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1. 3/2/2017 Working memory and literacy as predictors of performance on algebraic word problems
http://www.sciencedirect.com.ezproxy.utm.my/science/article/pii/S0022096504001055?np=y&npKey=1b0fa3d5d145dc83e09b6556563c96f040c5e6d6b7fc777fa8… 1/34
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http://dx.doi.org.ezproxy.utm.my/10.1016/j.jecp.2004.07.001
Journal of Experimental Child Psychology
Volume 89, Issue 2, October 2004, Pages 140–158
120043||
Working memory and literacy as predictors of performance on
algebraic word problems
Kerry Leea, ,
, SweeFong Ngb
, EeLynn Nga
, ZeeYing Lima
Show more
Abstract
Previous studies on individual differences in mathematical abilities have shown that
working memory contributes to early arithmetic performance. In this study, we extended
the investigation to algebraic word problem solving. A total of 151 10yearolds were
administered algebraic word problems and measures of working memory, intelligence
quotient (IQ), and reading ability. Regression results were consistent with findings from
the arithmetic literature showing that a literacy composite measure provided greater
contribution than did executive function capacity. However, a series of path analyses
showed that the overall contribution of executive function was comparable to that of
literacy; the effect of executive function was mediated by that of literacy. Both the
phonological loop and the visual spatial sketchpad failed to contribute directly; they
contributed only indirectly by way of literacy and performance IQ, respectively.
Keywords
Shortterm memory; Reading comprehension; Executive functions; Cognitive
processes; Mathematical ability; Problem solving
Introduction
Previous studies have shown that there are significant age and individual differences in
mathematical abilities. In an early study, Cockcroft (1982) reported sameage differences
that varied by the equivalence of a 7year achievement range. A more recent study
showed that the magnitude of individual differences varied across countries, with
variation in Singapore being smaller than that in most other countries (Singapore Ministry
of Education & Research & Testing Division, 2000).
Investigations into the causes of individual differences have considered a wide variety of
contributory factors such as biological (for a review, see Geary, 1993) and motivational
(e.g., Ashcraft, Kirk, & Hopko, 1998). Recently, an area of active research has focused on
the role of working memory. Working memory is involved in shortterm memory storage,
reasoning, problem solving, and other higher cognitive tasks that require simultaneous
representation and manipulation of information. In this study, we examined the relation
among working memory, reading abilities, intelligence, and children’s abilities to solve
algebraic word problems.
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10. 3/2/2017 Working memory and literacy as predictors of performance on algebraic word problems
http://www.sciencedirect.com.ezproxy.utm.my/science/article/pii/S0022096504001055?np=y&npKey=1b0fa3d5d145dc83e09b6556563c96f040c5e6d6b7fc777fa… 10/34
**
Path Model 1 Model 2 Model 3
CE → Literacy .36**
.36**
.36**
CE → Performance IQ .23**
.23**
.23**
VS → Performance IQ .31**
.31**
.31**
PL → MP −.04 — —
CE → MP .21**
— .21**
VS → MP .06 — —
Literacy → MP .36**
.47**
.36**
Performance IQ → MP .32**
.37**
.33**
Note. PL, phonological loop component; CE, central executive component; VS, visual spatial component;
MP, mathematical performance.
p < .01.
In summary, Model 3 provided the most parsimonious fit for the data. Again, we reran this
model using only data from the nine algebraic questions. The overall pattern was the
same. Taken together, these analyses showed that the only working memory component
that contributed directly to mathematical performance was the central executive
(standardized direct effect = .21). In addition, it contributed to mathematical performance
indirectly by way of literacy and performance IQ. Apart from the central executive, both
literacy and performance IQ contributed to mathematical performance. The standardized
total effect (i.e., the direct effect combined with the two indirect effects) of the central
executive (.42) was larger than that of both literacy (total effect = .36) and performance IQ
(total effect = .33).
Discussion
The findings showed reliable and moderate to strong correlations between all predictors
and mathematical performance. Children who had greater storage and greater executive
function capacities were better able to perform the mathematical problems. Similarly,
children with higher performance IQ and better reading and vocabulary abilities
performed better on the mathematical problems. As expected, many of the predictor
variables were intercorrelated. Results from the standard regression showed that after
such intercorrelations were controlled, the central executive, performance IQ, and
literacy measures provided unique contributions to the prediction of mathematical
performance. When all predictor variables were used, they accounted for 49% of
variation in mathematical performance.
The contribution of executive function
Findings on the contribution of executive function resemble those reported in earlier
studies. Compared with Bull and Scerif (2001), for example, both studies found that
executive function measures exhibited strong bivariate correlation with mathematical
performance. When literacy and IQ were taken into account, the contribution of executive
function was attenuated but remained reliable. In both studies, 2 to 3% of total variation in
mathematical performance could be uniquely attributed to central executive capacity.
Although reliable, direct executive function contribution was modest and smaller than
that of literacy. Given the complexity of algebraic word problems, a greater reliance on
executive function was expected. This is especially the case when most children found
the mathematical test challenging; the mean performance score was quite low.
There are several explanations for the contribution of working memory being lower than
expected. First, the WMTBC employed a span approach to measure capacity across the
three components. For executive function, three tasks were used: listening span,
counting span, and backward digit span. All three measures indexed capacity to store
and process simultaneously. In contrast, Bull and Scerif (2001) used measures that
targeted four aspects of executive function: perseveration, inhibition efficiency, capacity,
and coordination. Although the various measures were intercorrelated, the first three
contributed uniquely to mathematical performance. One possible implication of their
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