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The aim of the present study was to investigate the contribution of working memory and verbal ability (measured by vocabulary) to mathematical skills in children. A sample of 206 seven- and eight-year-olds was administered tests of these cognitive skills. A different pattern emerged that was dependent on both the memory task and the math skill. In the seven-year olds, visuo-spatial and verbal memory uniquely predicted performance on the math tests; however, in the eight-year olds, only visuo-spatial short-term memory predicted math scores. Even when differences in vocabulary were statistically accounted, memory skills uniquely predicted mathematical skills and arithmetical abilities. This pattern of findings provides a useful starting point that can add to existing research on the contributions of working memory and vocabulary to different mathematical skills.
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The relationship between working memory, IQ, and mathematical skills in children
Tracy Packiam Alloway
, Maria Chiara Passolunghi
University of Stirling, Italy
University of Trieste, Italy
abstractarticle info
Article history:
Received 5 October 2009
Received in revised form 21 September 2010
Accepted 26 September 2010
Working memory
Arithmetical abilities
Mathematical skills
The aim of the present study was to investigate the contribution of working memory and verbal ability
(measured by vocabulary) to mathematical skills in children. A sample of 206 seven- and eight-year-olds was
administered tests of these cognitive skills. A different pattern emerged that was dependent on both the
memory task and the math skill. In the seven-year olds, visuo-spatial and verbal memory uniquely predicted
performance on the math tests; however, in the eight-year olds, only visuo-spatial short-term memory
predicted math scores. Even when differences in vocabulary were statistically accounted, memory skills
uniquely predicted mathematical skills and arithmetical abilities. This pattern of ndings provides a useful
starting point that can add to existing research on the contributions of working memory and vocabulary to
different mathematical skills.
© 2010 Published by Elsevier Inc.
contributions of working memorythe ability to process and
remember informationand verbal ability (vocabulary) to mathemat-
ical skills. Baddeley's working memory model provides a useful
framework for understanding the role of the different memory
components in mathematical skills. The central executive is a
domain-general component responsible for the control of attention
and processing of information from long-term memory (Baddeley,
Emslie, Kolodny, & Duncan, 1998). The temporary storage of
information is mediated by the phonological loop for verbal material
and the visuo-spatial sketchpad for visual and spatial representations
(Baddeley & Logie, 1999). The fourth component, the episodic buffer,
is responsible for binding information into integrated chunks
(Baddeley, 2000). As measurement tasks have yet to be standardized
for children, this component was not considered in the present study
(but see Alloway, Gathercole, Willis, & Adams, 2004; Alloway &
Gathercole, 2005, for the links between the episodic buffer and
learning in children).
Although it is well-established that working memory is closely
linked to mathematical skills, this relationship is mediated by the task
as well as the child's age. Visuo-spatial memory (represented by
the visuo-spatial sketchpad) functions as a mental blackboard to
support number representation, such as place value and alignment in
columns, in counting and arithmetic tasks (D'Amico & Guarnera,
2005; Geary, 1990; McLean & Hitch, 1999). Specic associations have
also been reported between visuo-spatial memory and encoding in
problems presented visually (Logie, Gilhooly, & Wynn, 1994; Trbovich
& LeFevre, 2003), and in multi-digit operations (Heathcote, 1994).
Visuo-spatial memory skills uniquely predict performance in nonver-
bal problems, such as sums presented with blocks, in pre-school
children (Rasmussen & Bisanz, 2005), as well as problem-solving
(Passolunghi & Mammarella, 2010).
Verbal short-term memory (represented by the phonological
loop) has been linked to solving single-digit addition problems
(Hecht, 2002; Seyler, Kirk, & Ashcraft, 2003) and maintaining operand
and interim results in multi-digit problem (Fürst & Hitch, 2001;
Heathcote, 1994; Noël, Désert, Aubrun, & Seron, 2001; Seitz &
Schumann-Hengsteler, 2000, 2002). It is possible that verbal working
memory (represented by the central executive in Baddeley's model) is
a reliable indicator of mathematical disabilities in the rst year of
formal schooling (Gersten, Jordan, & Flojo, 2005; also Bull & Scerif,
2001), but not in older children (Reuhkala, 2001), as other factors,
such as number knowledge and strategies, play a greater role
(Thevenot & Oakhill, 2005).
The present study extends previous research by including a range
of working memory measures. On the basis of the differential links
between the memory components and arithmetical abilities, we
included measures of verbal and visuo-spatial short-term memory
and working memory (see Alloway, Gathercole, & Pickering, 2006;
Bayliss, Jarrold, Gunn, & Baddeley, 2003; for support of this theoretical
structure of working memory in development). This allowed us to
systematically investigate the links between the various memory
skills and mathematical skills and arithmetical abilities.
There is evidence that working memory tasks measure something
different from general ability tests, such as IQ and vocabulary (Cain,
Oakhill, & Bryant, 2004; Siegel, 1988). While these tests measure
Learning and Individual Differences 21 (2011) 133137
Corresponding author. Department of Psychology, University of Stirling, Stirling,
FK9 4LA, UK. Tel.: + 44 (0) 1786 467639.
E-mail address: (T.P. Alloway).
1041-6080/$ see front matter © 2010 Published by Elsevier Inc.
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knowledge that the child has already learned, working memory tasks
are a pure measure of a child's learning potential (Alloway & Alloway,
2010). Thus, working memory skills are able to predict a child's
performance in learning outcomes, even after their general ability has
been statistically accounted in reading and language skills (Gathercole,
Alloway, Willis, & Adams, 2006; Nation, Adams, Bowyer-Crane, &
Snowling, 1999; Passolunghi, Vercelloni, & Schadee, 2007; Stothard &
Hulme, 1992; for a review see Swanson & Saez, 2003). The present
study explored whether the same pattern of dissociation in the
contributions of verbal ability, measured by vocabulary, and working
memory would also be evident in tests that assessed a range of
mathematical and arithmetic abilities.
