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Creativity and problem-solving: Implications for classroom assessment

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Abstract

Four processes are at the core of “creative” problem-solving: finding problems, generating novelty, defining solutions, and recognizing solutions. The statement of the problem itself also influences the likelihood of creative solutions: In particular, “overdefined” problems inhibit creativity. It is also possible to focus on the product, distinguishing for instance between “routine,” “original,” “elegant,” and “innovative” products. This involves specifying aspects of products that are markers of creativity, such as diagnosis, redefinition, surprisingness, harmoniousness, and germinality. On the basis of these considerations, guidelines can be worked out for setting assignments in classroom teaching at all levels, and indicators identified that make it possible for teachers to assess in a consistent, understandable way the amount and kind of creativity in students’ work, as well as to indicate areas of strength and weakness.
This is the text of the 24th Vernon-Wall lecture to be presented at the annual meeting of the
Education Section of the British Psychological Society, Glasgow, November 6, 2004.
It was published by the BPS as
Cropley, A. J. (2005). Problem-solving and creativity: Implications for classroom assessment.
Leicester, UK: British Psychological Society.
Creativity and problem solving: Implications for classroom asssessment
Arthur Cropley
University of Hamburg
Arthur Cropley
Unit 3, 120 South Terrace
Adelaide, SA 5000
Australia
Email: ajcropley@gmail.com
Summary
Discussions of problem-solving not infrequently neglect four processes that are at the core of
“creative” problem-solving: finding problems, generating novelty, defining solutions, and
recognizing solutions. Furthermore, the problem itself influences the likelihood of creative
solutions: In particular, “overdefined” problems inhibit creativity. It is also possible to focus on
the product, distinguishing for instance between “routine,” “original,” “elegant,” and
“innovative” solutions. This involves specifying aspects of solutions that are favourable for
creativity, such as diagnosis, redefinition, surprisingness, harmoniousness, and germinality. On
the basis of these considerations, guidelines can be worked out for setting assignments in
classroom teaching at all levels, and indicators identified that make it possible for teachers to
assess in a consistent, understandable way the amount of creativity in students’ work, as well as
to indicate areas of strength and weakness.
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Creativity and problem solving: Implications for classroom assessment
Arthur Cropley
University of Hamburg
Guilford, the initiator of the modern era (e.g., 1950), described creativity as problem-solving,
and concluded (1959) that the creative process has four stages:
recognition that a problem exists;
production of a variety of relevant ideas;
evaluation of the various possibilities produced;
drawing of appropriate conclusions that lead to the solution of the problem.
Over the years, other writers too such as Newell, Shaw and Simon (1962) or Isaksen, Dorval
and Treffinger (1994) have linked creativity with problem-solving. In this paper, I will focus on
four aspects of Guilford’s outline listed above:
(a) defining the problem;
(b) defining the solution;
(c) producing solutions;
(d) recognizing a solution when one occurs.
Striking in Guilford’s approach is that the idea of “creativity” does not seem at first
glance to add much to understanding the steps in problem-solving given in his list. Indeed,
Land questioned the need for any such concept as “creativity” at all. He argued that he had
invented the polaroid camera by possessing detailed knowledge of relevant aspects of
photochemistry, applying logical thinking to these in order to proceed to a solution (a camera
that developed and printed its own pictures instantly), and possessing the energy to work
untiringly on solving the problem. At almost the beginning of the moden era, the cognitive
psychologist Campbell (1960) questioned whether there was any such thing as creativity and
by 1970, when a body of evidence based on differing samples and tests had accumulated,
Wallach (1970) argued that there was no need for a factor “creativity” to explain divergent
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thinking. By the 1990s, Milgram (1990) even asked whether creativity might not be a concept
whose time had come and gone. What then is the link between creativity and problem-solving,
apart from a vague notion that creativity helps, or the view that problem-solving is inherently
creative and no further discussion is therefore needed?.
Creative problem solving
In answering my own question I will distinguish between “creative” and “ordinary” problem-
solving. I will focus on the four elements I introduced above: discovering the problem, and
defining, generating, and recognizing the solution.The crucial thing about creative problem-
solving is that, in contrast to “ordinary” problem-solving, the problem is not specified exactly,
the nature of the solution is largely open, the pathway to the solution is not specified, and the
criteria for recognizing a solution are open.
