This article provides an overview of the relationships
among working memory, math performance, and math
anxiety. We provide examples from the mathematical
cognition literature to show: the critical role of working
memory in performing arithmetic and math; the relation-
ship between math performance and math anxiety, espe-
cially on standardized math achievement tests; and finally,
the way that math anxiety compromises the functioning
of working memory when people do arithmetic and math.
We conclude with some predictions concerning the risk
factors for math anxiety, and with some of the educational
implications of this work. See Ashcraft and Ridley (2005)
and Ashcraft, Krause, and Hopko (2007) for full-length
treatments of these issues. Excellent summaries of the
entire field of mathematical cognition can be found in
Campbell (2005).

We begin with a statement concerning just one justifi-
cation (of many) for this work. Math and science are in the
headlines these days, with research-based reports about
the relatively poor job American schools do in teaching
math and science, and the depressingly substandard job
many students are doing in mastering these topics. No one
doubts the importance of math and science to the work-
force in a technological society, or their importance in
general to an educated populace. So there is a general,
undeniable need for investigations about the learning and
mastery of math. And from a disciplinary perspective, the
rich complexity of math in all its facets suggests that it
should be an interesting topic for cognitive psychology
to address, and a critical one in any discussion of the rel-
evance of cognitive psychology to education.

Working Memory and Math Performance
Considerable evidence has appeared in the past 10 to

15 years concerning the vital role that working memory
plays in mathematical cognition. In LeFevre, DeStefano,
Coleman, and Shanahan’s (2005) view, the literature now
supports a clear generalization concerning the important
positive relationship between the complexity of arithmetic
or math problems and the demand on working memory for
problem solving. One aspect of this relationship involves
the numerical values being manipulated, and one aspect
examines the total number of steps required for problem
solution. We take these in turn.

It is now clear that working memory is increasingly
involved in problem solving as the numbers in an arith-
metic or math problem (the “operands”) grow larger. The
benchmark effect in this area is the problem-size effect,
the empirical result that response latencies and errors in-
crease as the size of the operands increases: For example,
6 7 or 9 6 will be answered more slowly and less
accurately than 2 3 or 4 5 (see Zbrodoff & Logan’s
2005 review). Part of this effect, we have argued, is due
to the structure of the mental representation of arithme-
tic facts in long-term memory, and the inverse relation-
ship between problem size and problem frequency—for
example, in textbooks (e.g., Hamann & Ashcraft, 1986).
That is, larger arithmetic problems simply occur less fre-
quently, and hence are stored in memory at lower levels of
strength (see Siegler & Shrager, 1984, for a comparable
approach); this is similar in most respects to the standard
word-frequency effect found in language processing re-
search. A second part of the effect, documented in the

243 Copyright 2007 Psychonomic Society, Inc.

Working memory, math performance,
and math anxiety

MARK H. ASHCRAFT AND JEREMY A. KRAUSE
University of Nevada, Las Vegas, Nevada

The cognitive literature now shows how critically math performance depends on working memory, for any
form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric litera-
ture is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious
avoid math: They avoid elective coursework in math, both in high school and college, they avoid college majors
that emphasize math, and they avoid career paths that involve math. We go beyond these psychometric relation-
ships to examine the cognitive consequences of math anxiety. We show how performance on a standardized
math achievement test varies as a function of math anxiety, and that math anxiety compromises the functioning
of working memory. High math anxiety works much like a dual task setting: Preoccupation with one’s math
fears and anxieties functions like a resource-demanding secondary task. We comment on developmental and
educational factors related to math and working memory, and on factors that may contribute to the development
of math anxiety.

Psychonomic Bulletin & Review
2007, 14 (2), 243-248

M. H. Ashcraft, mark.ashcraft@unlv.edu

244 ASHCRAFT AND KRAUSE

past 10 years, is the increasing tendency for larger op-
erand problems to be solved via some nonretrieval pro-
cess, whether it be counting, reconstruction from known
problems, or other strategies (see, e.g., Campbell & Xue,
2001; LeFevre, Sadesky, & Bisanz, 1996). Because non-
retrieval processing is invariably found to be slower and
more error prone than memory-based retrieval, the occur-
rence of strategy-based trials will slow down overall re-
sponse latencies, especially for larger problems. Critically
for the present discussion, strategy- or procedure-based
performance will rely far more heavily on the resources of
working memory in comparison with performance based
on relatively automatic memory retrieval.

We illustrate this with a series of experiments reported
in Seyler, Kirk, and Ashcraft (2003). In this work, we tested
college adults on the “basic facts” of subtraction—that is,
the inverses of the addition facts 0 0 up to 9 9. As
shown in Figure 1, there was a gently increasing problem-
size profile on response latency up to 10 n problems,
but then a dramatic increase in reaction times (RTs) be-
ginning with 11 n problems; error rates jumped from
below 5% to the 10%–22% range at the same point. The
dramatic change in the performance profiles suggested
strongly that the larger subtraction problems were being
solved via strategies. To test this possibility, we repeated
the study, asking participants to answer the question “How
did you solve the problem?” after each trial. The reported
incidence of strategy use matched the RT and error pro-
files very closely; strategy use was reported an average of
3% of the time on small subtraction problems, but on 33%
of the trials with large problems. On this evidence, simple

subtraction is heavily reliant on strategy use, a pattern
that should disadvantage participants if they are laboring
under limited working memory resources.

To document this f inal prediction, we tested simple
subtraction in a dual task setting: Participants held two,
four, or six random letters in working memory while per-
forming the subtraction; they then had to report the letters
in serial order. The dual task led to a significant decrement
in performance, as measured by accuracy of letter recall.
Importantly, this decrement was especially pronounced
for the large subtraction problems, those that relied heav-
ily on strategies rather than on retrieval. And the pattern
was exaggerated when participants’ own working memory
capacity was considered. There was substantially more in-
terference with letter recall for the low-working-memory-
span participants (a 56% error rate in the most difficult
condition) than for the medium- or high-span groups (re-
spectively, 46% and 31% error rates; Seyler et al., 2003,
Figure 7). In short, there was an increasing cost of the
dual task requirement for participants with lower work-
ing memory capacity. Simple subtraction, an arithmetic
operation introduced routinely in second grade, has a
substantial working memory component to it, especially
because even adults continue to rely heavily on strategy-
based processing instead of memory retrieval. Such reli-
ance disadvantages participants whose working memory
is occupied by a secondary task, and also those whose
working memory capacity is low.

The important point here is that strategy-based solu-
tions are not just slower, but far more demanding on work-
ing memory, whereas memory retrieval is usually found
to be a fast and relatively automatic process, with little
or no demand on working memory resources. Reports
consistent with this generalization are now common—for
example, work showing the dramatic decline in latencies
and working memory involvement as a function of prac-
tice on difficult math (Beilock, Kulp, Holt, & Carr, 2004;
Tronsky, 2005).

Similarly, the number of steps in a problem solution
is generally strongly correlated with response times, and
with the working memory resources necessary for correct
solutions; this is roughly analogous to the increase in pro-
cessing load with an increase in the number of clauses in a
sentence, for instance. As an example, Hecht (2002) found
that a concurrent articulatory task disrupted addition tri-
als performed via counting far more than it did trials per-
formed via retrieval (see comparable results in a test of
sequential adding by Logie, Gilhooly, & Wynn, 1994).

In our test of the relationship between number of steps
and working memory (Ashcraft & Kirk, 2001), we rea-
soned that the carry operation in addition should require
additional working memory processing, because carrying
adds yet another step to the processing sequence. We pre-
sented participants with addition problems ranging from
basic addition facts up to two-column additions; half of all
problems required a carry (e.g., 27 14; see also Fürst &
Hitch, 2000). The results were clear cut (see Ashcraft &
Kirk, 2001, Figure 1). Carry problems were considerably
slower than their noncarry counterparts, fully 1,200 msec
slower for the largest problems. Likewise, carry problems

60

0

800

1,000

1,200

1,400

1,600

1,800

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Minuend

M
e

an
R

T

Experiment

1

Experiment

2

Figure 1. Mean reaction time (RT) to simple subtraction facts
from 0 0 to 18 9 by minuend; for example, in 14 8, the
“minuend” is 14. From “Elementary subtraction,” by D. J. Seyler,
E. P. Kirk, & M. H. Ashcraft, 2003, Journal of Experimental Psy-
chology: Learning, Memory, & Cognition, 29, p. 1341, Figure 1.
Copyright 2003 American Psychological Association. Adapted
with permission.

WORKING MEMORY, MATH PERFORMANCE, AND MATH ANXIETY 24

5

invariably had higher error rates (from 5.2% to 9.4%) than
their noncarry counterparts (0.2% to 2.1%).

It appears that working memory processing is integral
to arithmetic and mathematics performance whenever a
procedure other than direct memory retrieval is operating.
That is, when simple one-column addition or multiplica-
tion is being performed, the underlying mental process
responsible is principally retrieval from memory, in which
case working memory plays a minor role, at best. But
when performance relies on algorithmic procedures—
say, carrying—or when other reconstructive strategies are
used, then working memory is crucial. Likewise, for multi-
step problems, there is an increasing reliance on working
memory as the number of steps increases (see, e.g., Ayres,
2001), and at points in problem solving when the need for
retaining intermediate goals and values is highest (see,
e.g., Campbell & Charness, 1990).

Math Performance and Math Anxiety
Serious research on math anxiety began to appear in

the early 1970s, when a suitable objective instrument for
measuring math anxiety became available. Since that time,
scores of articles have appeared on the various psychometric
properties of the original scale and its descendants, and on
the relationships between math anxiety and a host of other
characteristics. The best summary of this work remains the
Hembree meta-analysis (1990), which, for the most part,
is the source of the following correlations between math
anxiety and various aspects of math performance.

The story told by the correlations is sad indeed. The
higher one’s math anxiety, the lower one’s math learning,
mastery, and motivation; for example, a math anxiety
correlation of .30 with high school grades, .75 with
enjoyment of math, .64 with motivation to take more
math or do well in math, and .31 with the extent of high
school math taken. The overall correlation between math
anxiety and individuals’ math achievement, as measured
by standardized tests, is .31. Thus, highly math-anxious
individuals get poorer grades in the math classes they
take, show low motivation to take more (elective) math,
and in fact do take less math. They clearly learn less math
than their low-anxious counterparts.

These correlations mean, simply but importantly, that as
math anxiety increases, math achievement declines. This
seemingly inherent relationship between math anxiety
and achievement poses a genuine interpretive quandary:
Is lower performance on a math task due to math anxiety
or to lower mastery and achievement in math? Fortunately,
our work suggests a partial way out of the quandary. That
is, we collected scores from some 80 undergraduates on
a math-anxiety assessment and also on the Wide Range
Achievement Test (WRAT), a standard math achievement
test. The correlation between math anxiety and the com-
posite WRAT score was .35, very close to the value in
Hembree’s (1990) meta-analysis. But we then rescored
the WRAT performance, taking advantage of its line-by-
line increases in difficulty (e.g., whole-number addition
in Line 1, multiplication of fractions in Line 5, solving
for two unknowns in Line 8). When the test is scored in
this fashion, the impact of math anxiety is much clearer;

see Figure 2. Simple accuracy is at ceiling for all groups
on the initial lines of the test, suggesting no evidence of
lower achievement per se for math-anxious individuals on
the whole-number arithmetic taught in elementary school
(i.e., even high-anxious individuals can answer whole-
number problems correctly). Likewise, when we gave un-
timed paper-and-pencil tests of our whole-number arith-
metic stimuli, we found no math-anxiety differences on
accuracy, even though these same stimuli generated online
anxiety effects in an RT task (Faust, Ashcraft, & Fleck,
1996). But group performance on the WRAT does start to
diverge around Line 4 or 5: On the most difficult line of
the test, the high-anxious group averages fewer than one
in five problems correct. Thus, the lower achievement of
math-anxious individuals seems limited to more difficult
math, the math taught at or after late elementary school.

Note a second point as well. Scores on such achieve-
ment tests probably underestimate levels of math achieve-
ment among high-anxious participants. When students
take math tests, especially high-stakes math achievement
tests, it is very likely that their online anxiety reaction
is disrupting their performance. In agreement with this,
Hembree (1990) noted that for groups who undergo effec-
tive interventions for their math anxiety (cognitive behav-
ioral interventions), math achievement scores approach
those in the normal range. Given that the interventions do
not provide any instruction or practice in math, it follows
that previously low achievement-test results could be at
least partially explained by an online anxiety reaction that
depressed preintervention scores.

The negative relationship between math anxiety and
achievement is not universal across all forms of arithmetic
and math, and not universal across all testing situations.
Lab testing at the simpler levels of arithmetic need not
worry about a confounding relationship between achieve-

WRAT by Math Anxiety Group

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1 2 3 4 5 6 7 8

Line Number

M
e

an
C

o
rr

e
ct

Low anx
Med anx
High anx

Figure 2. Mean number correct per line (out of five) on the
Wide Range Achievement Test (WRAT) for low-, medium-, and
high-math-anxious groups.

246 ASHCRAFT AND KRAUSE

ment and math anxiety. Disentangling that confound at
higher levels of difficulty will be much more difficult.

Working Memory and Math Anxiety
The question of how math anxiety compromises work-

ing memory has a more subtle answer than merely saying
that math anxiety consumes the resources of the work-
ing memory system. For example, we used two different
verbal-based span assessments, and found no significant
anxiety-group differences at all. But when a computation-
based span task was administered, we found a pronounced
decline in assessed working memory capacity; the full-
scale correlation was a significant .40 (Ashcraft & Kirk,
2001, Experiments 1 and 3). We argue that a math-anxious
person’s working memory resources are drained—that the
individual suffers a compromised working memory—only
when the actual math anxiety is aroused, as in span tasks
that involve computations.

To demonstrate the joint effects of working memory and
math anxiety, we had our participants do two-column ad-
dition, either alone or in combination with a letter-recall
secondary task (Ashcraft & Kirk, 2001, Experiment 2). As
Figure 3 shows, errors to the letter task grew only mod-
estly for the low-, medium-, and high-anxiety groups in
the control conditions and in the two-letter load condition.
But in the difficult six-letter condition, with the working-
memory-demanding carry problems, the effect of the dual
task was quite strong, and affected the high-anxious group
the most. Clearly, when the math task becomes demanding,
and when the necessary resources from working memory
are occupied by the secondary task, performance suf-
fers. Highly anxious participants, who are already wast-
ing working memory resources by attending to their own
anxiety, suffer the most (if the dual task per se induced,
say, high-state anxiety, independent of working memory,
then errors should have increased on all dual task trials,
including the noncarry problems). We are currently explor-
ing other ways in which this diversion of working memory
affects the outcomes of mental processing.

