbal and visuospatial STM and WM. Children were individually tested with four computerized tasks: two STM tasks (forward verbal and visuospatial recall) and two WM tasks (backward verbal and visuospatial recall).

RESULTS

Relative to children with TD, those with DD did not show impairments on the forward or backward verbal tasks, but showed specific impairments in the visuospatial WM task. In contrast, children with MA were particularly impaired in the verbal WM task.

CONCLUSIONS

Knowing the underlying cognitive processes that differentiate why children with DD and MA fail in math could have both educational and clinical implications.

The differential role of verbal and spatial working memory in the neural basis of arithmetic

We examine the relations of verbal and spatial working memory (WM) ability to the neural bases of arithmetic in school-age children. We independently localize brain regions subserving verbal versus spatial representations. For multiplication, higher verbal WM ability is associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. For multiplication and subtraction, higher spatial WM ability is associated with greater recruitment of right parietal cortex, identified by the spatial localizer. Depending on their WM ability, children engage different neural systems that manipulate different representations to solve arithmetic problems.

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children's mathematical abilities

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability.

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills such as number system knowledge and estimation. This study of 3rd graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in 3 significant arithmetic skills: basic calculation fluency, written multidigit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill, and their contributions are independent of both each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: Most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multidigit skills. These findings indicate that many factors matter but multidigit skills matter most in 3rd grade mathematical achievement.

Early aging in adult survivors of childhood medulloblastoma: long-term neurocognitive, functional, and physical outcomes

Treatment for medulloblastoma during childhood impairs neurocognitive function in survivors. While those diagnosed at younger ages are most vulnerable, little is known about the long-term neurocognitive, functional, and physical outcomes in survivors as they approach middle age. In this retrospective cohort study, we assessed 20 adults who were treated with surgery and radiotherapy for medulloblastoma during childhood (median age at assessment, 21.9 years [range, 18-47 years]; median time since diagnosis, 15.5 years [range, 6.5-42.2 years]). Nine patients also underwent chemotherapy. Cross-sectional analyses of current neurocognitive, functional, and physical status were conducted. Data from prior neuropsychological assessments were available for 18 subjects; longitudinal analyses were used to model individual change over time for those subjects. The group was well below average across multiple neurocognitive domains, and 90% had required accommodations at school for learning disorders. Longer time since diagnosis, but not age at diagnosis, was associated with continued decline in working memory, a common sign of aging. Younger age at diagnosis was associated with lower intelligence quotient and academic achievement scores, even many years after treatment had been completed. The most common health complications in survivors were hearing impairment, second cancers, diabetes, hypertension, and endocrine deficiencies. Adult survivors of childhood medulloblastoma exhibit signs of early aging regardless of how young they were at diagnosis. As survival rates for brain tumors continue to improve, these neurocognitive and physical sequelae may become evident in survivors diagnosed at different ages across the lifespan. It will become increasingly important to identify factors that contribute to risk and resilience in this growing population.

The interrelationships of mathematical precursors in kindergarten

This study evaluated the interrelations among cognitive precursors across quantitative, linguistic, and spatial attention domains that have been implicated for math achievement in young children. The dimensionality of the quantity precursors was evaluated in 286 kindergarteners via latent variable techniques, and the contribution of precursors from each domain was established for small sums addition. Results showed a five-factor structure for the quantity precursors, with the major distinction being between nonsymbolic and symbolic tasks. The overall model demonstrated good fit and strong predictive power (R(2)=55%) for addition number combinations. Linguistic and spatial attention domains showed indirect relationships with outcomes, with their effects mediated by symbolic quantity measures. These results have implications for the measurement of mathematical precursors and yield promise for predicting future math performance.

Mathematical Disabilities: Reflections on Cognitive, Neuropsychological, and Genetic Components

The collection of articles in this special issue and related studies over the past decade provides a fine example of the substantial progress that has been made in our understanding and remediation of mathematical learning disabilities and difficulties since 1993 (Geary, 1993). The originally proposed procedural and retrieval deficits have been supported and a number sense deficit has been identified. There is evidence for visuospatial contributions to some aspects of mathematical learning, but identification of a core visuospatial deficit underlying some forms of mathematics learning disabilities and difficulties has been elusive. The contributions of working memory to the development and expression of these deficits is more nuanced than I originally proposed as are the brain systems supporting mathematical learning. Although much has been learned about children's difficulties in learning mathematics, but there is just as much and likely more than remains to be discovered.

Executive functions underlying multiplicative reasoning: problem type matters

We investigated the extent to which inhibition, updating, shifting, and mental-attentional capacity (M-capacity) contribute to children's ability to solve multiplication word problems. A total of 155 children in Grades 3-6 (8- to 13-year-olds) completed a set of multiplication word problems at two levels of difficulty: one-step and multiple-step problems. They also received a reading comprehension test and a battery of inhibition, updating, shifting, and M-capacity measures. Structural equation modeling showed that updating mediated the relationship between multiplication performance (controlling for reading comprehension score) and latent attentional factors M-capacity and inhibition. Updating played a more important role in predicting performance on multiple-step problems than did age, whereas age and updating were equally important predictors on one-step problems. Shifting was not a significant predictor in either model. Implications of proposing executive function updating as a mediator between mathematical cognition and chronological age and attention resources are discussed.

Mathematical learning disabilities in special populations: phenotypic variation and cross-disorder comparisons

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to mathematical learning difficulties and disabilities presented across the reviews. Specifically we consider how each of the reviews contributes to identifying the MLD phenotype by specifying the range of assets and deficits in mathematics, identifying sources of individual variation, and characterizing the natural progression of MLD over the life course. We show how principled comparisons across disorders address issues about the cognitive and behavioral co-morbidities of MLD, and whether commonalities in brain dysmorphology are associated with common mathematics performance profiles. We project the status of MLD research ten years hence with respect to theoretical gains, advances in methodology, and principled intervention studies.