An Inquiry Into The Spontaneous Transfer Of Problem-Solving Skill

CONTEMPORARY EDUCATIONAL PSYCHOLOGY 22, 472–494 (1997)
ARTICLE NO. EP970948
An Inquiry into the Spontaneous Transfer
of Problem-Solving Skill
Edward A. Price and Marcy P. Driscoll
Florida State University
Problem solving, by definition, involves achieving new understanding in unfamiliar
contexts, and is critical to all aspects of life, especially in the educational and scientific
arenas. Students learn from many experiences to develop a repertoire of abilities,
including the use of logic, which enable them to spontaneously transfer their problem-
solving skill to unfamiliar situations. The purpose of this study is to explore the mini-
mum conditions necessary to facilitate the spontaneous transfer of problem solving skill
in an unfamiliar context. One hundred and seventy-five subjects were presented with
logically identical problems based on the Wason selection task, which differed only in
the degree to which a familiar schema could be invoked to help solve the problem. In
the pretest stage, only 10.5% of subjects could solve the selection problem in an
unfamiliar context, whereas 57.3% could solve it in one that was familiar. The effect
of three interventions, prior exposure to a familiar scenario, repeat opportunities on
like problems, and process-oriented feedback, on selection task performance in an
unfamiliar context was assessed in a posttest stage. Overall, none of the interventions
were effective, indicating that the minimum threshold for spontaneous transfer may be
above the level of intervention included in this study. Schema theory, implications for
instruction, and directions for future research are discussed. q 1997 Academic Press
INTRODUCTION
Seventh-grade students have difficulty solving word problems, even when
they can successfully perform the mathematical calculations required by the
problem (e.g., Schoenfeld, 1988). Educated adults, competent with everyday
mathematical computations involved in shopping, managing money, and load-
ing trucks correctly, cannot do the same tasks when they are attempted in
abstract form in the laboratory (Lave, Murtaugh, & De La Rocha, 1984, cited
in Singley and Anderson, 1989). Subjects faced with a problem about radiating
a tumor fail to see the relevance of the solution provided in an analogous
problem until prompted with a hint by the experimenters (Gick & Holyoak,
1983). These examples all point to the significant effects that content and
context can have on problem solving even when tasks are logically identical.
Contrary to the classical theory of reasoning which holds that the rules of
Address correspondence and reprint requests to Edward A. Price, Department of Educational
Research, Florida State University, Tallahassee, FL 32306-3030.
472
0361-476X/97 $25.00
Copyright q 1997 by Academic Press
All rights of reproduction in any form reserved.

473
TRANSFER OF PROBLEM-SOLVING SKILL
logic are independent of context or content, what the problem is about has
an enormous impact on how people think about it. What a problem is about
also influences the degree to which people can apply what they know in one
context to solving the same or a similar problem in a new context.
Problem solving, by definition, involves achieving new understanding in
unfamiliar contexts. Problem solving is the process individuals engage in
when three conditions are met: first, there must be a ‘‘question,’’ task, or
challenge that requires an answer or solution; second, the problem solver
does not, for the moment, know how to reach the answer or solution; and,
third, there is a perceived need or desire for the answer. Absent these three
conditions the individual does not have a problem which requires solving
(Smith, 1991). As an ability, problem solving is critical to all aspects of life,
but it is particularly vital in the educational arena and scientific inquiry. Over
time, students learn from both successes and failures to develop a repertoire
of problem-solving abilities in many areas of knowledge. As this repertoire
expands, the students’ ability to approach the unfamiliar and the unknown
increases.
Applying knowledge or skill acquired in one context to new instances or
problems is a matter of transfer, and Salomon and Perkins (1989) suggested
that some kinds of transfer require mindful abstraction of a ‘‘rule, principle,
label, schematic pattern, prototype, or category’’ (p. 125). They called this
‘‘high road transfer’’ and contrasted it with ‘‘low road transfer,’’ which is
the unprompted use of well-learned behavior in new contexts. Low road
transfer appears to occur with extensive and varied practice so that behaviors
and cognitions become automatic and stimulus controlled. Given cues in a
new context that are taken to be prototypical of a particular category of
situations, the learned behavior is automatically applied. Driving a truck after
years of driving a car is an example of low road transfer. The conditions
necessary to facilitate the mindful abstraction on which high road transfer
depends, however, are less clear. Salomon and Perkins (1989) explicitly raised
the questions of what learning conditions promote high road transfer and
whether both kinds of transfer may contribute to some performances. In
problem solving some strategies may become automatic after years of practice
or study in a domain, but any given problem must first be approached mind-
fully if all relevant knowledge and skills are to be brought to bear on it. This
potential relation between automatic and mindful transfer intrigued us and
caused us to wonder what it would take to provoke spontaneous high road
transfer. After all, an essential condition of problem solving as a learning
outcome is the absence of guidance by the teacher; students must be able to
effectively solve problems in unfamiliar contexts on their own (Gagne,
Briggs, & Wager, 1992).
Research on the four card selection task (e.g., Wason, 1968) provided some

