1. science
2. mathematics

EUROPEAN JOURNAL OF BEHAVIOR ANALYSIS
2008, 9, 157 - 172
NUMBER 2 (WINTER 2008)
157
What is a problem? Theoretical conceptions
and methodological approaches to the study of
problem solving
Per Holth
Akershus University College, Norway
The current paper describes important events in the history of research on problem solving and
discusses questions regarding the classification of problems. First, the main research traditions and major
research findings in the field are described. Some major problems in the attempt to define a problem,
including the issue of novelty, are discussed. A solution is suggested, based upon the definition of a
problem situation as one that no prevailing three-term contingency has established as a discriminative
stimulus for an action that produces a reinforcer. The final section is concerned with some differences
between cognitivistic and behavioral treatments of problem solving.
Key words: problem solving, novelty, mediating behavior, cognition, behavior analysis.
The literature on problem solving
According to PsychInfo, the first publication to mention problem solving either in the
title or in the abstract was a paper by Willard
S. Small, published in 1900. Small investigated
what he called the “persistence of useless motor habits” and “fortuitous associations . . . in
problem solving.” The title of his article was
“An experimental study of the mental processes
of the rat.” After that, only two publications
on problem solving appeared in 1907, two in
1914/15, before the rate of publication began
to accelerate in the 1920’s and continued to do
so until the early 1990’s, when the rate leveled
off, but increased again from 2004 (see Figure
1). By the end of 2007, the sum total of such
publications was 22,088.
Some of the early studies on problem solving appear strikingly modern. For instance, the
research questions asked by B. W. Daily (1925)
to a large extent match research questions asked
in Hank Kahney’s (1993) book on current issues
Address correspondence to: Per Holth, Akershus University
College, Box 423, N-2001 Lillestroem, Norway. E-mail: Per.
[email protected]
Figure 1. The numbers of annual publications that,
according to PsychInfo, mention ‘problem solving’
either in the title or in the abstract from 1900
through 2007.
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Per Holth
158
in problem solving. On the other hand, the early
days of the problem solving literature showed
little sign of band-wagon research in which
particular research questions guided a larger
body of empirical or theoretical work. Some
early research was concerned with methods of
teaching arithmetic, some were concerned with
showing that “insight” in Köhler’s sense of the
word occurred or did not occur in children or in
adults in different types of problems, and some
were concerned with the special limitations of
‘idiots’. From 1930 to 1932, for instance, C.
G. Aldrich and coworkers published a number
of articles on problem solving in subgroups of
people (e.g., Aldrich, 1931; Aldrich & Doll,
1931).
Research traditions
In 1966, Forehand, among others, distinguished between four different bodies of
research into problem solving, which might be
designated as follows: (1) the Gestalt/cognitive
tradition, (2) the learning tradition, (3) the
computer/information-processing tradition,
and (4) the psychometric/component-analysis
tradition.
The Gestalt/cognitive tradition comprises a
large body of experiments aimed at demonstrating ‘insight,’ ‘productive thinking,’ and
‘structural reorganization.’ Early work included
both animal studies (Köhler’s monkey studies), and studies of human problem solving by
Wertheimer (1945; posthumously), Duncker
(1945), and Maier (1930, 1931). They were
interested in the extent to which problem solutions emerged in a step-by-step fashion versus
as a sudden, complete whole. Studies of animal
‘insight’ naturally went out of favor within
this tradition after Birch’s (1945) and Harlow’s
(1949) careful demonstrations of how ‘sudden’
solutions shown by their monkeys depended
upon specific types of individual histories.
As pointed out by Wertheimer (1945),
the Gestalt tradition was primarily interested
in what happened at the moment of ‘sudden insight’ in human subjects, but they did
not completely ignore the relevance of ‘past
experiences’. In fact much work was invested
in demonstrating how training histories often
hindered rather than fostered ‘insight.’ They
called it a functional ‘fixedness,’ ‘fixity,’ ‘einstellung,’ or ‘set.’ In Duncker’s candle problem,
for instance, subjects were given a candle, a
box of nails, and some other objects, and they
were asked to attach the candle to a wall above
a table so that it did not drip onto the table.
Duncker’s own solution was to use the nailbox
as a candle holder which could be nailed to the
wall, but very few subjects did that. According
to Duncker, subjects were ‘fixated’ on the normal function of the box, and problem-solving
success was hampered by ‘reproductive problem
solving behavior,’ consisting only of previously
directly reinforced responses. The results of
Maier’s string problem could be interpreted
similarly. Maier had two strings hanging from
the ceiling and certain objects, such as pliers,
lying around. When participants were asked
to tie the two strings together, they discovered
that when they took hold of one string, the
other was out of reach. After a while, some
participants would attach an object to one of
the strings and make it move like a pendulum
and, while holding one string, the other could
be caught on its up swing and then the two
could be tied together. However, two thirds of
Maier’s subjects failed to simultaneously grab
two ropes hanging from the ceiling – to tie them
together – although objects were present which
could have been tied to the end of one rope to
produce a pendulum effect which would obviously be helpful. Luchins (e.g., 1942; Luchins
& Luchins, 1950) went one step further and
actually provided his subjects with an experimental history that produced such rigidity in
problem solving.
