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Shifting ability predicts math and reading performance in children: A meta-analytical study

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Empirical evidence on the association between the shifting component of executive functioning and academic performance is equivocal. In two meta-analyses children's shifting ability is examined in relation to their perfor-mance in math (k=18, N = 2330) and reading (k=16, N = 2266). Shifting ability was significantly and equally associated with performance in both math (r=.26, 95% CI=.15–.35) and reading (r=.21, 95% CI=.11–.31). Intelligence was found to show stronger associations with math and reading performance than shifting ability. We conclude that the links between shifting ability, academic skills, and intelligence are domain-general.
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Shifting ability predicts math and reading performance in children:
A meta-analytical study
Nihal Yeniad, Maike Malda, Judi Mesman , Marinus H. van IJzendoorn, Suzanne Pieper
Centre for Child and Family Studies, Leiden University, Leiden, The Netherlands
abstractarticle info
Article history:
Received 27 April 2012
Received in revised form 18 July 2012
Accepted 8 October 2012
Keywords:
Shifting
Executive function
Math
Reading
Meta-analysis
Empirical evidence on the association between the shifting component of executive functioning and academic
performance is equivocal. In two meta-analyses children's shifting ability is examined in relation to their perfor-
mance in math (k=18,N= 2330) and reading (k=16, N=2266). Shifting ability was signicantly and equally
associated with performance in both math (r=.26, 95% CI=.15.35) and reading (r=.21, 95% CI=.11.31).
Intelligence was found to show stronger associations with math and reading performance than shifting ability.
We conclude that the links between shifting ability, academic skills, and intelligence are domain-general.
© 2012 Elsevier Inc. All rights reserved.
1. Introduction
The abilityto shift between conceptual representationsis critical for
the selection and maintenance of appropriate strategies and disengage-
ment from irrelevant ones, and represents skills that are necessary to
successfully perform academic tasks (Best, Miller, & Jones, 2009). It
has been argued that this ability is particularly important for perfor-
mance on complex academic tasks requiring alternation between
different aspects of problems or arithmetical strategies (Agostino,
Johnson, & Pascual-Leone, 2010; Blair, Knipe, & Gamson, 2008; Van
der Sluis, De Jong, & Van der Leij, 2007). This suggests that shifting abil-
ity (or cognitive exibility) would be mainly related to performance in
subjects like math, which has indeed been reported in several studies
(e.g., Bull & Scerif, 2001; Clark, Pritchard, & Woodward, 2010; Mayes,
Calhoun, Bixler, & Zimmerman, 2009), although others have failed to
nd this association (e.g., Espy, McDiarmid, Cwik, Stalets, Hamby, &
Senn, 2004; Lee, Ng, & Ng, 2009; Monette, Bigras, & Guay, 2011).
Although there is a less strong theoretical case for a link between
shifting ability and reading performance, several studies have examined
this association, with some reporting signicant results (e.g., Latzman,
Elkovitch, Young, & Clark, 2010; Van der Sluis et al., 2007), but others
showing no link between the two (e.g., Mayes et al., 2009; McLean &
Hitch, 1999). In the current study, a set of meta-analyses is performed
to investigate whether shifting ability is signicantly related to perfor-
mance in math and reading in children.
1.1. Shifting and academic performance
A growing body of evidence shows that executive function (EF) is
a crucial contributor to school achievement (Best et al., 2009; Müller,
Liebermann, Frye, & Zelazo, 2008). EF refers to higher-order cognitive
processes necessary for goal-directed problem solving in novel situa-
tions and planning. The term may encompass at least three separate
but related components: inhibition, working memory and shifting
(Lehto, Juujärvi, Kooistra, & Pulkkinen, 2003; Miyake, Friedman,
Emerson, Witzki, Howerter, & Wager, 2000). Broadly speaking,
shifting refers to changing the mental set that has been learned to a
new one. The rst step of shifting is to develop a representation of a
rule (i.e., a particular strategy for problem solving) in working mem-
ory and the second one is to shift to a new rule, which requires the
inhibition of the rule that has been already formed (Best & Miller,
2010; Garon, Bryson, & Smith, 2008). Although there is a substantial
amount of research linking EF to academic achievement, most studies
have focused on the contribution of working memory (Gathercole &
Pickering, 2000; Passolunghi, Mammarella, & Altoe, 2008; Swanson,
2006).
Previous meta-analyses by Carretti, Borella, Cornoldi, and De Beni
(2009), Swanson and Jerman (2006) and Swanson, Zheng, and Jerman
(2009) found clear evidence for lower working memory capacity of chil-
dren with math and/or reading disabilities compared to their peers with-
out such disabilities. In addition, a review by Raghubar, Barnes and Hecht
(2010) supports the role of working memory in math performance.
Regarding inhibition, recent conrmatory factor analyses show that EF
Learning and Individual Differences 23 (2013) 19
Corresponding author at: Centre for Child and Family Studies, Leiden University,
PO Box 9555, 2300 RB Leiden, The Netherlands. Tel.: +31 71 5273482; fax: +31 71
527 3945.
E-mail addresses: yeniadn@fsw.leidenuniv.nl (N. Yeniad),
m.malda@fsw.leidenuniv.nl (M. Malda), mesmanj@fsw.leidenuniv.nl (J. Mesman),
vanijzen@fsw.leidenuniv.nl (M.H. van IJzendoorn), S.Pieper@diabetesfonds.nl
(S. Pieper).
1041-6080/$ see front matter © 2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.lindif.2012.10.004
Contents lists available at SciVerse ScienceDirect
Learning and Individual Differences
journal homepage: www.elsevier.com/locate/lindif
measures load on two latent factors that might best be called working
memory and set-shifting (Huizinga, Dolan, & Van der Molen, 2006).