A related anxiety effect bears brief mention as well. Our
results show that high-math-anxious participants often sac-
rifice accuracy for speed, especially as problems become
more difficult, which we interpreted as an avoidance-like
effort to finish the testing session as quickly as possible
(Faust et al., 1996). Consequences of this—say, in terms
of achievement testing or learning from homework—have
yet to be investigated.

Applications to Education
Math is an important topic in schooling and in prepara-

tion for careers; skill at math is often a filter in terms of
career pathways. Math is also a cognitively challenging
topic, one that involves manipulation of symbols in an
often highly abstract setting. Furthermore, math must be
taught in school, unlike language, which children learn
naturally from their surroundings early in life. Presum-
ably, this should give cognitive psychology some advan-
tages in studying math, given that points in the math cur-
riculum can be specified—for example, the grade level at
which prealgebra is introduced.

It bears repeating that there is a pervasive reliance
throughout arithmetic and math on the working memory
system, from simple counting and estimation processes
(see, e.g., Siegler & Booth, 2005) up through algebra and
complex problem solving (Ayres, 2001). Indeed, even at
the earliest levels of formal education, there is a strong
relationship between a child’s working memory span and
performance on number-based tasks (see, e.g., Adams
& Hitch, 1997). The need for working memory may be
easy to overlook, given that even a difficult mathematics
problem can be presented with far fewer symbols than,
say, a complex, multiclause sentence. It is also the case
that sentences, and the words that compose them, gener-
ally refer to more concrete concepts and ideas (objects,
actions, events) than a typical math problem—even a
word problem in math—does. The very abstractness of

Six-Letter Load

0
5

10

15

20

25

30

35

40

45

No Carry Carry

Problem Type

P
e

rc
e

n
ta

g
e

E
rr

o
rs

Low control

Med control

High control

Low dual

Med dual

High dual

Two-Letter Load

0
5
10
15
20
25
30
35
40
45
No Carry Carry
Problem Type
P
e
rc
e
n
ta
g
e
E
rr
o
rs
Low control
Med control
High control
Low dual
Med dual
High dual

Figure 3. Percentage errors to the letter task in control and
dual task conditions, separately for two- versus six-letter memory
loads and low-, medium-, and high-math-anxious groups. From
“The relationships among working memory, math anxiety, and
performance,” by M. H. Ashcraft & E. P. Kirk, 2001, Journal of
Experimental Psychology: General, 130, p. 231, Figure 2. Copy-
right 2001 American Psychological Association. Adapted with
permission.

WORKING MEMORY, MATH PERFORMANCE, AND MATH ANXIETY 247

mathematical symbols surely adds to the difficulties that
people encounter when learning math, including difficul-
ties in storing and using information in working memory.
Acquiring the capacity for abstract thinking, of course, is
a late developmental milestone. So far, relatively few proj-
ects have explored math processing beyond the four basic
arithmetic operations, so the role of working memory at
higher levels of math has hardly been investigated at all.
Based on the central role identified so far, however, it can
only be the case that more difficult math will be even more
dependent on working memory. This would be especially
true given the heavier burden on procedural processing at
higher levels of math, and the lesser degree of automatic-
ity that might be attained by those procedures (the degree
to which math procedures themselves can become more
automatic is an almost totally ignored topic).

Turning now to math anxiety, several implications for
education can be drawn. Math anxiety seems to influence
cognitive processing in a straightforward way—working
memory resources are compromised whenever the anxiety
is aroused. Given the pervasiveness of working-memory-
dependent processing in arithmetic and math, this predicts
serious effects of math anxiety. It is easy to imagine how
math anxiety affects learning—say, in a high school math
classroom. A student whose math anxiety is aroused is
diverting needed attention away from the content of the
class and toward internal worries and anxieties over math.
This can only slow or degrade the mastery of the to-be-
learned information.

Further, the implications in the correlational literature
seem unavoidable. Math anxiety leads to a global avoid-
ance pattern—whenever possible, students avoid taking
math classes and avoid situations in which math will be
necessary, including career paths. In an important study of
math teachers’ approaches to teaching, Turner et al. (2002)
showed how students with an unsupportive, “cold” teacher
avoid in-school behaviors (making eye contact with the
teacher, going to out-of-class help sessions). These sound
like the ingredients for math anxiety. We predict that math
anxiety is learned in the classroom—for example, when
a student is called to the board to work a problem, does
poorly, and is embarrassed in front of the teacher and his
or her peers. In short, lower-than-average math abilities
and/or working memory capacity, susceptibility to public
embarrassment, and a nonsupportive teacher all may be
risk factors for developing math anxiety (Ashcraft et al.,
2007). Once math anxiety is established, it then seems to
be supported by a variety of cultural attitudes that under-
mine math achievement—for example, that math is hard,
one either is or is not good at math, regardless of how hard
one works, and so on.

We speculate one step further on the teacher’s role in the
development of math anxiety. When college majors are
given a math anxiety test, those who average the highest
are individuals preparing to be elementary school teach-
ers (Hembree, 1990). Compounding this, students earn-
ing such degrees are typically required to take very few
math courses (see also Ma, 1999). We thus suggest that
the stage is set early on in math education for students
to be “stranded” without a reasonable, instructive expla-

nation for many aspects of math, and/or in a classroom
in which the teacher, possibly defensively, adopts an un-
supportive, “cold” teaching approach. Placing an at-risk
child into such a teacher’s class may be the ideal recipe
for creating math anxiety, a hypothesis we are beginning
to investigate.

Cognitive psychology’s role should be to examine the
acquisition and mastery of math and math procedures, and
also the ways in which math anxiety has consequences
for cognitive processing. Cognition can also help deter-
mine the developmental course of this learned anxiety,
and explore the possibility that some genuinely cogni-
tive factors—for example, low math aptitude or working
memory capacity—may be risk factors for math anxiety.
Investigating the cognitive consequences of math anxiety
may provide a rather unique opportunity, testing the im-
pact of a malleable individual difference, math anxiety,
and its consequences on cognitive processing.

AUTHOR NOTE

Correspondence concerning this article should be addressed to M. H.
Ashcraft, Psychology Department, University of Nevada, Las Vegas,
Box 455030, 4505 South Maryland Parkway, Las Vegas, NV 89154-
5030 (e-mail: mark.ashcraft@unlv.edu).

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Perspectives on Psychological Science
2016, Vol. 11(1) 74 –100
© The Author(s) 2015
Reprints and permissions:
sagepub.com/journalsPermissions.nav
DOI: 10.1177/1745691615596790
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Many daily activities such as reading, writing, making a
shopping list, carrying on phone conversations, deciding
where to go on holidays, and many more require work-
ing memory. For example, when reading a text, mean-
ings expressed in the parts of a sentence are kept in
memory until they can be integrated in an overall mean-
ing at the end of the sentence. Besides memory storage
capacity, this task involves executive control to divide
attention over sentence processing and memory mainte-
nance of the sentence part. The term working memory
has been coined to refer to such combined usage of
memory and executive control to support an activity or a
skill. Language production and comprehension (e.g., Just
& Carpenter, 1992), mental arithmetic (e.g., DeStefano &
LeFevre, 2004), reasoning (e.g., Klauer, Stegmaier, &
Meiser, 1997), attentional control (Kane, Bleckley,
Conway, & Engle, 2001), and many other tasks require
working memory (WM) support to represent a situation,
to keep track of progress, and to maintain interim results.
In affective and emotional processing (e.g., Eysenck &
Calvo, 1992), especially in states of depression and anxi-
ety, people entertain worrying thoughts and engage in
rumination but also try to counteract or suppress such

thoughts, thus occupying memory and executive control
that otherwise would be available for other activities. The
degree to which such rumination consumes WM resources
varies across persons because the amount of WM capac-
ity (i.e., the ability to maintain information while per-
forming a demanding task) differs across individuals and
shows a robust and important relation to fluid intelli-
gence (e.g., Engle, Tuholski, Laughlin, & Conway, 1999).
WM capacity is predictive of a range of skills, including
reading comprehension (e.g., Unsworth & McMillan,
2013) and numerical skills (Rotzer et al., 2009). WM also
is considered to play a major part in the development of
mental capacity (Case, Kurland, & Goldberg, 1982), and
it is an important factor in psychopathology, particularly
in autism and attention-deficit/hyperactivity disorder
(e.g., Pennington & Ozonoff, 1996) but also in schizo-
phrenia and dementia (e.g., Baddeley, Logie, Bressi,
Della Sala, & Spinnler, 1986).

596790PPSXXX10.1177/1745691615596790VandierendonckDistributed Executive Control in Working Memory
research-article2015

Corresponding Author:
André Vandierendonck, Department of Experimental Psychology,
Ghent University, Henri Dunantlaan 2, B-9000 Gent, Belgium
E-mail: Andre.Vandierendonck@UGent.be

A Working Memory System With
Distributed Executive Control

André Vandierendonck
Department of Experimental Psychology, Ghent University

Abstract
Working memory consists of domain-specific storage facilities and domain-general executive control processes. In
some working memory theories, these control processes are accounted for via a homunculus, the central executive. In
the present article, the author defends a mechanistic view of executive control by adopting the position that executive
control is situated in the context of goal-directed behavior to maintain and protect the goal and to select an action to
attain the goal. On the basis of findings in task switching and dual tasking, he proposes an adapted multicomponent
working memory model in which the central executive is replaced by three interacting components: an executive
memory that maintains the task set, a collection of acquired procedural rules, and an engine that executes the
procedural rules that match the ensemble of working memory contents. The strongest among the rules that match the
ensemble of working memory contents is applied, resulting in changes of the working memory contents or in motor
actions. According to this model, goals are attained when the route to the goals is known or can be searched when the
route is unknown (problem solving). Empirical evidence for this proposal and new predictions are discussed.

Keywords
working memory, executive control, executive function, task switching

http://crossmark.crossref.org/dialog/?doi=10.1177%2F1745691615596790&domain=pdf&date_stamp=2016-01-27

Distributed Executive Control in Working Memory 75

After four decades of WM research, most present-day
WM theorists still rely on a homunculus to account for
the executive or attentional control that is considered to
be one of the core WM functions. This homunculus is
called central executive (e.g., Baddeley, 1986, 2000;
Baddeley & Hitch, 1974; Cowan, 1999, 2005), central
attention (e.g., Barrouillet, Bernardin, & Camos, 2004), or
executive attention (e.g., Engle, Tuholski, et  al., 1999).
Not only in WM but also in action control and behavior
change, control processes are attributed to a homuncu-
lus; however, understanding of how such control is per-
formed has not increased. For that reason, some
researchers have argued that all these homunculi must be
banished from theories (Verbruggen, McLaren, &
Chambers, 2014). In the present article, I pursue this
argument by presenting and elaborating a theoretical
model that accounts for executive control processes in
WM without the help of a homunculus.

The reason that the theoretical conception of WM
includes executive control (or whatever one chooses to
call it) originates from the assumption that WM uses
short-term memory resources to support other cognitive
activities, such as mental arithmetic, language, reasoning,
and problem solving. All these activities need memory
resources to attain their goal. Because these resources
have to be shared between these activities and memory
itself, the assignment of the resources typically occurs
under intentional control. Such an intentional or goal-
directed perspective requires proper control mechanisms
to facilitate goal attainment. Thus, WM not only provides
domain-specific memory resources to temporarily main-
tain information but also domain-general mechanisms to
support these goal-directed cognitive activities. For
example, in performing mental arithmetic, the WM sys-
tem not only provides verbal WM storage to maintain
interim results but also provides storage to maintain the
task goal and the selected method(s) to attain this goal
(Hitch, 1978; Imbo, Vandierendonck, & De Rammelaere,
2007).

In the model I describe in this article, the multicompo-
nent WM model of Baddeley and Hitch is used as a start-
ing point and as a reference (Baddeley, 2000; Baddeley,
Allen, & Hitch, 2010; Baddeley & Hitch, 1974). Several
reasons motivate this choice. First, although it is the old-
est model around,1 the multicomponent model still plays
a leading role in present-day WM research. Second, this
model has inspired a large share of the research on WM.
Finally, because of the diversity of the WM models
defined in the literature, it is not possible within the
scope of one article to formulate an account that fits all
models, even though the general ideas presented here
are assumed to be valid in the context of other WM mod-
els that rely on a homunculus to account for controlled
processes.

As the name suggests, the multicomponent WM model
consists of a collection of components or modules that
together constitute the WM system. At the top of the sys-
tem, the central executive component is assumed to
incorporate the control function. It oversees the ope-
ration of the domain-specific components of the WM
system: the phonological loop, which maintains phono-
logically coded verbal information for short periods of
time (Baddeley, 1986; Baddeley, Lewis, & Vallar, 1984);
the visuospatial sketch pad, which stores visual and spa-
tial information (Baddeley & Hitch, 1974; Baddeley &
Logie, 1999; Logie, 1995); and the episodic buffer, which
binds the contents of the modality-specific systems to
episodic long-term memory (Baddeley, 2000). The cen-
tral executive also supervises controlled and goal-directed
processes, including reasoning and problem solving. This
conceptualization of executive control has been defended
as representing an intermediate step toward a better
understanding of the WM system. Unfortunately, over
time, phenomena that could not be immediately under-
stood by the operation of the domain-specific modules
have been accounted for by the operation of the ill-
understood central executive.

Later on, Baddeley (1996a, 1996b) argued for a frac-
tionation of the central executive into simpler compo-
nents, which finally resulted in the addition of the
episodic buffer as another component in the multicom-
ponent model (Baddeley, 2000). The proposed function
of the episodic buffer consisted of binding features to
form a temporarily united representation (as in connect-
ing a specific color to a specific form or an action to an
actor in sentence processing). There is no doubt that the
inclusion of the episodic buffer improved the scope of
the model. Nevertheless, it did not result in a reduction
of the power of the central executive because further
research has shown that the hypothesized binding opera-
tions attributed to the episodic buffer do not involve
executive control (Allen, Baddeley, & Hitch, 2006; Allen,
Hitch, Mate, & Baddeley, 2012; Baddeley et  al., 2010;
Baddeley, Hitch, & Allen, 2009). In another effort to frac-
tionate the central executive, Miyake et  al. (2000) pro-
posed replacing it with specific executive functions, such
as changing focus from one intention to another (set
shifting); adapting the contents of WM by adding, replac-
ing, or deleting contents (memory updating); and sup-
pressing or decreasing the degree of activation of WM
contents (inhibition). Although Miyake et  al. took an
important step forward by rooting these executive func-
tions in measured variables, their attempt failed to
account for dual-task performance. In still another
attempt, Vandierendonck, Szmalec, Deschuyteneer, and
Depoorter (2007) tried to redefine the central executive
by specifying the basic processes underlying executive
control. Thus far, these efforts have failed to replace the

76 Vandierendonck

central executive with an account that does not involve a
homunculus and that is more defensible scientifically via
attribution of executive control to the operation of sim-
pler processes.

