Journal of Memory and Language 43, 652– 679 (2000)
doi:10.1006/jmla.2000.2720, available online at http://www.idealibrary.com on
A Procedural Explanation of the Generation Effect for Simple
and Difficult Multiplication Problems and Answers
Danielle S. McNamara
Old Dominion University
and
Alice F. Healy
University of Colorado at Boulder
Three experiments investigated the generation effect for the free recall of multiplication problems
and answers. In Experiment 1, a greater generation effect for answer recall was found for participants
presented with simple as compared to those presented with difficult multiplication problems. This
finding is inconsistent with an explanation of the generation effect in terms of effort. Experiment 2
replicated Experiment 1 and further demonstrated that participants show an equivalent generation
effect for problem operands (i.e., the cues) regardless of problem difficulty. Generation accuracy also
influenced the magnitude of the generation effect in the difficult problem condition. Experiment 3
replicated the results of Experiment 1, holding constant problem answers across simple and difficult
problems. These experiments collectively demonstrated a generation effect for the answers to
arithmetic problems only when participants reinstated at test the cognitive procedures used at study,
thus providing further evidence for the procedural account of the generation effect. © 2000 Academic
Press
Key Words: generation effect; procedural reinstatement; multiplication problem difficulty; arithmetic; cognitive procedures; memory; retrieval; effort.
The generation effect refers to a robust retention advantage found for material that is selfgenerated compared to material that is simply
copied or read. In a typical generation paradigm, participants are shown related word pairs
in either a read or generate condition (e.g.,
Slamecka & Graf, 1978). In the read condition,
We are indebted to Michael Ferris for help with Experiment 2 and to James Kole for help with Experiment 3. We
are also grateful to Dan Burns, Sal Soraci, and Bob Widner
for helpful comments on an earlier version of this article.
This research was supported in part by a Postdoctoral Fellowship (Grant 93-12) and by a Career Development Award
(Grant 95-56) from the J. S. McDonnell Foundation to
Danielle S. McNamara and by Army Research Institute
Contracts MDA903-93-K-00010, DASW01-96-K-0010,
and DASW01-99-K-0002 and Army Research Office Grant
DAAG55-98-1-0214 to the University of Colorado (Alice
F. Healy, Principal Investigator).
Address correspondence and reprint requests to Danielle
S. McNamara, Department of Psychology, MGB 250, Old
Dominion University, Norfolk, Virginia 23529-0267.
E-mail: [email protected].
both words are displayed (e.g., short–tall),
whereas in the generate condition, only the cue
word and a portion of the target word are displayed (e.g., short–t___) and the participant
generates the target word (i.e., tall). Many studies have demonstrated that items that are generated, compared to those that are read, have a
greater probability of being recalled or recognized (see McNamara & Healy, 1995a, 1995b,
for reviews of the literature). In sum, active
participation in the learning process leads to
greater retention than does passive perception.
The overarching goal of our research has
been to determine the parameters and limitations of the generation effect and to provide an
account of this basic cognitive phenomenon
within a relatively general theory of human
memory, the procedural account of learning
(Healy et al., 1992, 1993, 1995). The present
study provides a further test of the procedural
account of the generation effect (Crutcher &
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652
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
Healy, 1989; McNamara & Healy, 1995a,
1995b). There are two aspects to this account.
First, the critical factor leading to a generation
effect is that the participants engage in cognitive
operations that connect the target item to information stored in memory 1 rather than actually
generate, or produce, the target item. Second, it
is crucial that the participants be able to reinstate at the time of the memory test the cognitive operations, or learning procedures, that
were used at study. The generation effect occurs
because generating is more likely than reading
to promote procedures during encoding that can
be reinstated during a typical retention test (see
also Soraci et al., 1994). This process-oriented
account of the generation effect focuses on the
cognitive processes engaged in by the participants at both study and recall rather than on the
inherent nature of the target items or the relationship between the cue and target items.
In this study, we examine episodic memory
for multiplication problem answers that are either generated or read. Subjects either read or
generate the answers to multiplication problems
and then, after a short delay, recall the list of
answers (without the problems as cues). Although the generation effect is generally examined in the context of verbal stimuli, following
Gardiner and Rowley (1984) and Gardiner and
Hampton (1985), we have focused primarily on
the effects of generating in the context of arithmetic problems (Crutcher & Healy, 1989; McNamara, 1995; McNamara & Healy, 1995a,
1995b). In a typical generation effect condition,
the participant is presented with a cue word and
a word fragment (e.g., short–t___) and a relational rule (e.g., antonym) to generate the response (i.e., tall). The participant is typically
asked to recall all of the responses encountered
during study. In our case, the participant is
presented with an arithmetic problem (e.g.,
13 ⫻ 9 ⫽ _) which includes the relational rule
of multiplication. The participant responds with
1
Note that by this account the information in memory
need not reside in the lexicon; thus, this account resembles
but is not identical to the lexical activation hypothesis, so
that it can accommodate the findings of a generation effect
with nonwords (see, e.g., McNamara & Healy, 1995a;
Nairne & Widner, 1987).
653
the answer (i.e., 117) and is later asked to recall
all of the answers encountered during study. We
have used this paradigm because we are interested in further exploring the nature of the cognitive procedures, or mental operations, involved in the generation effect. The mental
procedures, namely the arithmetic operations
linking operands to answers, are straightforward
and well defined for arithmetic problems. In
contrast, the mental operations linking verbal
materials are more difficult to control experimentally and may vary considerably across participants. For example, whereas one individual
may link short and tall with a visual image of
Abbott and Costello, another may think of a
story involving an elf and a giant, and another
may form no image or story at all. In contrast,
the link between arithmetic problems and their
answers is relatively constant across individuals.
A second advantage of using arithmetic problems is that they allow us to examine the generation effect for episodic memory tasks
(Crutcher & Healy, 1989; McNamara & Healy,
1995b) as well as skill acquisition tasks (McNamara, 1995; McNamara & Healy, 1995a). As
in the present experiments, the generation effect
is typically examined using episodic memory
tasks; that is, tasks that require the participant to
remember the occurrence during the experimental session of the generated or read words or, in
our case, the answers to the arithmetic problems. In contrast, we have also compared the
advantages of repeated generating and reading
for arithmetic skill acquisition for both adults
(McNamara & Healy, 1995a) and children (McNamara, 1995). One strength of our procedural
account is that it has successfully predicted
findings for both episodic tasks and skill acquisition tasks.
The specific purpose of the present series of
experiments is to provide a more stringent test
of our procedural account by examining an unintuitive prediction from that account. Specifically, the procedural account leads to the prediction that the generation effect should be
larger for simple multiplication problems than
for difficult problems in an episodic memory
task. This prediction is unintuitive for at least
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MCNAMARA AND HEALY
two reasons. First, in an earlier study of skill
acquisition, we found the reverse—a larger generation advantage for difficult than for simple
multiplication problems (McNamara & Healy,
1995a). Second, by the intuitively plausible effort account of the generation effect (e.g., Griffith, 1976), as we discuss later, the generation
effect should be greater when the act of generation is more effortful. Hence, a greater generation effect would be expected for difficult
problems. However, our prediction of a greater
generation effect for simple problems follows
from the second aspect of the procedural account, namely that participants must be able to
reinstate at the time of the memory test the
cognitive operations that were used at study. To
understand how the procedural account leads to
this prediction, it is necessary to review details
concerning previous generation effect results
we found for multiplication and addition problems in a study involving episodic memory
(McNamara & Healy, 1995b).
In our previous study (McNamara & Healy,
1995b), we demonstrated a stable and robust
generation effect for simple multiplication
problems. In contrast, a generation effect for
addition problems was found only when participants were induced to reinstate at test the cognitive procedures they had used at study. To
increase procedural reinstatement, we led the
participants who were presented with addition
problems to use an operand retrieval strategy.
With this strategy, a participant recalls and
combines operands from problems seen during
study, derives answers by performing the relevant arithmetic operation on the operands (e.g.,
by multiplying the operands together), and then
checks the familiarity of the answers. For example, if a participant remembers that one of
the operands is 3, then by consecutively multiplying by 3, the participant can mentally check
the familiarity of the answers 6, 9, 12, and so
on, for which answer had actually occurred during study. In contrast to multiplication problems, the use of the operand retrieval strategy is
less efficient for addition problems because so
few answers are excluded. For example, given
the single operand (i.e., addend) 3, a participant
might derive the answers 4, 5, 6, 7, and so on. A
participant can use this test strategy with addition problems and ultimately it can be effective.
However, because of the greater number of answers to exclude, not only is this strategy inefficient with addition problems, but it is also
highly error prone.
According to our procedural account, the operand retrieval strategy leads to a greater generation effect because of the similarity between
the mental operations used for generating at the
time the problems are studied and the mental
operations used for this strategy at the time of
the memory test. The advantage of generating
is, thus, that it leads participants to engage in
cognitive procedures linking the cue and target
and that these same procedures can be reinstated
at test. For arithmetic problems, the relevant
cognitive procedures are the arithmetic operations linking the operands to the answers. The
participants in a generate condition, but not
those in a read condition, necessarily use the
relevant procedures at study whether the arithmetic operation is addition or multiplication.
When participants use the operand retrieval
strategy at test, they are reinstating the relevant
cognitive procedures. In a sense, they are regenerating the problem answer.
Participants are likely to use the operand retrieval strategy for all simple multiplication
problems, and thus, the generation effect is expected in all cases. In contrast, participants are
not likely to come up with the operand retrieval
strategy for addition problems, simply because
it is inefficient for this type of problem. Thus,
according to our procedural account, there is
typically no generation effect for addition problems because the relevant cognitive procedures
are usually not reinstated at test. In support of
this hypothesis (McNamara & Healy, 1995b,
Experiment 1), we demonstrated that when participants read and generated either multiplication or addition problems there was a strong
generation effect for simple multiplication
problems and a lack of one for addition problems. We also found fewer intrusion errors for
multiplication than for addition problems and a
predominance of “table-related” errors for multiplication problems; that is, the intrusions were
possible products of at least one of the presented
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
operands (see, e.g., Campbell & Graham,
1985). These latter two findings provided evidence that participants used an operand retrieval
strategy for the multiplication problems because
that strategy should limit the responses given
largely to the correct answers and the ones
sharing an operand with the correct answers.
However, we also predicted and found that a
generation effect does occur for addition problems as well as multiplication problems when
the participants are induced to use the operand
retrieval strategy for both types of problems
(McNamara & Healy, 1995b, Experiment 2).
Specifically, we found that a generation effect
did occur for addition problems when the participants also generated and read multiplication
problems within the same list. We had hypothesized that the presence of the multiplication
problems along with the addition problems
would promote the use of the operand retrieval
strategy for both types of problems. In other
words, if participants were naturally using the
operand retrieval strategy to recall the answers
to the multiplication problems, then they would
be led to use the same retrieval strategy for the
addition problems. We tested this hypothesis
again (McNamara & Healy, 1995b, Experiment
3) by giving participants an explicit suggestion
to use an operand retrieval strategy with addition problems. Immediately before recalling the
answers, they were told simply that one good
strategy for remembering the answer to a problem is to try to remember the problem itself and
if they could remember one or both of the
numbers added together, they would be more
likely to remember the answer to the problem.