Therefore, we focused on shifting as an important but not yet systemat-
ically reviewed component of EF in relation to academic outcomes. In
this study, the role of shifting in math and reading achievement is inves-
tigated through a set of meta-analyses. Further, possible factors that may
inuence the association of shifting with these two academic domains
are examined via moderator analyses to nd out what contributes to
the divergence of ndings.
1.2. Moderators
Divergent ndings regarding shifting and academic achievement
may result from heterogeneity of (1) shifting tasks, (2) shifting task
scoring, (3) sample characteristics, and (4) whether the impact of
intelligence is controlled for in statistical analyses. One of the sources
of heterogeneity in shifting tasks is variation in their level of com-
plexity. Clark et al. (2010) for instance found that the Flexible Item
Selection Task showed robust correlations with later achievement
scores whereas the Shape School-Switch Condition demonstrated
no association with achievement in preschool children after control-
ling for verbal intelligence, working memory and inhibition. The re-
searchers explained the mixed results with academic achievement
by pointing out the difference in the level of linguistic complexity be-
tween these two shifting tasks. Like other EF measures, shifting tasks
may also differ in terms of the cognitive processes operating in addi-
tion to shifting, which may affect the relations with academic scores.
Furthermore, shifting tasks differ in terms of rule presentation. On
some tasks, the rule is explicitly presented to the child (e.g., trail
making), whereas the sorting criterion is not explicitly revealed in
most of the card sorting tasks (see Dimensional Change Card Sorting
for exception) in which the rule should be deduced from the feedback
on the trials. The distinction in rule presentation may change the load
of nonexecutive processes (e.g., language and intelligence) or other
executive components (working memory or inhibition), which may
in turn moderate the relation of shifting with academic outcomes.
A second potential explanation for the heterogeneity of ndings is
the type of scoring of shifting tasks. Different tasks provide different
scores such as reaction time, accuracy, or efciency. In addition, some
tasks provide difference scores (e.g., RT difference between the Parts A
and B of Trail Making Task) whereas others give raw scores (e.g., total
RT to complete the task). Despite a wealth of research on EF tasks, it is
unclear whether different scores measure the same construct and
whether tasks with multiple scores differ from those with a single
score in terms of measuring shifting. Davidson, Amso, Anderson, and
Diamond (2006) provided striking evidence that score type matters
for different age groups. In their study with 4- to 13-year-olds and
young adults, accuracy was found to be a more sensitive measure for
young children than reaction time. Children were more impulsive
than adults, so their reaction time resisted changing with an accuracy
cost on difcult trials whereas adults tended to slow down (increasing
their reaction time) to be able to give accurate responses. Scoring type
of shifting tasks may thus moderate the relation between shifting and
academic achievement.
Third, diverging outcomes may also result from the variation in
age, gender, and SES of the samples in different studies. Shifting
shows a long developmental progression, as even 13-year-old chil-
dren do not reach the adult level (Davidson et al., 2006). It is unclear
whether the relation between shifting and academic achievement
differs across age. On the one hand, it has been found that shifting
in preschool does not contribute to math skills at the age of 6 when
the effect of age is controlled for (Espy et al., 2004). On the other
hand, in another study with third and fourth graders, Trail Making
Task, which is a commonly used shifting measure, showed signicant
correlations with math and reading scores, controlling for age
(Andersson, 2008). It is possible that the relation between shifting
and academic outcomes changes for preschoolers and school-aged
children partly because of the changing structure of EF with develop-
ment. Some studies, for instance support the unitary structure of EF in
preschool years (Hughes, Ensor, Wilson, & Graham, 2010; Wiebe,
Espy, & Charak, 2008; Wiebe, Shefeld, Nelson, Clark, Chevalier, &
Espy, 2011) as opposed to the fractionated nature of the same
construct in school-aged children (Huizinga et al., 2006; Lehto et al.,
2003). Gender has been reported to have no effect on the relation
between executive functions in general and academic domains
(e.g., Bull, Espy, & Wiebe, 2008; Clark et al., 2010). However, to our
knowledge, there are no studies that specically focus on the po-
tential moderating effect of gender on the relation between shifting
and academic achievement. There is also evidence that SES is related
to both shifting ability and academic achievement, with children
from low SES backgrounds performing less well than children from
higher SES backgrounds (Alexander, Entwisle, & Dauber, 1993;
Ardila, Rosselli, Matute, & Guajardo, 2005; Davis-Kean, 2005; Noble,
McCandliss, & Farah, 2007). Whether the relation of shifting with
academic outcomes differs for children coming from low-income
families compared to their socio-economically more advantageous
peers has not yet been explored.
1.3. The impact of intelligence
The fourth and last methodological issue is related to the question
whether the association between shifting ability and academic per-
formance is independent from the impact of intelligence on academic
achievement. The literature provides some evidence that shifting and
intelligence are associated in children (Ardila, Pineda, & Rosselli,
2000; Van der Sluis et al., 2007). Further, some studies have shown
that the relation between shifting and academic achievement disap-
pears after controlling for verbal intelligence in preschoolers (Espy
et al., 2004) and school-aged children (Bull & Scerif, 2001). On the
other hand, there has been research showing that shifting measured
in kindergarten remains a signicant predictor of academic perfor-
mance in the rst grade independent of covariates such as verbal
intelligence, social skills and current academic achievement (George
& Greeneld, 2005). An analysis of shifting ability in relation to aca-
demic achievement will thus have to take into account the potential
confounding inuence of intelligence.