In this article, I present an adaptation of the multicom-
ponent WM model in which the central executive is
deleted from the WM architecture and replaced by a ded-
icated WM component that maintains the conditions and
constraints of the currently scheduled intentional action
and relocates the control actions to the application of
specific rules that are automatically triggered when they
match the conditions and constraints represented in the
WM stores. The latter part is achieved in a so-called pro-
duction system, without a need for an autonomous con-
trolling agent or homunculus. The proposed changes are
substantiated in reference to published empirical find-
ings. For this reason, I first review the empirical findings
that help to constrain the WM architecture. Next, I elabo-
rate the implications of these findings for the conceptual-
ization of WM. Finally, I explain how conditions
represented in WM can automatically trigger rules that
result in intentionally controlled behavior.

Empirical Constraints on the WM
Architecture

WM provides domain-specific as well as domain-general
resources: On one hand, it provides temporary storage
for tasks that require maintenance of information for a
brief period of time; on the other hand, it supports con-
trol of intentional action. For example, in the execution
of a simple cognitive task such as judging whether a digit
is odd or even (parity task), not only are a temporary
representation of the digit and its activated associations
(e.g., “even”) needed for the duration of task execution,
but also storage must be made available for the represen-
tation of the goal and the way to achieve it (task set).
However, a mechanism that drives the control processes
(the realm of the central executive) also is needed
because temporary activations or representations of the
goal and the way to achieve it do not control other pro-
cesses, as they are merely temporary memory contents.
Before elaborating these storage and control mechanisms
in more detail, I summarize knowledge about controlled
processes and the role of WM in such processing, first
briefly presenting some relevant findings from task-
switching research and then discussing some relevant
findings from dual-task research.

Constraints from task switching

Switching between tasks occurs on several occasions
each day. While you are reading a text, a phone call may
remind you of a promise; you note down a reminder on

a post-it and return to reading, trying to figure out where
you left off. Switching is not always experienced as a
demanding event. However, research on task switching
has shown that a task switch almost always comes with a
cost expressed as a slower and more error-prone response
than a situation in which no switching is required.
According to the present state of task-switching research
(cf. Kiesel et al., 2010; Logan & Gordon, 2001; Monsell,
1996, 2003; Vandierendonck, Liefooghe, & Verbruggen,
2010), a successful task switch depends on the outcome
of a competition between processes related to the pres-
ent intention and processes that are driven by carryover
from activities related to the previous, no-longer-relevant
intention (e.g., task-set inertia; Allport, Styles, & Hsieh,
1994).

Task-control processes. Several kinds of processes are
involved in this competition. To clarify these processes,
let us take as an example switching from the execution
of a magnitude judgment task (deciding whether a digit
is smaller than or larger than 5) to a parity judgment task
(deciding whether a digit is odd or even). The parity task
requires the categorization of a digit as odd or even; in
the magnitude task, the same digit must be categorized
as small (smaller than 5) or large. In other words, the cor-
rect response to the digit depends on the task. In this
particular case, one of two keys must be pressed. For the
parity task, the instruction is to respond with a left key
press when the digit is odd and with a right key press
when it is even. Similarly, the magnitude task requires a
left response for a small digit and a right key press for a
large digit. Each trial starts with a cue that indicates which
task must be performed. The cue is followed by the pre-
sentation of a digit.

Using this pair of tasks, Figure 1 illustrates how the
execution of the parity judgment task may be affected by
previous executions of a magnitude judgment task. The
figure shows four pathways that are involved in the com-
petition between goal-directed (Pathway 1) and interfer-
ence-based (Pathways 3–4) processing. The cue initiates
goal-directed processing. Via a learned association, the
cue points to a task goal that after activation results in the
configuration of the task set (Pathway 1), which is an
ensemble of task-execution parameters (Logan & Gordon,
2001). For the tasks in the example, the task set includes
settings of the orientation of attention (attention focused
on a point in space where the digit will appear), stimulus
categorization rules (categories odd and even for the par-
ity task; small and large for the magnitude task), response
mappings (e.g., press left key for odd), stimulus modality
(visual or aural presentation of digits), response modality
(manual or vocal response), and speed-accuracy trade-
off (stress on accuracy, stress on speed, or equal stress on
both).

Distributed Executive Control in Working Memory 77

Activation of the goal and configuration of the task set
take some time, after which the conditions are set for
activation of processes that result in goal achievement
(Logan, 2003; Meiran, 1996, 2000; Monsell & Mizon, 2006;
Rogers & Monsell, 1995). These processes include activa-
tion of the target categorization (e.g., odd), activation of
the category-response mapping (if odd, press left), and
finally activation of the motor response (left key press).
Some of these processes are so well practiced that they
also occur via direct target associations (Pathway 2). Such
direct association may activate an irrelevant categoriza-
tion, which in turn may activate its associated response,
thus creating a competition with the task-relevant chain
of events.

Repetitions of stimuli or stimulus features prime repe-
tition of the associated response (Pashler & Baylis, 1991a,
1991b). The direct stimulus-response (S-R) association
(Pathway 3) can bypass the goal-directed pathway (1) to
the response. Task repetition enhances performance

efficiency, but when the task changes, application of the
S-R association may result in an error. Controlled process-
ing is needed for the goal-directed processing pathway to
be favored over the direct S-R link (Schuch & Koch, 2003;
Verbruggen, Liefooghe, & Vandierendonck, 2006).

Research has also shown that the target stimulus can
become associated with the task (Waszak, Hommel, &
Allport, 2003), resulting in the creation of a stimulus-task
association (Pathway 4). When a particular target is
uniquely linked to one of the tasks (e.g., when the digit
2 would only occur in the context of the parity task), a
direct stimulus-task association (2-parity) bypasses
effortful goal-directed processing and results in faster
goal achievement without risk of errors. However, when
occasionally the target occurs in the context of the other
task (e.g., the digit 2 unexpectedly occurs in the context
of the magnitude task), goal achievement of the magni-
tude task may completely fail. The occurrence of such a
bypass is difficult to control because the stimulus-task

Magnitude

Stimulus
Response

Goal

1

2

22

22

33

Parity

Task Set

44

Stimulus
Categorization

22
1

Fig. 1. Schematic description of the stages involved in goal-directed processing. In the top-down
pathway (1), first a goal is selected (parity: odd/even judgment). This leads to configuration of the
corresponding task set and biasing of the stimulus categorization towards the odd-even judgment
rules. In the bottom-up pathway (2), the stimulus is linked with both the magnitude (small/large)
and the parity categorization (in bold). Due to top-down biasing, the correct stimulus categorization
is selected, which leads to a correct response. In previous episodes, a stimulus-response associa-
tion (3) may have been learned; this association automatically triggers the previously associated
response. If this response is incorrect, the conflict between the incorrect and the correct responses
must be resolved. It is also possible that in previous episodes, a stimulus-task association has been
formed, for example, with the magnitude task (4). This leads to a goal conflict, which propagates
all the way down via task set and stimulus categorization to response.

78 Vandierendonck

association directly activates the task goal. If this activa-
tion is fast, the incorrect task goal may be the first one
becoming active so that it can easily win the competition
from the correct goal. If on the contrary, activation of the
correct goal occurs first, it is more likely to win the
competition.

This brief sketch summarizes the task-processing
stages at which biases and processing conflicts may
occur. At each of these stages, cognitive control opera-
tions resolve the conflicts to achieve the relevant task
goal. More detailed information can be found in the lit-
erature on task-switching and dual-tasking performance
( J. W. Brown, Reynolds, & Braver, 2007; Gilbert & Shallice,
2002; Kiesel et al., 2010; Logan & Gordon, 2001; Monsell,
2003; Vandierendonck et al., 2010; Waszak et al., 2003).

Interaction with WM. Notwithstanding the huge num-
ber of articles published on task switching in the last two
decades, the number of studies of the relationship
between task switching and WM is rather modest (Kiesel
et al., 2010; Vandierendonck et al., 2010) and addresses
only three research questions, namely, the role of verbal-
ization in task switching, the trade-off of WM and task-
switching efficiency, and the role of WM in voluntary task
choice. Because of their relevance to the present concern
(i.e., how task-switching processes constrain the WM
architecture), I consider each of these three lines of
research in some detail.

Inner speech and verbalization. By far, the largest
number of studies have been devoted to the first of these
three research questions: the role of verbalization and
inner speech in task switching. Goschke (2000) used let-
ter and color categorization tasks and reported smaller
switch costs when the task name (“letter” or “color”) was
verbalized before each stimulus (a colored letter) than
when a verbal distractor (“Monday” or “Tuesday”) was
named. This finding is consistent with the hypothesis that
task-set reconfiguration includes intention retrieval.

In a seminal study, Baddeley, Chincotta, and Adlam
(2001) investigated how a verbal memory load affects
task-switching performance. Participants applied simple
arithmetic operations (+1, −1) to lists of digits (1−9) in
either single-task (only addition or subtraction) or alter-
nating-task (+1, −1, +1, −1, . . .) lists, with or without task
cues (plus or minus signs). Confirming the typical switch
cost, responses were slower on alternating-task lists than
on single-task lists, but this overall cost was moderated
by the presence of task cues and by the type of verbal
memory load. Verbal load was varied in three levels: no
concurrent verbalization; simple irrelevant verbalization,
which required recitation of the months of the year ( June,
July, . . .); or cognitively demanding verbalization (i.e., the
trails task, Lezak, 1983), which consisted of alternating

recitation of the months of the year and the days of the
week (April, Tuesday; May, Wednesday; June, Thursday;
. . .). When task cues were shown, the alternating-list cost
was present only when a concurrent demanding verbal-
ization task was performed. Without cues, the alternat-
ing-list cost was present in the three types of verbal load,
and the cost increased with the amount of load imposed
by the verbalization task. These findings suggest that
only a demanding verbalization interferes with task-
switching performance, but that in the absence of exter-
nal cues, participants spontaneously use verbalization
(inner speech) to remind themselves of the present task,
thus creating for themselves a demanding verbal dual-
task situation.

Study of the role of inner speech was pursued further
by Emerson and Miyake (2003). Using a similar design
with arithmetic tasks (+3, −3) in single- and alternating-
task lists, they confirmed that switch costs increased
when the concurrent task was a verbal task (articulatory
suppression: fast continuous repetition of “a-b-c”) but not
when it was nonverbal (foot tapping). Emerson and
Miyake also varied the informativeness of the cues by
including conditions without task cues, with nonspecific
cues (colors; e.g., the number printed in red for addi-
tion), and with specific cues (+ for addition, − for sub-
traction). More informative cues resulted in smaller switch
costs. However, at all levels of informativeness, the switch
cost was larger in the conditions with articulatory sup-
pression than the conditions without a secondary task
(see also Saeki & Saito, 2004a; Saeki, Saito, & Kawaguchi,
2006, for similar results). These findings confirm that the
requirement to perform articulatory suppression impairs
the efficiency of verbal self-instruction via inner speech.
Such verbal self-instruction is needed to support selec-
tion of the correct task and to update progress in the
action plan in WM (see also Mayr & Bryck, 2005). Several
studies have shown that self-instruction plays a similar
role in other variations of the task-switching procedure,
such as alternating runs of twice the same task (Saeki &
Saito, 2004b), explicitly cuing the task (Liefooghe,
Vandierendonck, Muyllaert, Verbruggen, & Vanneste,
2005; Miyake, Emerson, Padilla, & Ahn, 2004), and cuing
the transition (switch or nonswitch) rather than the task
(Saeki & Saito, 2009).

In short, the studies on verbalization show that con-
current irrelevant verbalization impairs task-switching
performance. These studies hence support the conclu-
sion that maintaining a verbal goal representation plays
an important role in task switching: when the cues are
transparent, the verbal goal can be retrieved without any
additional verbal processing, but when the cues are
absent or nontransparent, additional verbal processing is
needed to establish the verbal goal.2 Inner speech may
be used to support this maintenance, and it takes the

Distributed Executive Control in Working Memory 79

form of verbalization of task goals, task cues, and possi-
bly category-response mappings (Liefooghe et al., 2005;
but see van’t Wout, Lavric, & Monsell, 2013). Thus inner
speech supports cue interpretation, particularly in situa-
tions in which the cues are arbitrary and do not provide
direct access to the task name or the task goal (Miyake
et al., 2004; Saeki & Saito, 2012). Inner speech also sup-
ports maintenance of the current goal and updating of a
plan (i.e., replacing a previous task set by a new task
goal and task settings; Bryck & Mayr, 2005).

Task-switching efficiency under WM load. The rela-
tionship between WM and task switching concerns
whether and to what extent task switching and WM
share executive control processes. This issue has been
addressed in a rather small number of studies.

Logan (2004) addressed this question by directly com-
paring memory and performance measures. He estimated
memory performance by means of the memory span,
which is defined as the number of memoranda that can
be recalled in the correct order on 50% of the trials. Lists
of between 1 and 10 task names such as “high-low,”
“odd-even,” or “digit-word” were presented for serial
recall. For each length, the proportion of completely cor-
rect recall trials was registered, and the length corre-
sponding to 50% correct performance yielded the
person’s memory span score. By the same logic, Logan
defined the task span as a measure of task performance,
namely, as the number of tasks that can be correctly
remembered and performed in correct order on 50% of
the trials. The same lists of task names were presented;
when list presentation was complete, the participants
were requested to apply the remembered tasks to a series
of targets such as “3,” “8,” and “2” in the correct order (the
first task to the first target, the second task to the second
target, and so on). The list length corresponding to com-
pletely correct performance on 50% of the lists was reg-
istered as the person’s task span. Despite the presence of
frequent task switching in the task-execution condition,
the task span and the memory span did not differ. Also a
comparison between strict scoring (recall the correct
task, and emit the correct response) and lenient scoring
(recall the correct task, but allow an incorrect response)
revealed no systematic differences between task spans
and memory spans. Hence, no trade-off between mainte-
nance and processing was observed in this setup (see
also Logan, 2006, 2007), and this result suggests that no
capacity must be shared between task performance and
task switching on one hand and maintenance of task
information on the other.