This suggestion also led to a generation effect
for addition problems.
In the present study, we compare the effects
of generating and reading for simple (e.g., 60 ⫻
8 ⫽ 480) and difficult (e.g., 16 ⫻ 8 ⫽ 128)
multiplication problems. We hypothesized that
the effects of generating for the difficult multiplication problems would follow a similar pattern to that for the addition problems in our
earlier study (McNamara & Healy, 1995b, Experiment 1). As explained earlier, a generation
effect is not normally expected for addition
problems because the operand retrieval strategy
655
is not typically used with this type of arithmetic
problem. Similarly, we hypothesized that most
participants presented with difficult multiplication problems would not use the operand retrieval strategy. It should be noted that the reasons why participants will tend not to use the
operand retrieval strategy for difficult multiplication problems and addition problems are
slightly different. For addition problems, we
have hypothesized that the operand retrieval
strategy is time consuming because of the large
number of answers to exclude (McNamara &
Healy, 1995b). In contrast, for difficult multiplication problems, we propose that the operand
retrieval strategy is time consuming because of
the need to compute the answers rather than
directly retrieve them from memory. The operand retrieval strategy consists of recalling problem operands, calculating an answer given those
operands, and then checking this answer for
familiarity. The mental operation of solving difficult multiplication problems is time consuming and error prone compared to that of solving
simple multiplication problems. Thus, participants should be less likely to use that strategy
with the difficult problems.
A second purpose of this study is to test
further the alternative hypothesis that the generation effect is due to the increased amount of
effort expended to process the cue and target in
the generate condition relative to the read condition (e.g., Griffith, 1976; McFarland, Frey, &
Rhodes, 1980). Even when effort has not been
the central theoretical construct explaining the
generation effect, it is often assumed that generation is “more effortful” than reading (e.g.,
Nairne, Pusen, & Widner, 1985, p. 190). Although the effort hypothesis is one of the most
intuitively appealing explanations of the generation effect, there is evidence to contradict it
(e.g., Glisky & Rabinowitz, 1985; Jacoby,
1978). For example, Jacoby (1978) failed to find
an effect of effort in a generation task when
difficulty was varied as a function of the number
of letters missing from a target word (cf.
Gardiner, Smith, Richardson, Burrows, & Williams, 1985). In addition, other researchers have
found generation effects even when the process
of generating required virtually no effort at all
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MCNAMARA AND HEALY
(e.g., Glisky & Rabinowitz, 1985; Nairne &
Widner, 1987). In spite of this evidence, effort
is often cited as the cause of the generation
effect (see, e.g., Anderson, 1990, p. 184). Moreover, the generation effect is often cited as
evidence for the importance of effort to learning
and memory (see, e.g., Tyler, Hertel, McCallum, & Ellis, 1979; but also see Zacks, Hasher,
Sanft, & Rose, 1983). Our intention here is to
provide a more direct test of the effort hypothesis by using more pronounced variations in the
amount of effort required to generate the response than used in previous studies. In this
study, we compare the magnitude of the generation effect for simple and difficult multiplication problems. If effort is operationalized by the
difficulty of the problem, in terms of both the
accuracy in solving the problem and the time
required to solve it, simple multiplication problems should require less effort to solve than do
difficult problems (see, e.g., McNamara &
Healy, 1995a; but also see Mitchell & Hunt,
1989). According to the effort hypothesis, if
increased effort is the source of the generation
effect, then a greater generation effect should be
found for difficult problem answers than for
simple problem answers. In contrast, as just
reviewed, according to the procedural account,
the reverse is expected: A greater generation
effect should be found for simple problem answers than for difficult problem answers. This
experiment should, thus, enable us to determine
the relative merits of the effort and procedural
accounts of the generation effect.
EXPERIMENT 1
In Experiment 1 we compared the generation
effect for simple and difficult multiplication
problems. Participants were presented with either 12 simple or 12 difficult multiplication
problems. Participants generated half of the
problems of either type and read the other half.
Participants’ memory for the answers to the
problems was tested with a free-recall procedure after a short distractor task. We hypothesized that participants would be less likely to
use the operand retrieval strategy with difficult
multiplication problems than with simple multiplication problems. Participants would be ex-
pected to have memorized the answers to the
simple multiplication problems so that they
could directly retrieve them from memory without any computation. In contrast, for the difficult problems the answers are not expected to be
directly linked to the operands in memory but
derived only through calculation. Hence, the
operand retrieval strategy is an easy strategy to
use for the simple problems because it requires
no computation, but is not easy for the difficult
problems because it requires computation in
that case. If participants are not required to do
any computation, they may not choose to do so.
The operand retrieval strategy is not impossible
when answers are not stored in memory; participants can still use the operands to help them
remember the answers, but the strategy is less
efficient and, thus, less likely to be employed in
that situation because computation is required
to retrieve the answers. Because participants are
less likely to use an operand retrieval strategy,
the generation effect should be reduced for difficult problems compared with simple problems.
We also tested two predictions of the procedural account. The first is that if participants use
the operand retrieval strategy for the simple but
not the difficult multiplication problems, then
fewer intrusion errors are expected for participants presented with the simple multiplication
problems than for those presented with the difficult problems. Second, and more specifically,
the use of the operand retrieval strategy with
multiplication problems should limit the recall
responses to possible problem answers having
at least one of the presented operands. This
assumption leads to the prediction that the majority of the intrusions should be table-related
for participants presented the simple multiplication problems.
Method
Participants and design. Twenty-four undergraduate students from the University of Colorado participated for credit in an introductory
psychology course. A 2 ⫻ 2 mixed factorial
design was employed, with one between-subjects variable, problem type (simple vs difficult), and one within-subjects variable, presen-
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
TABLE 1
Simple and Difficult Problems Presented to Participants
in Experiments 1, 2, and 3
Simple:
Experiments
1, 2, and 3
Difficult:
Experiments
1 and 2
Difficult:
Experiment 3
30 ⫻ 9 ⫽ 270
40 ⫻ 9 ⫽ 360
50 ⫻ 7 ⫽ 350
50 ⫻ 8 ⫽ 400
60 ⫻ 7 ⫽ 420
60 ⫻ 8 ⫽ 480
70 ⫻ 7 ⫽ 490
70 ⫻ 8 ⫽ 560
80 ⫻ 8 ⫽ 640
80 ⫻ 9 ⫽ 720
90 ⫻ 7 ⫽ 630
90 ⫻ 9 ⫽ 810
13 ⫻ 9 ⫽ 117
14 ⫻ 9 ⫽ 126
15 ⫻ 7 ⫽ 105
15 ⫻ 8 ⫽ 120
16 ⫻ 7 ⫽ 112
16 ⫻ 8 ⫽ 128
17 ⫻ 7 ⫽ 119
17 ⫻ 8 ⫽ 136
18 ⫻ 8 ⫽ 144
18 ⫻ 9 ⫽ 162
19 ⫻ 7 ⫽ 133
19 ⫻ 9 ⫽ 171
18 ⫻ 15 ⫽ 270
24 ⫻ 15 ⫽ 360
25 ⫻ 14 ⫽ 350
25 ⫻ 16 ⫽ 400
35 ⫻ 12 ⫽ 420
32 ⫻ 15 ⫽ 480
35 ⫻ 14 ⫽ 490
35 ⫻ 16 ⫽ 560
40 ⫻ 16 ⫽ 640
40 ⫻ 18 ⫽ 720
45 ⫻ 14 ⫽ 630
45 ⫻ 18 ⫽ 810
tation condition (generate vs read). Participants
were assigned to the problem type condition and
the counterbalancing subcondition according to
a fixed rotation on the basis of their time of
arrival for testing.
Materials. The multiplication problems consisted of 12 simple and 12 corresponding difficult multiplication problems. As shown in Table
1, both types of problems consisted of a twodigit multiplier followed by a one-digit multiplier. The products all consisted of three-digit
answers. For the simple multiplication problems, the second digit of the two-digit multiplier
was always 0 and the answer always ended in 0
(e.g., 30 ⫻ 9 ⫽ 270). For the difficult multiplication problems, the first digit of the two-digit
multiplier was always 1 and the answer always
began with 1 (e.g., 13 ⫻ 9 ⫽ 117). Apart from
the second digit of the two-digit multiplier in
the simple problems and the first digit of the
two-digit multiplier in the difficult problems,
the multipliers remained constant for both sets
of problems. The simple and difficult multiplication problems were each divided into two sets
of six problems of approximately equivalent
difficulty. Participants read one set and generated the other set. Order of presentation of the
two sets of problems and order of reading and
generating were counterbalanced across participants in each problem type condition.
657
Procedure. Participants were shown two sets
of shuffled index cards, each including six simple or six difficult multiplication problems. The
numbers were printed on 6 ⫻ 9⬙ index cards and
measured approximately 1⬙ tall. The problem
appeared on one side of the card; both the
problem and the answer to the problem appeared on the opposite side of the card. The
experimenter shuffled the index cards to randomize the order of problems within each set.
The first set of multiplication problems was
presented in either a read or a generate condition. The second set was presented in the other
condition. For the read condition, participants
were presented the side of the index card showing both the problem and the answer and told to
read the problem and the answer aloud twice in
a row. For the generate condition, participants
were presented the side of the index card showing only the problem and told to read the problem aloud, calculate the answer, and then say
the answer aloud. They were then shown the
problem with the correct answer printed on the
opposite side of the card, which they read aloud.
Thus, the problem and the answer were read
aloud twice in both conditions, and the participants in the generate condition said the correct
answer aloud at least once. After reading and
generating the multiplication problems, participants were given a self-paced distractor task,
which consisted of first reading a set of instructions and then reading a short passage while
circling predesignated target letters. Finally, the
participants were asked to write down all of the
answers to the multiplication problems that they
had seen. (They had not been forewarned of the
recall task; thus, this was an incidental test of
their memory for the problem answers.)
Results
The results are shown in Fig. 1 in terms of the
proportion of correct answers recalled as a function of problem type (simple vs difficult) and
presentation condition (generate vs read). A
mixed-multifactorial analysis of variance was
conducted on the proportion of correct responses including the between-subjects variable
of problem type and the within-subjects variable of presentation condition. There was a
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MCNAMARA AND HEALY
FIG. 1. Proportion of correct answers recalled in Experiment 1 as a function of problem type and presentation
condition, showing a greater generation effect for simple
than for difficult problem answers.
main effect of problem type, F(1,22) ⫽ 5.4,
MS e ⫽ 0.0515, p ⫽ .028, reflecting greater
recall for answers to simple problems (M ⫽
0.535) compared to difficult problems (M ⫽
0.382). There was also an overall generation
effect, F(1,22) ⫽ 43.6, MS e ⫽ 0.0334, p ⬍
.001, reflecting greater recall for generated answers (M ⫽ 0.632) compared to answers that
were read (M ⫽ 0.284). As predicted, there
was a significant interaction of problem type
and presentation condition, F(1,22) ⫽ 4.4,
MS e ⫽ 0.0334, p ⫽ .045. As shown in Fig. 1,
this interaction reflects the finding of a smaller,
though reliable, generation effect for difficult
problem answers [Difference ⫽ 0.238,
F(1,11) ⫽ 8.1, p ⫽ .015] than for simple
problem answers [Difference ⫽ 0.459;
F(1,11) ⫽ 50.3, p ⬍ .001].