474 PRICE AND DRISCOLL
insights because performance on this problem is widely discrepant depending
on the context in which the problem is encountered. The selection task requires
conditional reasoning (with propositions of the form, If p, then q) and is
considered to be the single most investigated problem in the deductive reason-
ing literature (Evans, 1996). The importance attached to this problem, from
an educational point of view, comes from the fact that logical deduction has
long been considered a primary means used by problem solvers to close the
distance between the problem and a solution. Moreover, conditional reasoning
plays an important role in scientific thinking. According to Ward, Byrnes,
and Overton (1990), ‘‘students need to become proficient in such conditional
reasoning in order to become successful practitioners of the scientific method
and to evaluate the validity of theoretical assertions in any of the scientific
disciplines’’ (p. 832). The fact that the selection problem yields such discrep-
ant performance in diverse contexts makes it a useful framework for studying
transfer.
The Four Card Selection Problem in Diverse Contexts
Peter Wason (1968) discovered that very few people could solve the selec-
tion task which involved determining which of four cards to turn over in
order to test a conditional statement (‘‘If a label has a vowel on one side,
then it has an odd number on the other side’’). Although the content of
Wason’s task was abstract and unfamiliar to his subjects, it was so simple
that then-current psychological theory was unable to explain why only 4%
of his subjects were able to do it. (See the Appendix and Fig. 2 for a full
explanation of the selection task.)
Since Wason’s study, a great many investigations have been undertaken
to try to improve performance on the selection task and to understand why
people have so much trouble doing it. Training in formal logic was no apparent
help. Cheng, Holyoak, Nisbett, and Oliver (1986) found that subjects per-
formed only 3% better following a full semester course in formal logic than
those who did not receive such training. Similarly, overall educational attain-
ment appeared to have no determinative effect on the outcome. According to
Jackson and Griggs (1990), people with Ph.D. degrees performed the selection
task no better than people with bachelor’s degrees.
When the selection task was put into a familiar context, however, perfor-
mance changed dramatically. In one of the earliest extensions, Wason and
Shapiro (1971) showed that presenting the conditional with content familiar
to subjects (‘‘Every time I go to Manchester I travel by train’’) enabled more
than 60% of the subjects to generate the correct card selections. Control group
subjects, faced with abstract content, were still mired at about 12%. Johnson-
Laird, Lagrenzi, and Lagrenzi (1972) gave a number of British subjects a
scenario relating to the British postal system with which they were familiar. In

475
the familiar condition 87.5% were able to do the selection card task correctly.
Interestingly, they found that other British subjects or foreigners living in
Britain who were not familiar with the postal system’s rules performed very
poorly.
D’Andrade (cited in Rumelhart, 1980; Rumelhart & Norman, 1981; and
D’Andrade, 1995), in the United States, also demonstrated the tremendous
impact of problem content on results. When presented within a familiar con-
text, known as the Sears Store Scenario (‘‘If the purchase receipt is over
$30.00, then it has the manager’s signature on the reverse side’’), 70% of
subjects were able to solve the problem, but when it was presented in an
unfamiliar context, known as the Label Factory Scenario (using Wason’s
original rule in the label factory scenario), only about 13% could do it. In a
related study, Griggs and Cox (1982) compared an unrealistic scenario with
a realistic one. While none of their subjects could perform the task correctly
with the unrealistic scenario, 73% could accomplish it when couched in terms
bound to be familiar to undergraduate students (‘‘If a person is drinking beer,
then the person must be over the age of 19’’).
Initially, the facilitation effect of familiar content appeared to be based on
subjects’ direct experiences. Griggs and Cox (1982) proposed the ‘‘memory
cue’’ hypothesis suggesting that the facilitation effect occurred when the
familiar problem content cued subjects’ memories. However, that view proved
to be both too broad and too narrow. On the one hand, efforts to replicate
the facilitation effect with familiar content yielded mixed results, indicating
that memory cueing was not always sufficient to produce a facilitation effect
(Griggs, 1983; Griggs & Cox, 1982; Wason, 1983). On the other hand, re-
searchers such as Cheng and Holyoak (1985) showed that generalized scenar-
ios with which their subjects were not directly familiar, and thus could not
be cued from memory, could lead to the facilitation effect.
A Schema-Based Explanation?
Researchers turned to schema theory in order to explain the disparity of
performance between familiar and unfamiliar scenarios (Anderson, 1977; An-
derson, Spiro, and Anderson, 1979; Rumelhart, 1980; Rumelhart & Norman,
1981; D’Andrade, 1995). Schemata are the basic units of knowledge that are
learned in the context of daily living. Schemata may concern objects, events,
processes, or attitudes (Driscoll, 1994). R. C. Anderson (1977) offers an effec-
tive description of the concept of schema.
A schema represents generic knowledge; that is, it represents what is believed to be
generally true of a class of things, events, or situations. A schema is conceived to
contain a slot or place holder for each component. For instance, a Face schema includes
slots for a mouth, nose, eyes and ears. (p. 2)

Some other examples of schemata are: ‘‘house,’’ ‘‘going to the restaurant,’’
‘‘taking a multiple choice test,’’ ‘‘writing a term paper,’’ and ‘‘getting ac-
quainted.’’ Rumelhart (1980) explained how schemata provide essential link-
ages between the concepts and patterns of behavior which are the substance
of what we know and do:
A schema theory is basically a theory about knowledge. It is a theory about how
knowledge is represented and how that representation facilitates the use of the knowl-
edge in particular ways. According to schema theories all knowledge is packaged into
units. These units are the schemata. Embedded in these packets of knowledge is, in
addition to the knowledge itself, information about how this knowledge is to be used.
(p. 34)
Each schema is made up of related concepts, involving both declarative and
procedural knowledge. For instance, the ‘‘getting acquainted’’ schema would
include such processes as giving a hand shake, saying something friendly,
asking a question about the other person, and so on. Rumelhart (1980) empha-
sized that ‘‘most of the reasoning we do apparently does not involve the
application of general purpose reasoning skills. Rather, it seems that most of
our reasoning ability is tied to particular schemata related to particular bodies
of knowledge’’ (p. 55).
As mentioned, Griggs and Cox (1982) proposed a ‘‘memory cue’’
schema explanation. If individuals have direct experience with the sce-
nario, prior schemata are activated and problem solving is facilitated.
According to this view, people rely mainly on very domain-specific knowl-
edge, wherein specific recollections of prior experiences are used to solve
problems. Singley and Anderson (1989) refer to this view as the ‘‘radical
specificity position’’ (p. 235).
Cheng and Holyoak (1985) offered a more general interpretation of schema
theory. They argued that even if people do not appear to use formal rules of
logic there are rule systems that people do use that are more general and
somewhat domain independent. These rule systems, which they argued are
acquired through everyday experience, are called pragmatic reasoning sche-
mas. According to Cheng and Holyoak (1985), their version of the selection
task, the drinking age scenario, involved an example of the pragmatic schema,
called the ‘‘permission schema.’’ In this schema the premise is that in order
to take one action, a precondition must be satisfied. They found that the
permission schema enabled 60% of the subjects to perform well, even when
the content was abstract, whereas only 20% could do the abstract problem
when the permission schema was not included.
Evans (1989) observed that the permission schema maps to the same solu-
tions as formal logic in the case of the four card selection problem. In other
words, using a permission schema produces ‘‘card choices which coincide