Kane, Conway, Hambrick, and Engle (2007) reached a
similar conclusion in a correlational study in which they
investigated task-switching performance by comparing
participants with high and low complex-span tasks.

Complex span tasks measure the amount of information
that one can retain while concurrently executing another
task, for example, remembering a series of digits while
performing a series of arithmetic operations (operation
span, Turner & Engle, 1989). Switch costs were present in
both groups, but the size of the switch cost did not differ
across high- and low-span subjects. In the same vein, a
structural equation modeling study showed no common-
ality between task switching and memory (Oberauer,
Süss, Wilhelm, & Wittman, 2003). Furthermore, presence
of a memory load does not seem to affect task-switching
performance (Kiesel, Wendt, & Peters, 2007). Hsieh (2002)
found that a concurrent arithmetic task impairs task
switching; however, Kessler and Meiran (2010) reported
no effect of a numerical judgment task on task-switching
performance. The contrast between the latter two findings
may be due to the larger verbal load present in an arith-
metic task (e.g., Imbo & Vandierendonck, 2007).

The thrust of these findings is that although WM may
play a role in task switching (as shown by the verbaliza-
tion studies), task switching and WM do not seem to call
on a common limited-capacity resource. In other words,
the limited-capacity resource needed to maintain the task
names is not needed for the control processes involved
in task switching, as is most clearly corroborated by the
task-span findings of Logan (2004). However, it may be
that the common practice of separately measuring latency
and accuracy switch costs results in an underestimation
of the true switch cost, in particular in situations in which
variations in speed-accuracy trade-off may play a role
(Hughes, Linck, Bowles, Koeth, & Bunting, 2014).

Goal selection under WM load. The third research
question about the relationship between WM and task
switching concerns the role of WM in task selection.
Instead of receiving instructions on which task they
should perform on each trial, in the voluntary task-
switching (VTS) procedure, subjects voluntarily select the
task they will perform (Arrington & Logan, 2004, 2005).
In addition to the usual performance measures (accuracy,
speed, and the associated switch costs), this procedure
allows researchers to measure task frequency and task-
switch frequency. In almost all VTS studies, investigators
have reported a task repetition bias (i.e., a bias toward
selecting a task repetition over a task switch). This bias
becomes smaller when there is more time to prepare
(Arrington & Logan, 2005) but is also influenced by exter-
nal factors (Arrington, 2008; Arrington & Rhodes, 2010;
Mayr & Bell, 2006; Weaver & Arrington, 2010). Clearly,
VTS is also vulnerable to interference effects (Mayr &
Bell, 2006; Yeung, 2010). Nevertheless, VTS leaves more
room for endogenous control than the standard task-
switching procedures do (Arrington & Logan, 2005;
Liefooghe, Demanet, & Vandierendonck, 2009).

80 Vandierendonck

To date, only a few studies have addressed the role of
WM in VTS. Weaver and Arrington (2010) presented a
letter and a digit on each trial and allowed the partici-
pants to perform either a consonant/vowel decision on
the letter or an odd/even decision on the digit. During
the execution of these tasks, WM was loaded with three
symbols (mixture of letter and digits) at three specific
locations. The letter or the digit presented on each trial
either matched one of the three symbols or one of the
three locations represented in WM; the other symbol did
not match an identity or a location of the elements in
memory. Participants more frequently selected the task
applicable to the symbol that matched the memory con-
tents, suggesting that the overlap between the target and
WM tends to activate the associated task, making it more
available.

Demanet, Verbruggen, Liefooghe, and Vandierendonck
(2010) investigated how a six-item memory load modu-
lated the effect of bottom-up interference on the repeti-
tion bias in VTS. Under conditions of interference, the
presence of a memory load resulted in a larger task
repetition bias. The investigators varied three types of
bottom-up interference: stimulus repetitions, repetition
of irrelevant stimulus features, and stimulus-task asso-
ciations. Only in the case of bottom-up interference
with stimulus repetitions was the effect of the memory
load larger when the stimulus actually repeated than
when it changed. This finding supports the view that
top-down control counteracts the automatic tendency to
repeat tasks (Vandierendonck, Demanet, Liefooghe, &
Verbruggen, 2012) and shows that the presence of a
WM load makes the top-down control less efficient.

Butler, Arrington, and Weywadt (2011) examined the
effect of stimulus repetitions in an individual differences
approach. Task repetition bias did not correlate with WM
capacity as measured by the operation span (Turner &
Engle, 1989). In contrast to the previous study (Demanet
et al., 2010), Butler et al. (2011) used less frequent stimu-
lus repetitions, and there was no memory load to aug-
ment the difficulty of interference resolution.

Conclusion. A few conclusions can be drawn from
this brief review of studies on the relation between task
switching and WM. First, the studies on the role of rel-
evant and irrelevant verbal memory loads and the infor-
mativeness of the task cues show that maintenance of
the task goal depends on verbal WM and inner speech.
Therefore, goal representation and maintenance require
verbal WM. Second, the findings that memory span and
task span do not differ (Logan, 2004) and that task-switch-
ing costs do not vary with WM capacity (Kane et  al.,
2007) show that maintenance of declarative information
does not interfere with task execution and task switching.
Although representation of the goal name does require

verbal WM, it does not create an extra burden on task-
switching performance because such goal representation
is probably present for any task that is being executed.
Therefore, it seems that the contribution of working WM
to task switching is not in providing extra (verbal) stor-
age but rather in providing another kind of resources.
Jointly with the findings in voluntary task switching that
a memory load and its maintenance result in less effi-
cient coping with bottom-up intrusions, the contribution
of WM to task switching seems to consist of providing
facilities to implement and maintain the task set, select-
ing appropriate means to attain the goal, and biasing the
competition between goal-relevant and goal-irrelevant
processes toward goal attainment.

Constraints from dual-task research

WM research heavily relies on dual-task methodology.
Only a few studies are relevant to the issues at stake here,
and in all of these studies, the methodology used was
inspired by the time-based resource-sharing (TBRS)
model of WM (Barrouillet et al., 2004). Memoranda are
presented one by one for later serial recall, and after each
memorandum or after a series of memoranda, a retention
interval that can be used for rehearsal or refreshment is
filled with strictly timed tasks that differ in the amount of
required cognitive control. These studies converge on the
finding that when the interval is filled with tasks that
require more executive control, serial recall of the memo-
randa is poorer (Barrouillet, Bemardin, Portrat, Vergauwe,
& Camos, 2007; Barrouillet et  al., 2004; Barrouillet,
Lépine, & Camos, 2008; Barrouillet, Portrat, & Camos,
2011; Oberauer & Lewandowsky, 2011; Portrat, Barrouillet,
& Camos, 2008; Vergauwe, Barrouillet, & Camos, 2010).
More executively demanding tasks usually take longer to
perform and occupy central attention (or the central
executive) for a longer time than less demanding tasks.
All these studies show that the same central attentional
resource is involved in serial memory performance as in
cognitively demanding tasks.

In the present context, it is interesting to have a closer
look at one study in which the same methodology was
used to investigate whether task switching also calls on
the same central attentional resource. Liefooghe,
Barrouillet, Vandierendonck, and Camos (2008) varied
the number of task switches during the retention/
rehearsal interval while keeping all other task parameters
constant. On each trial, a list of letters was presented for
serial recall, and in the interval between presentation and
recall, a series of digit-categorization tasks (magnitude
and parity judgment) were performed under strictly
timed conditions. Across and within several experiments,
the number of switches in the series of digit categoriza-
tion tasks varied. This procedure was based on the

Distributed Executive Control in Working Memory 81

hypothesis that switch trials involve task reconfiguration
and interference control so that series with more switches
impose a larger cognitive load. As predicted, when more
switches were required during the maintenance interval
(higher cognitive load), serial recall was impaired. In the
reverse direction, the size of the memory load did not
affect the switch cost.

Together with other published studies, the studies
reviewed here show that the WM system provides
domain-general support that is needed for memory
maintenance (in particular, serial recall) as well as for
execution of intentional tasks. If one assumes that the
attentional resource operates in an all-or-none fashion
and can only serve one task at a time, then it would
seem that larger the amount of time in the retention/
rehearsal interval that is occupied by attention-demand-
ing tasks, the smaller the amount of time that can be
invested in rehearsal or memory refreshment activities,
and the poorer serial recall will be.

An Adapted WM Architecture

This brief overview regarding interactions of WM and
task execution in the context of task switching and dual
tasking provides important and useful information for
refining the conceptualization of WM. I now use the
implications and restrictions that follow from this over-
view to build a new multicomponent model of WM. This
new model retains the components of the old model that
have proven to be most useful, namely, the phonological
loop, the visuospatial sketch pad, and the episodic buf-
fer; the central executive is replaced by more appropriate
components.

The first conclusion drawn from the overview shows
that WM maintains a goal representation during task exe-
cution. The sensitivity of this goal representation to both
facilitation and interference from external verbal and
phonological activity suggests that the goal is likely to be
maintained within the verbal storage system (phonologi-
cal loop). However, as I argue in a later section, goal-
directed responding requires binding of the goal
representation to other WM contents; if binding is needed,
the episodic buffer would seem more appropriate.3

Second, both task-switching and dual-task research
show that a task set must somehow be kept active in WM
during task performance. However, because the task
span (remembering the task names and executing the
tasks) does not differ from the memory span (remember-
ing only the task names), it is evident that the task set is
not maintained in domain-specific (verbal or visuospa-
tial) storage. Nevertheless, the task execution modalities
and constraints must be stored in some part of the WM
system.

Executive memory module

Because the central executive in the multicomponent
model is a processing unit and not a memory store, the
task set cannot be simply maintained in this module. As
suggested by Duncan et  al. (2008) in their research on
goal neglect (the failure to attain the goal due to the fail-
ure to attend to goal-relevant environmental features), a
task model (information about task execution modalities
and restrictions, i.e., the task set) could be maintained in
the episodic buffer throughout task execution. However,
in consideration of the conclusions drawn from the over-
view of findings, this option is not plausible because
information maintenance in WM does not interfere with
task execution. Moreover, in combination with the find-
ing that executive control is not implied in the binding
performed via the episodic buffer (e.g., Baddeley et al.,
2009), it seems that the episodic buffer cannot satisfy this
role. In other words, neither the domain-general nor the
domain-specific parts of the multicomponent WM model
provide a facility that is suitable for maintenance of the
currently active task sets. Therefore, in addition to the
phonological loop, the visuospatial sketch pad, and the
episodic buffer, the multicomponent model of WM
should be equipped with a dedicated storage component
for the maintenance of the currently and recently active
task sets. The executive memory (EM) component is pro-
posed to fulfill this role. The rationale is that every goal-
directed activity needs a memory trace of the goal, of the
means to achieve the goal, and of the restrictions and
constraints in the situation at hand. As intentional mem-
ory and recall are goal-directed activities, it would seem
that these activities are also supported by an active goal
representation and a task-set representation and that
alternation between task execution and memory refresh-
ment involves a task switch; the switch has a rather small
cost because the degree of overlap between memory
refreshment and a cognitive task is likely to be much
smaller than the overlap among the cognitive tasks typi-
cally used in task-switching research. Because of this dif-
ference in task overlap, memory refreshment and a
cognitive task can be more easily coordinated in a com-
mon plan (Lien & Ruthruff, 2004; Logan, 2007; D. W.
Schneider & Logan, 2006).

Figure 2 shows this new EM as one of the modules
placed at the same level as the other storage modules
(phonological loop, visuospatial sketch pad, and epi-
sodic buffer). The EM module is shown to interact with
long-term memory (LTM), the episodic buffer, and the
phonological loop. As previously discussed, during task
execution, EM is assumed to contain a representation of
the task set. This information encompasses S-R mapping
rules; a number of task-relevant settings, such as orienta-
tion of attention (Gopher, Armony, & Greenshpan, 2000),4

82 Vandierendonck

response threshold, and response bias (Logan & Gordon,
2001); and also some task constraints that are often speci-
fied in the task instructions, such as stimulus modality
(Hunt & Kingstone, 2004; Murray, De Santis, Thut, &
Wylie, 2009) and response modality (Koch, Gade, &
Philipp, 2004; Philipp & Koch, 2005). After the task is
finished, these elements are no longer kept active and
can be actively inhibited if necessary. The EM module is
a passive system in the sense that it only maintains infor-
mation for as long as it is needed, and although this sys-
tem is assumed to have limited capacity, it can contain
more than one active task set as long as the task sets do
not interfere with each other. The possibility that more
than one task set can be active in EM is considered to be
important when several tasks have to be coordinated as
in the context of complex skill acquisition. How many
task sets or task-set components the module can contain
is an empirical question but in practice also will depend
on the degree to which the active task sets are in a com-
petitive relationship.

Figure 2 also shows that the EM connects to proce-
dural LTM. The rationale for this connection is that EM

contents are filled in on the basis of procedural knowl-
edge available in LTM. As in typical production models
(e.g., Kieras, Meyer, Mueller, & Seymour, 1999; Lovett,
Reder, & Lebiere, 1999; W. Schneider, 1999), procedures
stored in LTM are assumed to take the form of condition-
action rules: “IF condition, THEN action” (e.g., “IF digit
is even, THEN remember digit category even”). Rules
that match information in the storage systems of WM
become activated, and their action parts are executed,
which sometimes consist of storing additional informa-
tion in WM.

Because of this link to procedural LTM, the EM is
similar but not identical to the procedural WM compo-
nent proposed by Oberauer (2009) in his WM model. In
the latter model, the WM is assumed to consist of acti-
vated LTM. Parallel to the distinction between declara-
tive and procedural LTM, this model distinguishes
between a declarative and a procedural WM module, so
that procedural WM is the activated part of procedural
LTM, just as declarative WM is the activated part of
declarative LTM. However, if declarative WM is simply
activated declarative LTM, it would not possible to

Visuospatial
Sketch Pad

Procedural
LTM

Episodic
LTM

Visual
Semantics

Language

Phonological
Loop

Episodic
Buffer

Executive
Memory

Central
Executive

Fig. 2. Architecture of the modified multicomponent working memory frame-
work. The modified model is shown in black and consists of the new compo-
nents and the part of the original model that is retained; the remainder of the
original model is shown in gray. The central executive (gray) is replaced by the
executive module (black) that connects to the episodic buffer, the phonological
loop, and long-term memory (LTM) and by a distributed control network that
consists of the knowledge base in procedural LTM (black) and a processing
engine (not shown because it connects to all the components).