1.4. Current study
In sum, empirical evidence on the association between shifting
and academic achievement is equivocal. In this study we investigate
shifting in relation to math and reading achievement in two meta-
analyses. The association between shifting and math seems to have
empirical support, whereas there is a less strong case for the associa-
tion between shifting and reading. Some studies also reported that
children with reading disability perform similarly to a control group
on shifting measures (Klorman et al., 1999; Van der Sluis, De Jong, &
Van der Leij, 2004), which supports the idea that there may be no re-
lation between shifting and reading. Therefore, we hypothesize that
shifting is positively associated with math performance, but not asso-
ciated with reading. We also search for explanations of the mixed
ndings by testing the effects of procedural moderators, including
rule presentation (whether the rule is explicitly revealed versus
kept implicit to be deduced by the participant), scoring type of the
shifting task (accuracy, reaction time, efciency, or combined),
study design (longitudinal versus concurrent), and time period
between the assessment of shifting and academic skills, as well as
sample moderators, including age, grade level (preschool versus
primary/secondary school), gender ratio, and socio-economic status
(SES). To evaluate the effect sizes obtained in the rst analyses in
light of the associations of our main variables with intelligence, we
will also present the results of four additional meta-analyses to assess
2N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
the associations of intelligence with math and reading, the associa-
tions between shifting and intelligence, and between math and
reading.
2. Method
2.1. Literature search
Three search methods were used to identify relevant studies. First,
we searched the electronic database Web of Science by using the
keywords executive funct*,shift*, set shift*”“task switch*,cognitive
exib*,mental exib*combined with academ* and school. Second,
we searched online dissertations via the database ProQuest Disserta-
tions and Theses with the same keywords. The search was nalized in
August 2011. Third, the reference lists of the collected articles and
dissertations and of the book chapter by Müller et al. (2008) were
checked for relevant studies. Studies were included if they reported
on the relation between shifting ability and any type of academic
achievement. Five additional inclusion criteria were used. (1) We in-
cluded studies with shifting tasks, which require changing the mental
set to a newer one that conicts with the rst; (2) shifting was
analyzed as a predictor of an academic outcome, or both constructs
were measured concurrently. If the academic assessment was con-
ducted prior to the measurement of shifting ability, the study was
excluded; (3) the sample consisted of children from the general
population. When information about the screening procedure was
not provided, the study was included; (4) both for shifting and aca-
demic performance, only the studies with performance-based tasks
were included. We excluded studies using only questionnaires and
studies using only observations; (5) we focused on math and reading
as academic outcomes since there were no sufcient results relating
shifting to other types of academic skills such as writing.
We found 20 studies with 34 outcomes that met our search
criteria with sample sizes ranging from 36 to 255 (see Table 2). Four-
teen of the studies provided separate outcomes for math and reading.
Four studies provided only math outcomes and two studies provided
only reading outcomes. Thus, 18 studies reported on shifting and
math (N=2330) and 16 studies reported on shifting and reading
(N=2266). The coding system for sample characteristics and study
methods is presented in Table 1. To assess intercoder reliability, all
studies were coded by two coders. Cohen's kappa was computed for
categorical variables, and intraclass correlations were computed for
continuous variables. The average agreement was .74 (86%) across
the categorical variables and .94 for the continuous variables. The
coders discussed disagreements in order to reach a consensus.
2.2. Moderators
We coded two types of moderators: sample and procedural
characteristics.
Sample moderators included age of the children as a continuous var-
iable and as a categorical variable (recoded into three categories by
using the 33rd and 67th percentile scores as younger than 6,
between 6 and 10 yearsand older than 10 years); grade level
(recoded into two categories as preschool/kindergarten vs. primary/
secondary school); gender ratio (% of girls), and socio-economic status
(recoded into three categories as low, middle and high). The predomi-
nant SES category of the sample was coded. Age of the children, grade
level and gender ratio were estimated for studies that do not provide
information for these moderators. Grade level was estimated based on
the mean age of the children. Similarly, age of children was estimated
based on the grade (e.g., 9 years for children in the grades 3 to 5).
Gender ratio of girls was estimated as 50%. Procedural moderators
included study design (longitudinal vs. cross-sectional), time period
between shifting assessment and academic testing, rule presentation
(explicit versus implicit), and scoring type of the shifting task (accuracy,
reaction time, efciency, or combined).
We coded the shifting tasks based on rule presentation. For
instance, the cards on the Wisconsin Card Sorting Test are sorted by
color, shape, or number of the objects. However, the sorting rule is
not revealed and remains implicit. The child has to deduce the correct
sorting principle by using the feedback (right or wrong) after each
trial. However, on most other shifting tasks the rule to sort and/or
switch is given explicitly. Thus, we coded the tasks as having either
explicit or hidden rules. One of the studies (Monette et al., 2011)
was coded as mixed since it included two tasks; one coded as explicit
and the other as implicit (hidden).
The shifting tasks also sh owed a great deal of variety i n terms of scor-
ing. Some studies used reaction time and others calculated the number
of correct responses as measures of performance. Likewise, some used
difference or costs between the versions of the task (e.g., RT difference
between the Parts A and B of Trail Making Task) whereas others pro-
vided only raw score. The task scoring is crucial to decide whether the
effect is in the hypothesized direction or not. We categorized the shifting
scores as reaction time, accuracy or errors, efciency (number of correct
responses divided by reaction time) or combined (when the task pro-
vided two or more different scores or when multiple shifting tasks
with a single score were used). When the task score was reaction time
or errors, the effect sign was reversed (i.e., higher shifting scores in
these cases would be expected to relate to lower academic achieve-
ment). We coded the type of scoring also for raw versus difference cat-
egorization. In the case of multiple correlation coefcients (e.g., when
there were multiple shifting scores and/or multiple academic scores),
these were averaged. If the averaged shifting scores were combinations
of various shifting indices (like accuracy and efciency), then th e scoring
type was coded as combined. In three studies, shifting was measured
by the Wisconsin Card Sorting Test (WCST), which simultaneously as-
sesses multiple cognitive processes related to shifting. We averaged
the WCST scores in order to obtain one single effect size for the
Table 1
Coding system for studies on shifting and academic achievement.