477
with those prescribed by the logical analysis of the problem’’ (p. 85). When
subjects interpret the card selection problem as one concerning permission, the
permission schema is evoked and enables them to make the correct selections.
The idea that subjects might be using a relevant schema to help them
solve the selection problem is supported by results of studies investigating
analogical reasoning as well as arithmetic problem solving. Gick and Holyoak
(1983), for example, conducted a series of studies in which subjects first read
one or more stories illustrating a problem and then attempted to solve a
different but analogous problem. Their results indicated that subjects who
induced a problem schema from the story had greater success in solving the
analogous problem than subjects who did not induce a problem schema. In
addition, Sweller (1989; Cooper & Sweller, 1987) argued that students solve
arithmetic problems rapidly and with relative ease when they access schemata
of problem types.
Does schema theory explain the disparity of performance among logically
identical situations that is seen in the investigations of the selection problem?
Can schema theory offer guidance in generating the conditions that will induce
people to make the transfer between identical problems in different contexts?
When we considered the array of prior research on the selection problem, we
noted that all of the studies exposed subjects to either an unfamiliar or a
familiar scenario, but never both and never the same scenario a second time.
Thus, the prior studies do not speak to the issue of potentially beneficial
effects of sequential or repeated exposure to the selection task, nor to the
effect of prior exposure to the familiar version on solving the one that is
unfamiliar.
If schemata are the operating mechanisms or knowledge structures that are
enabling or inhibiting performance when subjects encounter the unfamiliar
version of the selection task, and if possession of an applicable schema is
believed to be the reason why so many more subjects are able to perform
well in the familiar version, then it is possible that prior exposure to a familiar
scenario should facilitate problem solving when an unfamiliar scenario is
encountered right afterward. If all other conditions, such as wording, format-
ting, and problem structure, are held constant, we should be able to detect
the effect, thus supporting a schema-based explanation.
Mindful of the fact that performance was so much higher in the familiar
condition, we reasoned that prior exposure to a familiar scenario would be
one of the minimum conditions necessary to facilitate spontaneous transfer
of problem solving in the unfamiliar condition. Less likely, but also evidence
of a schema-based explanation, would be improved performance on the selec-
tion problem when encountered repeatedly in the unfamiliar scenario. Given
these supports, it may be possible for subjects to abstract a problem schema
and transfer it to the unfamiliar scenario.

Recognizing that people find the unfamiliar version of the four card selec-
tion problem difficult, however, we considered that prior exposure to the
familiar scenario and repeat exposures might still not be enough to facilitate
spontaneous transfer. Then the issue of additional factors leading to schema
building and schema extension becomes a primary concern. Thus, we hypothe-
sized that problem solving in the unfamiliar scenario could be enhanced by
a feedback intervention that induced schema restructuring or schema tuning,
two of the three ways schemata are assumed to be modified. (As noted below,
the third means of modifying schemata, accretion, does not apply to this
study.)
Our three research questions were generated, therefore, from our interpreta-
tion of schema theory and by our concern to know how much (or how little)
assistance problem solvers would require in order to spontaneously generate
their own correct solutions to problems of logic:
1. If a subject is exposed to the selection task in a familiar context before
immediately going on to one that is unfamiliar, does performance in the
unfamiliar context improve?
2. If subjects encounter the selection problem multiple times, does perfor-
mance improve?
3. If feedback is provided between attempts, does performance improve
and, if so, what kind of feedback is most effective?
Design and Rationale for the Study
Figure 1 portrays the three-stage structure of the study. Stage 1 replicates
the conditions of the D’Andrade study and establishes the existence of a
schema in our subjects. This enabled us to place the subsequent stages in the
same experimental context as the D’Andrade study. Stages 2 and 3 provide
our extensions of the original design. (A full description of the selection task
is provided in the appendix to this paper. See also Fig. 2.)
In stage 1, half the subjects began with the unfamiliar scenario in which
they were told to imagine themselves as label checkers in a label factory.
They were given the rule—‘‘If one side of the label has a vowel on it, then
the other side of the label has an odd number’’—and told to turn over only
those labels required to verify if the rule is being followed or not. The
remaining subjects began with the familiar scenario. They were told to imag-
ine themselves as clerks in a Sears store who were required to check receipts.
They were given the rule—‘‘If the store receipt is more than $30.00, then it
has the manager’s signature on the other side’’—and provided the same
instructions as the subjects in the unfamiliar scenario.
In both scenarios, the rules were carefully worded to exclude words such
as ‘‘must’’ or ‘‘should’’ in order to avoid inadvertently triggering one of the