Intrusions. Under the assumption that participants use the operand retrieval strategy more
often for simple than for difficult problems,
fewer intrusion errors would be expected for
participants given simple problems than for
those given difficult problems because that
strategy limits the answers given. Specifically,
the use of the operand retrieval strategy with
multiplication problems should limit the recall
responses to possible problem answers having
at least one of the presented operands. This
assumption also leads to the prediction that any
intrusions found for simple problems should be
table-related (see, e.g., Campbell & Graham,
1985); that is, the intrusions should be possible
products of at least one of the presented operands.
There was an average of 1.833 intrusion errors made by the participants. A mixed multifactorial analysis of variance was conducted on
the number of intrusion errors including the
between-subjects variable of problem type
(simple vs difficult) and the within-subjects
variable of error type (table-related vs non-table-related). As expected, participants who
were presented simple problems made fewer
intrusion errors (M ⫽ 1.000) than did participants who were presented difficult problems
(M ⫽ 2.667), F(1,22) ⫽ 5.7, MS e ⫽
1.4697, p ⫽ .025. The overall difference between table-related and non-table-related intrusion errors was not reliable, F(1,22) ⬍ 1.
There was, however, the predicted interaction
between problem type and error type,
F(1,22) ⫽ 9.1, MS e ⫽ 1.5530, p ⫽ .006.
This result reflects the finding that participants
given simple problems made predominantly table-related errors (M ⫽ 0.917, n ⫽ 11 errors)
and very few non-table-related errors (M ⫽
0.083, n ⫽ 1 error), whereas participants given
difficult problems made more non-table-related
errors (M ⫽ 2.000, n ⫽ 24 errors) than tablerelated errors (M ⫽ 0.667, n ⫽ 8 errors).
Discussion
The primary goal of Experiment 1 was to
demonstrate that a stronger generation effect
occurs for simple than for difficult multiplication problem answers and that this difference is
because participants are more likely to use the
operand retrieval strategy for the simple problems. As predicted, there was a reliable interaction of problem type and presentation condition,
indicating a stronger generation effect for the
simple problems. Also as predicted, there were
fewer intrusion errors for participants given
simple multiplication problems than for those
given difficult problems. This prediction was
based on the assumption that use of the operand
retrieval strategy would limit the number of
intrusion errors. Further as predicted, we found
that the majority of the intrusion errors were
table-related for the participants given simple
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
problems, whereas participants who were given
the difficult problems made fewer table-related
than non-table-related errors. This prediction
was based on the assumption that the use of the
operand retrieval strategy would limit intrusion
errors to numbers that were a product of at least
one of the presented operands. Finding few intrusion errors for the participants given simple
problems and finding that these errors were
table-related suggests that participants were
more likely to use an operand retrieval strategy
for simple problems. The opposite pattern of
results for the participants given difficult problems suggests that these participants were either
less likely to use the operand retrieval strategy
or less successful when using the strategy.
These findings, thus, support our hypothesis
that the successful reinstatement of the cognitive procedures engaged during study results in
a greater generation effect.
These findings also provide direct evidence
against the effort hypothesis as an explanation
of the generation effect. If the generation effect
resulted from a greater amount of effort in the
generate relative to the read condition, then a
greater generation effect for difficult than for
simple multiplication problem answers should
be observed. However, we found the opposite;
there was a greater generation effect for simple
than for difficult answers to multiplication problems.
EXPERIMENT 2
The results from Experiment 1 indicate that
there is a larger generation effect for simple
multiplication problems than for difficult multiplication problems. We have hypothesized that
participants presented with simple problems use
the operand retrieval strategy and that the use of
this strategy increases the advantage for generating in comparison to reading. According to
the procedural account, the generation advantage increases because the participants reinstate
the same mental procedures (i.e., solving the
problem) when using the operand retrieval strategy as they had when they first solved the
problems: When more similar mental procedures are engaged during encoding and recall,
memory is enhanced.
659
One alternative explanation for these results
is that participants are equally likely to use the
operand retrieval strategy with the simple and
difficult multiplication problems but they remember the operands with simple multiplication problems more easily than they do with
difficult problems. Simple problems are more
frequently encountered and may have a stronger
representation in memory. It follows that if participants were unable to remember the operands
of the difficult problems, then they may be less
likely to retrieve the answers as well. According
to this “operand memory” explanation, it is not
the reinstatement of the arithmetic procedures
that is the key to the recall of the answers, but
solely the recall of the operands at test.
If the finding of a greater generation effect for
simple multiplication problem answers than for
difficult multiplication answers was due to better memory for the operands, then the same
trend should be found for recall of the operands:
Participants should show a greater generation
effect for simple multiplication operand recall
than for difficult multiplication operand recall.
If, on the other hand, the finding of a greater
generation effect for simple multiplication
problem answers was due to the reinstatement
of the arithmetic procedures, then a generation
effect for memory of the operands, which does
not depend on performing the arithmetic procedures, should not depend on problem difficulty.
To examine the operand memory hypothesis,
we replicated Experiment 1, but asked participants first to recall the operands. After recalling
the operands and removing them from view,
participants in Experiment 2 recalled the answers to the problems as had participants in
Experiment 1. According to the operand memory explanation, a greater generation effect
should be found for the simple problems when
the operands are recalled. According to the procedural account, the generation effect for simple
and difficult problems should be comparable
when the operands are recalled but should still
differ when the answers are recalled.
A second purpose of Experiment 2 was to
determine whether the generation effect in the
difficult problem condition depended on the
participant’s ability to perform the difficult mul-
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tiplication procedures (as measured by the accuracy of the generated answers). If the majority of a participant’s generated answers were
incorrect, then the participant would be unlikely
to solve the problem correctly when checking
solutions based on retrieved operands. The participant would also be unlikely to solve the
problems in the same way both times and thus
would not reinstate at test the cognitive procedures used at study. According to our procedural account, the generate condition leads to
greater procedural reinstatement than does the
read condition because generating leads participants to engage in cognitive procedures linking
the cue and target, and these same procedures
can be reinstated at test. For arithmetic problems, the relevant cognitive procedures are the
arithmetic operations linking the operands to
the answers. If an individual has generally less
skill in difficult multiplication, it will be less
likely that the individual will be able to reinstate
correctly the same cognitive procedures at test
as used at study. To test this hypothesis, we
recorded the participants while they were generating and reading the answers to the multiplication problems in order to measure the accuracy of their generated answers.
Method
Participants and design. Forty-eight undergraduate students from Old Dominion University participated for credit in an undergraduate
psychology course. A 2 ⫻ 2 ⫻ 2 mixed factorial
design was employed, with one between-subjects variable, problem type (simple vs difficult), and two within-subjects variables, presentation condition (generate vs read), and recall
type (operands vs answer). Participants were
assigned to the problem type condition and the
counterbalancing subcondition according to a
fixed rotation on the basis of their time of arrival
for testing.
Materials. The multiplication problems were
identical to those used in Experiment 1 (see
Table 1) and were presented on the same type of
index cards. The simple and difficult multiplication problems were each divided into two sets
of six problems of approximately equivalent
difficulty. Participants read one set and gener-
ated the other set. Order of presentation of the
two sets of problems and order of reading and
generating were counterbalanced across participants in each problem type condition.
Procedure. Participants’ utterances were tape
recorded while generating and reading to determine the accuracy of each generated multiplication problem answer. Participants were
shown two sets of shuffled index cards, each
including six simple or six difficult multiplication problems. The first set of multiplication
problems was presented in either a read or generate condition. The second set was presented in
the other condition. The distractor task consisted of a word association task. Participants
were allotted 2 min to write three words associated with each of 22 nouns (e.g., flower, car,
etc.). Note that the distractor task in this case,
unlike the one used in Experiment 1, occurred
for a fixed duration.
Following the 2-min distractor task, participants were asked to write down the problems
(i.e., the operands) from the two sets of multiplication problems they had read and generated.
They were asked to write only the problem and
not the answer. They were then asked to write
down the answers to the two sets of problems.
They were asked to write only the answer and
not the problem and were not allowed to view
their previous recall of the problems. Operand
recall, like answer recall, was scored in an allor-none manner; participants had to recall both
operands for a correct response. Otherwise the
procedure was identical to that used in Experiment 1.
Results
The results are summarized in Fig. 2 in terms
of proportion of correct answers recalled as a
function of recall type (operands vs answer),
problem type (simple vs difficult), and presentation condition (generate vs read). A mixed
multifactorial analysis of variance was conducted on the proportion of correct responses
including the between-subjects variable of
problem type and the within-subjects variables
of presentation condition and recall type.
There was a main effect of problem type,
F(1,46) ⫽ 7.6, MS e ⫽ 0.1004, p ⫽ .009,
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
FIG. 2. Proportion of correct operands and answers recalled in Experiment 2 as a function of problem type and
presentation condition. An equivalent generation effect was
found for simple and difficult operand recall compared to a
greater generation effect for simple than for difficult answer
recall.
reflecting greater recall for operands and answers to simple problems (M ⫽ 0.413) compared to difficult problems (M ⫽ 0.289). There
was also an overall generation effect,
F(1,46) ⫽ 50.3, MS e ⫽ 0.0610, p ⬍ .001,
reflecting greater recall for generated operands
and answers (M ⫽ 0.477) compared to operands and answers that were read (M ⫽ 0.225).
The main effect of recall type reflecting the
difference between operand recall (M ⫽
0.329) and answer recall (M ⫽ 0.373) was not
reliable, F(1,46) ⫽ 2.6, MS e ⫽ 0.0377, p ⫽
.112. However, both the two-way interaction
between recall type and problem difficulty,
F(1,46) ⫽ 12.8, MS e ⫽ 0.0377, p ⫽ .001,
and the three-way interaction, F(1,46) ⫽ 8.8,
MS e ⫽ 0.0210, p ⫽ .005, were reliable. The
two-way interaction reflects a negligible effect
of problem difficulty for operand recall [difficult M ⫽ 0.316; simple M ⫽ 0.341;
F(1,46) ⬍ 1] compared to a large effect of
problem difficulty for answer recall [difficult
M ⫽ 0.261; simple M ⫽ 0.486; F(1,46) ⫽
14.45, p ⬍ .001].
The three-way interaction depicted in Fig. 2
reflects the finding that the generation effect
depended on both recall type and problem difficulty. Whereas the generation effect for operand recall did not depend on problem difficulty,
661
F(1,46) ⬍ 1, the generation effect for answer
recall did depend on problem difficulty,
F(1,46) ⫽ 4.6, MS e ⫽ 0.0389, p ⫽ .035.