Mathematical skills were measured by tasks involving ranking
numbers, translating numbers from one representation to another
(e.g., words to numbers), quantity discrimination, as well as more
complex number skills, such as arithmetic computation (Butterworth,
2005). Also of interest was whether working memory and vocabulary
would be differentially associated with mathematical skills as a
function of age (Holmes & Adams, 2006; Passolunghi et al., 2007). For
example, in the present study, verbal working memory may play a
greater role in supporting arithmetical ability in younger children (7-
year-olds), while visuo-spatial memory may be more closely linked to
such skills in older children (8-year-olds) since some arithmetic tasks
(e.g., more complex additions and subtractions) could require an
elevated demand of visuo-spatial processing. The link between
vocabulary and mathematical skills may be greater in the younger
cohort as the individual is learning new information, rather than in
the older group when gains made are likely the result of practice (see
Jensen, 1980).
1. Method
1.1. Participants
There were 206 typically developing children (109 boys) recruited
from four mainstream schools located in the north-west of Italy. The
majority of parents came from professional homes that were predom-
inantly middle class but included families from across the social
spectrum. For the statistical analyses, participants were divided
into two age groups: 7-year-olds (n=100; M=88 months,
SD=3.5 months; 50 boys) and 8-year-olds (n=106; M=103 months,
SD=3.6 months; 46 boys). None was receiving special education
services or had documented brain injury, or behavioral problems.
None of the assessed children belonged to families with socio-cultural
1.2. Measures
1.2.1. Working memory
All 12 tests from the Automated Working Memory Assessment
(AWMA, Alloway, 2007), a computer-based standardized battery that
provides multiple assessments of verbal and visuo-spatial short-term
memory, and of verbal and visuo-spatial working memory. There
were three measures of verbal short-term memory where the child
immediately recalls a sequence of information: digit recall, word
recall, and nonword recall. Testretest reliability is .89, .88, .69 for
digit recall, word recall, and nonword recall respectively.
There were three verbal working memory measures: listening
recall, backward digit recall, and counting recall. In the listening recall
task, the child veries a series of sentences by stating trueor false
and recalls the nal word for each sentence in sequence. In the
backwards digit recall task, the child recalls a sequence of spoken
digits in the reverse order. In the counting recall task, the child counts
the number of circles in an array and then recalls the tallies of circles.
Testretest reliability is .88, .84, .86 for listening recall, counting recall,
and backward digit recall respectively.
Three measures of visuo-spatial short-term memory were admin-
istered. In the dot matrix task, the child is shown the position of a red
dot in a series of four by four matrices and has to recall this position by
tapping the squares on the computer screen. In the mazes memory
task, the child is shown a maze with a red path drawn through it for
three seconds. S/he then has to trace in the same path on a blank maze
presented on the computer screen. In the block recall task, the child
views a video of a series of blocks being tapped and reproduces the
sequence in the correct order by tapping on a picture of the blocks.
Testretest reliability is .85, .86, .90 for dot matrix, mazes memory and
block recall, respectively.
Three measures of visuo-spatial working memory were adminis-
tered. In the odd-one-out task, the child views three shapes, each in a
box presented in a row, and identies the odd-one-out shape. At the
end of each trial, the child recalls the location of each odd one out
shape, in the correct order, by tapping the correct box on the screen. In
the Mr. X task, the child is presented with a picture of two Mr. X
gures. The child identies whether the Mr. X with the blue hat is
holding the ball in the same hand as the Mr. X with the yellow hat. The
Mr. X with the blue hat may also be rotated. At the end of each trial,
the child recalls the location of each ball in the blue Mr. X's hand in
sequence by pointing to a picture with six compass points. In the
spatial recall task, the child views a picture of two arbitrary shapes
where the shape on the right has a red dot on it and identies whether
the shape on the right is the same or opposite of the shape on the left.
The shape with the red dot may also be rotated. At the end of each
trial, the child recalls the location of each red dot on the shape in
sequence by pointing to a picture with three compass points. Test
retest reliability is .88, .84, .79 for the odd-one-out, Mr. X, and spatial
recall, respectively. Raw scores for all tests are reported in the present
Test reliability of the English AWMA is reported here and test
validity is reported in Alloway, Gathercole, Kirkwood, and Elliott
(2008). The tests were translated and voice recorded into Italian by
native speakers. As normative data for Italian is currently being
collected, we report the intercorrelations between working memory
composite scores in Table 1 based on the present sample. The
between-construct coefcients were high (rs ranging from .35 to .66),
suggesting good internal validity of the measures purportedly tapping
four subcomponents of working memory. On this basis, the following
analyses were based on the four memory components as reported in
Alloway et al. (2006). The range of scores for all 12 memory tests is
provided in Table 2 and the skewness and kurtosis values represent
normal distributions for both age groups.
1.2.2. Mathematical skills
All students were administered Italian AC-MT test, which consists
of four tasks with different levels of difculty depending on the age of
the student (Cornoldi, Lucangeli, & Bellina, 2002). In the rst task,
Number Operations, the student solves basic operations such as
single-digit addition (maximum score= 8). The second test measures
Quantity Discrimination, and the student makes number comparison
Table 1
Correlations between all memory scores; partial correlations (controlling for age in
months) in upper triangle (n=206).
Measures VSTM VWM VS-STM VS-WM Vocabulary
Verbal short-term memory
1 .44 .33 .21 .35
Verbal working memory (VWM) .50 1 .50 .50 .36
Visuo-spatial short-term
memory (VS-STM)
.43 .58 1 .59 .30
Visuo-spatial working memory
.32 .57 .68 1 .33
Vocabulary .46 .48 .53 .50 1
Note: All correlations are signicant at the .005 level.