479
Fig. 1. Design of the study.
pragmatic schemas—the ‘‘schema of obligation’’ that Manktelow and Over
(1992) discussed. Understanding the rules in terms of obligation tends to
change the nature of subjects’ reasoning in the selection task. Instead of
approaching the problem using logical deduction, they select cards based on
expected utility of conforming or not conforming to the rule. We wanted to
assure a clear test of schema-based logical reasoning and avoid introducing
an extraneous variable. In accord with D’Andrade’s results, we expected
that subjects given the familiar scenario would outperform those given the
unfamiliar scenario.
Stage 2 provides a test of the hypothesis that prior exposure to a familiar
scenario would assist problem solving by virtue of evoking an existing
schema. The question is whether apprehending the problem schema in the
familiar Sears story context will enable subjects to abstract a general problem
schema that they can then apply to the problem in the unfamiliar label factory
context. In stage 2, all subjects were presented with an unfamiliar scenario
(as label checkers) and the rule, ‘‘If one side of the label has the letter ‘P’
on it, then it has an even number on the other side.’’ The subjects exposed
first to a familiar scenario were expected to perform better on the problem
in the unfamiliar scenario of stage 2 than those exposed first to an unfamiliar
scenario. No feedback was provided between stages 1 and 2 for either group.
Stage 2 also answers the question of whether repeat exposures to the same
problem in the same context is enough for subjects to abstract a useful problem
schema. Should performance on the problem in the unfamiliar scenario im-

prove from stage 1 to stage 2, independent of the context seen before, then we
would conclude that multiple exposures are sufficient to induce spontaneous
transfer of problem solving.
Stage 3 enables us to examine the impact of an intervention—rule-based
feedback—that was designed to facilitate problem-solving transfer by modi-
fying subjects’ problem schemata. The selection of feedback types was guided
by schema theory. According to theory, schemata are extended in three ways:
accretion, restructuring, and tuning (Rumelhart, 1980; Rumelhart & Norman,
1978). Accretion refers to the encoding of new information in terms of existing
schemata. Since no new information was being provided to subjects in this
study, accretion was not applicable.
Restructuring occurs when information does not fit into an individual’s
existing collection of schemata and a new schema must be created. Restructur-
ing most commonly occurs by modeling the new schema on an existing
schema and modifying it slightly, i.e., reasoning by analogy (Rumelhart &
Norman, 1978, 1981). To support restructuring in stage 3 we used analogical
feedback in one of the two feedback conditions to be compared with no
feedback. Any analogy requires two elements for comparison. Thus no feed-
back could be given following stage 1 but was provided between stages
2 and 3. The analogical feedback for the Sears scenario was presented as
follows:
In the first scenario the rule you were asked to follow as a Sears Clerk was
‘‘If a receipt is over $30.00, the manager’s signature appears on the back.’’
In the second scenario the rule you were asked to follow as a Label Checker was
‘‘If there is a letter P on one side of the label, it has an even number on the other
side.’’
Please take note of the fact that having a receipt that is over $30.00 in the first scenario
is like having a letter P on one side of the label in the second scenario. Likewise,
having a receipt with the manager’s signature in the first scenario is like having an
even number on one side of the label in the second scenario. When you perform this
task one last time, please keep this in mind.
To help facilitate the creation of a problem schema for subjects who did not
spontaneously invoke it, the analogical feedback made the schema explicit
and linked it by analogy in the two scenarios.
Tuning, the third way by which schemata are modified, is a process of
refinement that adds and deletes characteristics to an existing schema. Tuning
leads to increased accuracy of a schema (Rumelhart & Norman, 1978). In
this study, declarative feedback (Dempsey, Driscoll, & Swindell, 1993) was
used in the second feedback condition of stage 3 to facilitate tuning.
Declarative feedback is rule-based and informative in nature. Declarative
feedback elaborates on the instructions given in the first stage. Briefly recall

481
that, in effect, the instructions were structured in this way: ‘‘The rule is if A
is true, then B is true. Using the items given, identify those which need to
be checked.’’ Chapman (1993) noted that the most common error that people
make on the selection involves affirming the consequent. In effect, affirming
the consequent logically reverses the rule into ‘‘If B is true, then A is true.’’
Chapman reported that people may not affirm the consequent when they are
provided direct information pointing away from that fallacy, hence our deci-
sion to include this form of declarative, rule-based feedback. We anticipated
that if subjects knew which error to avoid, they might then replace the wrong
item with a correct one. Specifically, declarative feedback provided in the
unfamiliar scenario was as follows (feedback provided in the Sears scenario
was nearly identical):
. . . the rule you were asked to follow as a Label Checker was
‘‘If a label has a vowel on one side, it has an odd number on the other side.’’
Please take note of the fact that the rule was NOT
‘‘If a label has an odd number on one side, it has a vowel on the other side . . .’’
When you perform this task one last time, please keep this in mind.
According to schema theory, this kind of feedback is most similar to tuning
because it helps the subject increase the clarity and accuracy of an existing
schema.
As noted, and consistent with Gick and Holyoak (1983), subjects were
invited to use the information provided in the feedback when they attempt
the selection task an additional time.
All subgroups in stage 3 performed the same task, that is, to examine the
set of labels provided in an unfamiliar scenario as follows: ‘‘If there is a
letter P on one side of the label, then there is an even number on the other
side.’’ The problem in stage 3 is identical to the problem in stage 2 in order
to avoid possible confounding caused by a problem change. The letters and
numbers used were changed, however, to prevent memorization of responses.
The hypothesis of this portion of the study was that, in keeping with
schema theory, analogical feedback should be more effective than declarative
feedback, which in turn should be more effective than no feedback at all. A
corollary of our earlier hypothesis is that the respective feedback effects were
expected to be greater among the subjects working within a familiar schema
than with those with the unfamiliar schema. Finally, if multiple exposures to
the problem have any effect, then the performance of all subjects should be
better in stage 3 than in the prior two stages.
Since our interest in this study was in discovering the minimum conditions
necessary to promote spontaneous transfer, we did not provide subjects with
correct response feedback, nor did we elaborate on how to solve the selection