Variable Coding system
Academic outcome 1= math
2= reading
3= other
4= aggregate
Sample
Mean age at T1 Continuous
Mean age at T2 Continuous
Grade level 1= preschool/kindergarten
2= primary/secondary
Gender ratio (% girls) Continuous
Socio-economic status 1= high
2= middle
3= low
4= not reported or mixed
Procedure
Research design 1= concurrent
2= longitudinal
Time period between the
measurement of shifting and
of academic achievement
Continuous
Rule presentation in the shifting task 1= explicit
2= implicit
(rule deduction by the participant)
The type of shifting scoring I 1= accuracy or errors
2= reaction time
3=efciency
4= combined
The type of shifting scoring II 1= raw
2= difference/cost
Covariates used in the statistical
analyses?
1= yes (partial correlations)
2= no (zero-order correlations)
Sample size Continuous
3N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
Table 2
Studies included in meta-analyses.
Study Effect sizes for
a
Shifting task
b
Shifting
scoring I
c
Shifting
scoring II
Shifting
rule
Sample
size
b
Mean age
(mo) T1
Mean age
(mo) T2
%
girls
Grade
d
Time
period
(mo)
Concurrent vs
longitudinal
SES IQ measure
Math Reading
Andersson (2007) .59*** .41*** Trail Making Reaction
time
Difference Explicit 69 119.5 48 2, 3 and 4 0 C No
info
Raven's
Andersson (2008) .61*** .42*** Trail Making Reaction
time
Difference Explicit 141 124 59 3 and 4 0 C Middle Raven's
Andersson (2010)
f
.33** Trail Making Reaction
time
Difference Explicit 95 125 141 65 3 and 4 16 L No
info
Raven's
Bull, Johnston, and Roy
(1999)
j
.17 Wisconsin CombinedRaw Implicit 44 87 41 3 0 C Low
Bull and Scerif (2001) .21* WisconsinCombined Raw Implicit 93 88 46 3 0 C No
info
Wechsler Block Design
and Vocabulary
Mayes et al. (2009) .02 .00 WisconsinCombined Raw Implicit 214 103.2 53 K-5 0 C No
info
WASI
Blair and Razza (2007) .26** .19* Flexible Item Selection Accuracy Raw Explicit 141 61 74.4 47 Preschool 13 L Low Raven's and PPVT
Turner (2010) .35*** .14 Flexible Item Selection Accuracy Raw Explicit 138 60 53 Preschool
i
0 C High Expressive Vocabulary
Mazzocco and Kover
(2007)
h
.13 .12 Contingency Naming Combined Raw Explicit 177 80.4 52 Primary
school
0C No
info
Wechsler Abbreviated
Latzman et al. (2010) .48*** .55*** D-KEFS Combined Raw Implicit 151 163.68 0 Middle
school
i
0 C High KBIT-2 Verbal and
Nonverbal
Bull et al. (2008)
g
.29** .29** Shape School, Switch Efciency Raw Explicit 82/83 54 92.52 52 Preschool 38 L Middle
Vitiello (2009) .29*** .17* Something's the same Accuracy Raw Explicit 179 51.4 52.4 50 Preschool 1 L Low PPVT
Altemeier, Jones, Abbott,
and Berninger (2006)
.00 Wolf Rapid Automatized Reaction
time
Raw Explicit 228 108
i
55 3 and 5 0 C High
Clark et al. (2010)
i
.32** .25* Flexible Item Selection
and Shape School, Switch
Combined Raw Explicit 102 48 72 50 Preschool 24 L Middle WPPSI-R
Lee et al. (2009)
k
.11 .09 Number Letter and Plus
Minus
Reaction
time
Difference Explicit 255 134.4 48 5 0 C Low Wechsler Vocabulary
Espy et al. (2004) .08 Spatial Reversal (SR) and
SR Irrelevant cues
CombinedRaw Implicit 96 50 57 Preschool 0 C High WJ Picture Vocabulary
Agostino et al. (2010)
e
.31*** Trail Making and
Contingency naming
Combined Both Explicit 155 122.1 56 360 C No
info
McLean and Hitch (1999) .23 .06 Trails Written, Verbal,
Color and Crossing Out
Reaction
time
Raw Explicit 36 108.96 58 3 and 4 0 C No
info
Monette et al. (2011) .06 .13 Trails-P and Card sorting Accuracy Raw Mixed 85 70 82 54 Preschool 12 L High
Van der Sluis et al. (2007) .24** .38*** Trails making, Object-S,
Symbol-S, and Place-S
Efciency Raw Explicit 172 128.08 51 4 and 5 0 C No
info
Raven's and RAKIT
Verbal Analogies
*pb.05, **pb.01, ***pb.001.
Notes for Table 2.
a
Academic outcomes were grouped as M= Math, R =Reading.
b
Shifting tasks and sample size as included in meta analyses. Those with refer to the tasks, for which scores were aggregated in order to obtain one single effect size for the association between shifting and academic outcome. When the
correlation between a single score and the academic outcome was reported as nonsignicant, it was estimated as zero.
c
Coding of the shifting task scores is described in detail in the text. Those with refer to the latent factors.
d
For longitudinal studies, the reported grade refers to the grade in which children were assessed for the rst time.
e
In the study by Agostino et al. (2010), academic outcome was based on the total sample and one attribute part of Contingency Naming Task.
f
In the study by Andersson (2010), reading performance on both foreign and native language tests was used.
g
In the study by Bull et al. (2008), the sample size is 83 for reading and 82 for math due to one missing case. The correlations of shifting with the 3rd wave academic scores were included.
h
In the study by Mazzocco and Kover (2007), the research design is longitudinal but the concurrent associations between the CNT and the academic scores were used.
i
Gender ratio was estimated (see Method section).
j
In the study by Bull et al. (1999), IQ was assessed, but the correlations of intelligence with academic scores and with shifting are not reported.
k
In the study by Lee et al. (2009), Block Design and Vocabulary subtests of WISC-III were used. However, only the correlations of Vocabulary with the variables of interest were reported.
