Understanding the contributions of working memory components over the primary school years to enable screening for future attainment in mathematics

Abstract

Interest in, and evidence for, the involvement of working memory in mathematics is increasing as the performance of school leavers is under constant scrutiny. Understanding how components of working memory relate to aspects of mathematics is, however, limited. The stability of this relationship when other cognitive predictors are included is not known, nor is whether the relationship is stable over time. This thesis contains a systematic review of the literature and four studies investigating relationships between working memory and mathematics performance.
As a first step, available literature on the relationship between visuospatial working memory and mathematics performance was reviewed in a systematic, thematic analysis of effect sizes. Results showed a significant influence on the effect size of standardised mathematics measures, but not the type of visuospatial working memory or mathematics being assessed. Crucially, the overall effect size was positive, demonstrating a positive association between visuospatial working memory and mathematics performance.
The first study built on these findings to identify the relative contributions of verbal, spatial-simultaneous, and spatial-sequential working memory in written mathematics. Year 3 children (7-8 years of age, n=214) in the UK completed a battery of working memory tasks alongside a standardised mathematics test. Results showed the largest individual contribution was from verbal working memory, followed by spatial-simultaneous factors. This suggests the components of working memory underpinning mathematical performance at this age are verbal-numeric and spatial-simultaneous. The study raised the question of whether this relationship is consistent across the primary school years.
The second study therefore examined the relative contributions of verbal and visuospatial simple and complex working memory to mathematics in primary school children. Children in Years 2 to 5 (6 to 10 years) were assessed (M age = 100.06 months, SD = 14.47, n=111). Results revealed an age-dependent relationship, with greater visuospatial influence in older children. Further analyses demonstrated that backward word span and backward matrices contributed unique portions of variance of mathematics, regardless of the regression model specified.
A further feasibility study (n = 28) investigated whether the relationships identified were resilient to the inclusion of other cognitive measures and whether there were any underlying cognitive deficits common in poor performers in mathematics. The study explored measuring working memory, speed of processing, g (intelligence), and number sense simultaneously. None of the regression models generated were significant, with no suggestions of fundamental differences between children who performed poorly in mathematics and their peers. Further analysis revealed considerable heterogeneity in the cognitive profiles of children showing a cause for concern in mathematics. The study demonstrated the approach is potentially feasible if the chosen measures thoroughly explore the child’s cognitive profile.
A final two-year follow-up to study 1 investigated how subcomponents of working memory measured in Year 3 related to mathematical performance in Year 5 (n = 159 M age = 115.48 months). Results show a shift from spatial-simultaneous to spatial-sequential influence, whilst verbal involvement remained relatively stable.
Possible explanations for the findings in relation to the existing literature are explored along with implications for educators and further research. Consideration is also given to the value of remediation strategies for poor mathematical performance.
The findings of the project as a whole indicate that there is a shift in the influence of the working memory components from spatial-simultaneous to spatial-sequential as children get older. The contributions of verbal working memory remain consistently important at all ages. These results suggest that a screener developed to predict future attainment should include measures of each of these areas in order to account for both shorter and longer term prediction.