There was a smaller, though reliable, generation
effect for difficult problem answers [Difference ⫽ 0.160, F(1,23) ⫽ 11.8, p ⫽ .003]
than for simple problem answers [Difference ⫽
0.332; F(1,23) ⫽ 25.6, p ⬍ .001]. The latter
finding replicates Experiment 1. The former
finding indicates that participants do not have
superior memory for the operands of simple
problems than for those of difficult problems,
and thus the operand memory hypothesis cannot
account for the results in Experiment 1 or for
the similar results involving answer recall in the
present experiment.
Answer recall conditional on operand recall.
According to the procedural account, the generation effect is increased when the mental procedures involved in generating are reinstated at
test. Recalling the operands before recalling the
answer should increase the likelihood that the
operands will be used to recall the answer. If
this is the case, and if it is procedural reinstatement that increases the generation effect, then
recalling the operands should have a greater
effect on the generate condition than on the read
condition. Operand recall should have little effect on the read condition because it should not
lead to reinstatement of procedures engaged in
the read condition. If, on the other hand, recalling the operands simply primes the subsequent
recall of the answer, then the effect of operand
recall should be equivalent across the read and
generate conditions.
To test these competing explanations, an
analysis was performed on the conditional proportions of answers recalled given prior recall
of the operands. This analysis provides an indication of the differential influence of operand
recall on answer recall in the read and generate
conditions. If operand retrieval facilitates recall
for the generate condition but not for the read
condition, then there should be a greater conditional proportion of answer recall given operand
recall from the generate condition than from the
read condition. This analysis was restricted to
those participants who recalled at least one
problem successfully in both the read and gen-
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erate conditions. After imposing this restriction,
this analysis included 15 participants in each of
the two problem type conditions.
There was a main effect of problem difficulty, F(1,28) ⫽ 26.96, MS e ⫽ 0.1369, p ⬍
.001, reflecting a greater conditional proportion
of answer recall given operand recall in the
simple condition (M ⫽ .786) than in the difficult condition (M ⫽ .290). There was also a
main effect of the within-subjects variable, presentation condition, F(1,28) ⫽ 4.36, MS e ⫽
0.0757, p ⫽ .043, reflecting a greater conditional proportion of answer recall given operand
recall in the generate condition (M ⫽ .612) as
compared to the read condition (M ⫽ .464).
The interaction between problem difficulty and
presentation condition was not reliable,
F(1,28) ⬍ 1. These results indicate that recalling the operands from the read condition is
indeed less likely to lead to recalling the answers associated with those operands than is
recalling the operands from the generate condition. This finding supports our hypothesis that it
is the reinstatement of the same mental operations at study and test that leads to enhanced
recall in the generate condition.
Intrusions. Participants made an average of
2.40 intrusion errors during recall. A mixedmultifactorial analysis of variance was conducted on the number of intrusion errors including the between-subjects variable of problem
type (simple vs difficult) and the within-subjects variable of recall type (operand vs answer). As expected, participants who were presented simple problems made fewer intrusion
errors (M ⫽ 1.60) than did participants who
were presented difficult problems (M ⫽ 3.19),
F(1,46) ⫽ 12.54, MS e ⫽ 4.7998, p ⫽ .001.
There was also a main effect of recall type,
F(1,46) ⫽ 11.98, MS e ⫽ 2.1730, p ⫽ .002.
Participants made more intrusion errors when
recalling the operands (M ⫽ 2.92) than when
recalling the answers (M ⫽ 1.87). The twoway interaction was not reliable, F(1,46) ⫽
2.76, MS e ⫽ 2.1730, p ⫽ .10.
Intrusions during operand recall were classified as set-related or non-set-related. Set-related
problems were defined as problems for which
each of the operands were among those pre-
sented. For both sets of problems, possible second operands were between 7 and 9. For the
difficult problems, possible first operands were
between 13 and 19, whereas for the simple
problems, possible first operands were between
30 and 90. A 2 ⫻ 2 mixed multifactorial analysis of variance including the between-subjects
variable of problem type (simple vs difficult)
and the within-subjects variable of intrusion
type (set-related vs non-set-related) was performed. The main effect of problem type was
marginally significant, F(1,46) ⫽ 3.21, MS e
⫽ 2.1911, p ⫽ .076, reflecting little difference in the number of recall intrusions for participants presented difficult problems (M ⫽
1.73) as compared to those presented simple
problems (M ⫽ 1.19). There were reliably
fewer non-set-related intrusions (M ⫽ 1.04)
than set-related intrusions (M ⫽ 1.88),
F(1,46) ⫽ 5.1, MS e ⫽ 3.2455, p ⫽ .027.
The interaction between problem type and intrusion type was not reliable, F(1,46) ⬍ 1.
These results indicate that participants did not
tend to guess the problem operands on the basis
of recognizing the limited set from which problems were chosen. Also, the likelihood of using
this guessing strategy was no greater or smaller
for simple problems than for difficult problems.
Intrusions during answer recall were classified as table-related and non-table-related, as in
Experiment 1. A 2 ⫻ 2 mixed factorial analysis
including the between-subjects variable of
problem type (simple vs difficult) and the within-subjects variable of intrusion type (table-related vs non-table-related) was performed.
There was a main effect of problem type,
F(1,46) ⫽ 20.1, MS e ⫽ 1.2953, p ⬍ .001,
reflecting more recall intrusions for participants
presented difficult problems (M ⫽ 1.46) than
for those presented simple problems (M ⫽
0.42). There were also more non-table-related
intrusions (M ⫽ 1.21) than table-related intrusions (M ⫽ 0.67), F(1,46) ⫽ 8.4, MS e ⫽
0.8388, p ⬍ .001. In addition, there was the
predicted interaction between problem type and
intrusion type, F(1,46) ⫽ 21.9, MS e ⫽
0.8388, p ⬍ .001. This result reflects the
finding that participants presented simple problems made predominantly table-related errors
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
(M ⫽ 0.58) and very few non-table-related
errors (M ⫽ 0.25), whereas participants given
difficult problems made more non-table-related
errors (M ⫽ 2.17) than table-related errors
(M ⫽ 0.75). These results replicate those in
Experiment 1.
Generation accuracy. Participants’ accuracy
when generating the answer to each problem
was recorded. Participants presented with difficult problems made more generation errors
(M ⫽ 2.0) than did those presented with simple
problems (M ⫽ 1.0), F(1,46) ⫽ 5.87, MS e ⫽
2.0435, p ⫽ .018. This finding provided evidence that the difficult problems require more
effort than do the simple problems (but see
Mitchell & Hunt, 1989). This finding also led us
to conduct separate analyses for participants
presented simple and for those presented difficult problems because of this difference in number of errors across participants in the two conditions.
Participants who were presented with simple
problems were classified as high or low accuracy according to whether they made no errors
versus made one or more errors when generating the answers to problems. Twelve participants made no errors (high accuracy), and 12
made between one and four errors (low accuracy; M ⫽ 2.0 errors). Separate analyses of
variance were conducted on operand and answer recall including the between-subjects variable of generation accuracy (high vs low) and
the within-subjects variable of presentation condition. Of greatest interest was the effect of the
between-subjects variable of accuracy on recall.
Accuracy had no effect on operand recall for
participants who were presented with simple
problems (high-accuracy M ⫽ 0.35, low-accuracy M ⫽ 0.33), F(1,22) ⬍ 1. However,
accuracy reliably affected answer recall,
F(1,22) ⫽ 6.9, MS e ⫽ 0.0836, p ⫽ .015,
reflecting the finding that high-accuracy participants recalled more problem answers (M ⫽
0.582) than did low-accuracy participants
(M ⫽ 0.363). The magnitude of the generation
effect for answer recall, however, did not depend on participants’ accuracy, F(1,22) ⬍ 1.
Participants who were presented with difficult problems were classified as high-, me-
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FIG. 3. Proportion of correct answers recalled from difficult problems in Experiment 2 as a function of participants’ accuracy when generating. The generation effect was
comparable for high- and medium-accuracy participants
compared to no generation effect for low-accuracy participants who incorrectly solved 50% or more of the problems.
dium-, or low-accuracy according to whether
they made zero to one error (n ⫽ 9), two errors
(n ⫽ 8), or three to six errors (n ⫽ 7) when
generating the answers to the difficult problems.
Separate analyses of variance were conducted
on operand and answer recall including the between-subjects variable of generation accuracy
(high, medium, and low) and the within-subjects variable of presentation condition. Once
again, of greatest interest was the between-subjects variable of accuracy.
As found for participants presented with simple problems, accuracy had little effect on operand recall for participants who were presented
with difficult problems (high-accuracy M ⫽
0.259, medium-accuracy M ⫽ 0.385, lowaccuracy M ⫽ 0.310), F(2,21) ⫽ 1.3. Although accuracy did not reliably affect answer
recall for difficult problems, F(2,21) ⫽ 2.3,
MS e ⫽ 0.0580, p ⫽ .122, the magnitude of
the generation effect for answer recall depended
on participants’ accuracy, F(1,22) ⫽ 4.07,
MS e ⫽ 0.0200, p ⫽ .032. As shown in Fig. 3,
the generation effect was comparable for highand medium-accuracy participants. On the other
hand, low-accuracy participants who had made
three or more errors showed no difference in
recall for problem answers that had been read or
generated.
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Based on the procedural account, our interpretation of the effect of generation accuracy is
that the participants who made three or more
errors during generation were less likely to reinstate the same mental procedures at study and
test because they did not possess the multiplication skills to do so. An alternative explanation
is that the magnitude of the generation effect is
reduced for these participants because if a problem is incorrectly generated, then the correct
answer is only seen once after the generation
attempt. In that case, a trial in the generate
condition effectively turns into a trial in the read
condition, at least at the behavioral level (i.e.,
after generating the answer, the participant
reads the complete problem and answer). To
test these competing hypotheses, an analysis
was conducted to compare the proportion of
recalled answers that had been incorrectly generated to the proportion of recalled answers that
had been correctly generated. If generating correctly is critical to the magnitude of the generation effect, then the conditional proportion of
answer recall given correct generation should be
higher than the conditional proportion of answer recall given incorrect generation. If procedural reinstatement is critical, and not correct
generation per se, then there should be no difference between the conditional proportion of
answer recall given correct generation and the
conditional proportion of answer recall given
incorrect generation.