task. We wanted to test first for the effects of rule-based feedback. In future
research, we intend to add both instructional and correct response feedback.
METHOD
Subjects
One hundred eighty (180) subjects were recruited for the study. Of these, 169 were recruited
from students in the College of Education at the Florida State University, Tallahassee, Florida.
Eleven were recruited from a local church in Tallahassee, Florida. Five packets were discarded
from the data set because they were not filled out (n Å 4) or were filled out incorrectly (n Å
1). Thus, the final sample size was 175. Subjects were divided into six subgroups (see Fig. 1)
that were equal in size initially. Subgroup sizes were 28, 29, 29, 30, 30, and 29, respectively.
Materials
All materials were in print format. The first page described the task and what the subjects
were supposed to do and included a consent form. Subjects were told that their names were not
required. The second page contained stage 1. On that page a brief description of the label
checking or Sears store scenario was provided along with the problem-solving task, depending
on the individual’s group assignment. The third page (stage 2) presented another label-checking
scenario with the same instructions as before.
At the fourth page (stage 3), subjects’ paths diverged. The no-feedback group encountered
their third and final exposure to the selection problem. The declarative and analogical feedback
groups were presented with feedback as previously described, followed by their third and final
exposure to the problem.
Procedure
The study was administered to small groups in the classroom. The researcher explained that
this was a study in human problem solving and that the task would take between 10 and 15
minutes, but they would be given all the time they required. Subjects were asked to note their
start and end times at the top of the first page. As explained above, the subjects were divided
into six categories, thus there were six different packets. Packets were placed in sequential order
and inserted into standard office envelopes ahead of time to assure that assignment to the six
subgroups would be random. The researcher did not know at the time the study was being
administered which subjects were being assigned to which groups. Packets were then collected
and scored.
Measures
Scoring of the selection task is straightforward. Subjects must select both affirming the anteced-
ent and denying the consequent. All other combinations are incorrect. (See the Appendix and
Fig. 2 for details.)
RESULTS
A summary of results indicating the percent of subjects responding correctly
in each stage of the study is presented in Table 1. Statistical significance is
also indicated using the x2
technique.

483
Fig. 2. The four possibilities of the four-card selection task.
Is There a Schema Effect in Stage 1?
In stage 1, we replicated the findings of the Wason and D’Andrade studies.
As expected, subjects performed significantly better in the familiar scenario
than they did in the unfamiliar scenario. In the familiar Sears scenario, 57.3%
of subjects were able to solve the problem correctly, whereas only 10.5% of
subjects were able to do so in the unfamiliar label-checker scenario. Therefore,
subjects were about 5.5 times more likely to solve the problem when it was
TABLE 1
Percent of Subjects with Correct Responses
Group One: Group Two: Statistical significance
Unfamiliar Familiar (x2
, a Å 0.05)
Stage One 10.5% 57.3% Significant, x2
Å 42.6,
df Å 4, p õ .0001
Stage Two 14.0% 12.4% Not significant
Stage Three
No feedback provided 14.3% 13.3% Not significant
Declarative feedback provided . . . 17.2% 16.7% Not significant
Analogical feedback provided . . . 3.4% 6.9% Not significant

TABLE 2
Number Who Selected the Correct Pair
Stage One Stage Two Stage Three
Familiar Scenario n Å 51 (All subgroups combined)
and of these c n Å 10 (19.6%)
Unfamiliar Scenario n Å 9
put in a familiar context. This difference in performance was statistically
significant (x2
Å 42.6, df Å 1, p õ .001, a Å .05).
Does Prior Exposure to a Familiar Scenario Facilitate Problem Solving?
Because problem-solving performance in an unfamiliar scenario is always
poorer than in a familiar scenario, we expected the performance to drop for
those subjects exposed to the Sears scenario in stage 1 followed by a label-
checker scenario in stage 2. It did (from 57.3 to 12.4%). But we hypothesized
that these subjects would outperform those who received the unfamiliar sce-
nario in both stages 1 and 2. The difference between the two groups in stage
2 would constitute the schema facilitation effect we expected to see. However,
that did not occur. Even though subjects could do the selection task more
successfully in the familiar scenario, the entire performance advantage disap-
peared as soon as they were in the unfamiliar scenario. The difference was
so dramatic that we think subjects did not even recognize that the familiar
and the unfamiliar scenarios were actually the same problem. This is all the
more remarkable since the materials were worded and formatted exactly alike.
So far, the data we reported for stage 2 include subjects who answered
correctly and incorrectly in stage 1. One might argue that the subjects in stage
1 who did not solve the selection task correctly should be excluded from the
analysis because they had no effective schema to be applied to stage 2. Indeed,
this is in keeping with our hypothesis that success with the familiar scenario
would provide facilitation when the unfamiliar scenario is encountered. Unfor-
tunately, when we looked only at those who answered correctly in stage 2,
prior exposure to the familiar scenario still did not appear to facilitate stage
2 performance in the unfamiliar scenario. Table 2 shows the situation quite
strikingly. If a subject solved the problem correctly in the familiar scenario,
the chances of getting it right in the subsequent unfamiliar scenario were less
than one in five (19.6%). On the other hand, although many fewer subjects
answered correctly in the unfamiliar scenario of stage 1, of those who did,