Useful as some of these experimental findings may be in predicting behavior, the overall
attempt to show that “organisms organize” may
add very little, and was what Boring (1957)
called “the great tautology of psychology.”
Moreover, the Gestalt question of whether problem solving is “productive” or just “reproductive” may constitute a pseudoempirical rather
than an empirical question – simply because
‘novelty’ may, as we shall see, constitute a defining characteristic of a ‘problem.’
What is a problem?
What has been called the learning tradition (sometimes, the S-R tradition) is hardly a
unitary approach except, perhaps, for a clearly
pronounced common interest in the relevance
of variables in the history of each subject.
Interestingly, Watson (1920) may, in fact,
have been the first to systematically use verbal
protocols in experiments on ‘thinking.’ For
instance, he asked subjects to talk aloud when
given assignments characterized by different
degrees of novelty to the subject. He could
observe characteristic response patterns under
these different conditions, with an increasing
number of errors, false starts, “hanging of the
head” and even “blushing” when subjects were
given the more novel assignments. Watson
pointed out that he had “often felt that a good
deal more can be learned about the psychology
of thinking by making subjects think aloud
about definite problems, than by trusting to the
unscientific method of introspection” (1920, p.
91). Although verbal protocols have been widely
used in the Gestalt tradition (e.g., Wertheimer,
1945) as well as in modern cognitive psychology
(see Ericsson & Simon, 1980), they have only
recently been employed seriously by others in
the radical behaviorist tradition (e.g., Hayes,
White, & Bissett, 1998).
After the work of Birch (1945) and of Harlow (1949), Kendler and Kendler (e.g., 1962)
analyzed problem solving in terms of combinations of separately established repertoires, and
such procedures were explicitly used by Epstein
and colleagues (Epstein, Kirshnit, Lanza, &
Rubin, 1984; Epstein, Lanza, & Skinner, 1980,
1981) to simulate ‘insight’ and other “higher
mental processes” in pigeons in what was called
the Columban simulation project. Beyond that,
behavior analysts were stuck with exploring
basic behavioral processes for a long time, and
their treatment of more complex and interesting
human phenomena have largely been theoretical interpretations as in much of Skinners later
work (e.g., Skinner, 1953, 1957, 1966, 1968,
1971, 1978). Direct experimental analyses of
more complex human performances, such as
stimulus equivalence, rule-governed behavior,
naming, and ‘joint control’ have only recently
begun to flourish within the behavioral tradi-
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tion (e.g., January issue of JEAB, 1998).
The Computer/information processing approach has been particularly influential in
modern cognitivist research and theorizing on
problem solving, and the work of Newell and
Simon (1972) has been called the bedrock of
the information-processing framework (e.g.,
Eysenck & Keane, 1995). In the ideal case, human problem solving is depicted metaphorically
in a computer language that allows for a direct
simulation of complex human phenomena in
the computer. Thus, input ‘information’ is taken
in by the organism, is ‘processed’ according
to a ‘program,’ the information is said to be
‘encoded,’ that is, converted to a form that can
be handled. It is ‘represented’ within and may
occupy ‘space,’ much like bytes in the ‘working
memory,’ and it may be ‘stored’ in ‘long-term
memory’ – such as on a hard disk – ‘tagged’ for
possible ‘retrieval’ in the future to produce an
‘output’ – a ‘printout.’ As pointed out by Davis
(1966), the computer simulation procedure
makes the demand that ‘prior information’ as
well as possible solutions and the sequences
of steps in problem solving are specified by
the researcher. This is typically attempted in
terms of problem space theory, which describes
the possible sequences of steps or states from
an initial state to a goal state in the form of a
flow chart.
Whereas a state space flowchart is considered
as an omniscient observer’s view of the structure
of a problem, the problem solver is construed
as going through corresponding sequences of
mental knowledge states. Derived from this
tradition are some widely used heuristic devices,
such as means-ends analysis, as well as partial
answers to some structural questions pertaining
to problem solving, such as what distinguishes
experts from novices.
The fourth line of research, the psychometric/
component-analysis line, aims to identify units,
called factors, of abilities or skills which, once
measured, allow for the prediction of success
on other tasks. Through factor analysis (the
multiple correlations of test scores across test
batteries), psychometricians have identified
variable numbers of intelligence factors, for
instance, ranging from Spearman’s (1923)
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original one, (‘g’), to Guilford’s (1967) 120,
but leveling out in more recent literature (e.g.,
Kahney, 1993) at around five or six. However,
cognitivists have moved on to try to answer not
just “What are the factors?” but also “How do
they work?” The cognitive-component method
of Sternberg (1977) with respect to problem
solving, for instance, is described as consisting of
two steps: (1) An armchair analysis of the kinds
of processes that might be involved, in accord
with information-processing theory, and (2)
an experimental test based on the assumption
that each component mental event takes time
to execute. Adding components to be repeated,
or subtracting components by guiding subjects
through some of the components in what is
called pre-cueing, helps decide whether each
hypothesized component actually takes time,
and how much.
Types of problems
In a paper titled “Current status of research
and theory in human problem solving,” Davis
(1966) wrote that “Research in human problem
solving has a well-earned reputation for being
the most chaotic of all identifiable categories of
human learning.” According to Davis (1966),
“. . . virtually any semi-complex learning task
which does not clearly fall into a familiar area
of learning can safely be called ‘problem solving’.” In fact, even wider definitions of problem
solving have been suggested. For instance, according to Radford and Burton (1974), “. . .
when psychologists investigate problems, they
are concerned with any situation in which the
end result cannot be reached immediately.”