An analysis of variance was performed comparing the conditional proportion of answer recall given correct generation and given incorrect
generation. This statistical analysis is restricted
to participants who made at least one error
during generation and to those who correctly
solved at least one problem. The analysis thus
included 12 participants in the simple problem
condition and 18 participants in the difficult
problem condition. This analysis is also restricted to the answers recalled from problems
presented in the generate condition (because
there were no errors in the read condition). The
effect of generation accuracy was not reliable,
F(1,28) ⬍ 1, reflecting the finding that participants were equally likely to recall an answer
regardless of whether it had been correctly gen-
erated (M ⫽ 0.428) or incorrectly generated
(M ⫽ 0.406). The effect of problem difficulty
was also not reliable in this analysis, F(1,28) ⫽
2.41, MS e ⫽ 0.1710, p ⫽ .132, nor was the
interaction, F(1,28) ⫽ 2.49, MS e ⫽ 0.0940,
p ⫽ .126. This analysis indicates that whether
or not an answer is correctly generated does not
determine the magnitude of the generation effect. Rather, this finding suggests that the critical aspect of the generation effect is that the
participants engage in the mental operations
involved in generation and that these operations
can be successfully reinstated at test.
To test our conclusions further, a mixed-factorial analysis of variance was conducted on the
proportion of correct answers conditionalized
on accurate generation. That is, a problem answer was included in the analysis only if it was
correctly generated. Therefore, if a participant
generated four answers correctly and recalled
two of those answers, the proportion correct
was calculated as .50. If a participant generated
four answers correctly and recalled only the two
answers incorrectly generated, the proportion
correct would be zero. The analysis included the
between-subjects variable of problem type and
the within-subjects variable of presentation condition.
The results for answer recall were virtually
unchanged by conditionalizing on accurate generation. There was a main effect of problem
type, F(1,46) ⫽ 17.8, MS e ⫽ 0.0872, p ⬍
.001, reflecting greater recall of answers to
simple problems (M ⫽ 0.502) compared to
difficult problems (M ⫽ 0.248). There was
also a reliable generation effect, F(1,46) ⫽
33.0, MS e ⫽ 0.0455, p ⬍ .001, reflecting
greater recall for generated answers (M ⫽
0.500) compared to answers that were read
(M ⫽ 0.250). As in the original analysis, the
generation effect for answer recall depended on
problem difficulty, F(1,46) ⫽ 7.0, MS e ⫽
0.0455, p ⫽ .011. The proportion recall for
difficult problems was 0.315 in the generate
condition and 0.181 in the read condition; the
proportion recall for simple problems was 0.685
in the generate condition and 0.319 in the read
condition. There was a smaller, though reliable,
generation effect for difficult problem answers
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
[Difference ⫽ 0.134, F(1,23) ⫽ 5.5, p ⫽
.027] than for simple problem answers [Difference ⫽ 0.365; F(1,23) ⫽ 30.9, p ⬍ .001].
Thus, this more conservative analysis of answer
recall accentuates our original interpretation of
the data.
Discussion
The results of this study provide strong evidence against the operand memory hypothesis
and support for the procedural account. According to the operand memory hypothesis, the generation effect should be larger for simple problems than for difficult problems both when the
operands are recalled and when the answers are
recalled. In both cases, the difference between
simple and difficult problems is explained by
the superior memory for the operands of the
simple problems. In contrast, according to the
procedural account, the generation effect for
simple and difficult problems should be comparable when the operands are recalled but should
be greater for the difficult problems than for the
easy problems when the answers are recalled.
The difference between simple and difficult
problems is explained by the participants’ superior ability to reinstate the multiplication operations for the simple problems than for the
difficult problems. In support of the procedural
account, we found that for operand recall there
was a generation effect of comparable magnitude for the simple and difficult problems,
whereas for answer recall the generation effect
was significantly larger for simple problems
than for difficult problems.
The finding of a reliable generation effect for
the multiplication problem, which acts as the
cue in this case, further demonstrates the importance of the cue–target relationship to the generation effect (Greenwald & Johnson, 1989).
Although Slamecka and Graf (1978) failed to
find a consistent generation effect for the cue,
they did find a small generation effect for the
cue in a cued recall task. Moreover, Greenwald
and Johnson (1989) subsequently found reliable
generation effects for the cues across three experiments. They argued that demonstrating that
memory for the cue benefits from the process of
generating is critical to accounts proposing that
665
the generation effect results from an enhanced
cue–target relationship (e.g., Donaldson &
Bass, 1980; Rabinowitz & Craik, 1986). The
procedural account is consistent with these accounts but goes further to emphasize the importance of procedural reinstatement.
For multiplication problems, recalling the operands is the first step toward procedural reinstatement: In order to re-solve the problem and
check the answer, the problem’s operands must
be remembered. A reliable generation effect for
the operands regardless of problem difficulty
indicates that the process of generating results
in better operand memory than does reading.
This finding was not specifically predicted by
the procedural account but can be easily understood within that framework simply by assuming that extra processing was devoted to the
operands during the problem solution that was
required in the generate condition but not in the
read condition. Generation probably also served
to strengthen the ties between the two operands
because they had to be interrelated during problem solution. In any event, finding a reliable
generation effect for the operands suggests that
superior operand memory partially explains the
generation effect for multiplication problem answers. However, this is not the whole story. The
generation effect for answer recall is dependent,
not just on recalling the problem’s operands, but
also on reinstating the cognitive procedures during study. This latter assumption explains the
greater generation effect for simple than for
difficult problem answers.
There are three additional observations in this
experiment providing support for the procedural
account and the hypothesis that the reinstatement of the same mental operations at study and
test leads to enhanced recall in the generate
condition. First, as in Experiment 1, in recalling
the answers, the participants made more intrusion errors with difficult than with simple problems and they made more table-related than
non-table-related intrusion errors with simple
problems, but more non-table-related than table-related intrusion errors with difficult problems. In contrast, in recalling the operands,
there was no reliable difference between participants presented with simple problems and
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MCNAMARA AND HEALY
those presented with difficult problems in terms
of whether the recall intrusions were set-related.
Second, the conditional proportion of answer
recall given operand recall was significantly
higher in the generate condition than in the read
condition, indicating that recalling the operands
from the read condition is less likely to lead to
recalling the associated answers than is recalling the operands from the generate condition.
These two findings suggest that (a) participants
given simple problems were more likely to use
the operands they recalled to derive and check
the answers than were participants given difficult problems and that (b) recalling the operands
leads to reinstating the cognitive procedures
relevant to generating, but not to reading.
A third observation in support of the procedural account concerns participants’ accuracy
of generating the problem answer. In answer
recall of difficult problems, the participants who
had shown the lowest accuracy at generating the
correct answers during the study phase showed
no generation effect at test. Clearly participants
who incorrectly generated the answers during
the study phase did not engage in an arithmetic
procedure that they could reinstate during the
test phase in order to derive the answer. This
finding cannot simply be explained by the fact
that the low-accuracy participants did not say
the correct answers during the study phase because all participants were shown and required
to read aloud the correct answer during the
generate task after they said aloud the answer
they generated. Moreover, this finding cannot
simply be explained by the fact that generating
correctly is critical to the magnitude of the
generation effect because it was found that participants were equally likely to recall an answer
that had been correctly generated as one that
had been incorrectly generated. Similarly,
Slamecka and Fevreiski (1983) found a generation effect for antonym pairs even when subjects failed to come up with the correct answer;
and Smith and Healy (1998) found a generation
effect for simple multiplication problems even
when subjects did not have time to complete the
generation process before the answer was provided. These results collectively suggest that the
critical aspect of the generation effect is that the
participants engage in the mental operations
involved in generation and that those operations
can be successfully reinstated at test.
EXPERIMENT 3
An alternative explanation for the results of
Experiments 1 and 2 is that the answers to the
simple multiplication problems are more likely
to be retrieved because they are more easily
encoded. That is, the simple problem answers
may be more easily encoded because they end
in a zero in contrast to the more complex, threedigit answers to the difficult problems. To examine this alternative explanation in Experiment 3, we held constant the answers to the
problems while varying the problem operands.
Thus, the problem corresponding to the answer
640 for the difficult problem version in Experiment 3 was 40 ⫻ 16. If the greater generation
effect for simple problems is due to the ease of
encoding the answers, and not due to the ease
and efficiency of re-generating the answer at
recall, then the interaction of problem type and
presentation condition found in Experiments 1
and 2 should disappear and only a main effect
for generating should emerge. If, however, the
generation effect is due to the reinstatement of
the mental operations, then Experiment 3
should replicate the results of Experiment 1.
A second purpose of Experiment 3 was to
examine whether the greater generation effect
for the simple problems was due to better recognition of the answers rather than to the reinstatement of mental procedures. That is, participants might be able to reproduce all possible
simple problem answers and subsequently “recognize” the answers they had generated. If this
is the case, then a greater generation effect
should be found for simple problems when testing is done with recognition as well as with
recall. On the other hand, if the generation effect for multiplication problem answers is dependent on the reinstatement of the mental operations, as predicted by the procedural account,
then eliminating the generation stage of recall,
by using a recognition test, should eliminate the
generation effect for both simple and difficult
problems. Specifically, recognition relies primarily on item information because it is primar-
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
ily the strength of the item in memory that
allows it to be recognized. However, the procedural account makes no assumptions regarding
the strength of the problem answers in the absence of the context provided by the problem
itself. Thus, there is no basis for predicting
greater item strength for generated multiplication problem answers than for those simply
read, and there is no mechanism for predicting a
generation effect for the recognition of multiplication problem answers on the basis of the
procedural account. To test these predictions,
retention was also examined in Experiment 3
with a recognition test.
We were also interested in whether participants would be more likely to report using the
operand retrieval strategy for problem answers
that had been generated in the simple problem
condition. Therefore, at the end of the experiment we asked participants to indicate what
type of strategy they had used to recall each
problem. They were asked to indicate whether
(a) they had relied on imagery (visual or auditory), (b) recalled one or more of the operands
to retrieve the answer (i.e., the operand retrieval
strategy), or (c) used an alternative or unknown
strategy. We predicted that participants would
be more likely to indicate having used imagery
to recall problem answers presented in the read
condition and to recall difficult problem answers. In contrast, we predicted that participants
would be more likely to report having used the
operand retrieval strategy for simple problem
answers that had been generated.
Experiment 3 also modified stimulus presentation to accommodate group presentation. To
do so, stimuli were presented in booklets. Each
task was presented on a separate page, with
presentation rate controlled by the participant.
In addition, participants in the generate condition did not read the correct answers following
generation, and the problems were seen only
once in both conditions. Thus, participants were
not provided with feedback concerning their
answers in the generate condition. However, to
decrease the answer generation error rate for
difficult problems, we permitted participants to
solve the problems using paper and pencil rather
than mentally.
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Method
Participants and design. Forty undergraduate
students from the University of Colorado participated for credit in an introductory psychology course. A 2 ⫻ 2 mixed-factorial design was
employed, with one between-subjects variable,
problem type (simple vs difficult), and one
within-subjects variable, presentation condition
(generate vs read). Half of the participants were
presented with simple problems, and half with
difficult problems. Participants were randomly
assigned to the problem type condition and the
counterbalancing subcondition.
Materials. The multiplication problems consisted of the 12 simple problems used in Experiments 1 and 2, and a new set of difficult problems (see Table 1). The answers to the simple
and difficult problems were identical. With a
few exceptions, the corresponding difficult multiplication problems were created by dividing
the first operand of the corresponding simple
problem by 2 and multiplying the second operand by 2. Exceptions to this procedure were
made when the resulting problem seemed too
simple. For example, the problem 40 ⫻ 9 would
have become 20 ⫻ 18, so we used 24 ⫻ 15
instead (which seemed more difficult).