Distributed Executive Control in Working Memory 83

distinguish between different occurrences or activations
of the same event. For example, to have an appropriate
representation of “One boy came, and another boy left,”
one must be able to distinguish the first occurrence of
“boy” from the second occurrence. With a WM that
is  only activated LTM, this distinction cannot be
made.  This difficulty is overcome if one assumes that
generic elements (types, e.g., the concept of “boy”) are
retrieved  from LTM and transformed into specific
instances (tokens) by the addition of input and context
information (e.g., boy1). This transformation process is
called instantiation. A consequence of the assumption
that LTM contains types and WM contains tokens is that
WM is considered to be a temporary store linked to but
separate from LTM. For procedural LTM, the situation is
slightly different. Because procedural LTM contains pro-
cedural rules, activation of these rules executes the
action part of the rules. As a consequence, EM in the
present model contains representations that result from
the actions performed when procedural rules are
activated.

Another important difference relates to the symmetry
in Oberauer’s model between the declarative and proce-
dural WM components; these components are structured
in a strictly similar and symmetric way, so that in both
components, the most activated element is in focus (focus
of attention, response focus) and is part of a set of highly
activated elements composing a subset of the activated
LTM elements. Such a strict symmetry makes it difficult to
define operational distinctions between procedural and
declarative WM because the elements in declarative WM
have to be linked to operations represented in proce-
dural WM; thus, degree of activation of an element in one
module tends to go hand in hand with the degree of
activation of the linked element in the other module.
There is no compelling reason to assume that declarative
memory and procedural memory operate in strictly simi-
lar ways; therefore, in the present model, no symmetry is
assumed between EM and the other modules that contain
declarative information. Finally, in contrast to procedural
WM that only contains the S-R mappings, EM also con-
tains other task-set parameters and constraints.

Distributed executive control processes

Figure 2 shows the central executive as part of the origi-
nal model, but this component is not a part of the new
WM architecture displayed in this figure; the adapted
model does not contain a central executive or another
autonomous agent that manages executive control or
supervises the distribution of the attentional resource
over different tasks. Nevertheless, the system must
include a mechanism that ensures that intentional actions
result in goal achievement. Although EM maintains

task-relevant settings, it is just a memory store and is not
equipped with any control mechanisms. In the present
model, executive control is proposed to result from pro-
cesses in a distributed procedural knowledge network.
Within this network, a procedural knowledge base (pro-
cedural LTM) contains rules that can be triggered by the
contents of WM. A processing engine then executes the
actions specified in the selected rule. How this result is
achieved and how it can account for executive control is
explained in the following section.

Procedural knowledge base. The procedural knowl-
edge base consists of condition-action rules. These rules
can be quite simple, such as “IF number is even, THEN
press right button” or “IF a plus cue is present, THEN
instantiate ‘addition of 1’ as the goal,” but they can have
rather complex condition parts such as “IF the goal is
parity judgment AND the number is 3, THEN categorize
the number as odd,” or “IF a plus cue is present AND the
goal is subtraction, THEN suppress the subtraction goal,”
or even “IF a goal is addition and a goal is subtraction,
THEN set the goal-conflict flag.” These examples show
that when applied, some of these rules initiate a motor
action (e.g., “press right button”); others update WM con-
tents either directly (e.g. “suppress subtraction goal”) or
after performance of a cognitive action (e.g., “categorize
as odd”); still others may simply change a parameter set-
ting in the task set (e.g., “set goal-conflict flag”).

The rules in these examples have all been acquired.
Although some procedural knowledge is innate (e.g., “IF
pain is felt, THEN cry,” or “IF feeling hungry, THEN eat”),
most of this knowledge is acquired from experience and
practice, but rules can also be acquired by instruction
(Cohen-Kdoshay & Meiran, 2007). Procedural learning
occurs in a number of ways: by adapting the rule strength
of existing rules, creating completely new rules, or com-
bining existing rules. Each production rule has a strength
or confidence value that changes on the basis of experi-
ence: the more often a rule has been successfully applied,
the more the confidence in the rule has accumulated;
similarly, after unsuccessful application, the confidence
decreases. Creation of a new production rule occurs if
the current WM content is taken as the condition and the
produced output is taken as the action. For example,
when the answer “5” in response to the attended stimulus
“2 + 3 = ?” is rewarded, the rule “IF goal is to add two
numbers AND the sum of 2 and 3 is requested, THEN say
5” may be created. Initially, this rule will have a rather
low confidence value, so that the likelihood of its being
activated is rather low. However, when one must solve
the same problem again, the rule may be recreated, lead-
ing to an increased rule strength. After a sufficient num-
ber of successful rule applications, the rule may have
gained so much strength that it always gains the

84 Vandierendonck

competition. As discussed previously, it is well known
that during execution of simple cognitive tasks, new S-R
rules (in line with Pashler & Baylis, 1991a, 1991b) and
new stimulus-task rules (in line with Waszak et al., 2003,
2004, 2005) are created. Apart from these two elementary
forms of rule learning, a new rule also can be created by
combining existing ones. If two rules with the same
action part have conditions that differ, a new rule encom-
passing both conditions may be created, which results in
a more general rule. This possibility is important in cat-
egorization; use of the rules “IF there is a square AND its
color is red, THEN say Category A,” and “IF there is a
square AND its color is blue, THEN say Category A” forms
the more general “IF there is a square AND it has any
color, THEN say Category A” (e.g., Anderson, Kline, &
Beasley, 1979). Other possible rule combinations may
result in rule specialization or even in the creation of
chained rules.

Processing engine. The procedural knowledge base in
LTM can thus be characterized as a repository of proce-
dural rules. A processing engine handles the activation
and selection of the relevant rules. Only when the condi-
tion part of a rule matches one or more WM contents, the
rule can be applied. The rules that match WM contents
are flagged as applicable, and from this applicable set,
only the most relevant rules are allowed to fire, which
means that their action part is executed.

How can it be determined that one rule is more rele-
vant than another one? Assessment of relevance may
depend on several features. Rule strength is a first possi-
ble feature. A rule with a high strength or confidence
value has proven to be successful and therefore may be
considered to be more relevant than rules that have accu-
mulated less strength. However, even when a rule has
built up strength in a particular context, it may be less
relevant for the present context than a weaker rule. For
example, the more general rule “IF it is cloudy, THEN it
will rain” may be stronger than the rule “IF it is cloudy
and it is freezing, THEN it will snow”; however, if both
match, the latter rule would be more relevant because it
applies to more specific conditions. For that reason, rule
specificity also should be taken into account on the
assumption that a more specific rule is more likely to be
useful in the present context than a more general rule
(see also Holyoak, Koh, & Nisbett, 1989). This point can
be clarified by comparing a few examples: “IF category is
even, THEN press right button”; “IF goal is parity AND
category is even, THEN press right button”; “IF goal is
parity AND number is 4 AND category is even, THEN
press right button”; and “IF binding contains parity goal
AND number 4 AND category even is present, THEN
press right button.” These examples have all the same
action part, but they differ in the generality of the

conditions so as to form a hierarchy. The fewer elements
that are specified in the condition, the more general the
condition is; conversely, the more elements the condition
contains, the more specific it is. The last rule in this list of
examples is very specific in that it specifies the current
goal, the digit, its categorization, and the existence of a
binding of these elements. If all these components are
present in WM, then it is quite likely that this rule is rel-
evant to the presently existing context. In contrast, the
first example in the series only mentions the category
“even.” Although the rule has some relevance, it is far less
specific because it also would match when another goal
is present and the category representation in WM is a
leftover from a previous event.

A further feature that can be used to assess relevancy
is the degree of match. In many production systems (e.g.,
Anderson et al., 1979), matching is either all or none, but
it is perfectly possible to consider matching as a matter of
degree (e.g., Vandierendonck, 1995); a higher degree of
matching corresponds to a higher degree of relevance of
the rule. In sum, the rules selected to be most relevant
will be the ones with the highest confidence value, the
highest degree of match to the existing conditions, and
the most specific conditions for the same proposed
action.

Checking of WM contents for applicable procedural
rules occurs according to a scheduled process. To that
end, the processing engine performs a continuously
cycling processing loop consisting of a series of actions,
including processing of environmental inputs, checking
for conflicts, adapting WM contents, and initiating motor
actions. In every cycle, some procedural rules that match
WM contents are applied. Each rule application takes
some time, so that the next cycle of checking can only
start after rule application has finished. It is also impor-
tant to note that not every rule applied contributes to
achieving the intended goal. For example, some rules
provide a shortcut between stimulus and response, actu-
ally bypassing the task set specifications. When other
processes do not block the bypassing action, an action
slip (error) is bound to occur.

Conclusion

The model proposed here is a modification of the multi-
component model of Baddeley and colleagues (Baddeley,
2000; Baddeley et  al., 2010; Baddeley & Hitch, 1974).
This modification retains the modality-specific storage
systems (phonological loop and visuospatial sketch pad)
and their relation to LTM via either a direct route or the
episodic buffer, which is a multimodal store that binds
information from the modality-specific storage systems
and LTM. The modified model does not include the cen-
tral executive but instead provides a temporary store to

Distributed Executive Control in Working Memory 85

maintain task-relevant settings. This store is directly
linked to procedural LTM. A processing engine selects
relevant procedural rules that match WM contents and
executes their action parts.

Contribution to Executive Control

How can this proposed system, which operates on the
basis of rules that are automatically triggered when their
conditions match WM contents, explain what is usually
called executive control? Executive or cognitive control
and automatic processing often are considered to be two
qualitatively distinct forms of processing. Typically, the dif-
ference between controlled and automatic processing is
assumed to be characterized as three qualitative dichoto-
mies. Controlled processes are capacity limited, occur
under intentional or planned control, and are used with an
awareness of the outcomes, whereas automatic processes
are not capacity limited (and hence do not suffer from
interference), occur under stimulus control, and are not
used with an awareness of outcomes (Neumann, 1984).
Nevertheless, empirical findings rather suggest that there is
a continuum from automatic to controlled processes (e.g.,
W. Schneider & Shiffrin, 1977; Shiffrin & Schneider, 1977).
In particular, it should be noted that actions that are exe-
cuted for the first time often require important amounts of
control, but with practice, execution becomes more auto-
matic (Shiffrin & Schneider, 1977). With learning and prac-
tice, new connections are formed and strengthened. While
initially the link among stimuli, representations, and
responses have to be retrieved separately and then bound
together, with practice the LTM association among these
components gets stronger. As a result of practice, a transi-
tion occurs from separate retrieval and temporary storage
of components to retrieval of a united representation. The
advantages conferred by this transition are that the call on
temporary storage decreases and thus bypasses the capac-
ity limitation and that execution becomes faster and thus
diminishes the chances of interference by other fast (bot-
tom-up or stimulus-driven) processes. In essence, due to
learning and practice, there is a shift from intentionally
driven to more stimulus-driven control. With more autom-
atization or more stimulus-driven control, task execution
becomes easier.

Task difficulty does not depend only on the degree of
automatization but also on the number of actions or the
complexity of the actions that must be performed. Hence,
task difficulty is often reflected in the complexity of the
task set in terms of number of rules, parameters, and
constraints. Repeating out loud the syllable “blah” at a
fast pace (articulatory suppression) is an example of a
quite simple task that does not require control processes
once the recitation is started. In contrast, counting back-
wards by 3 (191, 188, 185, and so on) is an example of a

more difficult, nonautomatized task. After encoding the
starting number in WM, one must apply a subtraction,
then replace the number in WM with the result of the
subtraction, and then continue executing the same
sequence over and over. As more action components are
added, the task grows in difficulty, and this increasing
difficulty goes hand in hand with increased amounts of
intentionally driven control processes.

Related to the contrast between automatized and non-
automatized tasks is the distinction between intentional
contexts in which the route to the goal is known and
intentional contexts in which the route to the goal is not
yet known. In the former category, the action reproduces
the achievement of a goal that has been reached previ-
ously; therefore, this action can be referred to as repro-
ductive goal achievement. In the latter category, the
means to achieve the goal still have to be found and
produced; therefore, the action can be referred to as pro-
ductive goal achievement. Because this constitutes a real
dichotomy with qualitative differences between the two
categories, these two cases are considered separately.

Control in reproductive goal
achievement

To understand how the procedural network in interac-
tion with WM contents can account for what is usually
called executive control, one must remember that each
intentional action requires an instantiation of the inten-
tion or goal and the retrieval and configuration of the
related task set in WM. Because this is the context of
reproductive goal achievement, the task set (i.e., the way
to achieve the goal and the constraints in doing so) must
be assumed to have a representation in LTM. I explain
how the system accounts for executive control in three
different cases: task switching, a memorization task, and
a dual-task context involving both memorization and task
execution.

Task switching. In many studies of task switching,
researchers have investigated switching between numeri-
cal judgment tasks, such as parity and magnitude judg-
ment (e.g., Logan & Bundesen, 2003). These tasks were
included in examples presented earlier in this article. To
illustrate how control processes are conceptualized in the
present model, I have used these tasks again. In the pres-
ent case, each trial starts with the presentation of a digit
shown either in blue (signaling the magnitude task) or in
red (calling for the parity task). The parity judgment task
requires a left key press for an odd number and a right
key press for an even number; the magnitude judgment
task requires a left key press if the number is smaller than
5 and a right key press if the number is larger than 5; the
digits are centered on a screen; responses are expected to

86 Vandierendonck

be fast but correct. All this information is presented in the
instructions and is stored in LTM. Notwithstanding evi-
dence suggesting that an immediate procedural encoding
occurs (Cohen-Kdoshay & Meiran, 2007; Liefooghe, De
Houwer, & Wenke, 2013), some practice is included to
stabilize the procedural encoding of all this information.