Thus phenomena described under the heading
of problem solving range from Thorndike’s
studies of cats in puzzle boxes through the human problem solving experiments carried out
within the tradition of Gestalt- and cognitive
psychology, to the discoveries of Galileo and
Einstein.
In an attempt to bring some order and
continuity into the field, Davis (1966) classified different types of problems according to
two broad sets of criteria. In problems of type
O (overt), the outcomes of different response
alternatives were not known to the problem
solver, so that overt testing of alternatives was
necessary. Hence, the problem solving behavior
was observable, and it was usually described by
what he called “behavioristic learning concepts.”
A prototypical example would be the behavior
of cats in Thorndike’s puzzle box studies. Once
outcomes of response alternatives are known to
the subject, however, these can be considered covertly, as Type C (covert). Such covert problem
solving tended to be described in mentalistic
terms, often within the Gestalt vocabulary. A
typical example would be the engagement in
‘mental arithmetic’ to solve math problems.
An overarching goal for research in problem
solving may still be as Kahney (1993) wrote, “to
be able to say, ‘Look, there are essentially five
(or ten or fifteen or whatever) types of problem.
Any problem you name can be categorized as
one of these types, or some combination of
them’.” (p.15). The standard practice is to classify problems mainly or solely in terms of their
structure. Thus, problems may be characterized
in terms of their “deep structure.” Different
problems are said to have the same deep structure on the basis of whether their state spaces
(derived from state space analyses) are identical
(e.g., Kahney, 1993). Problems with identical
“deep structures” are called isomorphic, but
the empirical evidence thus far suggests that
often surprisingly little transfer occurs even
between isomorphic problems (e.g., Reed,
Ernst, & Banerji, 1974). That is, of course, an
interesting research issue in its own right, but
it is not promising with respect to developing
structural classes that correspond to functional
classes of problems. In actual practice, the
problems studied experimentally are often
simply classified according to their structural
similarity with some prototypical experiments,
often named after the materials used and/or the
person who first described it. Hence, we have
Duncker’s candle problem, string problems of
the Maier type, Luchin’s water jar problem,
Tower of Hanoi problems, and Missionary and
Cannibals problems. Otherwise, problems are
said to be well defined when the problem space
is easily specified, and ill-defined if it is not, and
problems are called convergent or divergent
What is a problem?
depending upon whether there is only one, or
more possible solutions. Related to questions
concerning the ecological validity of laboratory
experiments on problem solving, a distinction
has also been made between “contrived” problems and real-life problems (Sinnott, 1989).
Whereas real-life problems are considered to
occur in a meaningful context and perceived
as worth solving, contrived problems are typically de-contextualized and abstract (Lebow &
Wagner, 1994). Accordingly, empirical studies
suggest that problem solving may be more adaptive and inventive in real-life than in contrived
laboratory problems.
Problems in defining a ‘problem’
(a) Related terms. Authors have often pointed
out a close relation between ‘problem solving’
and other concepts used as headings for research
areas in psychology, such as ‘learning,’ ‘thinking,’ and ‘creativity.’ For instance, Davis (1966)
wrote that “. . . virtually any semi-complex
learning task which does not clearly fall into
a familiar area of learning can safely be called
‘problem solving’.”
Both Radford and Burton (1974) and Skinner (1968) underscored the close relation between problem solving and thinking. According
to Radford and Burton (1974), J. P. Guilford
added ‘creativity,’ stating that ‘creative thinking’ can be equated essentially with ‘problem
solving.’
In a broader perspective, there is a
sense in which all basic research areas in psychology may be related to ‘problem solving,’
as pointed out by Kahney and by Skinner,
although in different terms (see Table 1).
However, attempting to define a particular
area of research that may require some sort of
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special treatment, different researchers have
postulated definitions of ‘problem’ and ‘problem
solving’ that vary in broadness.
(b) Some suggested definitions. Radford and
Burton’s (1974) definition of ‘problem’ as “. .
. any situation in which the end result cannot
be reached immediately” (p. 39) has already
been mentioned.
According to Kahney (1993), “whenever you
have a goal which is blocked for any reason –
lack of resources, lack of information, and so
on – you have a problem. Whatever you do in
order to achieve your goal is problem solving.”
(p. 15)
Newell and Simon (1972) wrote that: “A
person is confronted with a problem when he
wants something and does not know immediately what series of actions he can perform to
get it” (p. 72).
In Skinner’s (1966) terms, “behavior which
solves a problem is distinguished by the fact that
it changes another part of the solver’s behavior
and is reinforced when it does so (p. 225).
Finally, Davis (1973) suggested that “A
problem is a stimulus situation for which an
organism does not have a ready response” (p.
12)
(c) Problems with the definitions. Even if,
at first sight, the definitions may look clear
enough, “closer analysis easily muddies the
waters” (Davis, 1973, p. 13). Let us consider
some issues related to each of the definitions.