4N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
association between shifting and academic outcome (excluding failure
to maintain set, because this is considered to be independent of cogni-
tive exibility, see Greve, Love, Sherwin, Mathias, Ramzinski, & Levy,
2002; Greve, Stickle, Love, Bianchini, & Stanford, 2005).
2.3. Intelligence
Intelligence was measured only by a verbal (e.g., Peabody Picture
Vocabulary) or a nonverbal (e.g., Raven's Matrices) test in some studies,
whereas in other studies, a single quotient was estimated based on mul-
tiple subtests of a battery to indicate general intelligence. We coded
different types of intelligence, but due to the lack of studies tapping
each type of intelligence we were unable to use this moderator in the
analyses.
2.4. Statistical analyses
First, two meta-analyses were carried out, namely, one for the rela-
tion between shifting and math, and one for the relation between
shifting and reading. Second, we conducted two additional sets of
meta-analyses to investigate the relation between intelligence and the
two academic domains within the selected publications, which provid-
ed outcomes regardingthe association of intelligence with math and/or
reading. Third, we meta-analyzed the associations between shifting and
intelligence, and between math and reading within the set of selected
studies. The meta-analyses were performed using the Comprehensive
Meta-Analysis (CMA) program (Borenstein, Rothstein, & Cohen,
2005). For each outcome, an effect size (correlation) was calculated.
Effects in the hypothesized direction (i.e., a positive association
between cognitive exibility and academic achievement) were given
a positive sign. Effectsindicating anassociation opposite to the hypoth-
esized direction were given a negative sign. Studies reporting no exact
statistics but reported a non-signicant nding were assigned a conser-
vative non-signicant zero effect size (included using the study's
sample size and p=.50) (Mullen, 1989).
Using CMA, combined effect sizes were computed. Signicance
tests and moderator analyses were performed through random effects
models as the preferred mode of analysis (Borenstein, Hedges, &
Rothstein, 2007). Random effects models allow for the possibility that
there are random differences between studies that are associated with
variations in procedures, measures, settings, that go beyond subject-
level sampling error, and thus point to different study populations
(Lipsey & Wilson, 2001). To test the homogeneity of the sets of effect
sizes, we computed Q-statistics (Borenstein et al., 2005). In addition,
we computed 95% condence intervals (CIs) around the point estimate
of each set of effect sizes. Q-statistics and p-values were also computed
to assess differences between combined effect sizes for specicsubsets
of study effect sizes grouped by moderators. Contrasts were only tested
when at least two of the subsets consisted of at least four studies
(Bakermans-Kranenburg, Van IJzendoorn, & Juffer, 2003).
Funnel plots for both sets of studies were examined in order to
detect possible publication bias. A funnel plot is a plot of each study's
effect size against its standard error (usually plotted as 1/SE, or preci-
sion). It is expected that this plot has the shape of a funnel, because
studies with smaller sample sizes (larger standard errors) have in-
creasingly large variation in estimates of their effect size as random
variation becomes increasingly inuential, whereas studies with
larger sample sizes have smaller variation in effect sizes (Duval &
Tweedie, 2000b; Sutton, Duval, Tweedie, Abrams, & Jones, 2000).
However, smaller studies with nonsignicant results or with effect
sizes in the nonhypothesized direction are less likely to be published.
Therefore, a funnel plot may be asymmetrical around its base. The
degree of asymmetry in the funnel plot was examined by estimating
the number of studies, which have no symmetric counterpart on the
other side of the funnel. The trim and llmethod was used to test
the inuence of possible adjustments of the sets of studies for publi-
cation bias (Duval & Tweedie, 2000a,b).
For each study, Fisher's Z scores were computed as equivalents for
correlations. Fisher's Z scores have better distribution characteristics
than correlations, in particular better estimates of the standard
error (Lipsey & Wilson, 2001; Mullen, 1989). All Fisher ztransformed
effect sizes and all sample sizes were examined for outliers (dened
as standardized z-values exceeding +/3.29) (Tabachnick & Fidell,
2001). No outliers were detected.
Further, the 85% CIs were compared to explore whether the com-
bined effect sizes of six different sets of effect sizes were signicantly
different (Van IJzendoorn, Juffer, & Poelhuis, 2005). The sets of effect
sizes were partly based on the same subjects and therefore direct
statistical tests were not warranted. The absence of overlap between
85% CIs indicates a statistically signicant difference since producing
85% condence intervals guarantees that if the condence intervals
around the combined effect sizes of the two sets of meta-analyses
do not overlap then the level of statistical signicance between the
two groups would be 5% or lower (Goldstein & Healy, 1995; Julious,
2004; Payton, Greenstone, & Schenker, 2003). So, we used the 85%
CI around the point estimate as a conservative way of testing whether
the difference in effect sizes for the two comparison groups (intelli-
gence versus shifting as the predictor) for each of the academic skills
(math and reading) was signicant (see Fig. 1). Using 95% CIs did not
change our ndings and conclusions.
3. Results
3.1. Shifting and academic outcomes
The meta-analysis concerning the relation between shifting and
math included 18 studies, with a total sample of 2330 children. The re-
sults of the meta-analyses for math and reading are presented in
Table 3. The combined effect size for the relation between shifting and
math was substantial and signicant (r=.26, 95% CI= .15.35, pb.01)
in a heterogeneous set of studies (Q=113.31, pb.01). Overall, higher
levels of performance on shifting tasks were related to higher levels of
performance on math tests. Using the trim and ll method (Duval &
Tweedie, 2000a,b), we did not nd evidence for publication bias. The
fail-safe number for this set of studies was 614, i.e., it would take 614
null results to cancel out this signicant combined effect size.