134 T.P. Alloway, M.C. Passolunghi / Learning and Individual Differences 21 (2011) 133137
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and identies bigger and smaller numbers in a set (maximum
score= 6). In the third test, Number Production, the student
translates numbers from one representation to another (e.g., 4
dozen= 48; maximum score = 6). In the nal test, Number Ranking,
the student orders number sequences from the smaller to the higher
and vice versa (maximum score = 11). The reliability is: Number
Operations .74 (7 years) and .68 (8 years); Quantity Discrimination
.69 (7 years) and .65 (8 years); number production .75 (7 years) and
.72 (8 years); and .88 (7 & 8 years) for number ranking. The
concurrent validity, reported in the AC-MT manual is also good: .84
(Cornoldi et al., 2002).
Arithmetical abilities were also assessed using the Numerical
Operations subtest from the Wechsler Objective Numerical Dimen-
sions (WOND, Wechsler, 1996). It consists of 10 four-item tests. The
rst set assesses the ability to write dictated numerals. The
subsequent sets include computational problems addition, subtrac-
tion, multiplication and division. The correlation the Arithmetic
subtest from the WOND and Number Operations test from the AC-
MT is .42 (with age partialed out), which suggests that they assess
different mathematical components. As with most standardized
assessments, there is a discontinue rule, which means that not all
sets were presented to the children in the present study and the
younger children only completed a smaller number of sets compared
to the older children. As there are currently no Italian standard scores
are available for this standardized test, raw scores are reported in the
present study.
1.2.3. Vocabulary
In order to assess general ability, the children were administered
the PMA (Thurstone & Thurstone, 1968) vocabulary subtest, which
consists of 60 items. In half the items, the child indicates which word
has the same meaning as the target word. In the other half, the child
indicates which picture corresponds to the target word. Raw scores
were converted into standard scores, with a mean of 100 and a
standard deviation of 15 based on an Italian sample. The test-
reliability is .95. The correlations between vocabulary and the
memory measures are provided in Table 1 and the partial correlation
coefecients indicate a moderate association (rs ranging from .30 to
2. Results
Descriptive statistics for the cognitive measures as a function of
age-group are shown in Table 2. The following patterns emerged: the
7-year-olds scored lower than the 8-year-olds in all measures. In order
to compare the working memory prole between age-groups, a
MANOVCA was performed on the four memory composite scores,
with age (in months) as a co-variate. The overall group term associated
with Hotelling's T-test was not signicant (FN1, η
p=.02), suggesting
that the memory prole did not differ signicantly between the 7 and
8-year-olds once age was partialed out.
2.1. Working memory, vocabulary, and mathematical skills
In order to investigate which memory component was linked to
mathematical skills in 7 and 8-year olds, a series of stepwise
regression analyses were conducted on the raw scores on the four
sub-tests from the AC-MT and the Arithmetic subtest from the WOND.
The vocabulary raw score and all four memory composite scores were
entered simultaneously with a stepwise function. This approach
allowed us to identify the best predictive variables for various
mathematical skills as a function of age. Model statistics, as well as
standardized beta values and t-statistics, are provided in Table 3.
For the 7-year olds, vocabulary accounted for signicant propor-
tion of variance (13%) across all mathematical skills: Quantity
Discrimination (10%); Number Ranking (23%); Number Production
(16%); Number Operations (12%); Arithmetic (13%). Of the four
memory measures, visuo-spatial short-term memory accounted for
signicant additional variance to Quantity Discrimination (14%) and
Number Production (21%). Verbal short-term memory accounted for
signicant additional variance in the Arithmetic test from the WOND
(17%); and verbal working memory uniquely predicted Number
Ranking (18%).
For the 8-year olds, vocabulary accounted for signicant propor-
tion of variance (13%) across some mathematical skills: Quantity
Discrimination (9%); Number Ranking (30%); Number Operations
(27%); Arithmetic (26%); but not Number Production. Of the four
memory measures, only visuo-spatial short-term memory accounted
for signicant additional variance in predicting scores in Number
Table 2
Descriptive statistics of raw scores for cognitive measures as a function of age group (7 and 8 years).
7 yrs (n=100) 8 yrs (n=154)
Min Max Skewness Kurtosis Mean SD Min Max Skewness Kurtosis Mean SD
Memory tests
Digit recall 16 32 .260 .380 23.02 3.58 13 35 .303 .800 25.22 3.55
Word recall 8 24 .678 .198 18.91 3.51 12 28 .759 .423 20.29 3.20
Nonword recall 7 26 .318 .314 16.32 4.55 9 31 .302 .786 18.30 3.94
Verbal STM 12 26 .171 .479 19.42 3.0 12 30 0 .157 21.27 2.74
Listening recall 3 16 .324 .364 8.57 2.77 5 18 .416 .058 10.29 2.66
Counting recall 7 24 .011 .133 15.01 3.72 6 25 .370 .768 16.45 4.15
Backward digit recall 3 18 .400 .018 9.69 2.93 6 28 .111 .897 11.31 3.71
Verbal WM 7 17 .211 .175 11.09 2.24 7 21 .549 .274 12.69 2.65
Dot matrix 10 29 .211 .444 17.95 3.35 12 33 .278 .143 21.73 4.0
Mazes memory 5 26 .206 .413 15.98 4.70 8 27 .911 .083 20.14 4.67
Block recall 7 26 .300 .177 17.47 3.91 11 33 .176 .262 20.50 4.16
Visuo-spatial STM 10 26 .398 .192 17.13 2.93 12 29 .132 .059 20.79 3.51
Odd one out 6 23 .119 .016 13.75 3.47 9 26 .358 .135 15.90 3.53
Mister X 0 17 .428 .479 7.47 3.72 1 19 .284 .377 9.65 3.82
Spatial recall 0 23 .154 .439 11.18 4.84 1 24 .365 .032 14.00 4.28
Visuo-spatial WM 4 20 .148 .369 10.80 3.19 6 19 .106 .642 13.18 3.03
Number skills tests
Number Operations 0 4 2.21 1.15 1 8 5.59 1.64
Quantity discrimination 1 6 5.38 1.22 0 6 5.42 1.16
Number production 0 6 3.60 1.63 0 6 5.58 1.02
Number ranking 0 11 8.36 2.44 1 11 8.78 1.83
Arithmetic (WOND) 1 12 10.18 1.66 12 22 19.10 2.23
Vocabulary 27 57 44.91 6.82 36 59 52.55 5.02
135T.P. Alloway, M.C. Passolunghi / Learning and Individual Differences 21 (2011) 133137
Author's personal copy
Ranking (23%); Number Production (10%); Number Operations (19%);
and Arithmetic test from the WOND (35%); but not Quantity
Discrimination. Verbal short-term memory and working memory
did not uniquely predict scores in any scores in the mathematical
tests. The ndings suggest an age-related difference in the contribu-
tion of memory to arithmetical abilities.