First, if you are seated on a train on your way
from Oslo to Stockholm, for instance, the end
result cannot be reached immediately. According to the definition suggested by Radford
and Burton (1974), then, you would have a
problem whereas, in fact, you have not. Obviously, reaching the “end result” or “goal” must
depend upon some previous action by the
Table 1. Comparing Skinner’s (1966) and Kahney’s (1993) views on the relevance of basic processes
in the analysis of problem solving.
Every advance in understanding perception,
memory, language and problem solving will feed
into endeavours to help people become better
problem solvers.
(Kahney, 1993, p. 143)
Since there is probably no behavioral process which
is not relevant to the solving of some problem, an
exhaustive analysis of techniques would coincide
with an analysis of behavior as a whole. (Skinner,
1966, p. 225)
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Per Holth
problem solver. This is taken care of in Skinner’s
(1966) definition, but including all the cases in
which some behavior “changes another part of
the solver’s behavior and is reinforced when it
does so” also embraces cases which would not
normally be considered as problems. It would
include any regular behavioral chain, such as
making coffee, getting to work, getting started
on your computer, and so on, but standard usage suggests that these would not be considered
as problems unless some sort of ‘obstacle’ arises.
Raaheim (1988) criticized Skinner for “omitting ‘difficulty’ as a defining characteristic of
a problem” to which Skinner (1988) simply
replied that “There are easy problems and there
are hard ones, and they are both problems”
(p. 260). However, this may still require a
consideration of what characterizes a minimal
problem, because problem solving would otherwise actually coincide with the whole field of
operant behavior. Indeed, Reese (1994) listed
‘obstacle’ as a crucial feature of a problem: “If
no obstacle hinders progress toward a goal, attaining the goal is no problem” (p. 200). But
what constitutes an obstacle? There are certainly
problems without physical obstacles. If I ask
you to come up with the answer to 372 (square)
“in your head”, there are no particular physical
obstacles to stop you. You are free to tell the
answer, but it might still be a problem. Contrary
to Newell and Simons’ (1972) definition, you
may even “know immediately” a series of actions
would lead to the answer, but still be unable to
carry through with it. The cognitivist notion
of “lack of information”, as in Kahney’s (1993)
definition, may seem attractive from a colloquial
point of view, but such terms are, as we shall see,
undermined by experimental findings.
Finally, Davis’ (1973) definition is flimsy
for at least two reasons. First, it lacks a reference to what might be called the motivational
aspect of a problem. Luckily, not all stimulus
situations require ready responses. Second, and
less trivially, what, does it mean to “not have a
ready response”? Can it be determined ad hoc
only, or is it predictable, at least in principle,
from other variables? If we want to study how
people solve problems, we do obviously want
to know how to construct a problem.
Donahoe and Palmer (1994) have suggested
that the definition of a problem should include
the requirement that a solution must be possible for the subject. This is in agreement with
Saugstad (1977) who argued that “it does not
make sense to speak of a problem unless the individual is in some way capable of solving what
is regarded as the problem” (p. 115). However,
experiments on problem solving have, in fact,
occasionally used problems for which there is
no solution, although proving that there is no
solution is sometimes then itself the solution.
(e.g., J. R. Hayes, 1978; as referred to in Kahney, 1993).
A more important point brought up by
Saugstad (1977), among others, is that “problem solving cannot be said to take place when
an individual merely reproduces what he has
previously learnt.” (p. 116; also Davis, 1973).
Hence, as Saugstad (1977) pointed out, a “main
difficulty in making theoretical statements on
problem solving originates in the difficulty of
saying what is meant by ‘novelty’” (p. 115). In a
trivial sense, every stimulus and every response
are novel. They are never quite exactly like any
previous instance. The issue, therefore, is one
of characterizing the type or degree of novelty required for some situation to constitute
a problem.
The “novelty” in a problem.
Saugstad (1977) wrote that: “Apparently
if some definite task is mastered by an individual by an activity which may be described
as remembering, we should not regard this as
problem solving.” But certain types of remembering have been convincingly interpreted
precisely as problem solving by Palmer (1991),
Donahoe and Palmer (1994) and Delaney and
Austin (1998). In the following, a few technical terms will be needed: (1) The concept of
the three-term contingency, SD  R  SR,
that is, discriminative stimulus, response, and
a reinforcer, and (2) the concept of an establishing operation (EO). An EO serves two
functions: First, to establish the reinforcing
effect of certain stimulus changes and, next, to
initiate behavior previously followed by those
What is a problem?
stimulus changes.
Palmer (1991) distinguished between two
classes of contingencies for which the term
‘memory’ is usually said to be required. The first
is a matter of direct stimulus control, as when
you are asked to tell the answer to “5 times 7”,
or you answer Rome, promptly, to the question
“What is the name of the capital of Italy?” As
a result of standard education, your answer is
under direct stimulus control of the question
as a verbal discriminative stimulus, it does not
depend on some intermediate behavior on
your part, and it is explained satisfactorily by a
prevailing 3-term contingency in the presence
of relevant motivational variables – EO’s. There
is, of course, a temporal gap between the contingencies that established the behavior and the
current instance, and it is obviously tempting to
fill that gap in order to complete the account.
As Palmer pointed out, “for example, one may
propose that synapses have been modified or
created, resulting in an organism that responds
in a particular way in a particular setting, but
accounts of this sort are not necessary if our
criterion of explanation is to be the prediction
and control of behavior. A physiological explanation supplements the behavioral one; it does
not replace it” (1991, p. 266).
