Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade

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Abstract

This longitudinal study examined the relationship between working memory and individual differences in mathematics. Working memory measures, comprising the phonological loop, the visuospatial sketchpad, and the central executive, were administered at the start of first grade. Mathematics achievement was assessed 4 months later (at the middle of first grade) and 1 year later (at the start of second grade). Working memory was significantly related to mathematics achievement in both grades, showing that working memory clearly predicts later mathematics achievement. The central executive was a unique predictor of both first- and second-grade mathematics achievement. There were age-related differences with regard to the contribution of the slave systems to mathematics performance; the visuospatial sketchpad was a unique predictor of first-grade, but not second-grade, mathematics achievement, whereas the phonological loop emerged as a unique predictor of second-grade, but not first-grade, mathematics achievement.

Introduction

Working memory is an important factor in understanding individual differences in mathematics achievement in children. Research on the role of working memory in mathematics performance draws mainly on studies of children with mathematical disabilities, indicating that deficits in mathematics are linked to poor working memory (Bull et al., 1999, Gathercole and Pickering, 2000a, Geary et al., 2000, McLean and Hitch, 1999, Passolunghi and Siegel, 2004, Siegel and Ryan, 1989, Swanson and Beebe-Frankenberger, 2004, Swanson and Sachse-Lee, 2001, van der Sluis et al., 2005). Although there are many fewer studies in typically developing children, these also indicate that working memory plays an important role in (individual differences in) typical mathematics performance (Adams and Hitch, 1997, Bull and Scerif, 2001, Gathercole and Pickering, 2000b, Hecht et al., 2001, Holmes and Adams, 2006, Swanson and Kim, 2007).

The majority of these correlational studies in typically and atypically developing children are cross-sectional. Such a design does not allow us to determine the nature of the relationship between working memory and mathematics achievement. Therefore, we aimed to investigate whether working memory is a precursor of individual differences in mathematics achievement. We assessed measures of working memory at the beginning of first grade. Consequently, these assessments were not influenced by mathematics learning in primary school and allowed us to examine whether later mathematics achievement can be predicted by working memory. In the remainder of this section, the different components of working memory and their relationship with individual differences in mathematics are described first. After that, the design of the current study is presented.

Section snippets

Components of working memory

Baddeley’s influential three-component model of working memory (Baddeley, 1986, Baddeley, 2003, Baddeley and Logie, 1999) served as our framework to examine the influence of different working memory components on mathematics achievement. At the core of Baddeley’s model is the central executive, which is responsible for the control, regulation, and monitoring of complex cognitive processes. The model also encompasses two subsidiary subsystems of limited capacity that are used for temporary

Components of working memory and individual differences in mathematics

Each component of Baddeley’s working memory model is thought to have a specific role in mathematics performance (see DeStefano & Lefevre, 2004, for a review). Evidence from dual-task studies has consistently shown the involvement of the central executive in arithmetic, indicating that this component is responsible for the monitoring and coordination of different steps during arithmetic problem solving (Fürst and Hitch, 2000, Imbo and Vandierendonck, 2007b, Imbo et al., 2007). Turning to the

The current study

We aimed to examine whether initial measures of working memory predicted subsequent mathematics achievement by conducting a longitudinal correlational study. We also sought to determine the unique contributions of working memory components in explaining variability in mathematics performance in first and second grades. The current study extended previous research in three ways. First, our study was longitudinal with the working memory data collected before mathematics achievement data, allowing

Participants

Participants were 106 first graders (63 boys and 43 girls) from five primary schools in Flanders, Belgium. At the start of first grade, when the working memory measures were assessed, the mean age of the children was 6 years 4 months (SD = 4 months). First-grade mathematics data were available for 77 children (mean age = 6 years 8 months, SD = 8 months). Second-grade mathematics data were available for 83 children (mean age = 7 years 4 months, SD = 3 months). Three children did not complete the test of

Descriptive statistics

The means, standard deviations, ranges, and maximum possible scores for all administered measures and age are displayed in Table 1. This table indicates that the data were well distributed without ceiling or floor effects. Reliability coefficients of all measures are also presented in this table.

Correlational analyses

Pearson correlation coefficients were calculated to examine the associations between the administered tasks (Table 2). The working memory measures that were thought to measure the same working memory

Discussion

This study aimed to examine the predictive relationship between working memory and later mathematics achievement in first and second grades by means of a longitudinal correlational design. Therefore, we assessed each working memory component at the beginning of first grade and collected mathematics achievement data 4 months later (in the middle of first grade) and 1 year later (at the start of second grade). The correlational analyses showed that each working memory component was predictively

Acknowledgments

Bert De Smedt and Bart Boets are postdoctoral fellows of the Research Foundation Flanders (FWO). We are grateful to all of the children and teachers (and their respective schools) who participated in this study. Special thanks are due to Jo-Anne LeFevre and two anonymous reviewers for their helpful comments on earlier versions of this manuscript.

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