Discussion

A growing body of work is suggesting that working memory is related to performance in

mathematics from an early age and right through the school career (e.g., Bull et al., 2008; Holmes

& Adams, 2006; Holmes et al., 2008; Passolunghi & Cornoldi, 2008; Simmons et al., 2012). Each of

83 these studies has been very informative; however there have been some cross-study issues that have resulted in somewhat inconsistent conclusions. Examples of issues that may have influenced the conflicting results might be; the use of a wide variety of both mathematical and working memory tasks that are not necessarily standardised against one another, the use of numerical working memory measures, the use of only one measure per working memory domain, and the varying age ranges assessed. In the present study in order to attempt to combat some of these issues the number of working memory measures used was increased to two per WM component, and refrained from the use of numerically grounded tasks. A further strength of this study was that a cohort of children was followed over a three year period during their early schooling. This allowed the study to elucidate further the specific elements of working memory that were thought would be involved expressly in Calculation performance over a three year period.

Overall the results across the three year period further substantiate the close links evidenced between the Baddeley and Hitch (1974a) model of working memory and performance on a curriculum based mathematics test (Bull et al., 2008; Holmes & Adams, 2006). The cross-sectional results confirmed that working memory is accounting for between 17% and 36% of the unique variance in mathematics raw scores after age related variance has been partialled out. Agreement with the Rasmussen and Bisanz study (2005) is noted insofar as WM is predicting a significant amount of unique variance at this specific age range. This finding also lends support to previous evidence that suggests that there is a relationship between working memory and National Curriculum performance given that the administered mathematics test was heavily influenced by the teaching of the National Curriculum (Gathercole & Pickering, 2000b; Holmes & Adams, 2006;

Jarvis & Gathercole, 2003). Moreover these data extend previous findings by applying the working memory theoretical principles to curriculum based mathematics at a younger age range than measured in the previously cited studies.

5.10.1 Reception

While NV-STM and CE-CWM both significantly correlate with Mathematics 5 raw scores, the in-depth statistical analyses demonstrated that at this age CE-CWM is the only significant

84 independent predictor variable for performance on the mathematics test. The CE-CWM finding in this phase of testing supports some previous studies (Bull et al., 2008; Holmes & Adams, 2006), and corroborates the idea that carrying out mathematical operations is likely to involve executive functions such as inhibition, task switching, strategy adoption and updating (see also Bull et al., 1999). However, while support for (Bull et al., 2008; Bull et al., 1999) is proffered, direct comparisons cannot be immediately drawn as the tests utilised as measures of central executive/executive function in the Bull et al studies were different from those in the present work. In relation to the functional similarity of executive function and central executive tasks Lehto (1996) reports that Wisconsin Card Sorting Task (WCST), the Tower Of Hanoi, and the Global Search Task each appear to tax different aspects of executive function, with only the WCST being dependent on working memory. As such it is thought that more meaningful comparisons may be drawn from studies where the WCST was used as a measure of executive

function/working memory (Bull et al., 1999).

Bull and colleagues also reported that Corsi Block was not related to mathematical ability (at mean age 7.3y), and with this measure a more meaningful comparison can be drawn, as the Block Recall task is a computerised version of Corsi block task. In this present study, the Reception data agree with Bull and colleagues showing that at this age grouping Block Recall (as a measure of NV-STM) is not a significant predictor of mathematics (as a whole) even though Block Recall and Mathematics 5 do correlate strongly.

5.10.2 Year One

At Year One (mean age 72.7 month, SD 3.91) as with the results from the Reception year at school, these data advocate links between the Baddeley and Hitch (1974a) tripartite model of working memory and performance on this curriculum based mathematics test, with the working memory measures accounting for 36% of the unique variance in overall mathematics raw scores. This figure is after taking statistical account of both age and the newly introduced Performance Measures. All six WM measures correlate significantly with Mathematics 6 raw scores, yet the in-depth statistical procedures indicate that at this age the verbal working memory measure and

85 V-STM are both significant independent predictors of performance on the mathematics

assessment after all the other variables have been accounted for. Similarly Gathercole et al (2006) also found tests of central executive and verbal term memory, but not non-verbal short-term memory to be indicative of mathematics performance. Additionally Holmes and Adams (2006) established that verbal short-term memory skills were related to mental arithmetic, but not to other mathematics skills measured in 8-10 year olds.