However, it is the second memory class characterized by Palmer which is of primary interests
here. Consider a somewhat more complex math
question, like “67 times 73.” Standard math
education has not prepared us to answer this
question directly, that is, we have not encountered the relevant 3-term contingency in which
the question could be established as an SD for
the correct response. Similarly, a question such
as “What did you have for dinner last Tuesday”
does not usually work directly as an SD for the
correct answer, because the appropriate events
according to the three-term contingency have
not occurred. In sum, then, the novelty which
should enter into the definition of a ‘problem’
occurs when some behavior is scheduled for
reinforcement (that is, an EO is in effect),
but no prevailing three-term contingency has
established the current situation as an SD for an
action that produces the reinforcer.
Additional complexities arise here. How
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do we know that some behavior can not be
ascribed directly to the relevant three-term
contingency? The three-term contingency is
sometimes described as the A–B–C of behavior
analysis, suggesting an antecedent, behavior,
and a consequence, but the formula does not
apply to just any arbitrary subdividing of successive events into Antecedent, Behavior, and
Consequence. Sometimes the formula does
not seem to readily fit the observed facts. Yet,
behavior analysts have often neglected to state
the criteria for when the formula applies and
when it does not.
Identifying instances of SDs and Rs. The SD is
defined as a stimulus in the presence of which
a particular response is typically reinforced and
which, as a result, controls the response in the
sense that in the presence of the stimulus, the
response is more likely to occur than in the
absence of that stimulus. According to the definition, then, a history of direct reinforcement of
the response in the presence of that stimulus is
in some sense required in order for the stimulus
to qualify as an SD. However, as Skinner (1935)
pointed out, “it is very difficult to find a stimulus and response which maintain precisely the
same properties upon two successive occasions”
(p. 347). Thus, Skinner (1935) showed that it
was necessary to consider classes of stimuli and
classes of responses. The class concept requires
some defining property that allows for the
determination of class membership. Hence, as
pointed out by Skinner (1969): “The topography of an operant need not be completely fixed,
but some defining property must be available
to identify instances.” (p. 175).
In accord with Skinner’s previous work,
Catania (1973) argued that the concept of the
operant grew out of a correlation between two
response classes, one descriptive and one functional. The descriptive operant is the class of
responses for which consequences are arranged
and the functional operant is the class generated by that contingency. While any instance
of the descriptive operant class can be identified
when it occurs, we can only infer that particular
instances are also members of the functional
class. A functional class involves a controlling
relation, and controlling relations are never
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Per Holth
directly observable (cf., Sidman, 1979). Several
manipulations, and observations of instances
and non instances may be required for the
identification of controlling relations, and even
when a rat “lever presses for food” in an experimental chamber, any particular instance of lever
pressing might occur “for other reasons.”
A descriptive operant class sometimes involves only response-descriptive features. In
discriminated operants, however, the descriptive
classes also involve stimuli or stimulus properties
in the presence of which responses are followed
by certain consequences. By extending Catania’s
(1973) analysis of the operant class to the case
of the discriminated operant, it is clear that the
class of antecedents called SD similarly requires
a correlation between a descriptive and a functional class of “SDs.” Evidence of SD control,
therefore, requires a demonstration of a correlation between the stimulus class in the presence
of which particular responses are reinforced and
the stimulus class in the presence of which those
particular responses subsequently are more
likely to recur. The existence of a descriptive
discriminated operant class (such as responding
correctly to some specific types of multiplication
tasks) may not be accompanied by a corresponding functional class (i.e., actually responding
correctly to all such multiplication tasks) unless
specific precurrent behavior is established. If so,
the presented task is not an SD for uttering or
writing the correct answer, but for the precurrent behavior which may lead, eventually, to the
correct answer. In ‘Relational Frame Theory,’
Hayes and coworkers have described a number
of different complex relational frames in accord
with which humans sometimes respond, such
as coordination (equivalence is one example),
opposition, distinction, comparison, and hierarchical, temporal, and spatial relations . In
their chapter on thinking and problem solving,
Hayes, Gifford, Townsend, and Barnes-Holmes
(2001) defined “thinking in a verbal sense” as
“a reflective behavioral sequence, often private,
or pragmatic verbal analysis that transforms
the functions of the environment so as to lead
to novel, productive acts” (p. 95), and “verbal
problem solving” as “framing events relationally
under the antecedent and consequential control
of an apparent absence of effective actions” (p.
96). Hence, it seems clear that these proponents
of relational frame theory recognize examples
of problem solving that consist of “behavioral
sequences” that can mediate “novel, productive
acts”. However, according to Hayes, BarnesHolmes, and Roche (2001), complex relational
responding is typically established through
multiple exemplar training, and they see no
need to posit mediating behavioral responses
to account for ‘derived relational responding’
(Hayes, Fox, Gifford, Wilson, Barnes-Holmes,
& Healy, 2001). Yet, the prerequisites for, and
the generality of relational responding without
such mediation or precurrent behavior remain
to be explored. For instance, it is not yet obvious
that the initial trials of a stimulus equivalence
test do not constitute a problem in the sense that
precurrent responses of some sort are typically
necessary in order to respond in accord with
equivalence. Some experimental data suggest
that the initial test trials do constitute a problem in this sense. For one thing, reaction times
typically increase initially during testing, and in
a study that more or less eliminated the possibility of precurrent responding by constraining
reaction times initially during testing to 2s, the
subjects did not respond in accord with equivalence (Holth & Arntzen, 2000). Although a
‘relational frame’ (such as coordination in this
case) may suffice as a descriptive class, it may not
be accompanied by a corresponding functional
class. We do not know ‘the lines of fracture’
along which new instances actually emerge in
the repertoires of organisms in the absence of
functionally relevant intermediate behavioral
events. Presumably, a problem only exists when
they do not.