The meta-analysis concerning the relation between shifting and
reading included 16 studies with a total of 2266 children. The
SHIFTING ABILITY IN RELATION TO MATH AND READING
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Shifting
&
Math
IQ
&
Math
Shifting
&
Reading
IQ
&
Reading
Shifting
&
IQ
Math
&
Reading
N = 1751
N = 2330
N = 1539
N = 2266
N = 1657
N = 1283
Fig. 1. Comparison of the 85% condence intervals of the meta-analyses regarding
shifting and intelligence (IQ) in relation to math and reading. Note. The combined effect
size (correlation) is shown with x.
5N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
combined effect size for the relation between shifting and reading
was moderate and signicant (r=.21, 95% CI= .11.31, pb.01) in a
heterogeneous set of studies (Q=90.85, pb.01). Overall, higher levels
of performance on shifting tasks were related to higher levels of per-
formance on reading tests. Using the trim and ll method (Duval &
Tweedie, 2000a,b), no asymmetry was found in the funnel plot;
therefore evidence for publication bias was absent. The fail-safe
number for this set of studies was 344.
We examined the papers included in our meta-analyses for reliability
estimates. We used the Spearman's (1904) correction for attenuation
formula based on the reliabilities of the measures. The mean reliabilities
were as follows: .74 for the shifting measures (k= 4), .82 for the math
measures (k=4), and .86 for the reading measures (k=2). We found
truepopulation effect sizes for the association between shifting ability
and math performance of .33 and for the association between shifting
ability and reading performance of .26. Since a very small number of
studies reported reliability estimates of the measures on the sample
involved, the results based on this correction should be interpreted
tentatively.
3.2. Moderators
We tested whether moderators regarding sample characteristics
(age, grade level, gender ratio and socio-economic status) and proce-
dure (study design, time period between shifting and academic testing,
rule presentation and scoring type in shifting tasks) were associated
with effect size separately for math and reading (Table 3). For exploring
the effect of a continuous variable, weighted regression models were
used. None of the sample characteristics and none of the procedural
moderators showed signicant effects on the association between
shifting and math or reading performance. However, the lack of moder-
ation effects is tentative due to the small numberof studiesin particular
subsets. The moderating effects of SES (k=3 low SES for reading), rule
presentation (k=2 implicit for reading), shifting scoring as difference
versus raw (k= 3 difference for math) and a covariate used in the
statistical analyses (k=3 partial correlations for both math and read-
ing) could not be tested due to an insufcient number of studies per
subset i.e., less than four (Bakermans-Kranenburg et al., 2003).
3.3. Intelligence, shifting and academic outcomes
The meta-analysis concerning the relation between intelligence
and math that included 12 studies with a total sample of 1751 chil-
dren showed a signicant and large combined effect size (r= .47,
85% CI=.41.52) in a heterogeneous set of studies (Q=40.86,
pb.01). The CI around the point estimate for the relation between
intelligence and math did not overlap with the CI for the relation
between shifting and math (r=.26, 85% CI=.18.33), which means
that the relation between intelligence and math was signicantly
stronger than between shifting and math. The meta-analysis con-
cerning the relation between intelligence and reading, which in-
cluded 11 studies with a total of 1657 children showed a signicant
and large combined effect size (r= .43, 85% CI = .37.49, pb.01) in a
heterogeneous set of studies (Q=46.27, pb.01). The absence of
overlapping 85% CI with the CI for the relation between shifting
and reading (r=.21, 85% CI=.14.28) suggested that the relation
between intelligence and reading was signicantly stronger than
that between shifting and reading.
The relation between shifting and intelligence was reported in 11
studies with a total sample of 1539 children. The combined effect size
for the relation between intelligence and shifting was signicant and
substantial (r=.30, 85% CI=.18.41, pb.01) in a heterogeneous set
of studies (Q=107.54, pb.01). Last, we conducted a meta-analysis
with 10 studies that provided results for the association between
math and reading. The combined effect size within a total of 1283
children was signicant and large (r=.56, 85% CI=.50.62, pb.01)
in a heterogeneous set of studies (Q= 22.24, pb.001). Comparison
of the 85% condence intervals of the meta-analyses regarding
shifting and intelligence in relation to math and reading is presented
in Fig. 1.
Table 3
Meta-analytic results of studies relating shifting with math and with reading.
Math Reading
kn r 95% CI Q
a
pkn r 95% CI Q
a
p
Total set 18 2330 .26 [.15, .35] 113.31 .00 16 2266 .21 [.11, .31] 90.85 .00
Sample characteristics
Age .66 .72 3.30 .19
Youngest 7 823 .22* [.04, .39] 12.88* 6 728 .20* [.03, .35] 2.02
Medium 6 633 .23** [.03, .42] 23.03** 5 724 .09 [.09, .28] 12.01*
Oldest 5 874 .32** [.12, .50] 73.23** 5 814 .32** [.15, .47] 59.10**
Grade .23 .63 .04 .84
Preschool/K 7 823 .22* [.05, .38] 12.88* 6 728 .20* [.02, .36] 2.02
Primary/secondary 11 1507 .27** [.13, .40] 100.26** 10 1538 .22** [.08, .34] 88.78**
SES
b
1.26 .26
High/middle 7 795 .32** [.14, .47] 29.92** 7 928
Low 4 619 .15 [.09, .38] 24.41** 3 575
Procedure characteristics
Study design .00 .92 .07 .79
Concurrent 13 1682 .26** [.16, .41] 108.00** 10 1581 .20** [.07, .33] 86.39**
Longitudinal 5 648 .25* [.04, .43] 4.14 6 685 .23* [.06, .38] 3.08
Rule presentation
c
1.72 .42
Explicit 12 1647 .30** [.17, ..42] 80.51** 13 1816
Implicit 5 598 .18 [.04, .38] 27.32** 2 365
Shifting scoring I .98 .61 .92 .63
Accuracy/errors 4 543 .25* [.01, .46] 4.96 4 543 .16 [.05, .36] .33
Reaction time 4 501 .36** [.12, .56] 74.51** 6 824 .18 [.00, .34] 42.08**
Efciency/combined 10 1286 .22* [.06, .36] 32.96** 6 899 .27** [.11, .43] 39.78**
Shifting scoring II .33 .56
Difference/costs 3 465 4 560 .26* [.05, .45] 35.88**
Raw 14 1710 12 1706 .19* [..07, .31] 54.94**
Note: *pb.05, **pb.01.