3. Discussion
The aim of the present study was to investigate the contributions
of working memory and vocabulary to mathematical skills in children.
The comparisons of the younger (7 years)and older (8 years) children
showed slightly different patterns in the contribution of memory to
mathematical skills and arithmetical abilities. Verbal memory pre-
dicted Number Ranking and Arithmetic skills in 7-year-olds, while
visuo-spatial short-term memory predicted these same skills in 8-
year olds. The latter also predicted performance in Quantity
Discrimination and Number Production in the younger group.
In line with previous research, verbal short-term memory was an
important predictor of performance in single-digit addition and
subtraction problems (e.g., Hecht, 2002; Seyler et al., 2003). However,
it did not predict scores in Number Operations, which may be due to
the fewer number of items that the 7-year-olds solved (4 items).
These items were also relatively easy and may have involved
information that was automatically activated as a result of frequent
repetition. Verbal working memory was uniquely linked to Number
Ranking, which required the student to order number sequences from
the smaller to the higher and vice versa. This task appeared to tap
executive resources as they had to hold the items in mind while
placing them in the correct numerical order.
The pattern of association between memory scores and mathe-
matical skills was slightly different for the eight-year-olds. In
particular, only visuo-spatial short-term memory accounted for
signicant additional variance in predicting the mathematical tests
(except for Quantity Discrimination). The importance of visuo-spatial
short-term memory ts well with evidence that it functions as a
mental blackboard to support number representation particularly
when problems are presented visually (Trbovich & LeFevre, 2003).
One issue worth addressing is the unique contribution of visuo-spatial
short-term memory, but not visuo-spatial working memory. One
possibility is this age group (78 years) may have drawn more on
executive resources when performing the visuo-spatial short-term
memory tasks (see Alloway et al., 2006; Cowan et al., 2005).
Inspection of the association between these two constructs for the
present sample conrms that they share almost 50% of their variance,
which is larger than any other of the memory constructs. Thus, given
the close relationship between these two constructs, it is possible that
the visuo-spatial short-memory tasks captured any additional
variance of the visuo-spatial working memory ones.
Vocabulary scores uniquely predicted performance on all mathe-
matical tests across the age groups, with the exception of Number
Production in eight-year-olds. There was not an age-difference in the
contribution of vocabulary to mathematical skills, which may be due
to the nature of the math tests used in the present study. As the older
cohort were presented with more items in some of the tests (e.g.,
Number Operations and Arithmetic) compared to the younger group,
they were exposed to new information which likely tapped general
ability. Indeed, the variance that the Vocabulary scores accounted for
in both these math tests was twice as much for the older group. A key
point is that short-term and working memory signicantly predicted
mathematical skills and arithmetical abilities after the variance
associated with vocabulary was accounted, which indicates that
working memory is not a proxy for intelligence and measures a
dissociable cognitive construct (Gathercole et al., 2006; Passolunghi,
Mammarella, & Altoè, 2008).
In summary, this exploratory study provides a useful starting
point that can add to existing research on the contributions of
working memory and vocabulary to different mathematical skills. A
novel and signicant nding was that even when differences in
vocabulary were statistically accounted, memory skills uniquely
predicted mathematical skills and arithmetical abilities. The pattern
of ndings reported in the present study can provide the rst step of
a series of subsequent investigations on underlying mechanisms
related to mathematical skills, such as phonological processing skills
(Hecht et al., 2001) and strategy use (Geary, Hamson, & Hoard,
Alloway, T. P. (2007). Automated Working Memory Assessment. London: Harcourt
Alloway, T. P., & Alloway, R. G. (2010). Investigating the predictive roles of working
memory and IQ in academic attainment. Journal of Experimental Child Psychology,
Alloway, T. P., & Gathercole, S. E. (2005). The role of sentence recall in reading and
language skills of children with learning difculties. Learning and Individual
Differences,15, 271282.
Alloway, T. P., Gathercole, S. E., Kirkwood, H. J., & Elliott, J. E. (2008). Evaluating the
validity of the Automated Working Memory Assessment. Educational Psychology,7,
Table 3
Stepwise regression analyses predicting numerical skills as a function of age group.
Dependant variables Age group Independent variables R2 ΔR2 df ΔFΒt
Quantity Discrimination (ACMT) 7 1 Vocabulary .10 1, 98 11.43 * .32 3.38*
2 Visuo-spatial STM .14 .04 1, 97 4.84* .21 2.12*
8 1 Vocabulary .09 1,104 10.44* .30 3.23*
Number Ranking (AC-MT) 7 1 Verbal WM .18 1, 98 21.53* .42 4.64*
2 Vocabulary .23 .05 1, 97 6.87* .25 2.62*
8 1 Visuo-spatial STM .23 1,104 31.15* .48 5.58*
2 Vocabulary .30 .07 1,103 10.28* .29 3.21*
Number Production (AC-MT) 7 1 Vocabulary .16 1, 98 18.07* .40 4.25*
2 Visuo-spatial STM .21 .05 1, 97 6.75* .25 2.60*
8 1 Visuo-spatial STM .10 1,104 11.74* .32 3.43*
Number Operations (AC-MT) 7 1 Vocabulary .12 1,98 12.73* .34 3.57*
8 1 Visuo-spatial STM .19 1,104 25.02* .44 5.00*
2 Vocabulary .27 .08 1,103 10.72* .30 3.27*
3 Verbal STM .30 .03 1,102 4.78* .20 2.19*
Arithmetic (WOND) 7 1 Vocabulary .13 1, 98 15.07* .37 3.88*
2 Verbal STM .17 .04 1, 97 4.26* .21 2.07*
8 1 Vocabulary .26 1,104 37.12* .51 6.09*
2 Visuo-spatial STM .35 .09 1,103 14.41* .33 3.80*
Note: STM=short-term memory; WM =working memory; * pb.05; Β=standardized beta values.