Basic, unmediated SD R relations can
be blurred by different variables, such as: (a)
the lapse of time between the “SD” and the R,
and (b) the complexity of a relational pattern
between the “SD” and the corresponding R.
In both cases, at some level, the SD ceases to
function as such with respect to that particular
response. When, in spite of this, some apparent functional relation between the S and the
R still remains, the relation must be bridged
or mediated by additional events. We have
What is a problem?
already discussed the case of the time delay in
the example of memory as problem solving.
Basic research with both humans and animals
shows that in the absence of potentially mediating events, the basic functional relation breaks
down if the interval exceeds a few seconds (e.g.,
Blough, 1959; Peterson & Peterson, 1959).
As the complexity increases, the less likely it
seems that the appropriate novel responding
results automatically from a particular identifiable contingency. For instance no number of
multiple exemplars with the multiplication of
three- and four-digit numbers would suffice to
establish the appropriate problem solving skills
with respect to novel exemplars in the absence
of precurrent problem solving skills.
An example: Precurrent responses in
continuous repertoires
As Skinner (1968) has pointed out, precurrent responses need not be explicitly reinforced.
But neither does the terminal response or
“solution”. When precurrent behavior is not
terminated by some explicit reinforcement of
a successful response, we must point to other
variables to account not only for why the precurrent behavior starts, but also for why it stops,
i.e., when we “know we are right.”
In some performances, such as imitation,
instances cannot be identified in terms of
stimulus and response properties alone, but in
terms of correspondences between response dimensions and stimulus dimensions. Such cases,
in which reinforcement is contingent upon a
correspondence between response and stimulus
dimensions, were described by Skinner (1953)
as continuous fields. Wildeman and Holland
(e.g., 1972) reported a couple of experiments
on such contingencies and called the resulting
behavior continuous repertoires. They found that
such repertoires were easily established in young
school children but not in pigeons. However,
little more of the basic research was carried out.
In a simple case of a potentially continuous
repertoire, let us say we reinforce the selection
of RIGHT 1 in the presence of LEFT 1 (see Figure 2, upper panel),
LeftRIGHT 2 in the presence
of LEFT 2, and RIGHT 5 in the presence of
165
LEFT 5. Now, what will happen if we present,
say, LEFT 3 or LEFT 6? A subject could, for
instance, respond in accord with a continuous
repertoire by horizontal eye movements or by
drawing a line from left to right and by stopping
when arriving at a stimulus in the right-hand
column. However, this strategy would have
limited success across different task - as in the
rotated dimension task (Figure 2, lower panel),
or in arbitrarily-related dimensions task, or in,
say, multiplication. If, instead, the subject emits
a differential response, such as pronouncing the
number (possibly as a result of counting) and
rehearses it until the same topography is jointly
controlled by a second stimulus, this would
be applicable to a range of different kinds of
problems (e.g., Lowenkron, 1991, 1996, 1998).
Even in some cases that typically involve specific
types of explicitly trained precurrent responses,
joint control is involved when we are checking
up on ourselves, as in self editing. For instance,
1
1
2
2
3
3
4
4
5
5
6
6
1
2
3
4
5
6
6
5
4
3
2
1
Figure 2. Continuous repertoire training
materials. Upper panel: A vertical stimulus
dimension to the left, and a corresponding
response dimension to the right. Lower panel:
A vertical stimulus dimension to the left, and a
corresponding rotated 90O response dimension.
166
Per Holth
having a couple alternative solutions to “73
multiplied with 77,” we might do “3 times 7
equals 21” and, as a result, decide on the one
that “ends with 1.”
A few words need to be said about the
general reluctance among behavior analysts as
regards what is conveniently called mediating
or precurrent performances. This is clearly not
an absolute question of accepting or rejecting
the inclusion of mediating behavior in one’s
analyses, since the area of problem solving is
defined by the functional relevance of such
performances. Thus, rather than questioning
whether or not mediating performances should
be accepted as part of the picture, we may be
concerned with the levels of complexity at
which some sort of problem solving is necessarily, or most likely, part of a successful repertoire.
An important task, then, is (1) to find out when
basic SDR relations actually break down, (2)
to identify the types of events (such as transpositional repertoires) capable of mediating the
still occasionally apparent Stimulus  Response
relation, and (3) to specify histories that give rise
to those mediating performances.
I will now turn to methodological and theoretical issues related to such mediating events,
and to certain contrasts between cognitive and
behavioral accounts.