Once again, at this age range as with Bull et al (1999) no evidence is found to suggest that nonverbal short-term memory is contributing to predicting the Mathematics 6 outcome.

5.10.3 Year Two

The pattern of the Year 2 data follows a similar blueprint to the previous two years with working memory as a whole being a significant predictor of Mathematics 7. Also evident is that a central executive task is emerging as a consistent unique predictor of performance on this curriculum based mathematics assessment. However at this time point the significant independent predictor was Listening Recall (V-WM).

As with Reception and Year One, the nonverbal short-term memory measures showed no

influence over performance on the mathematics task. It was also noted that two nonverbal short-term memory variables failed to intercorrelate at Year 2 (Mazes Memory and Block Recall) but both did correlate with Mathematics 7. There are several feasible explanations for this anomalous data pattern. Two ideas that stand out are that this age grouping may indicate a developmental fractionation time point (Alloway et al., 2006; Hitch, 1990). A second explanation may be that the difference between the Mazes Memory static presentation format and the Block Recall dynamic presentation format may prove to be the key factor in the disparity between the two tasks. Pickering and colleagues (Pickering, 2001; Pickering et al., 2001) have reported evidence of a developmental dissociation in performance on static and dynamic versions of the matrices task suggesting that it may not be the visual and spatial properties of two tests used in their study of visuospatial memory (Corsi blocks and the visual pattern test) but the static and

86 dynamic nature of the tasks that taps different subcomponents of this memory system. It is possible, therefore, that NV-STM may comprise of separable components for dealing with visuospatial information in the form of static patterns and paths of movement. It is tentatively proposed that this may only become evident at around the age of 6 to 7 years old, as previously in this study the NV-STM measures correlated adequately for tasks reputed to be measuring the same construct.

5.10.4 Predicting Later Mathematics with Early Working Memory

Some studies have claimed that intelligence tests are a reliable index to predict later scholastic attainment (Colom & Flores-Mendoza, 2007; Stanovich, Cunningham, & Feeman, 1984). Recent works however, have strongly intimated that working memory represents a dissociable cognitive skill from intelligence, with unique links to learning outcomes, and it is also relatively culture free (Alloway, 2009; Fischer, 2008). It is arguably too soon into the theoretical understanding and debate about this topic to adopt the working memory approach to replace intelligence testing, but it is proving over and over to be a robust finding that working memory can predict later school progress (Gathercole et al., 2003; Gathercole & Pickering, 2000b; Gathercole, Pickering, Knight, et al., 2004; Holmes & Adams, 2006; Jarvis & Gathercole, 2003; Mayberry & Do, 2003; St Clair-Thompson & Gathercole, 2006). This present study has demonstrated that working memory measured upon school entry can uniquely predict 14% of variance in overall mathematics scores at age 7. This figure is obtained after the variance pertaining to both age and Performance Measures has been statistically removed.

Other studies such as Passolunghi et al (2007) have also identified WM as a predictor of maths over a period of time. In their instance mathematics was measured four months post working memory testing. In a similar type of study Noël, Seron and Trovarelli (2004) provided evidence that phonological loop capacity was indicative of later mathematics ability, with particular reference to addition skills and strategies in first graders, who are roughly age comparable with the present cohort. Clearly these studies link well with our finding that working memory

significantly predicts a portion of later overall curricular mathematics ability. Interestingly there is

87 a minor incongruity between the present study and the Noël et al research in that no strong evidence is found that verbal short-term memory is significantly predictive of later maths ability.

In the Noël study the emphasis was placed upon addition and addition strategies rather than general mathematical skills. Therefore at this stage this study cannot discount the notion that phonological processing may well be significantly involved in more “specific” or separable mathematics abilities which will be discussed in later chapters.