136 T.P. Alloway, M.C. Passolunghi / Learning and Individual Differences 21 (2011) 133137
Author's personal copy
Alloway, T. P., Gathercole, S. E., & Pickering, S. J. (2006). Verbal and visuo-spatial short-
term and working memory in children: are they separable? Child Development,77,
Alloway, T. P., Gathercole, S. E., Willis, C., & Adams, A. M. (2004). A structural analysis of
working memory and related cognitive skills in early childhood. Journal of
Experimental Child Psychology,87,85106.
Baddeley, A. D. (2000). The episodic buffer: A new component of working memory?
Trends in Cognitive Sciences,4, 417423.
Baddeley, A. D., Emslie, H., Kolodny, J., & Duncan, J. (1998). Random generation and the
executive control of working memory. The Quarterly Journal of Experimental
Psychology,51A, 819852.
Baddeley, A. D., & Logie, R. H. (1999). The multiple-component model. In A. Miyake & P.
Shah (Eds.), Models of working memory: Mechanisms of active maintenance and
executive control (pp. 2861). New York: Cambridge University Press.
Bayliss, D. M., Jarrold, C., Gunn, M. D., & Baddeley, A. D. (2003). The complexities of
complex span: Explaining individual differences in working memory in children
and adults. Journal of Experimental Psychology: General,132,7192.
Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children's
mathematics ability. Shifting, inhibition and working memory. Developmental
Neuropsychology,19, 273293.
Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child
Psychology and Psychiatry,46,318.
Cain, K., Oakhill, J., & Bryant, P. (2004). Children's reading comprehension ability:
concurrent prediction by working memory, verbal ability and component skills.
Journal of Educational Psychology,96,3142.
Cornoldi, C., Lucangeli, D., & Bellina, M. (2002). AC-MT test di valutazione delle abilità di
calcolo. Erickson: Trento.
Cowan, N., Elliott, E. M., Saults, J. S., Morey, C. C., Mattox, S., Hismjatullina, A., & Conway,
A. R. A. (2005). On the capacity of attention: Its estimation and its role in working
memory and cognitive aptitudes. Cognitive Psychology,51,42100.
D'Amico, A., & Guarnera, M. (2005). Exploring working memory in children with low
arithmetical achievement. Learning and Individual Differences,15, 189202.
Fürst, A. J., & Hitch, G. J. (2000). Different roles for executive and phonological
components of working memory in mental arithmetic. Memory & Cognition,28,
Gathercole, S. E., Alloway, T. P., Willis, C., & Adams, A. M. (2006). Working memory in
children with reading disabilities. Journal of Experimental Child Psychology,93,
Geary, D. C. (1990). A componential analysis of an early learning decit in mathematics.
Journal of Experimental Child Psychology,49, 363383.
Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical
cognition: A longitudinal study of process and concept decits in children with
learning disability. Journal of Experimental Child Psychology,77, 236263.
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identication and interventions for
students with mathematics difculties. Journal of Learning Disabilities,38,
Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition
of multi-digit addends. Current Psychology of Cognition,13, 207245.
Hecht, S. A. (2002). Counting on working memory in simple arithmetic when counting
is used for problem solving. Memory & Cognition,30, 447455.
Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations
between phonological processing abilities and emerging individual differences in
mathematical. Journal of Experimental Child Psychology,79(2), 192227.
Holmes, J., & Adams, J. W. (2006). Working memory and childrens mathematical skills:
Implications for mathematical development and mathematics curricula. Educa-
tional Psychology,26, 339366.
Jensen, A. R. (1980). Bias in mental testing. New York: Free Press.
Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in
arithmetic problem solving. Memory & Cognition,22, 395410.
McLean, J. F., & Hitch, G. H. (1999). Working memory impairments in children with
specic mathematics learning difculties. Journal of Experimental Child Psychology,
74, 240260.
Nation, K., Adams, J. W., Bowyer-Crane, C. A., & Snowling, M. J. (1999). Journal of
Experimental Child Psychology,73, 139158.
Noël, M. -P., Désert, M., Aubrun, A., & Seron, X. (2001). Involvement of short-term
memory in complex mental calculation. Memory & Cognition,29,3442.
Passolunghi, M. C., & Mammarella, I. C. (2010). Spatial and visual working memory
ability in children with difculties in arithmetic word problem-solving. European
Journal of Cognitive Psychology, 22, 944963.
Passolunghi, M. C., Mammarella, I., & Altoè, G. (2008). Cognitive abilities as precursors
of the early acquisition of mathematical skills during rst through second grades.
Developmental Neuropsychology,33,3.
Passolunghi, M. C., Vercelloni, B., & Schadee, H. (2007). The precursors of mathematics
learning: working memory, phonological ability and numerical competence.
Cognitive Development,22, 165184.
Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early
arithmetic. Journal of Experimental Child Psychology,91, 137157.
Reuhkala, M. (2001). Mathematical skills in ninth-graders: Relationship with visuo-
spatial abilities and working memory. Educational Psychology,21, 387399.
Seitz, K., & Schumann-Hengsteler, R. (2000). Mental multiplication and working
memory. European Journal of Cognitive Psychology,12, 552570.
Seitz, K., & Schumann-Hengsteler, R. (2002). Phonological loop and central executive
processes in mental addition and multiplication. Psychologische Beiträge,44,
Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary subtraction. Journal of
Experimental Psychology. Learning, Memory, and Cognition,29, 13391352.
Siegel, L. S. (1988). Evidence that IQ scores are irrelevant to the denition and analysis
of reading-disability. Canadian Journal of Psychology,42, 201215.