Each trial of the experiment starts with the appearance
of a digit in the center of the screen—say, for example, a
red digit 3 on the current trial. As the appearance of the
digit involves a change in the visual environment, it (auto-
matically) captures attention. This capture leads to its
instantiation in WM, presumably in the episodic buffer
but possibly also in the phonological loop.5 The color
feature of the digit matches the rule that translates the
color into a goal (“IF color is red, THEN select parity
goal”), which results in the instantiation of the goal name
in the episodic buffer. Next, the task set is retrieved from
procedural LTM and configured in the executive module.
The present example includes two category-response
rules (“IF odd, THEN press left,” and “IF even, THEN press
right”), a parameter setting that a manual motor response
is required, and a parameter setting that both speed and
accuracy are required. Thus far, the WM contents match
rules regarding parity goals, parity task sets, and digits.
The combination of goal and digit matches some rules,
for example, a rule such as “IF goal is parity and digit is 3,
THEN retrieve category odd.” If this rule is applied, the
digit parity (odd) will be added to the episodic buffer. On
a next processing cycle, the presence of the goal, the digit
(target), and the category may trigger a rule to create a
binding of these elements in the episodic buffer. This
binding may then trigger a rule to activate the correspond-
ing response rule that is part of the task set. After suffi-
cient activation has been accumulated, a left key press
response will be executed. This sequence of processes
corresponds to Pathway 1 of Figure 1, and involves both
the episodic buffer and the executive memory module.

With more practice in the task, the LTM rule linking
the digit and the parity category becomes stronger and
may be triggered automatically, resulting in simultaneous
instantiation of the digit and its parity category in the
episodic buffer (Pathway 2 in Fig. 1). Thus, the time
needed to complete processing of the target is shortened,
with as a consequence faster correct responding.

When the category “odd” is instantiated in the epi-
sodic buffer, irrespective of whether this occurs due to
activation of the shortcut just mentioned or whether the
category is retrieved on the basis of the combination of
digit and goal, an error may occasionally occur. For
example, when the present digit (3) and the category
“odd” are in the episodic buffer while the previous cate-
gory (“even”) is still present, both the triplet “parity goal,
3, odd” and the triplet “parity goal, 3, even” meet the
conditions of a rule to form a binding. Only one of those

bindings can be implemented because each particular
element can be present in only one binding at any time.
Whichever of the two bindings is implemented first will
constrain further response selection. In other words, if
the parity-3-even binding is implemented first, the even-
right rule in EM will be triggered, even though the pres-
ent digit is odd.” This example shows that the processes
involved in binding the WM elements are “blind” to the
precise features of their inputs and hence do not “know”
which binding is the correct one.

In contrast to repeat trials (trials in which the task or
goal remains the same), switch trials require retrieval and
configuration of a different task set, which makes perfor-
mance vulnerable to sources of interference such as tar-
get-response associations and target-task associations. In
typical task-switching contexts, all the targets are ran-
domly distributed over the tasks, so that each digit occurs
about equally frequently in each task. Thus, if an associa-
tion between a particular digit and a specific task is
formed, the association between the same digit and the
other task are roughly equally strong, so that there is no
real danger of such an association bypassing processing.
Similarly, if an association between a particular digit and
a correct response under a particular task is formed, the
association between this digit and the alternative response
has a similar strength. The likelihood that such an asso-
ciation bypasses processing is also rather small.

Nevertheless, it is worthwhile to explore what would
happen if such associations could acquire enough
strength to affect performance. First, I examine the case
of a target-response association (Pathway 3 in Fig. 1).
Consider the case that over a series of magnitude judg-
ment trials, an association between the digit 7 and the
response right (IF digit 7, THEN respond right) has built
up strength and that the present trial shows the digit 7 in
a parity task. If the association has sufficient strength, the
right key press may be gaining strength while instantia-
tion of the parity goal and the corresponding task-set
reconfiguration still have to be completed (as in Pathway
1 of Fig. 1). If the strength of the respond-right process
reaches threshold before target-related processing is
complete, an incorrect and, in fact, unintended response
will be made. The only way to safeguard against such fast
errors is to make it more difficult for the unintended
response to be made by raising the response-threshold
setting (in EM) so that responding overall becomes
slower.6 This extra time before responding completes
allows goal-directed processing to configure the task set
and to build up strength in favor of the correct response.
The result is that on some occasions the incorrect
response will be executed while on other occasions the
correct response will be produced.

Next is the case of target-task associations (Pathway 4
of Fig. 1). This case is based on the acquisition of an

Distributed Executive Control in Working Memory 87

association between the target digit and the task name
(“IF digit 7, THEN instantiate magnitude goal”) within the
context of the same example of the digit 7 occurring only
in the magnitude task over a series of trials. When the
digit 7 occurs while the magnitude task set is already
configured, application of the rule only strengthens the
present goal and task-set representations. However, if the
digit 7 is presented for parity judgment (as indicated by
its color), two incompatible goals may become instanti-
ated in the episodic buffer: the parity goal (on the basis
of the color cue) and the magnitude goal (on the basis of
the acquired association). These instantiations will be
accompanied by instantiation of the corresponding task
sets in EM. The presence of incompatible goals in the
episodic buffer or incompatible task sets in EM consti-
tutes a goal conflict. If a conflict-detection rule fires in
response to the goal conflict, a goal-conflict flag is set
because further processing of two incompatible inten-
tions is bound to result in incoherent responding. As a
safeguard, when the goal-conflict flag is on, only goal-
and task-set-relevant rules are allowed to fire. When the
conflict is resolved, the conflict flag will be turned off. In
the meantime, only goal instantiation, goal inhibition,
and task-set-configuration rules are allowed to fire, with
the result that one of the two goals wins the competition.
Because goal and task-set instantiations of both tasks
start at about the same time, either of the two may win
the competition, resulting in either a slow correct or a
slow incorrect response.

This account of the rule applications in a task-switch-
ing context shows that there is no need for a special
agent to control the events and actions. Instead, in the
four processing pathways that have been well docu-
mented by previous task-switching research, the actions
performed are completely accounted for by the contents
of the WM modules and the rules available in procedural
LTM. Because the rules vary in strength, the time course
of WM instantiations shows some variation, resulting also
in variable responses and response times. So, even
though the interaction of conditions and rules follows
fixed principles, the resulting behavior of the system still
is variable.

Intentional memorization. Although memorization
without explicit intention to retain the information for
later usage does occur, in the context of WM research
with its focus on serial recall, storage is driven by an
intention to use the stored information. Because of this
intentional basis, this activity is assumed to involve, like
any other intentional activity, a representation of the
memorization goal and a corresponding task set. Given
that the task set specifies the means to attain the goal, it
seems evident that the task set encoded in EM would

include one or more of the “strategies” that could be used
to efficiently store and maintain information in memory,
such as encoding, chunking, grouping, rehearsing, or
refreshing. To cope with anticipated requirements of
recall (e.g., a focus on item information, particular item
features such as location or color, or the serial order of
items), one selects a suitable memorization method, and
it is encoded in the task set. Other task constraints such
as expected modalities of recall also are part of the con-
figured task set.

The presence of a memorization intention thus affects
the maintenance operations performed during a reten-
tion interval. In a typical WM task, serial position of the
memoranda is important, so rehearsal and refreshment
have to respect order coding. Similarly, if chunking is
used, the chunks have to respect the order of the indi-
vidual memoranda.

Once the memorization goal and task set are prepared,
each occurrence of a new memorandum has to be stored
in WM in accordance with the memorization rule and
parameters specified in the task set. In the interval
between successive memoranda and during the retention
interval at the end of the list of memoranda, some opera-
tions are performed to enhance the likelihood of later
retrieval of the memoranda. These operations are speci-
fied in procedural LTM and result in different actions
depending on the modality of the memoranda. For mem-
oranda stored in the phonological loop, regular rehears-
als are performed, whereas for memoranda in the
episodic buffer, refreshments are more likely to be used
(for more details about this difference, see Camos, Lagner,
& Barrouillet, 2009; Camos, Mora, & Barrouillet, 2013;
Camos, Mora, & Oberauer, 2011; Mora & Camos, 2013).

When recall is requested, the memorization goal is
replaced by a recall goal and corresponding task set. This
task set specifies the output modality required for recall
(oral recitation, written recall, old/new decision, and so
on). A recall loop is started, such that in each cycle of the
loop, the WM contents are scanned, and the memoranda
recovered are encoded in the output buffer and eventu-
ally emitted.

Dual-task: Task execution during retention interval.
The model’s account of the control processes occurring
in a dual-task context involves both memorization and
task execution. In the case considered here, a series of
tasks must be performed during the retention interval of
a memorization task. Many dual-task studies have
reported an impairment of serial recall when a secondary
task is performed during the encoding interval, the reten-
tion interval, or both. Controlling for time available for
memory maintenance and secondary task execution, the
methodology introduced by Barrouillet et al. (2004) has

88 Vandierendonck

become a standard in the field to test TBRS theory.
A  simple experiment reported in Barrouillet, Portrat,
Vergauwe, Diependaele, and Camos (2011) is used here
to illustrate how the model accounts for control pro-
cesses in such a dual-task setting.

In this experiment, memoranda were seven conso-
nants, each followed by an interval during which either
four or eight squares were presented at a slow (1,190 ms
per square), medium (990 ms per square), or fast pace
(790 ms per square). The participants judged whether the
location of the square was above or below the screen
center. In the theory tested in this experiment, memory
refreshment and task execution are assumed to require
attention, which is a resource that can be shared in an
all-or-none manner among different tasks. Hence, during
the retention interval, attention allocation rapidly switches
between the location decision tasks and memory refresh-
ment. That means that while attention is occupied by the
location decision task, attention is not available for mem-
ory refreshment: The larger the proportion of the reten-
tion interval that is occupied by decision tasks, the
smaller the proportion of time that will be left for mem-
ory refreshment, and the more recall will be impaired. As
expected on the basis of the theory, recall was poorer
with faster presentation rates, but the number of squares
in the interval did not affect recall performance because
the cognitive load (proportion of the interval occupied
by the decision tasks) did not change.

How does the present model account for such find-
ings? At the start of each trial, the memorization goal is
instantiated in the episodic buffer, and the memorization
task set is configured in EM. Next, the first memorandum
is presented and encoded in the episodic buffer. Soon
after encoding and refreshment have started, the first
square is presented. As appearance of the square consti-
tutes an environmental change, attention is captured,
resulting in the instantiation of the location-judgment
goal in the episodic buffer and configuration of the cor-
responding task set in EM. With this shift from memoriza-
tion to location judgment, the memorization task set must
be inhibited. However, the amount of inhibition applied
to the memorization task set can be assumed to be lim-
ited because the memorization rules and the location-
judgment rules respond to different conditions, so that
there is little opportunity for overlaps between applica-
tion of the memorization and the location-judgment task
sets. As a consequence, the chances for mutual interfer-
ence are rather small, and it suffices to ensure that the
location-judgment task set is more strongly activated than
the memorization task set. Furthermore, execution of the
memorization task has to continue afterwards, so that it
is more advantageous to keep the memorization task set
in WM so that it can be swiftly reactivated when the

opportunity arises. In fact, the context of the retention
interval may be considered as one in which the memori-
zation task is interrupted in favor of execution of another
task.

When the location-judgment task set becomes the
dominant one (i.e., is more activated than the memoriza-
tion task set), the location of the square must be judged.
The features of the square (form and location) become
encoded in the visuospatial sketch pad, procedural rules
to determine the location with respect to the reference
become active, and the result of the process is a catego-
rization response (“above” or “below”) that is instantiated
in the episodic buffer, where it can be bound with the
goal and the target to activate the appropriate task-set
rule (e.g., “IF a square is above center, THEN press left
key”). After response execution, application of a rule
matching the condition that a response has been emitted
reactivates the memorization goal and task set and sup-
presses the no-longer-relevant location-judgment goal
and task set so as to make the memorization task set
dominant. The memoranda are now further refreshed
until the next square is presented, which leads to a
switching back to the location-judgment task. The
remainder of the trial entirely consists of such switching
back and forth between the memorization and the
square-judgment task, and this switching continues until
the next memorandum is presented or recall is requested.
This state of affairs involving task-set switches ensures
that the two tasks are performed strictly sequentially: No
memory refreshments occur during location judgment,
and no square processing occurs during memory refresh-
ment. Without any need for additional assumptions, it
follows that if more of the interval is occupied by loca-
tion judgment, less time will be available for memory
refreshment and that consequently more memory loss
may occur. Clearly, this account makes the same predic-
tion as Barrouillet’s TBRS theory. Moreover, this predic-
tion can be made without any call on a central executive
or an attentional resource.

Interim conclusion. Clearly, for the all situations con-
sidered here, goal achievement is possible without an
autonomous agent such as a central executive. In all the
examples, the conditions represented in WM are suffi-
cient to trigger specific condition-action rules that either
change WM contents or initiate a response that achieves
the goal. Occasionally, shortcut rules may be applied that
sometimes result in the selection of an incorrect action or
lead to a conflict that must be resolved and again may
result in an error. In fact, the presence of such rules pro-
vides a more straightforward explanation of the occur-
rence of errors than a central executive that fails on some
occasions.

Distributed Executive Control in Working Memory 89

Control in productive goal
achievement

In a situation in which one lacks experience or in which
the route to the goal is unknown, activation and instan-
tiation of the goal will not result in a successful retrieval
of a complete task set because the task set has not been
learned yet. Finding a method to attain a goal is the con-
text of problem solving. Even in the early days of the
information-processing approach to cognition, this was
the subject of computer-simulation programs such as the
Logic Theorist (Newell & Simon, 1956) and the General
Problem Solver (Newell & Shaw, 1959). These programs
solve problems by searching the so-called problem space
for combinations of means that lead to the goal. In terms
of goals and task sets, this means that at first, a subgoal
acts as a substitute for the goal during a search of the
problem space (Newell, 1981) for a suitable way to
achieve the goal. Usually a solution consists of finding
one or more intermediate goals that can be achieved. For
example, if the goal is to find the sum of 324 and 489, a
subgoal first may be set up to find the sum of the hun-
dreds (300 + 400), next the sum of the tens (20 + 80),
then the sum of the units (4 + 9), and finally the sum of
all the intermediate results. In general, a solution can be
obtained by finding intermediate steps that can be
achieved by already acquired means and then stepwise
by applying the solution steps to reach the final goal (see
also de Groot, 1965). The pioneering work of Alan
Newell, Herbert Simon, and others (e.g., Newell & Simon,
1956) in the early attempts of computer simulation and
artificial intelligence and also later work leading to the
different versions of the adaptive control of thought
(ACT) model (Anderson, 1983, 1990, 1996; Anderson &
Bower, 1973; Anderson & Lebiere, 1998) already have
shown that even solving difficult problems does not need
a “ghost in the machine” (Ryle, 1949, p. 17) and can sim-
ply be achieved by applying rules and heuristics (Newell,
Shaw, & Simon, 1958a, 1958b; Newell & Simon, 1961).