Contrasting cognitive and behavioral
accounts
(a) The question of mediation. That different
sorts of covert mediation of behavior occurs in
very much of human behavior is such an obvious fact that no one can seriously question it. If
you just watch someone being asked when they
went to bed last night, or to come up with the
square of 65 with no aids, many very anomalous
results, including very unpredictable response
latencies, will be found in the area of stimulus
control if you exclude from consideration some
mediating events that are even quite obvious to
anyone who has engaged in a little self observation. Moreover, the cognitive literature is replete
with empirical results that make sense only on
assumptions of certain mediating events, such as
in experiments on ‘mental rotation,’ by Shepard
and coworkers (Cooper & Shepard, 1973;
Shepard & Metzler, 1971), in experiments on
visual tracking – even in the pigeon (Neiworth
& Rilling, 1987), and in Kosslyn’s (1975, 1976)
experiments on image tracing tasks.
So, the question is really not at all whether
such functional mediation takes place but, first,
what are the criteria for inferring it and, second,
in what terms should those mediating events
be described? The criteria are different within
cognitivist and behaviorist frameworks and, of
course, so are the terms in which the inferred
mediating events are described.
Before contrasting behavioral and cognitive
interpretations of cognition and problem solving, it is tempting to describe some essential
features of the behavioral view that are often
misrepresented in psychology. For instance, the
behavioral perspective is actually a selectionist
view rather than a stimulus – response view, it is
concerned with events that take place inside the
skin of organisms, it does not depict behavior
according to an input-output formula, and it
does not generally ignore ‘cognitive’ phenomena, but it ignores internal duplicates or representations of those phenomena – particularly as
automatically explanatory entities. Anyone can
find out about that easily by checking primary
behavioral literature sources. Moreover, the continuing misrepresentations of behavioral views
in psychology are amply documented elsewhere
(e.g., Catania, 1991; Schlinger, 2002; Todd &
Morris, 1992).
Several authors have been concerned with
what is sometimes called a Procrustean bed of
behavior analysis. For instance, Davis (1973)
wrote:
By dissecting human thinking and
problem solving into the theoretical language of simple conditioned responses,
the theorist must ignore too much beautifully conscious and deliberate mental
behavior. . .To even attempt a complete
picture of such activities, one must use
a phenomenological language which
accepts the complexity of the conscious,
thinking, and feeling human being (Davis, 1973, pp. 58-59).
What is a problem?
The same problem, however, is faced by
other sciences. I recall an incident where a
physiology teacher said that: “Erection is a
vascular-dilatation phenomenon which can be
understood from the structure of the penis.”
Some of his students disagreed red-bloodedly.
We often want more than the dry and narrow
scientific facts, but it is not obvious that the
typical cognitive vocabulary will come off much
better here.
(b) Cognitivist guidelines for inferring cognitive events. As pointed out by Reese (1994), even
the most ardent cognitivist, such as a Piagetian,
does not freely invent cognitive phenomena,
but actually constrains the inventions on the
basis of quite objective evidence. Such objective
evidence can consist of at least one of the following: (1) Behavior occurring in accord with
a certain pattern or a specific rule, (2) verbal
self reports on cognitive activity, (3) behavioral
discontinuity (as in ‘insight curves’), (4) long
reaction times, (5) basic behavioral processes,
such as ‘reinforcement,’ ‘extinction,’ ‘generalization,’ or ‘discrimination,’ or (6) the survival of
behavior over time.
As Reese (1994) also pointed out, no such
evidence is very compelling by itself, and the
inference that an unobservable cognitive event
occurred is fundamentally a syllogism of the
following form:
Major premise: If a person performs A (a
specified cognitive activity), then the person will
exhibit B (e.g., a specified behavioral pattern).
Minor premise: The person exhibits B.
Conclusion: The person performed A.
Although this involves the logical fallacy
of affirming the consequent, it is the standard
pattern of scientific inference, and it does not
distinguish cognitivist from behaviorist inferences.
(c) Behaviorist guidelines for inferring mediating behavior. The main distinguishing feature of
interpretations in behavior analysis as compared
with traditional cognitive psychology is that the
terms and principles relied on in a behavioral
interpretation are restricted to those obtained
directly from the experimental analysis of behavior. An interpretation that includes private
167
events makes the provisions that the private
event is probable, given current controlling
variables, and that control by these variables
is plausible considering the phylogenic and
ontogenic histories of the organism (Palmer,
1991). Computer simulations of ‘cognitive’
phenomena are increasingly popular within
the behavioral tradition but, then, the same
criteria apply - no new principles may be introduced: the principles informing the program
are restricted to those that are derived from
research on the relevant biobehavioral processes.
As Donahoe and Palmer (1994) recounted:
“[Scientific] interpretation is a consumer, not
a producer of principles” (p. 127). Why, then,
would some researchers impose such restriction
upon their own activities at odds with the psychological community at large and, definitely,
at odds with the prestigious field of modern
cognitive psychology?
Problem solving as behavior: The utility of
the behavioral view
As pointed out by Catania (1992), when
math problems are solved by paper and pencil,
the intermediate products obviously serve as
discriminative stimuli that may occasion the
solution. Furthermore, “presumably, the intermediate products would still enter into the
solution, even if there was no written record of
them. If we did not say them aloud, an observer
might say we had engaged in ‘mental arithmetic’
. . . But the role of the intermediate products is
the same even if they are more public and more
permanent in the first case than in the second.
We still have much to learn about such processes, but we need not treat them as something
other than behavior” (p. 348).