Stothard, S. E., & Hulme, C. (1992). Reading comprehension difculties in children.
Reading and Writing: An Interdisciplinary Journal,4, 245256.
Swanson, H. L., & Saez, L. (2003). Memory difculties in children and adults with
learning disabilities. In H. L. Swanson, S. Graham, & K. R. Harris (Eds.), Handbook of
learning disabilities (pp. 182198). New York: Guildford Press.
Thevenot, C., & Oakhill, J. (2005). The strategic use of alternative representations in
arithmetic word problem solving. The Quarterly Journal of Experimental Psychology,
58A, 13111323.
Thurstone, N. L., & Thurstone, T. G. (1968). PMA Primary Mental ability (trad. it. Batteria
Primaria di Abilità). Firenze: Organizzazioni Speciali.
Trbovich, P. L., & LeFevre, J. A. (2003). Phonological and visual working memory in
mental addition. Memory & Cognition,31, 738745.
Wechsler, D. (1996). Wechsler Objective Numerical Dimensions. London: Harcourt
137T.P. Alloway, M.C. Passolunghi / Learning and Individual Differences 21 (2011) 133137
... Other studies have examined WMC concerning topics such as math ability, math anxiety, gender (H. Miller & Bichsel, 2004), IQ (Alloway & Passolunghi, 2011), and mathematical reasoning (Palengka et al., 2021). However, it is very rare to find researches that examine WMC with mathematical problem-solving based on the Polya's steps. ...
... WMC increases, the students' mathematical abilities also tend to increase. The results of this study are in line with the results of related studies that have examined the relationship between children's working memory and their learning achievement in various fields, some of which being mathematics (Alloway & Passolunghi, 2011;Friso-Van Den Bos et al., 2013;H. Miller & Bichsel, 2004) which stated that there is a relationship between working memory and mathematical achievement. ...
p style="text-align: justify;">Problem-solving process requires information processing, and the information processing is related to working memory capacity (WMC). This study aims to determine the effect of WMC on students' mathematical abilities and to describe the ability of the students with high and low WMC in solving mathematical problems. This research used mixed method with Sequential Explanatory Design. The quantitative data were collected through the provision of OSPAN tasks and math tests to 58 students aged 15-17 years, while the qualitative data were collected through interviews based on mathematical problem-solving tasks. The results showed that WMC had a significant effect on students' mathematical abilities (R=0.536; p=0.000). Researchers found differences in students' mathematical problem-solving abilities with high and low WMC. Students with high WMC can remember and manage information well which supports the determination of more advanced problem-solving strategies and have better attention control so that they find varied appropriate solutions. Students with low WMC experienced decreased attention control as the complexity of the tasks increased, missed important information in problem solving strategies, and did not recheck their work, leading to wrong solution/answer. The mathematical performance of students with high WMC outperformed the mathematical performance of students with low WMC.</p
... Collectively, children with ADHD had experienced di culties in different mathematic skills. Evidence demonstrates that mathematics is closely associated with executive functions such as attention [11,13] and working memory [14,15]. However, the contributions of processing speed (PS) to mathematic performance are relatively understudied, particularly in children with impaired PS like those with ADHD [16,17]. ...
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ADHD is associated with processing speed (PS) deficits and mathematic difficulties. However, the relationships between PS and mathematics in children with ADHD were understudied. The current study investigated the contributions of PS to math fluency (MF) and tested the mediating role of working memory (WM) in the relationships between PS and MF in children with ADHD. Seventy-eight third to fifth graders (ADHD children, n = 52; Typically developing children, n = 26) were tested on their PS (perceptual, graphomotor-cognitive, and phonological), MF, and WM using standardized measures. Hierarchical regression analyses showed that only graphomotor-cognitive PS significantly predicted MF in children with ADHD. Besides, mediation analyses revealed that graphomotor-cognitive PS had both direct and indirect effects via WM on MF. Although such results suggested that slow PS contributed to impaired WM, the current study is unable to determine the directionality of effects due to the nature of research design.
... A further 10 studies were initially considered to meet inclusion criteria, however, on closer inspection they were excluded due to key methodological differences that prevented comparison with other included studies. Of these 10 'near-miss' studies: three reported only partial correlations (rather than bivariate correlations provided by the majority of included studies) (DeNigris & Brooks, 2018;Henry & Maclean, 2003;Rasmussen et al., Focal colours are common chromatic colours (e.g., blue, green), and non-focal colours are hues between common colours (e.g., turquoise, aqua) 2009), two reported a composite memory score for analyses (where such composites comprised memory tasks that were judged to assess different aspects of visual memory, such as a spatio-temporal span task and a visuo-perceptual array task) (Lum et al., 2012;Vukovic et al., 2014), two reported age-standardised scores (rather than raw scores) (Alloway & Elsworth, 2012;Metcalfe & Stratford, 1986), one used a mixed vocabulary task (assessing both receptive and expressive vocabulary) (Alloway & Passolunghi, 2011), one combined receptive and expressive vocabulary scores for analyses (Joseph et al., 2005), and one reported z-scores (rather than raw scores) (Hooper et al., 2011). Characteristics and results of these 10 'near miss' studies are provided in supplemental document (Table S5). ...
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Although attention and early associative learning in preverbal children is predominantly driven by rapid eye-movements in response to moving visual stimuli and sounds/words (e.g., associating the word “bottle” with the object), the literature examining the role of visual attention and memory in ongoing vocabulary development across childhood is limited. Thus, this systematic review and meta-analysis examined the association between visual memory and vocabulary development, including moderators such as age and task selection, in neurotypical children aged 2-to-12 years, from the brain-based perspective of cognitive neuroscience. Visual memory tasks were classified according to the visual characteristics of the stimuli and the neural networks known to preferentially process such information, including consideration of the distinction between the ventral visual stream (processing more static visuo-perceptual details, such as form or colour) and the more dynamic dorsal visual stream (processing spatial temporal action-driven information). Final classifications included spatio-temporal span tasks, visuo-perceptual or spatial concurrent array tasks, and executive judgment tasks. Visuo-perceptual concurrent array tasks, reliant on ventral stream processing, were moderately associated with vocabulary, while tasks measuring spatio-temporal spans, associated with dorsal stream processing, and executive judgment tasks (central executive), showed only weak correlations with vocabulary. These findings have important implications for health professionals and researchers interested in language, as they advocate for the development of more targeted language learning interventions that include specific and relevant aspects of visual processing and memory, such as ventral stream visuo-perceptual details (i.e., shape or colour).