Discussion

From the first publication about the multicomponent
working model by Baddeley and Hitch in 1974 until
today, the model has proven to be a productive tool for
new research, providing understanding of the operation
of WM. All the components of the model have their func-
tion and are rooted in empirical findings, except for the
central executive. Although evidence supports the
involvement of executive processes, the central executive
component is vaguely defined, with unlimited powers of
control. As eloquently argued by Verbruggen et al. (2014),
there is an urgent need to replace such explanations
of  control by a mechanistic account that refers to

well-understood processes. In this vein, I propose in the
present article that the central executive in the multicom-
ponent WM model is replaced by a memory module that
temporarily maintains task-execution-related information
(task set) and that the control is performed by actions
executed when the conditions match WM contents.

Given the description of the present modification of
the model, a few critical questions deserve further atten-
tion. The first question is whether the proposed model is
sufficient to replace the central executive. The second
concerns the role of the proposed processes in an indi-
vidual differences context. A third critical question con-
cerns the validation of the adapted model.

Is the central executive made
redundant?

The elaborative description of the model and its account
of performance in executively demanding situations has
shown that basic processes triggered by the congruency
of WM contents and the condition part of rules stored in
procedural LTM can account for selection of goal-directed
action. The same mechanism also accounts for the occa-
sional lapses that occur due to interference and noise in
the WM representations. Actually, the processes involved
in reproductive goal achievement cover all types of tasks
that have been used in dual-task studies of the central
executive. To substantiate this point, I consider the tasks
used in such dual-task research one by one. In each case,
the present account suffices to explain the observed
dual-task interference effects.

Backward counting. Backward counting by 3 as in
the early studies of decay in short-term memory ( J. A.
Brown, 1958; Peterson & Peterson, 1959) is one of the
first tasks ever used to interfere with memory refresh-
ment. Backward counting requires the repetitive applica-
tion of a “minus 3” operation. This task can be performed
by implementing the appropriate task set: subtracting 3
from the target number and then replacing the target
number with the result of the subtraction. Application of
condition-action rules in response to current WM con-
tents suffices to perform this task repetitively.

Random generation of elements from a set. Another
often-used task consists of random generation of ele-
ments from a set. For example, imagine repetitively
throwing a die and announcing the upcoming number.
Such tasks have been performed with letters or numbers
(Baddeley, 1966; Robbins et al., 1996; Towse & Cheshire,
2007; Towse & Valentine, 1997), with selection of keys on
a key pad (Baddeley, Emslie, Kolodny, & Duncan, 1998),
and with time intervals (Vandierendonck, De Vooght, &
Van der Goten, 1998a). All these variations of random

90 Vandierendonck

generation involve simple control processes that mostly
are triggered by instructions not to repeat the same item
too often or not to produce familiar patterns or orders.
Consequently, the task set specifies not only the require-
ment to retrieve elements or maybe strings of elements
(Vandierendonck et al., 2012) but also the constraints that
have been stressed in the instructions. All processes
needed for executing such a task rely again on condition-
action rules that are applied when they match the WM
contents. The additional constraints stored with the task
set activate rules that check for the presence of repeti-
tions or familiarities.7

In random-interval repetition (Vandierendonck, De
Vooght, & Van der Goten, 1998b), auditory stimuli
(bleeps) are presented at random time intervals, and
each detected bleep requires a fast detection response.
The random variation of the time intervals discourages
automatization of the detection response and again con-
dition-action rules suffice to correctly execute the task.

Choice response. Most frequently, choice response
tasks (Szmalec, Vandierendonck, & Kemps, 2005) are
used in dual-task studies. Such tasks (e.g., parity judg-
ment, location judgment, and so on) require selection of
an appropriate response. Also the trails task (Lezak, 1983)
has been used in some studies (Baddeley et  al., 2001).
The most difficult version of the task requires alternating
between two well-known series (e.g., alternate between
reciting days of the week and months of the year:
Wednesday, March; Thursday, April; and so forth). Even
though each series is well known, progress in each series
must be remembered. Again, condition-action rules com-
bined with the appropriate task set account for correct
task performance.

Memorization. In a few studies, memorization has
been used as a secondary task in recall (Depoorter &
Vandierendonck, 2009). As explained previously, memo-
rization requires a task set and is further governed by
condition-action rules. When a memorization task is exe-
cuted in the retention interval of another memorization
task (with different contents), application of the condi-
tion-action rules matching WM contents completely
accounts for controlled task execution.

In other words, existing dual-task research on the role
of the central executive in WM has called on only repro-
ductive-goal-achievement tasks, so there is no need to
call on productive-goal-achievement actions. Although
the present model accounts for productive-goal-achieve-
ment processes, in view of the kinds of tasks used to
interfere with the central executive, one may ask whether
productive-goal-achievement actions should also be part
of the central executive. They are, no doubt, part of the
cognitive repertoire, but is it necessary to assume that

they are part of the executive control processes as needed
in WM?

In an attempt to achieve a more restraining conceptu-
alization of the central executive, Baddeley (1986) pro-
posed that this agent corresponds to the supervisory
attention system described by Norman and Shallice
(1986).8 Their model assumes two levels of control. As
long as a well-trained skill is being executed, the system
operates largely automatically; the occasional conflict is
resolved semiautomatically on the basis of learned habits
(contention scheduling). However, in novel situations or
failures of the automatic conflict resolution, the supervi-
sory attentional system comes into action. It intervenes in
favor of one of the competing actions or can call on strat-
egies for finding alternative solutions. The distinction
between contention scheduling and supervisory atten-
tion seems to run parallel to the distinction made here
between reproductive and productive goal achievement,
although it is difficult to tell whether the two distinctions
are completely equivalent. If this interpretation is correct,
it follows that the present modeling can also account for
actions subsumed by Norman and Shallice’s (1986) super-
visory attention system. The remaining question of
whether it is necessary to assume that WM functioning
calls on supervisory attention and problem solving
requires further research.

In the present proposal, I clearly have gone beyond a
simple fractionation of the central executive into a
restricted set of smaller components. Instead, I have tried
to identify the processes underlying executive control.
However, because the proposal is based on ideas from
research on task switching, some may argue that the
present modeling is representative of only one executive
function: (task-)set shifting. Indeed, in the classification
of executive functions proposed by Miyake et al. (2000),
the latent variable of set shifting corresponds to the com-
mon variance in a number of task-switching contexts.
However, the common variance among three variations
of task switching might involve more than simply set
shifting. In fact, the latent variable is defined as the com-
monality in task demands of the various task-switching
contexts involved; as documented in the present article,
this involves much more than replacing one intention by
another one. Similarly, the latent variables of memory
updating and inhibition also are defined as the common-
ality in a series of task demands. For memory updating,
it concerns demands common to a number of memory-
updating procedures (see also Szmalec, Verbruggen,
Vandierendonck, & Kemps, 2011), and for inhibition, it
concerns demands common to a number of situations in
which an automatic response must be suppressed in
favor of another response. Because the processes
described in the present model include not only switch-
ing between tasks but also intentionally adapting

Distributed Executive Control in Working Memory 91

memory contents (memory updating) and selecting some
action sequences above other ones (selection and inhibi-
tion), it is clear that the model covers not only set shifting
and task switching but also processes related to memory
updating and inhibition.

Individual differences

Apart from being a central notion in experimental
approaches to cognition, WM capacity—the number of
chunks of information that can be kept active during per-
formance of other tasks—is a property of the cognitive
system that varies across persons. Complex-span tasks
measure WM capacity in a standardized dual-task con-
text; well-known examples are the reading span task
(serial recall of words while processing sentences,
Daneman & Carpenter, 1980), the counting span task
(counting dots and remembering the results of a series of
counts, Case, 1985), and the operation span task (serial
recall of words while performing arithmetic operations,
Turner & Engle, 1989). With the development of such
complex WM span tasks, a correlational approach to WM
was initiated. A popular and successful alternative to the
experimental approach, the complex span measure is
used in typical latent variable studies as well as in experi-
mental designs in which one or more experimental vari-
ables are crossed with the contrast between subjects with
a high and low complex-span performance. Important
achievements of this approach include a large body of
findings regarding the relation between WM capacity and
other performance variables (for a review, see Barrett,
Tugade, & Engle, 2004); robust results about the relation-
ship between WM and fluid intelligence (Conway, Kane,
& Engle, 2003; Unsworth & Engle, 2005); and new theo-
retical models of WM (e.g., Engle, Kane, & Tuholski,
1999).

Although the correlational approach to WM was not
addressed in the present article, it is important to discuss
the potential contribution of the proposed distributed
control processes to individual difference approaches of
WM. Just as the views on WM are rooted in experimental
approaches, the correlational approach to WM some-
times calls on a control homunculus to account for indi-
vidual differences in WM capacity. In the theoretical
model of Engle, Kane, and Tuholski (1999), for example,
the notion of executive attention plays a critical role.
According to Unsworth, Schrock, and Engle (2004), exec-
utive attention plays a role in situations that require “inhi-
bition of prepotent responses, error monitoring and
correction, and decision making and planning” (p.
1302)—in other words, in situations that typically call on
executive functions as defined by several other authors
(e.g., Burgess, 1997; Miyake et  al., 2000; Norman &
Shallice, 1986). This list of situations also defines the

scope of the supervisory attention model and the central
executive in the multicomponent model of WM. This
actually means that the labels central executive and exec-
utive attention refer to basically the same concept, and
although executive attention has not been profiled as a
homunculus, replacing this construct by distributed con-
trol processes is as valid as it is for the notion of central
executive. However, because I did not refer explicitly to
individual differences in this proposal, there is a need to
specify how these control processes can account for indi-
vidual differences in WM capacity.

In fact, the literature contains already a number of
indications of how this can be achieved. For example,
experiments with demanding tasks such as the Stroop
task (naming the print color of nonmatching color words,
Stroop, 1935) have shown that high-span individuals are
better able than low-span individuals to keep the task
goal active in WM (e.g., Kane & Engle, 2003; Kiefer,
Ahlegian, & Spitzer, 2005; Long & Prat, 2002; Meier &
Kane, 2013). This account is related to the notion of goal
neglect (failure to attain the activated goal, Duncan et al.,
2008) and corresponds to the present proposal that the
task goal and, in particular, the task set are maintained in
an active state in WM. It suggests that these processes are
subject to individual differences and are part of what is
measured by complex span tasks.

Similarly, several studies have shown that high-span
persons are faster and more accurate than low-span per-
sons in resolving conflicts between automatically trig-
gered courses of action and intended actions; examples
are the execution of controlled eye movements (e.g.,
Kane et al., 2001; Unsworth et al., 2004) and some visual
attention tasks (see Vandierendonck, 2014, for an over-
view). Such conflict resolution processes typically occur
in task-switching contexts, which were used for the pres-
ent model. Again, the efficiency with which such pro-
cesses can be performed seems to differ across persons
with low and high WM capacity.

It is important to note that in these situations, there is
a conflict or competition between an automatically trig-
gered action (e.g., reading the color word in a Stroop
task) and an intended action (naming the print color of
the word). In some instances, the automatic action wins
the competition; in other instances, the intended action
does. Simply building up activation of the intended
action at a faster rate or to a higher level, possibly jointly
with lateral inhibition of the automatic action, suffices to
let the intended action win this competition.

Some authors have assumed that active inhibition of
the automatic action is needed in these and some other
contexts. Although inhibition of a no-longer-needed task
set is part of the present model, a general active inhibi-
tion process is not included and is not necessary. The
model seems to do fine without direct inhibition (except

92 Vandierendonck

for task sets). The present model assigns a key role to
activation: WM contents have to be kept active and pro-
cesses that boost activation of these contents achieve this
goal. Activation of WM contents decays over time or can
be inhibited indirectly by lateral inhibition. To directly
inhibit (declarative) WM contents requires accessing
these contents with the aim of decreasing their activation;
however, accessing WM contents increases their activa-
tion. Hence, including active inhibition would require
additional processes to make it work. Furthermore, the
operationalization of the construct of inhibition in the
model of Miyake et al. (2000) does not suggest that inhi-
bition works in a direct way. In that model, the executive
function of inhibition is a latent factor based on the com-
mon variance in three tasks: the (exogenous) anti-sac-
cade task (executing an eye movement in the opposite
direction of a peripheral cue), the Stroop task, and the
stop-signal task (responding quickly to a target but with-
holding the response when a stop signal appears). All
three tasks require the resolution of a conflict between
two courses of action, so that it suffices to assume a com-
petition between the activation of these two courses of
action.9

The same processes that were proposed to account for
executive control in general seem to be applicable in the
context of the individual differences approach to WM.
However, attention must also be paid to the observation
that measures of WM capacity (complex span tasks)
share an important amount of variance with fluid intelli-
gence tasks such as the Raven’s progressive matrices
(Raven, Court, & Raven, 1977). As the relation to intelli-
gence was not a theme in the present article, one may
ask whether the model can account for such a relation-
ship. This is largely an empirical question. It is difficult to
see a direct link between the kind of processes needed
in task-set control (reproductive goal achievement) and
intelligence. However, in the context of problem solving
(productive goal achievement), a relationship to intelli-
gence seems evident. Because at present the importance
of the contribution of each of these two sets of processes
is not known, a substantiated answer can only be
obtained on the basis of further empirical research.

Empirical support

Thus far in this discussion, I have addressed the claims
that the present model can account for executive control
processes in WM without invoking a homunculus and
that the model can also account for individual differences
in WM. Next, I address how empirical research can fur-
ther substantiate the claims made in the model. One of
the basic assumptions of the present model adaptation
concerns the position that intentional memorizations as
well as cognitive tasks require a task set for selection of

the appropriate intentional actions. On the basis of this
assumption, the model predicts the same effects of cogni-
tive load in strictly timed dual-task designs that the TBRS
model of Barrouillet and colleagues does (Barrouillet
et al., 2007; Barrouillet et al., 2004; Barrouillet & Camos,
2010; Barrouillet, Portrat, & Camos, 2011; Portrat et  al.,
2008). Besides, because according to the present model,
the cost of switching between the primary memorization
task and the secondary task depends on the degree of
overlap between the two task sets, an additional cost of
switching may be expected. In particular, the greater the
overlap of the two task sets, the larger the switch cost will
be; as a result, there will be less time for memory refresh-
ment and, consequently, a further impairment of recall.

