Short-Term Memory, Working Memory, and Executive Functioning in Preschoolers: Longitudinal Predictors of Mathematical Achievement at Age 7 Years

TLDR: Correlational and regression analyses revealed that visual short-term and working memory were found to specifically predict math achievement at each time point, while executive function skills predicted learning in general rather than learning in one specific domain.

Abstract: This study examined whether measures of short-term memory, working memory, and executive functioning in preschool children predict later proficiency in academic achievement at 7 years of age (third year of primary school). Children were tested in preschool (M age = 4 years, 6 months) on a battery of cognitive measures, and mathematics and reading outcomes (from standardized, norm-referenced school-based assessments) were taken on entry to primary school, and at the end of the first and third year of primary school. Growth curve analyses examined predictors of math and reading achievement across the duration of the study and revealed that better digit span and executive function skills provided children with an immediate head start in math and reading that they maintained throughout the first three years of primary school. Visual-spatial short-term memory span was found to be a predictor specifically of math ability. Correlational and regression analyses revealed that visual short-term and working memory were found to specifically predict math achievement at each time point, while executive function skills predicted learning in general rather than learning in one specific domain. The implications of the findings are discussed in relation to further understanding the role of cognitive skills in different mathematical tasks, and in relation to the impact of limited cognitive skills in the classroom environment.

Figures

Table 2 Growth Curve Modeling—Results of the Unconditional Models

Table 1 Demographic Information and Descriptive Statistics for Mathematics Outcomes and Predictor Variables

Table 5 Percentage Variance Accounted in Math Controlling for Reading Achievement at Each Time Point (or Reading Controlling for Math Achievement at Each Time Point)

Table 3 Growth Curve Modeling—Results of the Conditional Models

Table 4 Correlations between Predictor Variables and PIPS Mathematics and Reading Scores

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University of Nebraska - Lincoln University of Nebraska - Lincoln
DigitalCommons@University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln
Developmental Cognitive Neuroscience
Laboratory - Faculty and Staff Publications
Developmental Cognitive Neuroscience
Laboratory
10-30-2008
Short-term memory, working memory, and executive functioning Short-term memory, working memory, and executive functioning
in preschoolers: Longitudinal predictors of mathematical in preschoolers: Longitudinal predictors of mathematical
achievement at age 7 years achievement at age 7 years
Rebecca Bull
University of Aberdeen, United Kingdom
, r.bull@abdn.ac.uk
Kimberly A. Espy
University of Nebraska-Lincoln
, kespy2@unl.edu
Sandra A. Wiebe
University of Nebraska Lincoln
, sandra.wiebe@ualberta.ca
Follow this and additional works at: https://digitalcommons.unl.edu/dcnlfacpub
Part of the Neurosciences Commons
Bull, Rebecca; Espy, Kimberly A.; and Wiebe, Sandra A., "Short-term memory, working memory, and
executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7
years" (2008).
Developmental Cognitive Neuroscience Laboratory - Faculty and Staff Publications
. 40.
https://digitalcommons.unl.edu/dcnlfacpub/40
This Article is brought to you for free and open access by the Developmental Cognitive Neuroscience Laboratory at
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Published in Developmental Neuropsychology 33:3 (2008), pp. 205–228; doi 10.1080/87565640
801982312 Copyright © 2008 Taylor & Francis Group, LLC. Used by permission.
Corresponding author — Rebecca Bull, School of Psychology, William Guild Building, Uni-
versity of Aberdeen, Aberdeen, Scotland, UK, AB24 2UB. Email r.bull@abdn.ac.uk
Short-Term Memory, Working Memory,
and Executive Functioning in Preschoolers:
Longitudinal Predictors of Mathematical
Achievement at Age 7 Years
Rebecca Bull
School of Psychology, University of Aberdeen
Aberdeen, United Kingdom
Kimberly Andrews Espy and Sandra A. Wiebe
Ofce of Research & Department of Psychology
University of Nebraska–Lincoln
Abstract
This study examined whether measures of short-term memory, working mem-
ory, and executive functioning in preschool children predict later prociency in
academic achievement at 7 years of age (third year of primary school). Children
were tested in preschool (M age = 4 years, 6 months) on a battery of cognitive
measures, and mathematics and reading outcomes (from standardized, norm-ref-
erenced school-based assessments) were taken on entry to primary school, and at
the end of the rst and third year of primary school. Growth curve analyses ex-
amined predictors of math and reading achievement across the duration of the
study and revealed that better digit span and executive function skills provided
children with an immediate head start in math and reading that they maintained
throughout the rst three years of primary school. Visual-spatial short-term
memory span was found to be a predictor specically of math ability. Correla-
tional and regression analyses revealed that visual short-term and working mem-
ory were found to specically predict math achievement at each time point, while
executive function skills predicted learning in general rather than learning in one
specic domain. The implications of the ndings are discussed in relation to fur-
ther understanding the role of cognitive skills in different mathematical tasks, and
in relation to the impact of limited cognitive skills in the classroom environment.
205