a
Q statistic for moderator stands for effect of contrasts (df =number of subgroups 1), Q statistic for subgroup stands for homogeneity (df= k1).
b
The studies that do not report SES information were excluded.
c
The study by Monette et al. (2011) was excluded.
6N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
4. Discussion
4.1. Discussion of the ndings
Our meta-analyses showed that the association between shifting
ability and math as well as the association between shifting ability
and reading performance were substantial and signicant. The varia-
tion in effect sizes between studies for the association between
shifting and academic achievement was not related to differences in
rule presentation or type of scoring on the shifting task, or to differ-
ences in research design, time period between the measurement of
shifting and academic outcomes, children's age, grade level, SES
or gender. Intelligence was found to be a stronger contributor to
academic performance than shifting, and shifting was substantially
associated with intelligence. Lower reliabilities of shifting measures
compared to IQ assessments were not responsible for the weaker
contribution of EF to school achievement compared to IQ. Even after
correction for attenuation combined effect sizes for shifting were
considerably smaller than those found for IQ.
First of all, the results of our main meta-analyses indicate that
children with a higher capacity to switch a conceptual representation
(i.e., goals, rules or strategies for problem solving) to a newer one
show better performance on math and reading. The combined effect
sizes of the associations of shifting with math and with reading were
quite similar. This is contrary to our hypothesis that shifting would be re-
lated to math but not to reading. Whereas shifting is considered to be
necessary for alternating between different strategies in complex math-
ematical problem solving (Agostino et al., 2010; Bull et al., 2008; Mayes
et al., 2009; Van der Sluis et al., 2007), the literature does not offer a
clear explanation for the relation between shifting and reading. Given
the results of our meta-analysis of the association between math and
reading skills, it is likely that our results are due to the substantial shared
variance between the two constructs. Apparently, competence in both
math and reading taps into a common more general cognitive ability.
This is conrmed by our nding that the associations of math and read-
ing skills with intelligence are very similar in size. These results all point
to a domain-general interpretation of the links between shifting ability,
academic skills, and intelligence. According to a new framework pro-
posed by Miyake and Friedman (2012), each EF component involves a
common (across all three EFs) and a specic part (unique to that partic-
ular ability). Taken this new conceptualization of the EFs into account, it
might be possible that common EF may enable children to maintain the
goal of a task, whereas shifting-specic abilities may contribute to partic-
ular domains of achievement (e.g., alternate between different arithmet-
ical strategies in complex math tasks). Since in the included studies
shifting ability was not decomposed as it is proposed by Miyake and
Friedman (2012), the question of how the common and specicparts
of shifting ability are related to achievement remains unanswered.
Second, the results of the moderator analyses did not support
the hypothesis that the diverging outcomes regarding the relation
between shifting and academic achievement may result from the
heterogeneity of procedural or sample characteristics in different
studies. It is important to note however, that the lack of moderation
effects may be due to the small number of studies in particular subsets.
The reasons for including most of these moderators (e.g., rule presenta-
tion and scoring type on the shifting task) were based on theoretical
considerations rather than on empirical evidence, because the effect of
these variables on the association between shifting and academic per-
formance has never been investigated before. For a moderator like
child agethere has been some empirical work, but with contradicting re-
sults. Our meta-analyses therefore provide a much-needed clarication
of the (lack of) effects of these moderators. However, we could not test
the effects of all possible interfering variables for the association be-
tween shifting and academic performance in this study. For instance, it
is important to note that the substantial variety in shifting tasks
remains a methodological challenge mostly due to task impurity
(Miyake et al., 2000). Shifting tasks, like other EF measures, differ in
terms of complexity as a result of different amount of loadings on
other executive (inhibition and working memory) and nonexecutive
processes (e.g., linguistic skills). Unfortunately, the literature does not
provide a well-dened framework to categorize shifting tasks by taking
into account these levels of complexity. Instead, it has been proposed
that the relatively pure EF components can be extracted by conrmatory
factor analysis (Lehto et al., 2003; Miyake et al., 2000) and the
nonexecutive processes operated by EF tasks should be accounted for
by using control tasks, which are quite similarto their EF correspondents
except that they do not require the operation of the given EF component
(Van der Sluis et al., 2007). It is important to note that conclusions
regarding the specic role of EF components in academic achievement
without controlling for the common executive and nonexecutive
(e.g., intelligence) variance are limited. Future studies that employ these
kinds of methods may be more promising to overcome task impurity,
and therefore allow for more straightforward conclusions regarding the
unique relations of EF components with academic performance.