The simple and difficult multiplication problems were each divided into two sets of six
problems of approximately equivalent difficulty
(as in Experiment 1). Participants read one set
and generated the other set. Order of presentation of the two sets of problems and order of
reading and generating were counterbalanced
across participants in each problem type condition.
Procedure. Participants were tested individually and in small groups of two to three. Each
participant was provided with a booklet. On the
first page, participants were instructed that they
should complete the booklet one page at a time
and that they should never return to a page after
going on to the following page (unless instructed to do so). A reminder not to turn back
to a previous page was presented on the top of
each page in the booklet (a pilot study had
shown this tendency to be problematic). The
second and fourth pages consisted of the read
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and generate problems (with a third blank page
inserted to prevent seeing the following page).
Problems presented in the read condition consisted of the problem and the answer with an
answer blank next to each one. The participant
was instructed to read the problem and the answer and copy the answer to the problem in the
space provided. Problems presented in the generate condition consisted of the problem followed by a blank space. The participant was
instructed to read each problem and write the
answer to each problem in the space provided.
They were allowed to use paper and pencil to
solve the problem if necessary, but were told to
use that page as the scratchpad. The fifth page
consisted of the distractor task. Participants
were presented with nine common words (e.g.,
flower and fish) and asked to write the first three
words that came to mind after reading the word.
The sixth page consisted of the recall task.
Participants were asked to write down all of the
answers to the multiplication problems (and not
the problems) from both lists, the ones copied,
and the ones solved. The seventh page was a
blank filler sheet followed by the recognition
task. Participants were presented with 24 numbers and asked to place a check beside each of
the 12 numbers recognized as being an answer
to a problem that had been read or generated.
They were also asked to rate the confidence of
their answers (those checked and those that
were not checked) from 1 (low) to 5 (high). The
12 distractors were created by either subtracting
or adding 20 to the problem answers (i.e., 290,
330, 340, 380, 440, 470, 500, 580, 610, 620,
740, and 830).
On the last page, participants were asked to
turn back to the recall page and indicate the type
of strategy used to retrieve each problem answer
recalled. Specifically, they were asked to write
the letter A next to the answer to indicate “I just
remembered the answer— don’t know how”;
the letter B to indicate “I used imagery to recall
the answer (visual or auditory)—I could see the
answer in my mind, or I could hear the answer
in my mind”; the letter C to indicate “I recalled
some or all of the problem to recall or verify the
answer”; or the letter D to indicate that they had
FIG. 4. Proportion of correct answers recalled in Experiment 3 as a function of problem type and presentation
condition, showing a reliable generation effect for simple
problems answers and the lack of a generation effect for
difficult problem answers.
used some other strategy (they were also asked
to describe the strategy in that case).
Results
The results are shown in Fig. 4 in terms of the
proportion of correct answers recalled as a function of problem type (simple vs difficult) and
presentation condition (generate vs read). A
mixed-multifactorial analysis of variance was
conducted on the proportion of correct responses including the between-subjects variable
of problem type and the within-subjects variable of presentation condition. There was a
main effect of problem type, F(1,38) ⫽ 12.15,
MS e ⫽ 0.0773, p ⬍ .001, reflecting greater
recall for answers to simple problems (M ⫽
0.496) compared to difficult problems (M ⫽
0.279). The effect of presentation condition
was marginal, F(1,38) ⫽ 3.36, MS e ⫽
0.0596, p ⫽ .075, reflecting slightly greater
recall for generated answers (M ⫽ 0.437) compared to answers that were read (M ⫽ 0.337).
As predicted, there was a significant interaction
of problem type and presentation condition,
F(1,38) ⫽ 5.24, MS e ⫽ 0.0596, p ⫽ .028.
As shown in Fig. 4, this interaction reflects the
lack of a generation effect for difficult problem
answers [Difference ⫽ ⫺ 0.025, F(1,19) ⬍
1] compared to a reliable generation effect for
simple problem answers [Difference ⫽ 0.225;
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
F(1,19) ⫽ 9.29, p ⫽ .007]. Thus, in contrast
to Experiments 1 and 2, there was no generation
effect for difficult problems in this experiment.
Intrusions. There was an average of only
0.488 intrusion errors made by the participants
in this experiment, much less than in Experiments 1 and 2. A mixed multifactorial analysis
of variance was conducted on the number of
intrusion errors including the between-subjects
variables of problem type (simple vs difficult)
and the within-subjects variable of error type
(table-related vs non-table-related). The effect
of problem difficulty was not reliable,
F(1,38) ⫽ 2.0, MS e ⫽ 0.513, p ⫽ .168
(simple M ⫽ 0.375; difficult M ⫽ 0.600).
There were reliably more table-related errors
(M ⫽ 0.700) than non-table-related errors
(M ⫽ 0.275), F(1,38) ⫽ 6.3, MS e ⫽ 0.576,
p ⫽ .017, but there was no interaction, F ⬍ 1.
Hence, in contrast to Experiments 1 and 2, we
did not find a significantly greater number of
intrusions for difficult than for simple problems,
and we did not find a greater predominance of
table-related intrusions for simple problems
than for difficult problems. There are a number
of reasons why this pattern of results may have
occurred. The most probable cause of the different pattern of intrusions is the greatly reduced number of intrusions. The reason for this
reduction is not clear but it may have something
to do with the use of testing packets, which
were employed in this experiment but not in
Experiments 1 and 2.
Generation accuracy. Participants presented
with difficult problems made only slightly more
generation errors (M ⫽ 0.55) than did those
presented with simple problems (M ⫽ 0.20),
F(1,39) ⫽ 2.88, MS e ⫽ 0.4250, p ⫽ .098.
This error rate translates to 90% accuracy in the
difficult problem condition and 97% accuracy
in the simple problem condition. Thus, there
were fewer errors overall in comparison to Experiments 1 and 2 and little effect of problem
difficulty on generation accuracy. Accuracy was
higher in this experiment presumably because
we allowed the participants to use pencil and
paper to solve the problems, whereas in Experiments 1 and 2 participants were required to
solve the problems mentally.
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Nevertheless, to verify further that generation
accuracy did not affect the results, a mixedmultifactorial analysis of variance was conducted on the proportion of correct answers
conditionalized on accurate generation. That is,
a problem answer was included in the analysis
only if it was correctly generated. The analysis
included the between-subjects variable of problem type and the within-subjects variable of
presentation condition.
The results for answer recall were virtually
unchanged by conditionalizing on accurate generation. There was a main effect of problem
type, F(1,38) ⫽ 11.18, MS e ⫽ 0.0767, p ⫽
.002, reflecting greater recall of answers to
simple problems (M ⫽ 0.502) compared to
difficult problems (M ⫽ 0.295). There was
also a reliable generation effect, F(1,38) ⫽
4.73, MS e ⫽ 0.0638, p ⫽ .036, reflecting
greater recall for generated answers (M ⫽
0.460) compared to answers that were read
(M ⫽ 0.337). As in the original analysis, the
generation effect for answer recall depended on
problem difficulty, F(1,38) ⫽ 4.17, MS e ⫽
0.0638, p ⫽ .048. The proportion recall for
difficult problems was 0.299 in the generate
condition and 0.292 in the read condition; the
proportion recall for simple problems was 0.622
in the generate condition and 0.383 in the read
condition.
Recognition. A mixed-multifactorial analysis
of variance was conducted on the proportion of
correctly recognized old numbers (i.e., hits) including the between-subjects variable of problem type and the within-subjects variable of
presentation condition (read vs generate). There
was a main effect of problem type, F(1,38) ⫽
26.13, MS e ⫽ 0.0417, p ⬍ .001, reflecting
better recognition of answers to simple problems (M ⫽ 0.800) compared to difficult problems (M ⫽ 0.567). There was no effect of
presentation condition, F(1,38) ⬍ 1, reflecting
equivalent recognition for items that were read
(M ⫽ 0.679) and generated (M ⫽ 0.688).
Problem type and presentation condition did not
interact, F(1,38) ⬍ 1. A separate analysis of
variance was also performed on correctly rejected new items. There was a main effect of
problem type, F(1,38) ⫽ 26.62, MS e ⫽
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TABLE 2
Recall Strategies Reported by Participants as a Function of Problem Type and Presentation Condition in Experiment 3
Problem type
Simple
Generate
Read
Average
Difficult
Generate
Read
Average
Overall average
Answer imagery
Problem recall
Other
Unknown
Average
1.16
0.37
0.77
2.16
1.00
1.58
0.16
0.26
0.21
0.32
0.63
0.48
0.95
0.57
0.76
0.25
0.45
0.35
0.56
0.55
0.25
0.40
0.99
0.40
0.85
0.63
0.42
0.40
0.20
0.30
0.39
0.40
0.44
0.42
2.394, p ⬍ .001, reflecting higher proportions
of correct rejections by participants who solved
simple problems (M ⫽ 0.856) than by those
who solved difficult problems (M ⫽ 0.654).
Average signed confidence ratings were calculated by considering ratings for correct responses as positive and ratings for incorrect
responses as negative. Thus, if an individual
missed an item with a confidence of 5, this
rating would be entered as ⫺5. A mixed-multifactorial analysis of variance was conducted on
the average signed confidence ratings for the old
items including the between-subjects variable
of problem type and the within-subjects variable of presentation condition (read vs generate). There was a main effect of problem type,
F(1,38) ⫽ 26.26, MS e ⫽ 0.0417, p ⬍ .001,
reflecting higher confidence for answers to simple problems (M ⫽ 2.845) compared to difficult problems (M ⫽ 1.072). There was no
effect of presentation condition, nor was there
an interaction of problem type and presentation
condition, both Fs ⬍ 1. An analysis of variance
was also performed on participants’ confidence
for rejecting new items. There was a main effect
of problem type, F(1,38) ⫽ 34.95, MS e ⫽
1.416, p ⬍ .001, reflecting higher rejection
confidence by participants who solved simple
problems (M ⫽ 3.120) than by those who
solved difficult problems (M ⫽ 0.900).
Strategy protocols. Participants identified at
the end of the experiment which strategy they
remembered using to recall each of the problem
answers. The list of strategies provided to the
participants were (a) “I used imagery to recall
the answer (visual or auditory)—I could see the
answer in my mind, or I could hear the answer
in my mind”; (b) “I recalled some or all of the
problem to recall or verify the answer”; (c)
some other strategy; and (d) “I just remembered
the answer— don’t know how.” Reported strategies were summed for each participant as a
function of problem condition (generate vs
read). When participants reported using both
imagery and recalling the problem to verify the
answer, the response was summed with the latter category (i.e., problem recall). One participant in the simple problem condition was not
included in the analyses due to not recalling any
problem answers correctly.
A mixed-multifactorial analysis of variance
was conducted on the number of strategies reported including the between-subjects variable
of problem type and the within-subjects variables of presentation condition (read vs generate) and strategy type (imagery, problem, other,
and unknown). The means as a function of these
variables are presented in Table 2.