206 Bu l l , Es p y , & Wi E B E i n De v e l o p m e n t a l ne u r o p s y c h o l o g y 33 (2008)
Children’s performance in mathematics and reading achievement in
schools is inuenced by a number of contributing factors. Higher level
achievement will depend to some extent on the basic skills that feed into
more complex reading and mathematical abilities. Tymms (1999) referred
to these as “general developed abilities,” which includes skills (at school
entry) such as letter recognition, spelling, and phonemic awareness as pre-
cursors to reading, and number recognition, magnitude understanding,
and counting as precursors to mathematics (see Geary, Hamson, & Hoard
2000; Geary, Hoard, & Hamson, 1999). Clearly, these predictor variables
are a simplied form of the complex skill they are predicting, and Gath-
ercole, Pickering, Knight, and Stegman (2004) argued that such basic skills
represent crystallized knowledge (or what Cattell referred to as crystallized
intelligence (Gc)) built up on the basis of experiences in the home, nurs-
ery school, and other social settings, and referenced by over-learned skills
and knowledge such as vocabulary. However, such learning opportunities
also interact with a basic cognitive capacity for learning, and Gathercole et
al. pointed out that it is essential to assess these uid cognitive capacities,
skills that are not knowledge based and generally less determined by socio-
economic factors, but which allow us to engage in complex cognitive op-
erations. Such abilities can also be referred to as uid intelligence (Gf) and
represent a biologically based ability to acquire skills and knowledge dur-
ing the lifespan (see Geary, 2007 for a review). As such, it is argued that
such uid cognitive capacities (or Gf) should predict learning in evolution-
arily novel contexts such as school and the workplace.
Cognitive studies of mathematical achievement and disorder provide a
valuable insight into the decits that might underlie difculties in learn-
ing mathematics. Many studies have used the working memory model of
Baddeley and Hitch (1974, see also Baddeley, 1996, 2000) as a framework
within which to study a range of cognitive skills, and recent work indicates
that working memory is a core mechanism underlying individual differ-
ences in Gf. The two “slave” systems of working memory, the phonolog-
ical loop and the visual-spatial sketch pad, are specialized for processing
language-based and visuo-spatial information, respectively. Assessment
of these slave systems is typically made using short-term memory tasks
where small amounts of material are held and reproduced in a sequential
fashion, with minimal resources needed from long-term memory to inter-
pret the task and no additional competing cognitive demands (e.g., digit
span, word recall, Corsi blocks, visual-patterns task). The central execu-
tive controls the allocation of resources between the phonological loop and
the visual-spatial sketch pad, schedules multiple cognitive activities, and is
able to revise the content of memory in light of new and relevant informa-
tion. Experimental tasks assessing the central executive typically attempt to
obtain a measure of the participants’ abilities to combine concurrent pro-