Because to the best of our knowledge only one study reports on
the association between shifting and academic outcomes correcting
for IQ (Mayes et al., 2009), the literature did not provide enough ev-
idence to disentangle the contributions of shifting and intelligence
to academic outcomes. To gain at least some insight into the role of
intelligence, we analyzed the associations of intelligence with math
and reading using the publications selected for the main meta-
analyses. Our results showed that the relations of intelligence with
math and reading were signicantly stronger than the relations of
shifting with these academic outcomes. The large combined effect
size between intelligence and the academic outcomes seems to sup-
port previous ndings reporting high correlations between intelli-
gence and achievement tests (Psychological Corporation, 2002). The
similarity in the combined effect sizes for the associations of intelli-
gence with math and reading supports the fact that intelligence is a
higher-order, domain-free contributor to school achievement much
like shifting ability. What remains unclear however, is whether
shifting ability predicts achievement beyond the effect of intelligence.
In most of the previous studies, the association between academic
and executive functions has been explored without controlling for in-
telligence. One study showed that the WCST perseverative responses
score, a measure of the inability to shift, was one of the very few
scores that predicted math (but not reading) beyond intelligence,
which led the researchers to conclude that switching ability is neces-
sary for math performance (Mayes et al., 2009). Consequently,
the unique contribution of shifting to math independent of intelli-
gence has some support, but needs replication. It remains to be seen
whether shifting predicts reading in a similar fashion, when control-
ling for intelligence in general and verbal intelligence in particular.
Our ndings showed a signicant and substantial association
between shifting and intelligence consistent with previous research
(e.g., Ardila et al., 2000). In contrast, some studies have reported
that the association of shifting with intelligence disappears when
the intercorrelations among the three EF components are controlled
for (Duan, Wei, Wang, & Shi, 2010; Friedman et al., 2006). In these
studies, working memory was the only EF component that remained
signicantly correlated with intelligence after controlling for the
other components. In the present study, it was impossible to remove
the variance of other EF components from the relation between
shifting and intelligence. Nevertheless, our ndings support the
growing evidence reporting moderate to high correlations between
EF components and intelligence scores (e.g., Blair & Razza, 2007;
George & Greeneld, 2005; Latzman et al., 2010).
4.2. Limitations
It is important to note some limitations of this study. First, due to
the small number of studies in particular subsets (e.g., implicit subset
7N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
of rule presentation), we had to merge different subcategories into
one subset in statistical analyses (e.g., efciency and combined
scoring of shifting tasks), which may have reduced the clarity of the
results regarding the moderator effects. For the same reason, we
were unable to test the moderating effects of SES (for reading), rule
presentation (for reading), and covariates (for both math and read-
ing). Second, due to the lack of studies including partial correlations
controlling for intelligence (only the study by Mayes et al., 2009),
we could not investigate whether shifting is associated with academic
achievement beyond the inuence of intelligence. Some studies
reported regression analyses controlling for intelligence in addition
to the effects of several other covariates such as age, maternal educa-
tion or effortful control in predicting academic outcomes by EF com-
ponents (e.g., Blair & Razza, 2007; Espy et al., 2004), thus making it
more difcult to estimate the inuence of intelligence on the associa-
tion between shifting and academic outcome.
4.3. Implications
On a theoretical level, our results provide evidence that shifting abil-
ity is a domain-general cognitive process for predicting academic per-
formance, as is the case for intelligence. However, more research is
needed to explore the nonshared variance of these higher-order cogni-
tive processes to determine whether they are unique predictors of
achievement. There is an ongoing debate about the nature of shifting
ability (Chavelier & Blaye, 2008). Based on the new unity and diversity
framework (Miyake & Friedman, 2012), future studies decomposing
shifting ability into common and specic parts and examining the asso-
ciations of these parts with academic performance could provide a
better understandingof the role of shifting in achievement. From a prac-
tical point of view, identifying the potential contributors to school
success is necessary to improve the effectiveness of assessment at edu-
cational settings. Selecting assessment tools, which tap domain-general
abilities contributing to achievement, may help practitioners and edu-
cators to evaluate children's competencies at the time of school entry
that are important for later success. In this sense, measuring shifting
ability may provide crucial information to target at-risk children, who
may experience difculties on reading or math performance. In addi-
tion, the knowledge about the contribution of shiftingability to achieve-
ment combined with evidence showing positive effects of some training
programs on EF performance (Diamond, Barnett, Thomas, & Munro,
2007; Dowsett & Livesey, 2000; Karbach & Kray, 2009) suggests that it
is worthwhile to further investigate the potential effects of experimen-
tally enhanced shifting ability on academic performance. However,
there are some concerns regarding the utility of working memory train-
ing programs due to various methodological challenges (Melby-Lervåg
& Hulme, 2012; Shipstead, Redick, & Engle, 2012). Therefore, future
work in this area should explore whether shifting ability can be im-
proved independent of task-speciclearning(Shipstead et al., 2012),
whether this improvement can be long-lasting and transferable to
other cognitive skills (e.g., intelligence), and how the presumed rela-
tions of common and specic parts of shifting ability are inuenced by
training.
4.4. Conclusion
In sum, our meta-analyses showed that shifting, the ability to exi-
bly switch between different rules, strategies or tasks, is a domain-
free contributor to academic achievement, regardless of variations in
samples and procedures. Although previous studies have shown that
the working memory is an important contributor to academic success,
the evidence was not that clear for the shifting component of EF. In
addition, our analyses provide an insight into the relative contributions
of intelligence and shifting to academic outcomes. By showing the
substantial association between shifting and intelligence, the current
study addresses the importance of taking into account the impact of
intelligence in exploring the contribution of shifting and other EF com-
ponents to academic performance.
Acknowledgement
This study was conducted with a grant from New Opportunities for
Research Funding Agency Co-operation in Europe (NORFACE, grant 292).
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9N. Yeniad et al. / Learning and Individual Differences 23 (2013) 19
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Chapter
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Thesis
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Thesis
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