1. Defining the problem—problem finding
At least until the dawning of the modern creativity era, the idea of problem-solving was
encapsulated in intelligence testing: The person being tested is presented with a clearly defined
problem, about which there is no ambiguity and for which there is a known answer (i.e., the
solution to the problem is already known). If the person taking the test does not already know
the answer, it can be worked out by applying known techniques or logic (i.e., the pathway to
the solution is known). The examiner merely has to check whether or not the person has given
the one and one only correct answer (which is to be found in the test manual). Becoming good
at this was, by and large, what was regarded as the purpose of teaching and learning, and of
course, was emphasized in setting and marking assignments.
However, from the beginning of modern interest in creativity some writers argued that
the special thing about creative problem-solving is that it involves not solving well-defined
problems that have already been constructed by somebody else, but clarifying ill-defined
problems in a process of finding or defining your own problems (e.g., Torrance, 1965).
Creativity researchers spoke of “problem awareness,” “problem recognition” and the process of
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“problem finding” or “problem definition”. As Dillon (1982) pointed out, problem finding is
not as straightforward as might seem: It is possible to distinguish between recognizing
problems that are already evident in the present organization of available information and are
obvious to any qualified observer, discovering hidden problems, and inventing problems. In
modern times, it has been recognized that invented problems have most to do with creativity
(Jay and Perkins, 1997), and Mumford and co-workers (1996) identified “problem
construction” as one of the main cognitive processes involved in creative problem-solving.
A simple example of the first kind of problem from our field (the obvious problem that
is the same for everybody and inevitably leads to the one and one only correct answer—or is
unsolvable for people without the necessary knowledge and/or reasoning skills) is to be seen in
standardized achievement tests. The instructions to these tests often contain elaborate details
that have the purpose of excluding any uncertainty about what is required. In my terms, the
tester’s intention is to exclude the possibility of any test candidate discovering or inventing a
problem.There is a payoff to defining the problem in a highly circumscribed manner and
precluding problem-finding, i.e., in concentrating on “ordinary” problem-solving—for the
problem solver it simplifies the search for a solution and for the assessor it standardizes the
kind of solution likely to be reached. In education, such problems are greatly admired by
testers and examiners, since all relatively knowledgable persons being tested quickly recognize
what is required by the problem, and confine themselves to the limited range of possible
solutions implied by the problem’s definition—indeed, it is quite possible, or even usual, that
there may only be a single answer. Even those who do not possess sufficient knowledge to
solve the problem usually play by the rules.
This greatly simplifies scoring and grading, and eliminates arguments about the
accuracy of assessment. However, such problems discourage creativity. From the point of view
of creative problem-solving, they are overdefined. None the less, it is extremely hard for
teachers to break away from the habit of overdefining the problem. The majority of students
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like such problems (despite what they may say to the contrary), because in effect, the solution
is also overdefined,.since there is always an answer. This is known to the teacher who has
already given guidance on how to find it, or can give such guidance on request, and the
learners’ task is clearcut (learn the “facts” by heart), even if many of them do not relish the idea
of doing the necessary work. For students who are extrinsically motivated (they seek simply to
pass the exam, regardless of contents) or achievement motivated (they wish to get the best
possible grade), such problems are ideal, even if they discourage the deep learning of
intrinsically motivated students, who wish to understand the structure of the discipline.
Tardiff and Sternberg (1988) also stressed the importance in creativity of sensitivity to
problems, but went further and emphasized an additional element of problem-finding: finding
good problems. Getzels and Csikszentmihalyi (1976) concluded that this is as much the case in
artistic as in scientific creativity. A striking example of both these aspects of creative problem-
solving is Einstein’s recognition that existing theories of electrodynamics were inadequate in
dealing with moving bodies. He (a) “invented” a problem where others saw none, and (b)
identified the “good” aspect of this problem. This quickly led to the special theory of relativity,
revealed the need for a general theory of relativity, and ultimately resulted in lasting fame. In
terms of the hierarchy I will introduce below, “good” problems are those that not only provoke
a helpful answer to a specific situation, but also yield or even require what I call “elegant” and
“generalizable” solutions, i.e., they lead on to new things that go beyond the present situation.
Solutions to the “best” problems lead to Nobel prizes and similar awards.
However, problem-finding is not as straightforward as might be thought. Sosa and Gero
(2003) recently argued that many creative products are developed “to satisfy the needs of …
social groups”. As I see it, the “needs” may be concrete and down-to-earth, such as cheaper
power, or a cure for a particular disease, but they may also be more general such as better
educational methods or more beautiful ways of combining colours on canvas, or more abstract
such as improved ways of expressing feelings through music. Generally, the “social groups”
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whose needs must be satisfied are (a) people who are knowledgable in a domain—specialists or
experts, or (b) users of the domain—people who are in some way affected by it. The people
who are motivated to solve the problem are most commonly active in the domain as
practitioners, experts, researchers, and the like. Those who have no contact with an area,
seldom (although perhaps not never) experience the need for solutions to problems or produce
solutions in that domain.