... show positive correlations (Alloway & Passolunghi, 2011), neither is an isomorphic construct (Nakamura, 2015). What this means is that while intelligence, a fundamentally explicit cognitive ability with a proven relationship with working memory capacity, is hypothesized (A. S. Reber, Walkenfeld, & Hernstadt, 1991) and found to have no relationship with implicit abilities, it does not preclude the existence of a relationship between implicit abilities and working memory, due to the independent operative nature of the latter. ...
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Is there is a common implicit ability analogous to I.Q. (i.e., a latent factor determined by strong inter correlations of psychometric measures)? Based on my Ph.D. research, there is just enough evidence to argue both ways.
... Many researchers have repeatedly demonstrated the importance of working memory for mathematical achievement in typically developing (TD) children (Alloway & Passolunghi, 2011;Berg, 2008;Bull et al., 2008 for a review, see Raghubar et al., 2010). Working memory is the ability to store information while doing other cognitively draining tasks (Gathercole et al., 2006), and many studies have shown that poor working memory is a primary cognitive signature of dyscalculia (Allen et al., 2020;Andersson, 2008;Swanson & Sachse-Lee, 2001). ...
Developmental dyscalculia (DD) has long been thought to be determined by multiple components. Dyscalculia has high comorbidity with other learning and developmental disabilities, including reading and writing disorders, attention deficits, and problems in visual/spatial skills, short memory, and working memory. This study aims to assess prevalence rates for isolated as well as comorbid DD in a sample of Italian-speaking children. In addition, we studied the neuropsychological profile of children with isolated or combined dyscalculia. We tested 380 children (176 males and 204 females) between the ages of 8.17 and 9.33 years using an extensive battery to determine the neuropsychological profile. The assessment included an arithmetic battery and nonverbal intelligence, short-term memory, reading, and writing tests. The results indicated that children with DD more frequently have a reading disorder and writing disorder. They also have a lower nonverbal intelligence quotient (IQ) and obtain significantly lower scores in short-term memory tests and on a visuospatial skills questionnaire. They also had significantly higher scores (indicative of greater attentional difficulties) in the Conners subscale for attentional problems. Children with DD present different cognitive and neuropsychological profiles.
This chapter reviews research on the efficacy of training Working Memory (WM) in an educational context. We begin with a brief description of WM, its relation to classroom constructs, an overview of WM training programs, followed by classroom recommendations pertaining to several case studies. We characterize WM training programs into two categories: those that are narrow in scope and those that are broad in scope. Narrow-scope WM training programs are similar to a WM test, while broad-scope WM training programs train WM in the context of broader abilities, such as executive function, attention, or learning skills. Additionally, we discuss the efficacy of WM training with respect to near- or far-transfer effects. Near transfer refers to improvements that are similar to the training program, such as improvements in WM tasks, while far-transfer effects refer to improvements in skills related to the area of training, such as other executive function skills such as inhibition, updating, and planning, as well as attention and fluid intelligence (IQ). We also report whether transfer effects are short-lived or long-lasting (maintenance effects). Finally a discussion regarding implementing WM training in the classroom and future directions are provided.
Background Previous research suggests that visuospatial working memory (WM) is a unique predictor of mathematics. However, evidence from neuropsychology and cognitive studies suggests dissociations between visual and spatial WM. Procedure We examined the differential relationships between visual and spatial WM with mathematics using a new task that 1) utilized the same paradigm across visual and spatial tasks and 2) required executive WM. Main findings We found that our new spatial WM task related to mathematics scores while visual WM did not. Spatial WM related to mathematics scores for fourth-graders and not second graders, consistent with previous findings on the relationship between spatial skills and mathematics as mathematics becomes more complex. No relationship was found between spatial WM and reading scores at either grade level. Conclusions Our results highlight the dynamic relationship between WM components and mathematics over the elementary school years and suggest that spatial WM is a unique predictor of mathematics starting from middle childhood.
Conference Paper
This study aims to determine the relationship among working memory capacity (WMC) and students' mathematical ability, then to describe the high and low students' working memory capacity in solving mathematical problems. This research mixed method uses the Sequential Explanatory Design (SED) model with the research sample are 52 students of 13-14 years old. Instruments of research are OSPAN task, the mathematical test, and a mathematical problem-solving task. Technique of data analysis used quantitative and qualitative method. The results point out that there was a significant positive relationship between working memory capacity and students' mathematical ability (R = 0.51 and P = 0.00011). Students with the high working memory capacity tend to be quick to understand problems and implement a solution plan, their written completion steps are quite simple, and they have other strategies for solving problems. Students with low working memory capacity tend to take longer to understand the problem and need more time to implement the solution plan, and do not have other strategies to solve the problem.
The essence and reason for the inability to master mathematics are described as a lack of working memory. This paper describes two main approaches to solving the problem of teaching mathematics to students with learning difficulties in mathematics (MLD): (1) training working memory and (2) reducing the load on working memory in the instructional process. It was found that the results of the first approach are ambiguous: Training working memory leads to its improvement, which is confirmed by the test results but may not lead to improvement of the mathematical learning process associated with the student’s working memory. This justifies the primacy of the second approach. Both previously known methods for reducing the load on working memory in mathematics instruction are presented. A computer-based mathematics learning system developed by the author aims at automating basic computational skills (arithmetics, trigonometry, geometry). It is explained how to work with the developed computer-assisted learning system, which is based on the method of interval repetitions, and empirical data on the results of the system implementation are given.