Mirroring the results for recall accuracy,
there were reliable main effects of problem
type, F(1,38) ⫽ 12.69, MS e ⫽ 0.701, p ⬍
.001, and presentation condition, F(1,37) ⫽
4.51, MS e ⫽ 0.511, p ⫽ .040, as well as a
significant interaction of problem type and presentation condition, F(1,37) ⫽ 6.70, MS e ⫽
0.511, p ⫽ .014 (see Table 2).
More importantly, there was a main effect of
strategy type, F(3,37) ⫽ 3.97, MS e ⫽ 1.518,
p ⫽ .010, reflecting a greater overall tendency
to recall the problem in order to retrieve and
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
verify the answer (i.e., the operand retrieval
strategy) as compared to other strategies. However, the reliable interaction of strategy type and
presentation condition confirms our prediction
that the use of the operand retrieval strategy
would be more frequent for problem answers
that were generated than for those that were
read, F(3,37) ⫽ 4.57, MS e ⫽ 0.826, p ⫽
.005. Moreover, the interaction of strategy type
and problem type confirms our prediction that
the use of the operand retrieval strategy would
be more likely for participants presented with
simple problems than for those presented with
difficult problems, F(3,37) ⫽ 5.59, MS e ⫽
1.518, p ⫽ .001. Finally, there was a reliable
three-way interaction of strategy type, problem
type, and presentation condition, F(3,37) ⫽
4.57, MS e ⫽ 0.826, p ⫽ .005. This interaction reflects the moderate tendency to use the
operand retrieval strategy for difficult problem
answers that were generated compared to the
tendency to use imagery of the answer or some
other strategy to recall difficult problem answers that were read. In contrast, for simple
problem answers, there was a clear tendency to
use the operand retrieval strategy in both presentation conditions, but the tendency was
greater for answers that were generated than for
those that were read.
Discussion
Experiment 3 confirmed that the greater generation effect for simple problem answers was
not due to the greater ease of encoding the
simple problem answers. Indeed, when the answers were identical for the simple and difficult
problems, we found a substantial generation
effect for simple problem answers and no generation effect for difficult problem answers.
These results support our predictions, but contrast somewhat with the results of Experiments
1 and 2, which showed a reliable, though small,
generation effect for difficult problem answers.
We doubt that this difference in outcome is
attributable to the differences in the problems
and answers across experiments. Rather, this
difference is more likely attributable to the absence of feedback provided to participants regarding their generated answers in Experiment
671
3. In Experiments 1 and 2, feedback was provided because of the difficulty of generating the
answers mentally—resulting in numerous generation errors. In Experiment 3, we increased
generation accuracy by allowing participants to
use paper and pencil to solve the problems—
eliminating the need for problem answer feedback. We suppose that the feedback provided in
Experiments 1 and 2 strengthened the relationship between multiplication problem and the
answer, thus increasing the likelihood of reinstating the relevant mental operations for the
difficult problems at test. Similarly, Johns and
Swanson (1988) found a generation effect for
nonwords when feedback was provided and
failed to find an effect when it was not provided.
We also examined participants’ recognition
of the problem answers after they had recalled
the answers. We found better recognition of the
simple than difficult answers, presumably because simple problem answers have a stronger
representation in memory. We also found
equivalent recognition of answers that had been
read and generated. We had predicted this outcome based on the assumption that the generation effect for multiplication problem answers
depends on the reinstatement of the mental operations engaged at study and that this process is
not necessary to complete a recognition test.
Finally, we substantiated our claims by asking participants to report what strategy they had
used to retrieve each of the successfully recalled
problem answers. As predicted, the use of the
operand retrieval strategy was more frequently
reported for problem answers that were generated than for those that were read and more
frequent for participants presented with simple
problems than for those presented difficult
problems. We also found that for simple problem answers, there was a clear tendency to use
the operand retrieval strategy for both presentation conditions but a larger tendency for the
generate than for the read condition. This result,
in conjunction with the results for recall accuracy, indicates that, whereas the participants in
the simple problem condition attempt to use this
strategy for all of the problem answers, the
operand retrieval strategy is most often employed and is most effective for problems pre-
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sented in the generate condition. According to
the procedural account, the operand retrieval
strategy is more effective for generated answers
because the participants reinstate the same cognitive procedures at test that were used during
encoding.
GENERAL DISCUSSION
In our first experiment of this study we demonstrated that a generation effect for the answers to multiplication problems is stronger for
simple than for difficult problems. We also
found that participants presented with simple
multiplication problems had fewer intrusion errors and that more of these errors were tablerelated, suggesting that participants are more
likely to use an operand retrieval strategy for
these problems. In Experiment 2, we replicated
these findings when participants were required
to recall the answers to multiplication problems,
but found a generation effect of equal magnitude for simple and difficult problems when
participants were required to recall the operands
rather than the answers. Experiment 3 refuted
the possibility that our findings were due to a
confounding stemming from differences in response terms. In addition, we found a lack of a
generation effect for recognition. We had predicted this outcome based on the assumption
that the generation effect for multiplication
problems was attributable to the reinstatement
of the mental operations, which was not necessary for recognition of the answers. We also
found that participants were most likely to report using the operand retrieval strategy for
simple problem answers that were generated.
We have provided a relatively simple explanation of our findings. According to the procedural account, retention is enhanced when (a)
participants engage at study in cognitive operations that connect the target item to information stored in memory and (b) the test allows or
induces participants to reinstate the same cognitive operations that were used at study. The
generation effect occurs because generating is
more likely than reading to promote procedures
during encoding that can be reinstated during
the retention test. For arithmetic problems, the
relevant cognitive procedures are the arithmetic
operations linking the operands to the answers.
We hypothesized that the operand retrieval
strategy (i.e., recalling and combining operands
to reproduce and check answers) leads to a
greater generation effect because the mental
operations used for generating and the mental
operations used for this strategy are similar if
not identical. Because individuals are likely to
use the operand retrieval strategy for all simple
multiplication problems, the generation effect is
expected with these problems. In contrast, individuals are less likely to use the operand retrieval strategy for difficult problems, simply
because it is inefficient for this type of problem.
This study has provided converging evidence
in support of our procedural account of the
generation effect by replicating our previous
findings (McNamara & Healy, 1995b) with a
different type of arithmetic stimuli (i.e., we
compared simple and difficult multiplication
problems here, but earlier we compared multiplication and addition problems). Moreover, the
second experiment in the present study has allowed us to rule out an alternative explanation
for our findings in terms of operand memory as
opposed to memory for the cognitive operations
or procedures. In addition, we have extended
our previous findings by examining the influence of generation accuracy on the generation
effect in this paradigm. Generation accuracy
turned out to be a critical factor in determining
when a generation effect would occur.
Effortful Processing
One purpose of this study was to examine
further the hypothesis that the generation effect
is a result of a greater amount of effort to
process the cue and target in the generate condition than in the read condition (e.g., Griffith,
1976; McFarland et al., 1980; cf. Glisky &
Rabinowitz, 1985; Jacoby, 1978). We found in
Experiment 2 that the answers to the difficult
problems were generated less accurately than
those to the simple problems. Although we did
not measure generation response times in the
present study, we have found previously that
difficult problems like those we used here are
generated more slowly as well as with lower
accuracy than simple problems like those we
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
used here (McNamara & Healy, 1995a). If increased effort were the source of the generation
effect, then a greater generation effect for both
problems and answers should have been observed in the difficult problem condition relative to the simple condition. However, this was
not the case in any of our three experiments,
where instead the opposite effect was found.
Thus, if effort is operationalized by the difficulty of the problem in terms of both accuracy
and response time, these experiments provide
clear and direct evidence against the effort hypothesis. Although the effort hypothesis is no
longer generally favored by researchers of the
generation effect, effort is still widely attributed
as a cause of the generation advantage in many
secondary sources (e.g., Anderson, 1990).
Hence, our clear and direct refutation should
dispel any claims that effortful processing is
related to the generation effect.
Three Sources of Information
According to multifactor accounts of the generation effect, generating is superior to reading
because it strengthens three sources of information: from the item, from the stimulus–response
relationship, and from the whole list. For example, Hirshman and Bjork (1988) proposed that
generating activates features of the response
term in memory (i.e., lexical or semantic activation) and strengthens the cue–target relationship in memory and, furthermore, that the importance of these two sources of information is
determined by the type of retention test. Specifically, free recall is facilitated by the activation
of the response term, whereas cued recall is
facilitated by both factors. Thus, these assumptions collectively accounted for larger generation effects for cued recall than free recall when
generating versus reading was manipulated between subjects (Begg & Snider, 1987; Hirshman & Bjork, 1988; Nairne, Riegler, & Serra,
1991; Schmidt & Cherry, 1989). These assumptions also accounted for the finding that the
generation effect in cued recall increased when
relational processing was increased (Burns,
1990). McDaniel, Waddill, and Einstein (1988)
further proposed that free recall also depends on
whole list information and the task of generat-
673
ing enhances the stimulus–response relation at
the expense of whole-list information. Hence,
the generation effect for free recall was predicted to, and did, occur in a between-subjects
design when the response words were structured
by categories and the cue words were the category names, thus enhancing whole-list information. Similarly, Nairne and his colleagues
(Nairne et al., 1991; Serra & Nairne, 1993)
examined the generation effect for order and
item information to demonstrate that generation
enhances item memory but impairs memory for
the serial order of list presentation.
Thus, according to multifactor accounts the
three factors that influence the generation effect
stem from the availability of information from
the item, from the stimulus–response relationship, and from the whole list. Moreover, performance on retention tests tends to rely more or
less on certain types of information depending
on the specific test employed. Recognition is
assumed to rely primarily on item information
because it is primarily the strength of the item in
memory that allows it to be recognized. Recall
tends to rely on both item and whole-list information, whereas cued recall relies on both item
and relational information.
Procedural Reinstatement
How does our procedural reinstatement account compare to multifactor accounts? According to our procedural account of the generation effect, successful performance at test
depends on whether the cognitive operations
used at study are reinstated at the time of the
retention test. The generation effect occurs because generating is more likely than reading to
promote procedures during encoding that can be
reinstated during a typical retention test. The
parameters for predicting when reinstatement
will occur depend partially on the type of information enhanced by generating and whether the
retention test taps into that source of information (as outlined by multifactor accounts). However, we also assume that recall relies in some
cases on the stimulus–response relationship.
Specifically, when the response items do not
have a strong representation in memory (e.g.,
digits and nonwords), recall will rely more on
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the stimulus–response relationship, and more
specifically on the reinstatement of this relationship to retrieve the items at test. The generation
condition improves recall in comparison to
reading in this case due to procedural reinstatement. When conditions of procedural reinstatement are not met, a generation effect is not
expected for less meaningful items or items that
depend on context to derive their meaning (e.g.,
Gardiner & Hampton, 1985; Graf, 1980; McElroy & Slamecka, 1982; Nairne & Widner,
1987). In contrast, when the generated items
have a strong semantic representation in memory, then recall is more likely to rely on the
activation of the response items in memory and
whole-list information (as described earlier).