Where there is no awareness that a problem exists, there will be no problem-finding, no
drive to produce solutions, and no creative problem-solving. A simple example is the area of
design: A common artefact may be awkward to use and ineffective, perhaps even dangerous.
However, it may be so familiar to so many people that everybody has become accustomed to
its disadvantages, and may be able to use it very effectively, despite the disadvantages and
inconvenience. In this case there is no pressure to introduce effective novelty and, in a sense,
no problem, no matter how bad the design may be. An example is the automobile. The internal
combustion engine is inefficient and wastes energy, cars are very dangerous, and they pollute
the environment. However, novelty in automobile design is limited to tinkering with details,
and no genuinely radical originality has been seen since the introduction of the horseless
carriage about 120 years ago. Problem awareness is limited to the issue of how to polish what
already exists. Solutions that emerge in this area are not what I would call “good” solutions,
since they are in essence dead ends.
A further, simple, everyday example can be taken from my experiences in Canada in
the 1960s and 1970s. I was astonished to find that people baked using plain flour, to which
baking soda had to be added. They did not see the need to add baking powder as a disadvantage
or inconvenience, and were amazed when I told them about the self-raising flour I was
accustomed to using in Australia. Lack of knowledge of any alternative and sheer familiarity
with what already existed led to a situation where there was no problem awareness and no
pressure to improve things. (Interestingly, self-raising flour was introduced briefly in the
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1970s, but did not sell well, and was removed from sale. People were so accustomed to the
inconvenient version that they resisted changing to the more convenient. No problem
awareness meant no solution pressure, and no solution pressure meant no generation of
effective novelty.)
As the plain flour example shows, there may be a tension between the society’s
problem awareness and that of individuals. The problem may be apparent only to people who
are well informed in an area (sometimes even only to one person, as in the Einstein example
already given), because it arises from a discrepancy between what already exists and what
these people think things should be like, not from a publicly perceived problem—only
knowledgable insiders are dissatisfied and experience the urge to produce a creative solution
(when Einstein was dissatisfied with existing theories of thermodynamics, others were
experiencing no such dissatisfaction, and thus perceived no problem). In this case, lack of
problem awareness inhibits creativity. This suggests that a culture of problem awareness would
foster creativity. This could be in school, but also in higher education or in organizations such
as companies or factories.
2. “Creative” solutions
Even creative solutions to problems must be “appropriate,” “correct,” “useful,” or
“valuable”, as Amabile and Tighe (1993, p. 9) put it. Poincaré made the same point more than
100 years earlier, and Bruner (1962) referred to the necessity of relevance and effectiveness.
But appropriateness and correctness are required in conventional solutions too: You do not get
many points on an IQ test or on a conventional school achievement test for irrelevant, incorrect
answers, nor in the real world either. At the practical level, this is particularly obvious in
domains such as engineering, where usefulness and similar properties are easy to define and
are uncompromisingly expected (with a few exceptions, as will be discussed below). How,
then, does creativity go beyond correctness, appropriateness, or usefulness to expand the idea
of a solution?
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It seems more or less self-evident that the first characteristic of a creative solution to a
problem is novelty—creativity always leads to something new, as Morgan (1953) pointed out at
the beginning of the modern creativity era. However, novelty, unexpectedness, surprisingness,
and the like are not required for “ordinary” problem-solving, and indeed, are likely to be
rejected or punished. Creativity thus expands the idea of “solution” by adding the criterion of
novelty. The order of the criteria “relevance and effectiveness” and “novelty” is not arbitary:
Although novelty seems intuitively to take precedence over effectiveness in any discussion of
creativity, my view is that in the case of problem-solving there can be no discussion of
creativity without first dealing with the issue of relevance and effectiveness. To take a simple
example, a bridge must first solve the problem of getting traffic across a river. If it does not do
what the engineers were hired to build it for, it does not solve the problem, no matter how
beautiful or how surprising it is. In this sense, creative problem-solving may well differ from
other forms of creativity such as aesthetic creativity, where novelty may well have precedence.1
There may even be a conflict between the two ways of looking at a solution to a
problem. A famous example in my homeland is the Sydney Opera House. After several decades
it is still hailed as a piece of extraordinary architectural creativity, because of its high level of
novelty: For instance, it introduced novel design principles and new building techniques that
are still being used today. Its only fault is that it is a less than optimal solution to the problem
of large-scale staging of operas, the purpose for which it was originally commissioned! Critics
who dwell on this (i.e., who place relevance and effectiveness before novelty) and insist that
the opera house should be capable of doing what it was built for (provide a venue for grand
opera) are dismissed as soulless curmudgeons by those who give preference to the criterion of
novelty.