ME M o r y a n d Ex E c u t i v E Fu n c t i o n i n g i n pr E s c h o o l E r s 207
cessing and storage by using measures such as listening span (Daneman
& Carpenter, 1980), counting span (Case, Kurland, & Goldberg, 1982) or
backward digit span.
More recent conceptualizations of the central executive (e.g., Baddeley,
1996; Miyake et al., 2000) support the idea of distinct executive functions,
some of which are more strongly related to general uid abilities (or Gf)
than others. These distinct executive functions include inhibition (suppres-
sion of dominant action tendencies in favor of more goal-appropriate be-
havior), shifting (disengagement of an irrelevant task set or strategy and the
subsequent activation of a more appropriate one), and updating (encoding
and evaluation of incoming information for relevance to the task at hand
and subsequent revision of the information held in memory, most closely
associated with complex span tasks). Friedman et al. (2006) reported that in
healthy adults, updating (or what others would refer to as working mem-
ory) is most closely related to intelligence, whereas the links between inhi-
bition and shifting to intelligence were much lower and signicantly me-
diated by the variance shared with updating. However, where frontal lobe
functioning is compromised (as we might expect early in development),
executive function skills may not be so easily differentiated, resulting in
higher and more general executive function- intelligence correlations.
Many studies have examined the relationship between working mem-
ory subsystems, executive functioning, and arithmetic or mathematics abil-
ity. Some studies have attributed individual differences in mathematical
problem solving (particularly arithmetic) to inefciencies in the utilization
of the phonological system (e.g., Furst & Hitch, 2000; Gathercole & Pick-
ering, 2000; Gathercole et al., 2004; Geary, Brown, & Samaranayake, 1991;
Siegel & Ryan, 1989; Swanson & Sachse- Lee, 2001), with the role of the
phonological loop being to encode and retain verbal codes used for count-
ing and/or retain interim solutions. However, a number of studies of chil-
dren with poor mathematical skills have revealed no signicant limitations
in verbal short-term memory, or limitations being due to a third factor such
as processing speed or co-occurring reading difculties (e.g., Bull & John-
ston, 1997; Geary et al., 1999; Geary et al., 2000).
Recent research is placing more emphasis on the important role of the
visual- spatial sketch pad in children’s early arithmetical skills (McKenzie,
Bull, & Gray, 2003; Holmes & Adams, 2006). Visual-spatial skills and vi-
sual-spatial working memory have been found to be related to children’s
early counting ability (Kyttala, Aunio, Lehto, van Luit, & Hautamaki,
2003), and to mathematics ability in children aged 10 years (Maybery & Do,
2003), 11 years, and 14 years (Jarvis & Gathercole, 2003). Studies of children
with specic mathematical difculties have shown that they typically per-
form poorly on visuo-spatial span measures (McLean & Hitch, 1999; van
der Sluis, van der Leij, & de Jong, 2005; White, Moftt, & Silva, 1992). One
of the identied subtypes of mathematical learning disabilities includes
those individuals believed to have decits in visual-spatial skills (Geary,

208 Bu l l , Es p y , & Wi E B E i n De v e l o p m e n t a l ne u r o p s y c h o l o g y 33 (2008)
1993). Visual-spatial skills may impact math at various levels—number in-
versions and reversal, misalignment of column digits, problems in visual
attention and monitoring such as ignoring signs or changing operation
part-way through completion of problem, and acquiring concepts of bor-
rowing and carrying. The visual- spatial system also supports other aspects
of non-verbal numerical processing such as number magnitude, estimation,
and representing information in a spatial form, as in a mental number line
(Dehaene, 1997; Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999; Zorzi,
Proftis, & Umilta, 2002). Therefore, spatial visualization and understanding
and manipulation of spatial relations appear to be particularly important in
math skill development (Dark & Benbow, 1990; Geary et al., 2000; McGrew,
Flanagan, Keith, & Vanderwood, 1997).
Many studies now also report a direct association between executive
functioning and children’s early emerging and developing mathemati-
cal skills across a wide age range (e.g., Bull, Johnston, & Roy, 1999; Bull &
Scerif, 2001; Espy, McDiarmid, Cwik, Stalets, Hamby, & Senn, 2004; Gath-
ercole & Pickering, 2000; Gathercole et al., 2004; McLean & Hitch, 1999;
Passolunghi & Siegel, 2001). Many of these studies choose to focus on
span tasks thought to measure updating within working memory. How-
ever, a number of studies have tried to specify the functional relations be-
tween different aspects of executive functioning (e.g., inhibition, shifting,
and updating) and their relationship to a range of numerical and mathe-
matical skills. These studies show that in young preschool children (Espy
et al., 2004), and in children aged around 7 (Bull & Scerif, 2001) and 11
years (St Clair-Thompson & Gathercole, 2006) inhibitory skills are predic-
tive of mathematics ability, although the relationship may be less clear cut
in older children (van der Sluis, de Jong, & van der Leij, 2004). More com-
plex shifting skills have been found to be predictive of performance in chil-
dren aged 7 years and older (Bull et al, 1999; Bull & Scerif, 2001; McLean
& Hitch, 1999; van der Sluis et al., 2004). Finally, whereas some studies re-
port a specic relation between executive functioning and mathematics in-
dependent of reading skills (e.g., Bull & Scerif, 2001), it is clear that execu-
tive functioning skills have been implicated in many aspects of learning,
including language comprehension, reading, and writing (e.g., Gathercole,
Alloway, Willis, & Adams, 2006; Gathercole & Pickering, 2000; Gathercole
et al., 2004; Swanson & Jerman, 2007). Therefore, one of the aims of this
study is to determine the specicity of the relationship between early cog-
nitive and academic skills (in this case reading and mathematics).
Although evidence has amassed for the link between working memory,
executive functioning, and mathematics, it is not clear whether these uid
abilities would actually contribute to the prediction and identication of
later mathematical skills and difculties, that is, would they provide teach-
ers with a useful diagnostic tool that could be administered in the early
school years. Given the evidence noted earlier that central executive func-
tions predict concurrent and longitudinal mathematical achievement in