485
100% of them got it right when they faced another unfamiliar scenario in
stage 2. Contrary to our hypothesis, prior exposure to the familiar scenario
accomplished nothing.
Does Multiple Exposure to the Problem Facilitate Transfer?
Most subjects who failed to solve the selection task correctly in the unfamil-
iar scenario appeared to have no existing problem schema to work with in
stage 1, and they did not apparently build a useful problem schema in stage
2. Their performance remained low regardless of their multiple exposure to
the selection problem. For the subjects who initially encountered the problem
in a familiar scenario, the availability of an existing schema in stage 1 provided
no benefit to problem solving in stage 2. As Table 2 shows, multiple exposures
to the same type problem, regardless of its context, had no facilitative effect
on performance.
How Does Feedback Affect the Transfer of Problem Solving?
In stage 3, we wanted to determine what kind of feedback, if any, improves
the transfer of problem solving. Three types of feedback conditions were
provided: no feedback, declarative feedback, and analogical feedback. We
hypothesized that declarative feedback and analogical feedback would im-
prove problem-solving performance, but the data did not confirm our predic-
tion. As Table 1 shows, the differences among subgroups in stage 3 were not
significant, nor was performance in stage 3 better than performance in stage
2 for any group. Therefore, this study provided no evidence that rule-based
feedback facilitates the spontaneous transfer of problem-solving skill, at least
within the confines of this design.
What Can Be Learned from the Errors Subjects Made?
When two of our three primary hypotheses were not confirmed, we exam-
ined the error patterns made by the subjects. Although response patterns of
one, three, or four selections may include the correct options of affirming the
antecedent and denying the consequent, they are counted as errors because
they violate the instructions given to subjects to turn over only those cards
that require verification, no more and no less. While virtually all the subjects
correctly chose to affirm the antecedent, the most common error pattern
involved affirming the consequent. This error is tantamount to arbitrarily
reversing the rule. If the rule is ‘‘if vowel, then odd,’’ affirming the consequent
transforms the rule to ‘‘if odd, then vowel.’’
Stage 2 tells a striking story in comparison to stage 1 as both the familiar
and the unfamiliar groups appeared nearly identical in their response pattern
distribution. In stage 2 both groups displayed the same error patterns of
affirming both the antecedent and the consequent (50%) and affirming the

TABLE 3
Frequency and Percentage of Subjects Who Made a Change after Receiving Feedback
Subgroup Frequency Percentage
Unfamiliar, no feedback 0 out of 28 0.0%
Familiar, no feedback 4 out of 30 13.3%
Unfamiliar, declarative feedback 19 out of 29 65.5%
Familiar, declarative feedback 16 out of 30 53.3%
Unfamiliar, analogical feedback 8 out of 29 27.6%
Familiar, analogical feedback 1 out of 29 3.4%
antecedent only (20%). No statistical difference exists between the two groups
in Stage 2. This means that many subjects who correctly selected denying
the consequent in conjunction with affirming the antecedent in the familiar
scenario of stage 1 abandoned denying the consequent (which was correct)
for affirming the consequent (which was not correct) in stage 2 when they
got to the unfamiliar scenario.
Stage 3 follows the feedback treatments. We have already seen that the
feedback used did not lead to a statistically significant improvement in perfor-
mance in any group. Nonetheless, there was an observable effect regarding
those who made a change following feedback. The change could be of any
kind: from correct to incorrect, from incorrect to correct, or from one incorrect
response pattern to another.
As shown in Tables 3 and 4, the feedback we provided was effective only
in the declarative condition and then only in eliminating one error response,
affirming the consequent, which our feedback targeted. The degree of impact
was about the same for all subjects who received this type of feedback, so it
is safe to assume the change is caused by the feedback treatment rather than
any residual schema effect based on prior exposure to the familiar scenario.
TABLE 4
Frequency and Percentage of Subjects Who Eliminated ‘‘Affirming the Consequent’’
after Receiving Feedback
Subgroup Frequency Percentage
Unfamiliar, no feedback 0 out of 28 0.0%
Familiar, no feedback 0 out of 30 0.0%
Unfamiliar, declarative feedback 16 out of 29 55.2%
Familiar, declarative feedback 12 out of 30 40.0%
Unfamiliar, analogical feedback 0 out of 29 0.0%
Familiar, analogical feedback 1 out of 29 3.4%

487
Other than this, the number who changed to the correct pair following any
of the feedback conditions is negligible.
DISCUSSION
We began this study with the question, What does it take to provoke
spontaneous high road transfer? We hypothesized that invoking an appropriate
schema from a problem in a familiar context would facilitate solving the
same problem in an unfamiliar context when it was encountered right after.
Although our subjects demonstrated that they had an appropriate schema that
assisted them in solving the problem in the familiar context (stage 1 results),
they did not transfer this schema to the unfamiliar context (stage 2 results).
Moreover, subjects who did not have a problem schema for solving the
problem in the unfamiliar context did not build one with multiple exposures
to the problem (also stage 2 results). Finally, contrary to expectation, rule-
based feedback designed to facilitate schema tuning and restructuring did not
improve subjects’ problem solving performance (stage 3 results). Declarative
feedback, however, did have the effect of eliminating the most common error,
affirming the consequent.
Schema theorists, such as Anderson (1977), Rumelhart (1980), Johnson-
Laird (1983), and Cheng and Holyoak (1985), have argued that subjects
depend on schema building in learning how to solve problems. Salomon
and Perkins (1989) argued further that the problem schema must be mind-
fully abstracted or decontextualized from specific instances of a problem
in order for high road transfer to occur. This study adds strength to the
idea that schemata exist and that they powerfully influence problem solving
(from stage 1 results). However, there is no evidence that our subjects
spontaneously abstracted a useful schema while trying to solve the selec-
tion problems nor did the feedback conditions appear to promote such
abstraction.
In one respect, our results seem surprising. Subjects in Gick and Holyoak’s
(1983) research demonstrated increased transfer when they were cued as to
the relevance of the first story to the solution of the problem in the second
story and when two prior analogs were provided. In contrast, our subjects
could not solve the selection problem in the unfamiliar context even when
provided with feedback analogously linking it to the problem in the familiar
context, which they could solve. Two prior analogs were of little benefit to
our subjects even when subjects were cued to the relevance of the earlier
scenarios and when encouraged to use the information on the third and final
problem-solving attempt.
So what did the subjects in this study actually do? In the unfamiliar scenario,
given the absence of a relevant schema, we think they acted with what Evans
(1984, 1989, 1996) and others have referred to as matching bias. The rule