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This study examined the contributions of the different components of the working memory (WM) model to a range of mathematical skills in children, using measures of WM function that did not involve numerical stimuli. A sample of 148 children (78 Year 3, mean age 8 years and 1 month, and 70 Year 5 pupils, mean age 9 years and 10 months) completed WM measures and age‐appropriate mathematics tests designed to assess four mathematical skills defined by the National Curriculum for England. Visuo‐spatial sketchpad and central executive, but not phonological loop, scores predicted unique variance in children's curriculum‐based mathematical attainment but the relative contributions of each component did not vary much across the different skills. Subsequently, the mathematics data were re‐analysed using cluster analysis and new performance‐related mathematics factors were derived. All three components of WM predicted unique variance in these performance‐related skills, but revealed a markedly distinct pattern of associations across the two age groups. In particular, the data indicated a stronger role for the visuo‐spatial sketchpad in the younger children's mathematics performance. We discuss our findings in terms of the importance of WM in the development of early mathematical ability.
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Although various studies support the multicomponent nature of visuospatial working memory, to date there is no general consensus on the distinction of its components. A difference is usually proposed between visual and spatial components of working memory, but the individual roles of these components in mathematical learning disabilities remains unclear. The present study aimed to examine the involvement of visual and spatial working memory in poor problem-solvers compared with children with normal level of achievement. Fourth-grade participants were presented with tasks measuring phonological loop, central executive, and visual versus spatial memory. In two separate experiments, both designed to distinguish visual and spatial component involvement, poor problem-solvers specifically failed on spatial—but not visual or phonological—working memory tasks. Results are discussed in the light of possible working memory models, and specifically demonstrate that problem-solving ability can benefit from analysis of spatial processes, which involves ability to manipulate and transform relevant information; instead, no benefit is gained from the analysis of visual pictorial detail.
In the present study, the relationship between working memory (WM ) capacity, particularly visuo-spatial working memory (VSW M), the ability to mentally rotate three-dimensional objects and mathematical skills was investigated. In Experiment 1, the two VSW M components, viz. static visuo-spatial storage component and dynamic visuo-spatial storage component, were examined separately. The ability to retain gradually increasing square patterns (static VSW M capacity), the ability to retain movement sequences (dynamic VSWM capacity) and the ability to mentally rotate abstract figures were related to mathematical skills (n = 0.44 - 0.57). In Experiment 2, the contribution of other W M components to mathematical skills was examined. The results suggest that performances in the static visuo-spatial task (visual matrix pattern task) and in the mental rotation task are related to a mathematics test score (n = 0.42 - 0.58). Other WM components, viz. the central executive and phonological WM , did not relate to mathematical skills in the present study.
This paper is concerned with the role of working memory resources in mental multiplication. In two experiments a dual-task paradigm was used. In the first experiment neutral tapping was contrasted to three modalityspecific secondary tasks: Irrelevant speech and articulatory suppression were used to disrupt the phonological loop and a visuo-spatial tapping was used to disrupt the visuo-spatial sketchpad. Multiplication sums needed to be solved mentally and results needed to be spoken aloud. Sums varied in difficulty (easy, e.g., 3 x 4 =, difficult, e.g., 8 x 17 =). Results from the first experiment revealed declines in performance on difficult sums under articulatory suppression but no interference effect for easy sums. To investigate the role of central executive processes, a second experiment extended the range of interference conditions to a central executive interference task (random letter generation). Now articulatory suppression and random generation caused a decrease of performance on difficult sums. In addition, performance on easy sums was negatively impacted by random letter generation as well. We infer that solving complex multiplication sums demands phonological loop and central executive processes, whereas retrieving numerical facts in solving simple multiplication sums requires only central executive processes. We found no evidence of modality-specific access to numerical facts stored in long-term memory.
Working memory is currently a 'hot' topic in cognitive psychology and neuroscience. Because of their radically different scopes and emphases, however, comparing different models and theories and understanding how they relate to one another has been a difficult task. This volume offers a much-needed forum for systematically comparing and contrasting existing models of working memory. It does so by asking each contributor to address the same comprehensive set of important theoretical questions on working memory. The answers to these questions provided in the volume elucidate the emerging general consensus on the nature of working memory among different theorists and crystallize incompatible theoretical claims that must be resolved in future research. As such, this volume serves not only as a milestone that documents the state-of-the-art in the field but also as a theoretical guidebook that will likely promote new lines of research and more precise and comprehensive models of working memory.
Investigates the role of subsystem-specific working memory resources in mental arithmetic. The dual-task paradigm was used to present addition and multiplication sums with subsystem-specific concurrent tasks. In the 1st experiment, neutral tapping (NT) was contrasted to articulatory suppression (AS), canonical number articulation (CN), and random number generation (RN) as secondary tasks. AS primary task sums (2 levels of difficulty) had to be solved mentally, and results had to be spoken out loud. AS mainly affected difficult addition sums, CN decreased performance on easy and difficult addition sums and difficult multiplication sums, and RN produced interference on all sums. In a 2nd experiment researchers used random letter generation (RL) and canonical letter articulation (CL) in addition to NT and AS in order to rule out effects of semantic interference. A result-pattern comparable to the 1st experiment was observed. It is concluded that the elementary process of fact retrieval requires central executive resources, that temporarily storing partial results relies on phonological loop resources, and that keeping track of a carry operation is monitored by the central executive. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Examined the role of visuo-spatial working memory in the solution of mental addition problems in 3 experiments with a total of 12 adults. A standard task was devised in which Ss were required to mentally summate 2 3-digit addends presented either visually or auditorily. Exp 1 demonstrated that during mental addition both spatial interference and articulatory suppression were each capable of disrupting the working storage of initial problem information. While visual interference failed to disrupt performance in zero-carry problems, when the working retention of partial results and carrys was examined, evidence of selective interference was found. Results converge on the view that mental addition involves the deployment of a working memory constellation in which both the visuo-spatial scratch pad and the articulatory loop participate. (PsycINFO Database Record (c) 2012 APA, all rights reserved)