Varying the requirements and demands of the memo-
rization task can test the latter expectation. I argued that
the overlap between a memorization task set and typical
cognitive tasks (choice-response tasks) that are used in
dual-task designs is rather low. By varying the demands
of the memorization task, one also can vary the degree of
overlap with secondary tasks, making it possible to com-
pare a condition with low overlap to a condition with
high overlap between memorization and secondary task.
Such an increased overlap could be achieved by adding
a task requirement to the memorization task. For exam-
ple, instead of simple refreshment of the memory con-
tents, the memory task could demand that after every
task execution, the memoranda be changed on the basis
of some memory-updating tasks (e.g., Oberauer, Suss,
Schulze, Wilhelm, & Wittmann, 2000). With a larger over-
lap between memorization and task execution, switching
between task execution and memorization would be
expected to cost more time, which in a strictly timed
design would be expected to result in poorer recall.

Another way to manipulate the overlap between mem-
orization and secondary task concerns the inclusion of
operations to be performed on the memoranda. To the
extent that these operations overlap or are similar to
actions required in the secondary tasks, the similarity
between the task sets of memorization and secondary
will be increased. One can think of conditions requiring
a decision on each memorandum (cf. levels of processing
methodology, Craik & Lockhart, 1972). Overlap between
the memorization task and the secondary task then can
vary with the degree of similarity between the required
decision and the secondary task action. An example of
such a task is one in which letters are presented to sub-
jects for later recall but instead of recalling the letters that
were presented, subjects are asked to perform an alpha-
bet arithmetic task on each letter (e.g., “Replace each let-
ter by the letter n positions later in the alphabet,” Zbrodoff,
1999), then maintain the outcome of this operation, and
recall it at the end of the task. If the secondary task calls
for mental arithmetic, the overlap will be large, but if the

Distributed Executive Control in Working Memory 93

secondary task requires another type of response, over-
lap will still be substantial but smaller. With increases in
overlap, the chances of interference between the two
task sets (of the memorization task and the secondary
task) increase, making recovery or reactivation of the
maintenance task set more difficult.

In contrast, if the operations to be performed during
memorization do not overlap with the secondary task
and are memorable, it may be expected that adding an
additional task enhances memory, in line with typical
levels-of-processing findings (Craik & Lockhart, 1972).
This also applies when specific actions are applied to the
memoranda, as in the so-called enactment effect: When
during encoding, an action must be performed on each
of a series of objects, this enactment results in improved
recall compared with an equivalent time of encoding
without the opportunity to manipulate the objects
(Engelkamp, Zimmer, & Kurbjuweit, 1995; Engelkamp,
Zimmer, Mohr, & Sellen, 1994; Mulligan & Hornstein,
2003; Steffens, Jelenec, Mecklenbra, & Thompson, 2006;
Yang, Gathercole, & Allen, 2014). Furthermore, according
to the present model, if enactment is studied with a sec-
ondary task that overlaps in task set with the memoriza-
tion task, memory gain should be lowered in comparison
to conditions with smaller degrees of overlap.

Another issue of interest is that the task set includes
a parameter setting that determines the orientation of
attention. Several studies have shown that performance
on selective attention tasks is poorer when a memory
load is present than when there is no memory load
(e.g., Lavie, Hirst, de Fockert, & Viding, 2004). Similarly,
subjects with a low WM capacity tend to perform more
poorly on attention tasks than subjects with a high
WM  capacity (e.g., Kane & Engle, 2003; Kane, Poole,
Tuholski, & Engle, 2006; Poole & Kane, 2009). For a
review of the main findings regarding the interaction
of selective attention tasks with WM and an explana-
tion of the observed effects in terms of the model pre-
sented here, see Vandierendonck (2014). According to
the present view, when a selective attention task is
performed under memory load (i.e., during a memori-
zation interval), secondary task performance may suf-
fer to the extent that there are overlaps in the attentional
settings of both task sets.

Another avenue for model testing consists of imple-
menting a computational model based on the present
assumptions and comparing performance of the model
with human performance. A computational model based
on assumptions that are quite close to the ones elaborated
in the present article has been applied to a few experi-
ments published in the literature (Vandierendonck, 2012).
Performance of the model corresponded well to human
performance. However, it is not easy to assess the extent
to which the observed degree of correspondence to the

data depends on the central assumptions made here. In
each computational implementation, additional assump-
tions are needed to make the model run, so clearly more
work along these lines is required. Nevertheless, together
with other work (e.g., Kieras et  al., 1999; Lovett et  al.,
1999; W. Schneider, 1999), this demonstrates that it is pos-
sible to account for executive control without invoking an
autonomous agent such as a central executive.

Relation to other work

The version of a multicomponent WM model elaborated
in the present article has not been developed in isolation
of other views on WM. As was evident in the body of this
article, the EM module resembles procedural working
memory in Oberauer’s (2009, 2010) WM model. The main
differences between the present modeling and Oberauer’s
view were already clarified. In the present model, WM is
not considered to be activated LTM but concerns a sepa-
rate representation combining information from LTM with
information from sensory input and mental states. Another
difference concerns the architecture of the model: Instead
of assuming a completely similar hierarchy of processes
for activated declarative and procedural LTM as in the
model of Oberauer, the present model assumes that the
episodic buffer (similar to Oberauer’s declarative WM)
and EM (similar to Oberauer’s procedural WM) not only
have different contents but also operate in a manner that
is adapted for the type of content.

The model also shows important similarities to the
views developed by Barrouillet and colleagues (2004,
2011). Their TBRS model is based on the assumption that
there is a structural bottleneck that prohibits the central
attentional resource to be allocated to more than one
activity at a time, so the usage of time is crucial. In the
present model, usage of time is similarly critical, not
because of a basic assumption about serial processing
but because the model assumes that goal-directed activi-
ties have representations in WM; these representations
are the conditions that activate the procedural rules, so
that only the rules that match the representations that are
relevant to the currently dominant task set will be trig-
gered at any time. This difference between the present
model and the TBRS model pertains to the hypothesized
underlying processes and is the basis for variance of task-
set overlap between memorization and secondary tasks.
Such an overlap can lead to additional impairment of
recall if the cost of switching between the two tasks is too
large. Apart from that, the present model basically makes
the same predictions as the TBRS model, because the
present model also assumes decay of WM contents that
are not refreshed or rehearsed.

Finally, the present model shares many similarities
with models developed as follow-ups to early computer

94 Vandierendonck

simulation and artificial intelligence projects, the best
known of which probably are the ACT model and its
variants (Anderson, 1983, 1996; Anderson & Lebiere,
1998; Lovett et  al., 1999). Using similar approaches,
researchers developed several models of general cogni-
tive function and WM, such as the executive process-
interactive control (EPIC) model (Kieras et  al., 1999;
Meyer & Kieras, 1997a, 1997b), Soar cognitive architec-
ture (Young & Lewis, 1999), and others (W. Schneider,
1999). Also a few specifically designed models were pro-
posed as alternatives to traditional WM views (Barnard,
1999; O’Reilly, Braver, & Cohen, 1999).

In view of all these efforts, one may ask whether these
modeling efforts have not solved the homunculus prob-
lem already. Indeed, the present proposal bears many
similarities to production models such as adaptive control
of thought-rational (ACT-R) and EPIC. In fact, these mod-
els are powerful computational devices with the potential
to include executive control processes in the more spe-
cific models developed with these tools. An ACT-R model
of WM has been published (Lovett et  al., 1999). In this
model, WM is the activated part of LTM, and although the
model does account for dual-tasking effects, it does not
include control mechanisms to link WM to higher cogni-
tive processes. The WM modeling within the EPIC frame-
work (Kieras et  al., 1999) comes much closer to the
present claim that it is possible to replace the central
executive by specific control processes embedded in pro-
duction rules by giving an account of executive processes
involved in verbal WM. In the present model, I extend this
previous work by trying to account for the complete
scope of a central executive agent in WM.

Conclusion

The model presented here—an adaptation of the multi-
component WM model—eliminates the central executive
as a homunculus by replacing it with a passive store, a
procedural LTM network, and an engine governing their
interaction. The passive store contains information rele-
vant to task execution—the task set. These contents and
those of the other WM components trigger matching
rules in the procedural LTM network, which results in
automatic application of the most relevant matching rules
to change the WM contents in any of its storage modules
(phonological loop, visuospatial sketch pad, episodic
buffer, and EM) or to initiate a motor action. This model
accounts for both productive and reproductive goal
achievement.

Declaration of Conflicting Interests

The author declared no conflicts of interest with respect to the
authorship or the publication of this article.

Notes

1. It is indeed the first model explicitly proposed to account
for WM, even though Miller, Galanter, and Pribram (1960)
were probably the first to use the term working memory, and
Atkinson and Shiffrin (1971) were the first to indicate that short-
term memory could be referred to as working memory because
of the many control processes involved (coding, chunking, and
so on).
2. Note, however, that although the presence of a verbal goal
may be useful in task switching, it does not seem to be sufficient
for goal attainment, as the verbal goal is merely a reminder of
the current goal state.
3. Note that because the phonological loop and the episodic
buffer have different functions, it is perfectly possible for some
piece of information to be maintained in both modules.
4. Like the other parameter settings of the active task set, the
specification of the orientation of attention is needed for the
processes related to task execution. If this parameter specifies
that attention be focused on the central area of the visual field,
this implies that stimuli occurring in that part of the field will be
processed and encoded within the episodic buffer, but stimuli
outside this area are less likely to be processed. On the con-
trary, when the parameter indicates that attention is spread over
the major part of the visual field, all stimuli within that part of
the field will be processed. There is no homunculus to make
any decisions about attentional orientation; instead the atten-
tional orientation is installed with the task set on the basis of
information retrieved from LTM.
5. Because the information in this and following examples is
in the verbal modality, the phonological loop may be used to
maintain this information. However, as in the present example
binding is required, it is necessary to assume that the episodic
buffer is involved.
6. This can occur after an error has been committed by applying
a rule that changes the response threshold.
7. This account of the control processes required in random
generation suggests that random generation is not a difficult
task. However, most people who have tried to generate random
events know from experience that random generation is in fact
quite difficult. This subjective difficulty stems from the fact that
random generation (i.e., producing a series of events such that
these events are equiprobable and independent) is not part of
our behavioral repertoire. It is next to impossible for humans to
select a series of events that obeys the statistical criterion of sto-
chastic independence. Even though every generated sequence,
whatever its statistical properties, can be produced by a purely
random process, most people will have doubts about the ran-
dom qualities of the series because they are aware of the many
times corrections have been made to the spontaneously gener-
ated events. Moreover, spontaneously produced sequences can-
not be trusted to be random either because of the occurrence of
priming and retrieval of known sequences from LTM.
8. At the time of this writing, this position is still maintained by
Alan Baddeley as he confirmed in personal communications I
had with him at the occasion of the International Conference
on Working Memory in Cambridge ( July 2014) and the Seventh
European Working Memory Symposium (EWOMS 7) confer-
ence in Edinburgh, Scotland (September 2014).

Distributed Executive Control in Working Memory 95

9. Note that this competition also applies for the stop-signal
task. Accounts of the stop-signal task assume a competition
between two processes: execution of the response required
for the target and a process that blocks responding (Logan &
Cowan, 1984).

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Cog. Psych WWR #1

In class last week the Chinese Room argument was brought up in reference to how symbols are grounded. I had never heard of the Chinese Room or John Searle so I wrote it down to investigate after class. Further into the discussion the analogy of trying to discern symbols with more symbols struck an immediate cord with me. My six year old daughter had recently finished reading a beginners chapter book on Helen Keller and in the story it tells of this momentous moment where Helen finally understood that the hand movements she was making equated to a symbol for the water she was feeling. In the book Helen poignantly describes this as her soul’s birthday. My little one had a lot of questions about what that meant and I fumblingly try to convey the meaning. Finally I asked her to close her eyes and cover her ears tight while I made movements in her hand. I think in some small way she was able to appreciate what it would be like to have communicate that way.

In an effort to try and learn more about that moment I pursued more information about the Chinese Room and Helen Keller. Indeed I found an article published in Minds & Machines in 2006 titled “How Helen Keller used syntactic semantics to escape from a Chinese Room” by William J. Rapaport. He posits that computers can learn natural language through syntax semantics which he says is how Helen Keller came to know language. In a dictionary analogy Rapaport clearly identifies the circular process of defining word with another. At some point you must have understanding or meaning of a word to get out of this loop. He calls this a closed loop. Our minds work in much the same way per Rapport “More significantly, our brain is just such a closed system: all information that we get from the external world, along with all of our thoughts, concepts, etc., is represented in a single system of neuron firings. Any description of that real neural network, by itself, is a purely syntactic one” (Rapport, 2006).

Ultimately, Rapport explains that Helen had some semantic correspondence because she had her own rudimentary version of signs and ways of communication before her teacher Ann Sullivan arrived. While this article certainly helped me to understand how it was Helen was able to make such an extraordinary leap in understand I was not able to see how this could be applied to computers. That

could be due to my own lack of understanding rather than fault in the author’s logic. There is another article out there titled Helen Keller was not in a Chinese Room. I intend to read that as well to see if I can get anything further of the subject

Remember, reactions are the amount of material that will fit on a one page, double-spaced, typed document. Part of the exercise is for you to get right to your point and justify it briefly. Sources are open, but I’d prefer some element of empirical research. So, if you see something in the newspaper and want to react to it, try to track down the original research. Or, find some research that supports or refutes the information in the newspaper and discuss that. Show me that you’re thinking, include some cognitive stuff, and read some of the primary literature and I will be pleased.

What will get me excited about a reaction paper:

· React based on something else you’ve learned in the class (“when we discussed language, you said…but this article said…” or “here’s another example of…”). Bring things together in a new and interesting way.

· React based on something you know about your area of psychology that relates to Cognitive Psychology.

· How does this idea lead to new research questions?

· Make me say “this person is insane, but that’s a really cool idea.” Explore absurd places to take the research.

What won’t get me excited about a reaction paper:

· “This article was really easy/hard to read/understand.”

· A personal anecdote; overturning data with an anecdote

· “There were only five participants in the study which seems like too few.” I don’t want a showboating critique, talk to me about ideas.

· Two pages of summary followed by “I really liked this article.”

· A “reflection.” In fact, calling it a reflection report will piss me off.