said, ‘‘If vowel, then odd,’’ so they tended to notice the items mentioned in
the rule, select them, and then quickly turn the page. In the familiar scenario,
possession of a relevant schema (i.e., familiarity with store receipts and getting
forms signed) enabled them to score higher, but with no visible transfer of
this ability to the unfamiliar context. Simply put, they saw two items in the
rule, so in most cases those were the ones they selected. We doubt the thinking
was any more mindful than that.
In a study conducted after ours, Evans (1996) suggested that the matching
bias is cued by a preconscious determination of relevance that is qualitatively
different from formal logical reasoning. Using the drinking age version of
the selection problem (Griggs & Cox, 1982), which has a reliable facilitation
effect, Evans (1996) noted that subjects required little time to make correct
selections. His study, which was computer-based, was designed to collect
data on time spent considering card choices, as well as the actual selections.
Evans reported that
the subjects who think about the card for a reasonable amount of time—as measured
by inspection times—end up selecting it. Those who do not think about the card (there
are many zero times at the level of individual subjects) or inspect it only briefly do
not end up selecting the card . . . . Individual differences in perceived relevance (as
measured by inspection times) are also strongly correlated with selection decisions on
particular cards. (p. 223)
Does this mean that subjects are deciding what cards they will pick before
they think about them? Although this is counterintuitive, Evans thinks so.
If, as we have seen, problem-solving ability is heavily content and context
dependent, and yet, as we also have seen, not entirely dependent on direct
experience, then what Evans is proposing makes sense. In everyday life
individuals seldom have the time or the opportunity to search through all the
possibilities of a problem space before a decision is required. Often key facts
are missing, parts of a problem are difficult to understand, or sufficient time
is not available to fully analyze a problem. And yet, despite these limitations,
people are often able to discern a correct problem solution in situations where
they have an incomplete set of relevant knowledge to draw upon.
Such an ability would essentially consist of pattern recognition (Margolis,
1987). These patterns would be stored and organized as schemata, ready
for use on demand when needed. Living in a complex and ever-changing
environment would require that these schemata be fairly durable in the sense
of being correctly tuned to appropriate contexts, so that the right schemata
would be triggered in the right context. Some of them would be very specific
and not very transferable. The demands of survival would also require some
moderately generalizable schemata as well in order to promote learning and

489
adaptation. Nesting schemata within schemata, as schema theory proposes,
would certainly add to this flexibility.
Given the usual constraints of both time and limited working memory,
most individuals, most of the time, will not search through an entire problem
space; indeed, the habit of doing so could often create an overwhelming
cognitive burden (Carlson, 1997). As Perkins and Salomon (1989) noted
with the example of famous chess masters, the number of combinations and
permutations on a typical chess board is far too large for an individual to
explore fully. The chess master does not attempt this futile task, however,
for he or she has already memorized thousands of patterns that commonly
occur on the chess board along with their probable strengths and weaknesses.
Using these patterns as a heuristic, the chess master rapidly recognizes a few
of the most promising moves and then concentrates all of his or her analytical
ability on those.
On this account, patterns are judged relevant or worthy of further cognitive
attention as a result of the interaction between the schemata that individuals
possess and the contexts in which they find themselves. The schemata people
use could be based on direct experience as Griggs and Cox (1982), Johnson-
Laird (1983), Evans (1984, 1989), D’Andrade (1995), and others have pro-
posed. When these are absent, the schemata can be moderately generalized,
as in the pragmatic schemas proposed by Cheng and Holyoak (1985), Mank-
telow and Evans (1979), Manktelow and Over (1992), Cosmides (1989), and
others. What does appear clear, however, given the long history of research
on the selection task and other problems, is that fully context-independent
logical analysis is not the normative response for most people.
Thus, it may well be that the judgment of relevance is determined heuristi-
cally and preconsciously, through pattern recognition of subtle pragmatic cues
(Evans, 1984, 1996; Margolis, 1987). Evans (1996) noted:
Not only is attention selectively focused on the presented information, but the retrieval
of relevant prior knowledge, including rules, heuristics or schemas, also occurs the
same way. The success of such conscious, analytic reasoning as does occur is very
highly constrained by the ‘‘relevant’’ information on which it is focused. (p. 223)
In sum, this study reinforces the point that new schemata do not easily
arise spontaneously, nor are they easily transferred. We were not able to
develop evidence supporting our hypotheses that exposure to a familiar sce-
nario would facilitate the transfer of problem-solving skill to an unfamiliar
scenario, nor that practice opportunities alone enhance performance, nor that
the rule-based feedback that we provided in this study by itself leads to
enhanced performance. We do have evidence that declarative feedback may
help eliminate errors, which is valuable to know. If these factors are to have