Frequently asked questions

Q1. What are the contributions in "Short-term memory, working memory, and executive functioning in preschoolers: longitudinal predictors of mathematical achievement at age 7 years" ?

This study examined whether measures of short-term memory, working memory, and executive functioning in preschool children predict later proficiency in academic achievement at 7 years of age ( third year of primary school ). Growth curve analyses examined predictors of math and reading achievement across the duration of the study and revealed that better digit span and executive function skills provided children with an immediate head start in math and reading that they maintained throughout the first three years of primary school. The implications of the findings are discussed in relation to further understanding the role of cognitive skills in different mathematical tasks, and in relation to the impact of limited cognitive skills in the classroom environment. 

Q2. What future works have the authors mentioned in the paper "Short-term memory, working memory, and executive functioning in preschoolers: longitudinal predictors of mathematical achievement at age 7 years" ?

A combination of knowledge-based assessment plus cognitive measures may provide a good estimate of the child ’ s ability to learn and hence their future academic success. 

Q3. What predictors were not significantly associated with reading achievement at this stage?

Backward digit span, inhibition, and Tower of London did not significantly predict reading achievement at this stage, although correlations indicated that higher reading achievement was associated with better performance on all cognitive tasks. 

Q4. What is the importance of the visual-spatial sketch pad at this young age?

The importance of the visual-spatial sketch pad at this young age is in line with recent research suggesting that before the age of 7, and particularly before the onset of spontaneous verbal rehearsal, children rely heavily on visual-spatial representations to support the maintenance of information in short-term storage (McKenzie et al., 2003). 

Q5. Why was the intercept set at P3?

Because the outcome measures being used are normative referenced and use standardized scores, the average linear rates of change were not expected to be significant (which would indicate that the subjects are gaining ground across time relative to the standardization sample). 

Q6. What is the way to measure cognitive flexibility in preschool children?

Measuring cognitive flexibility in preschool children has proven to be challenging, as reversal task performance (as used in many previous studies) may discriminate only those with severe disturbances in flexibly shifting between response sets, such as children diagnosed with severe disorders . 

Q7. What is the role of visual-spatial representation in the development of mathematic skills?

Deficits in the ability to represent visual-spatial information in working memory may be particularly detrimental to early developing non-verbal numerical skills such as estimation and manipulation of visual representation of magnitude using a number line, skills found to be predictive of later achievement in school (see e.g., Booth & Siegler, 2006; Jordan, Hanich, & Kaplan, 2003). 

Q8. What is the significance of working memory and inhibition in academic achievement?

In a study of 11 year olds, St Clair-Thompson and Gathercole (2006) found that working memory and inhibition both uniquely predicted curriculum attainment in mathematics and English indicating that these skills support general academic learning rather than the acquisition of skills and knowledge in specific domains. 

Q9. What is the significance of the correlations between the cognitive predictor variables and mathematics?

If certain cognitive skills place general, rather than specific, constraints on reading and mathematics abilities, associations between the cognitive predictors and, for example, mathematics should be abolished when differences in reading ability are taken into account (and vice versa). 

Q10. What would be the way to examine whether cognitive skills at preschool also predict differential rates of growth?

Use of equivalent tests across the different time points and use of raw scores would allow an examination of whether cognitive skills at preschool also predict differential rates of growth in academic skills.