However, the question for many psychologists remains: Why should we treat problem
solving strictly in terms of behavior? ‘Reflection’
and ‘ratiocination,’ for instance, are not intuitively examples of behavior, and Harré (1988),
for example, stated that “such problem solvings
. . . are precisely not behavior” (p. 246). In reply,
here are a few things that I believe will have to
be seriously considered:
1. The case of negative information. The
168
Per Holth
common finding that people learn more from
positive instances than from negative ones, even
when they are equally ‘informative,’ poses a
particular problem for information processing
theories. Wason (1960; see also Wason & Johnson-Laird, 1972), for instance, presented four
cards with a letter on one side and a number
on the other, with the upsides typically showing
one vowel, one consonant, one odd, and one
even number (such as A, D, 7, 4), and told
his subjects to turn only the cards they would
have to in order to find out if the following was
true: “If there is a consonant on one side of
the card, then there is an even number on the
other.” Subjects rarely turned over the card(s)
that could, in fact, have disproved the rule. This
phenomenon was investigated in more detail by
Dinsmoor (1983) in an experiment on observing behavior in pigeons. During a mixed EXT/
VR schedule of reinforcement, a pigeon can be
taught to peck an additional key that produces
stimuli correlated with each component schedule. In colloquial terms, the pigeon pecks one
key to see if there’s any reason to peck the second
key. But does it really? Dinsmoor modified the
procedure so that the first peck only produced
one of the stimuli – either the one correlated
with extinction or the one correlated with variable ratio reinforcement. The results showed
that the pigeon continued pecking on the first
key only when it produced the stimulus that
was correlated with reinforcement, even if the
stimulus correlated with extinction was equally
‘informative.’ Hence, it is the reinforcing rather
than the informative value of stimuli that affects
observing behavior. This suggests that the basic
idea of information processing may need to be
reconsidered.
2. Interpretation of imaging, image tracing,
and mental rotation. According to Kosslyn
(1981), cognitivists generally hold the view
that images are quasi-spatial entities generated
from some store of perceptual experiences in
long-term memory. As pointed out by Eysenck
and Keane (1995), two worries accompany such
symbolic-representation theories: First, they
tend to become quite complicated, even with
respect to simple tasks and, second, “we are left
with no idea of how these symbols are repre-
sented and manipulated at the neural level.” In
contrast, the operant view is fairly simple. First,
as expressed by Skinner: Seeing can occur “in
the absence of the thing seen” (e.g., Skinner,
1974), but “so far as we know, nothing is ever
seen covertly which has not already been seen
overtly at least in fragmentary form.” This view
is fully in accord with Kosslyn’s (1975, 1976)
experiments on image tracing tasks, experiments
on so-called ‘mental rotation’ by Shepard and
coworkers (Cooper & Shepard, 1973; Shepard
& Metzler, 1971), and so on. Second, the
behavioral perspective makes no claim to even
suggest what happens at the neural level, but is
concerned with specifying the behavioral facts
which the neurologist must have in order to
complete the task. Moreover, as Skinner (1988,
p. 337) pointed out, whatever symbolic representations may or may not occur, something
called ‘seeing them’ would still be required.
3. Interpretation of introspective data and verbal protocols. The standard practice in cognitivist
interpretations is to make some resigned reservations as to the accuracy of self reports. Kahney
(1993), for instance, wrote that “the best we can
hope for is information in a subject’s statements
that permits us to infer that particular mental
processes occur in a given task situation” (p. 54).
Although the warnings of Nisbett and Wilson
(1977) are often echoed, no serious efforts are
made to tackle basic issues concerning the limits
to self observation and its nature of origin in
the first place. In addition to the obvious limits
set by the structure of the nervous system, the
behavioral view is that awareness of private
events depends on some sort of correspondence
between private and public events – accessible
to the verbal community (see Skinner, 1957,
p. 131ff). Hence, for instance, visual imaging
must have something in common with regular
seeing, just as auditory imaging must have
common properties with regular hearing, and
so on. This is actually an exciting view, because
it suggests that the covert actions performed
during problem solving, for instance, can be
taught at the overt level.
4. Reinterpretation of ‘cognitive’ findings.
Finally, if empirical findings in the cognitive
literature on problem solving are reinterpreted
What is a problem?
in terms of behavior, there is a substantial body
of basic research which may be immediately relevant. For instance, there are impressive bodies
of research on complex stimulus control, multiple exemplar training, and on rule-governed
and contingency-shaped behavior, which seem
directly relevant, respectively, to the questions
of the characteristics of ‘expert behavior,’ of
variables that influence transfer of problem
solving skills across tasks, variables involved
in the heuristics or in the contingency shaping of ‘avoiding loops.’ According to Kahney
(1993):
The idea, simply put, is to try to figure out how to make ‘C’ students into
‘A’ students. That’s a worthy goal. But
at the moment the goal has not been
achieved. (p. 148)
In conclusion, although a behavioral view
of problem solving is clearly less intuitively
attractive than cognitivist formulations, the
behavioral view is more parsimonious, and it
has an enormous advantage in its potential with
respect to practical applications. I suppose that
if Kahney’s goal is ever to be reached, cognitive
psychology cannot afford to neglect the basic
knowledge of behavioral principles that behavior analysis has to offer.
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