We assume that recall relies on procedural
reinstatement for arithmetic problems because
the response items (i.e., the problem answers)
do not have a strong representation in memory.
In essence, the answers are meaningless in the
absence of the context provided by the arithmetic problems. Similar to recall, recognition
relies on the strength of item information because it is primarily the strength of the item in
memory that allows it to be recognized. Why
did recognition not rely on reinstatement of the
problems, as did recall? The answer is that there
was essentially no need in that case. We assume
that reading as well as generating the answers
sufficiently increased the activation of the problem answers for successful recognition to occur.
Hence, procedural reinstatement of the problem
solving operations did not produce a generation
effect because that process was unnecessary to
complete the recognition task.
The concept of procedural reinstatement
builds on previous findings of transfer appropriate processing (e.g., Morris, Bransford, &
Franks, 1977) and encoding specificity (e.g.,
Tulving & Thomson, 1973). Accordingly, the
relative levels of performance on retention tests
depend on the particular task performed during
encoding, and it is easier to access a memory
trace when the context at retrieval is similar to
the encoding context. Evidence that encoding
specificity and transfer appropriate processing
play important roles in the generation effect can
be found in studies looking at explicit memory
tasks such as recall and recognition (e.g., Glisky
& Rabinowitz, 1985; Nairne & Widner, 1987)
as well as those using implicit measures (see
Roediger & McDermott, 1993, for a review).
Glisky and Rabinowitz demonstrated that the
benefits of generating were enhanced by the
repetition of the crucial mental operations.
Moreover, Nairne and Widner demonstrated
that reinstating the same mental operations at
test that were used during encoding is critical to
obtain a generation effect for nonwords.
Kolers and Roediger (1984) argued that
many learning and memory phenomena are explicable within a procedural framework. They
postulated that memory for episodic information is stored together with memory for the
processing of the information when it is acquired. Specifically, they showed that the manner in which information is acquired is highly
associated with its representation in the mind.
Hence, recognition of learned material will vary
with the similarity of the processes involved in
acquisition and test, and transfer between tasks
will depend on the degree of correspondence of
underlying cognitive procedures. However,
Kolers and Roediger’s procedural theory does
not always lead to the prediction of a generation
effect. According to this theory, implicit memory measures are predicted to show advantages
for the read condition rather than a generation
effect. Reading should be more likely than generating to enhance performance on retention
measures that tap into the same perceptual encoding operations used in reading. Although
there have been some exceptions (e.g., Masson
& MacLeod, 1992; Schwartz, 1989), the general
finding has been, in accordance with the procedural theory, that generating has positive effects
on conceptual tests such as recall and recognition, whereas reading is superior to generating
on perceptual memory tests such as word identification, word-fragment completion, and
word-stem completion (e.g., Blaxton, 1989;
Jacoby, 1983; Smith & Branscombe, 1988;
Srinivas & Roediger, 1990; Winnick & Daniel,
1970). These findings collectively demonstrate
the importance of procedural reinstatement to
explain the generation effect.
The effects of procedural reinstatement also
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
contribute to the increased benefit of generating
for cued recall tasks in comparison to free recall
and recognition tasks (e.g., Begg, Snider, Foley,
& Goddard, 1989). That is, the cued recall task
is more similar to the generation task than to
reading, and thus some of the benefit from generating stems from an increased match between
the encoding and retention tasks. Begg et al.
(1989) based their conclusions on the lack of a
generation effect for cues—arguing that this
finding refutes the importance of stimulus–response relational processing for cued recall
tasks because the stimulus should also benefit
from this processing. However, the present Experiment 2 and other investigations (Greenwald
& Johnson, 1989; McDaniel & Waddill, 1990)
have revealed generation effects for cues under
incidental learning conditions. Nevertheless,
these latter findings do not negate the importance of procedural reinstatement but rather indicate that the stimulus terms for read items are
not afforded extra processing when a retention
test is not expected. Thus, another factor that
must be considered to determine the likelihood
of the generation effect is the processing that
occurs for items in the read condition.
Encoding Processes
According to the procedural account, it is not
important whether an item is generated but
rather how it is processed. Specifically, during
the encoding stage participants must engage in
cognitive operations that serve to connect the
target item to information stored in memory. To
the extent that the items in the read condition
are processed as such, the generation effect is
reduced or disappears. The most convincing
evidence indicating the importance of encoding
processes for the generation effect was provided
by Crutcher and Healy’s (1989) study. In a
typical generation paradigm, the read and generate conditions differ primarily in whether the
to-be-remembered items are present (i.e., read)
or absent (i.e., generate) during encoding.
Crutcher and Healy showed that the presence or
absence of the to-be-remembered item was not
the most important factor in obtaining the generation effect for the answers to simple multiplication problems. They manipulated two fac-
675
tors relevant to encoding: (a) whether the
problem was solved mentally and (b) the presence or absence of the answer to the problem in
the stimulus display. They found a retention
advantage only for tasks requiring mental solution of the multiplication problems and no effect
of whether the answer was present or absent.
Further evidence along these lines comes
from studies showing enhanced read performance with intentional testing conditions (e.g.,
Watkins & Sechler, 1988) or with the use of
mnemonics (e.g., Begg, Vinski, Frankovich, &
Holgate, 1991; Donaldson & Bass, 1980; McNamara & Healy, 1995a). Begg and his colleagues (1991) demonstrated that having participants either imagine the words or rate their
memorability eliminated the generation effect.
Donaldson and Bass (1980) also found that a
read task that required the evaluation of the
goodness of the relationship resulted in a memorial advantage for the target items similar to
that found for a generate task. Similarly, McNamara and Healy (1995a) showed that when
learning word–nonword pairs, reading was as
effective as generating for participants who
spontaneously used mnemonics to associate the
pairs. Thus, cognitive processes similar to those
used in a generate condition can be induced in a
read condition when it is combined with additional processing demands such as verification,
imagery, memorability ratings, or the use of
mnemonics. These studies collectively show
that generating the target items is not necessary;
the critical factor leading to a generation effect
is that the participants themselves perform the
necessary cognitive procedures to derive the
target items.
Skill Acquisition
In the present investigation, we demonstrated
a stronger generation effect for simple than for
difficult multiplication problems. In contrast,
we previously found a generation advantage for
difficult, but not for simple, multiplication problems during skill acquisition (McNamara &
Healy, 1995a). The principal difference between the present study and our previous one on
skill acquisition is that in the present study,
participants were asked to recall the answers to
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MCNAMARA AND HEALY
the problems without the problems as cues,
whereas in the previous study participants were
always given the multiplication problems and
asked simply to solve them. In the previous
study, we trained participants on either simple
or difficult multiplication and found that repeatedly generating, as compared to repeatedly
reading, difficult multiplication problems resulted in higher accuracy and faster solution
times for these problems. In contrast, reading
and generating were equally effective for the
refinement of the skills involved in solving simple multiplication problems. Although performance after training approached ceiling in terms
of accuracy for the simple multiplication problems (M ⫽ .93), the same trend was found in
terms of response time, ruling out an explanation of our findings based solely on ceiling
effects. We also explained these findings in
terms of the procedural account. Accordingly,
in skill and knowledge acquisition paradigms,
cognitive procedures must be developed during
training for learning to occur and generating is
more likely than reading to promote the formation of new and stable cognitive procedures. We
predicted that a generation advantage would
occur for difficult multiplication problems but
not for simple problems because little change in
cognitive procedures would be expected for
simple multiplication problems, whereas difficult problems would be expected to require the
development of new cognitive procedures. That
is, college students already possess the cognitive procedures necessary to retrieve the answers to simple multiplication problems, but do
not have well-established cognitive procedures
to solve more difficult multiplication problems
with operands greater than 12 (e.g., Ashcraft,
1992; Bourne & Rickard, 1991; Fendrich,
Healy, & Bourne, 1993).
How can the procedural account explain a
larger generation effect for simple than for difficult multiplication problems in an episodic
memory paradigm and at the same time explain
a generation advantage for difficult but not for
simple multiplication problems in a skill acquisition paradigm? We assume that in both the
episodic memory and skill acquisition tasks,
generating is more likely than reading to pro-
mote the relevant cognitive procedures (i.e., the
mental multiplication operations) during study
or encoding. When the operands are provided at
test, as they are in the skill acquisition task, then
the cognitive procedures used at test or retrieval
will naturally match those used at study or encoding. However, when the operands are not
provided at test, as in the episodic memory task,
then the cognitive procedures used at test will
only match those used at study if the participants adopt an operand retrieval strategy.
Hence, what is crucial in the episodic memory
task is that participants be led to adopt the
operand retrieval strategy, and that is most
likely with simple problems. On the other hand,
what is crucial in the skill acquisition task is that
participants be led to develop new cognitive
procedures during study, and that is most likely
with difficult problems. Therefore, we predict
that under most circumstances, a generation effect will occur for episodic memory tasks requiring familiar cognitive processes that can be
reinstated at test, and a generation effect will
occur for knowledge and skill acquisition tasks
that require participants to form new cognitive
procedures.
The Procedural Account
In summary, the procedural account of the
generation effect embraces multifactor accounts
and further assumes the importance of both
procedural reinstatement and encoding processes. One advantage of the procedural account is that it provides a framework to understand positive generation effects in both
episodic memory (McNamara & Healy, 1995a)
and skill acquisition paradigms (McNamara,
1995; McNamara & Healy, 1995b) as well as
negative generation effects (i.e., advantages for
reading relative to generating) that have been
found in many studies involving implicit priming measures at test (see Roediger & McDermott, 1993, for a review). One aspect of our
procedural account is that it is more process
oriented rather than item oriented. Processing
factors, in contrast to item-related factors, are
recognized by an increasing number of researchers as crucial to the understanding of the
generation effect (e.g., Begg et al., 1991; Mc-
PROCEDURAL EXPLANATION OF THE GENERATION EFFECT
Daniel, Riegler, & Waddill, 1990; McDaniel &
Waddill, 1990; McDaniel et al., 1988; Nairne et
al., 1991). Moreover, the importance of focusing on process-oriented principles to explain
other cognitive phenomena is presently given
greater emphasis (e.g., Jacoby, 1991; Kolers &
Roediger, 1984; Roediger, 1990). Hence, the
procedural account has been useful for better
understanding a large range of long-term retention phenomena (e.g., Healy et al., 1992) and
other cognitive processes (Kolers & Roediger,
1984). Thus, the procedural account provides a
general cognitive principle that has wide applicability.
Developing a complete understanding of the
generation effect is crucial to the understanding
of retention processes, primarily because the
generation effect is a basic phenomenon, but
also because of the importance of its implications for improving learning and memory. We
believe that 2 decades of research on this phenomenon is finally painting a more complete
picture of the parameters involved in the generation effect and thus of the factors that lead to
more successful learning and memory.
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(Received November 4, 1999)
(Revision received February 21, 2000)