any value in instruction of problem-solving skill they may well need to be
combined with other kinds of instructional assistance.
These reflections suggest some implications for instruction as well as direc-
tions for further research. First, instruction should focus more on schema-
building strategies as foundational to problem-solving ability. An integral
component of building these schemata for logical deduction would concentrate
explicitly on increasing the problem solver’s ability to deny the consequent
as well as to affirm the antecedent. Problem solvers should be guided explicitly
to avoid affirming the consequent when inappropriate. Instruction should
pursue these goals in the context of realistic, familiar scenarios rather than
in more conventional abstract contexts.
Second, instruction should facilitate schema building by providing learner
feedback in the form of numerous fully worked out and explained examples
or worksheets that explicitly guide learners in building their own schemata.
This relates to what Cormier (1987) refers to as the principle of ‘‘encoding
specificity’’—wherein the probability of retrieving a schema that has been
built ‘‘is a joint function of the way in which the material was originally
encoded and the cues of information available at the time of retrieval’’ (pp.
153–154). As shown in this study, feedback that was limited to a process or
rule orientation was not sufficient to facilitate spontaneous problem-solving
performance.
Third, single exposures to problem-solving situations are unlikely to pro-
vide enough material for schema building to occur. If high road transfer
is desired following instruction, multiple schema-building experiences are
probably required just as they are for low road transfer. How many and what
kind is still a subject for additional research.
Corollary to this implication is that instructors and instructional designers
should assume that problem-solving ability is cumulative not only over time
but over numerous experiences. This study points in the direction of multiple
exposures to problem solving scenarios, probably from differing perspectives,
as the most probable way to assure that the learner actually notices that a
newly encountered problem is really a previously encountered problem in a
new context (Driscoll, 1994; Cheng et al., 1986). Once the learner recognizes
the relevance of other schema to the current problem, he or she can bring his
or her repertoire of problem-solving abilities and prior knowledge to bear
upon the present situation, thus setting the stage for high road transfer to
occur.
Given these implications for instruction, a new focus on individuals, rather
than just groups, is desirable. Research utilizing thinking aloud protocols
would greatly add to this effort. We agree with Evans’ (1996) concern that
‘‘surprisingly, very few reports are available of thinking aloud protocols on
the selection task’’ (p. 223).

491
Finally, whatever plan instructors adopt, they must not leave schema build-
ing or knowledge transfer to chance. It does not arise spontaneously and its
development cannot be assumed.
APPENDIX: THE FOUR CARD SELECTION TASK
Wason (1968) introduced the selection task to test the classical view that
human reasoning operates according to the rules of formal logic. Subjects are
shown four cards as in Fig. 2 and told that a letter appears on one side and
a number on the other side. Subjects are asked to determine which cards need
to be turned over to check if a rule is being followed or not. The rule is, ‘‘If
a card has a vowel on one side, then it has an odd number on the other side.’’
While subjects are instructed to turn over only those cards required to make
the determination, they are not told how many cards need to be turned over.
The four cards (E, F, 7, 8) represent the four logical possibilities created
by the if-then conditional: affirm the antecedent, affirm the consequent, deny
the antecedent and deny the consequent. Only 4% of Wason’s subjects identi-
fied the correct pair of cards, the letter ‘‘E’’ and the number ‘‘8,’’ which
represent affirming the antecedent and denying the consequent, respectively.
Affirming the Antecedent. Selecting the ‘‘E’’ is a called affirming the ante-
cedent and, in formal logic, it leads to a valid conclusion. If there is an even
number on the other side, the rule is being followed and the card is correct.
In this case we could let the card by without looking at it. However, if there
is an odd number on the other side, the rule would be violated and the card
would be wrong. We cannot let a bad card through, so we have to turn the
card over to make sure there is not an odd number on the other side.
Denying the Antecedent. Selecting the ‘‘F’’ is a called denying the anteced-
ent and, in formal logic, it leads to an invalid conclusion. Since the rule does
not tell us to look for consonants, it does not matter if there is an odd or an
even number on the other side. Therefore, we do not turn over this item.
Affirming the Consequent. Selecting the ‘‘7’’ is called affirming the conse-
quent and, in formal logic, it leads to an invalid conclusion. We do not turn
this item over since the rule does not say to do anything in the case of odd
numbers, rather only vowels. Thus, if there is a vowel or a consonant on the
other side, it makes no difference. Seventy-nine percent of Wason’s (1968)
subjects made this error even though it is logically invalid.
Approximately 70% of our subjects made this error as well.
Denying the Consequent. The remaining response, selecting the ‘‘8,’’ is
called denying the consequent, and, in formal logic, it leads to a valid conclu-
sion. It does not matter if there is a consonant on the other side, but if there
is a vowel on the other side the rule is being violated. Thus, we must turn
over this item to check. When we deny the consequent we are looking for
information that is missing rather than for information which is present. Since

the information we require is missing, more people are likely to miss this
option. In fact, that is what happens. 96% of Wason’s subjects failed to
combine this option with the more obvious and equally essential affirming
the antecedent option.
In this study, 89.5% of our subjects in the unfamiliar scenario missed this
as well.
D’Andrade (cited in Rumelhart, 1980; D’Andrade, 1995) modified Wason’s
original design. Half of D’Andrade’s subjects repeated the original abstract
and unfamiliar conditions of the Wason study. The other half were asked to
imagine themselves as clerks at a Sears store with the responsibility of check-
ing the validity of store receipts. They were told ‘‘If the receipt is over $30,
then it has the manager’s signature on the back of the receipt.’’ In the Sears
scenario four receipts as shown in Fig. 2 were presented: a purchase over
$30, a purchase under $30, a receipt that is signed on the back, and a receipt
that is not signed on the back. Logically identical to the Wason version, the
correct answer is to select just the receipt over $30 and the receipt without
the manager’s signature on the back, that is, to affirm the antecedent and to
deny the consequent.
As we can see, the logical form of the Sears problem is the same as the
earlier letter and number scenario. The two scenarios differ in that one has
a familiar context and the other has an unfamiliar one. One is realistic in
content, the other is arbitrary. As mentioned earlier, in the familiar Sears
scenario 70% of D’Andrade’s subjects selected the correct combination of
responses (cited in Rumelhart, 1980). However, only 13% of D’Andrade’s
subjects could perform the task when based on the abstract rule, ‘‘if vowel,
then odd.’’
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