1 Although the idea of problem-solving is most obvious in, let us say, engineering, where the problem may be concrete,
specific, easily evaluated, and so on, in principle, I see the task of an artist, a sculptor, a musician, a poet, a novelist,
or similar workers in aesthetic domains as also amenable to discussion in terms of problem-solving: For instance, how
can a feeling or an emotion be expressed in an effectively novel way?
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In aesthetic creativity the relationship in solutions between relevance and effectiveness,
on the one hand, and novelty, on the other, may be more or less open, or even favour novelty at
the expense of effectiveness. However, in the case of practical problem-solving, effectiveness
is essential: Otherwise the “official” problem has not been solved, although some other
problem may have been solved on the side (as in the case of the Sydney Opera House). Jackson
and Messick (1965) made a helpful distinction in this context: They distinguished between the
“internal” relevance and effectiveness of a product and its “external” relevance and
effectiveness. The novelty and beauty of the Opera House are aspects of its internal creativity,
the question of whether it actually works as an opera house is related to its external creativity.
In discussing the creativity of products various researchers have gone beyond novelty.
Taylor (1975), for instance focused on generation, reformulation, originality, relevancy,
hedonics, complexity and condensation. Besemer and O’Quin (1999) added resolution (the
product is valuable, logical, useful and understandable) and elaboration and synthesis (the
product is organic, elegant, complex and well crafted). I thus propose two additional criteria of
creative problem solutions, in addition to effectiveness and novelty:
Elegance: Einstein argued that it is not difficult to find novel solutions to problems:
The difficult part is finding solutions that are elegant (see Miller, 1992). Grudin
(1990) reinforced this idea when he referred to “the grace of great things [my italics]”.
What Grudin was referring to is what might be called the “internal” elegance (see the
reference above to Jackson and Messick, 1965) of the product (it is well worked out,
logical and complete). Creative solutions cause surprise in beholders (Bruner, 1962)
and possibly a more or less instantaneous “shock of recognition”, even provoking a
“Why didn’t I think of that?” or an “Of course; it’s obvious!”reaction. Indeed, an
elegant solution may be so obviously just right that—after the fact—viewers may
underrate its creativity or denigrate it as banal. This is possibly the highest praise
that can be conferred on a solution to a problem! Rechtin and Maier (1997) quoted
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Wernher von Braun’s aphorism: “The eye is a fine architect. Believe it!” This
principle captures what is intuitively understood by many problem-solvers—good
solutions often look like good solutions, or to put it slightly differently, they possess
not only “internal” (see above), but also “external” elegance.
Generalizability: In 1605 Francis Bacon developed a binary cipher using only
five bit combinations of the letters a and b, thus showing that complex messages
could be represented without loss of information, using only two values. Gottfried
Leibnitz built on this to invent the binary number system late in the same century.
The two could scarcely have conceived of modern computers, but they laid the
foundation for modern digital computing. This is a dramatic example of
generalizability.
The special quality of generalizable solutions is that they not only solve a particular
problem, but also
• solve problems in other apparently unrelated situations (i.e., they are transferable to
other situations, whether or not the problem solver intended this at the time);
• introduce a new way of conceptualizing a whole area, or open up new approaches to
existing problems, possibly in many areas (i.e., they are germinal);
demonstrate the existence of previously unnoticed problems and suggest the need for
new work (i.e. they are seminal);
• lay a foundation for later solutions to new problems, although the original problem-
solver may have had no idea of the future problems (i.e., they are foundational).
One way of classifying problem solutions is to use the four dimensions just listed to arrange
them in a hierarchy ranging from the “routine” solution (characterized by effectiveness
alone) at one pole to the “innovative” solution (characterized by effectiveness, novelty,
elegance and generalizability) at the other, with “original” and “elegant” solutions between
these poles. This relationship is shown in Table 1 (see next page), where a plus sign means
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that a property is necessary for this kind of solution, a minus sign that it is not. The
schematic in Table 1 can also be used to demonstrate the position of “aesthetic” creativity,
where the only necessary property of solutions seems to be novelty. Additional properties
may or may not be present. The table shows that each solution higher in the hierarchy
incorporates all the properties of those at lower levels, but adds something to them.
According to our criteria, routine solutions to products are not creative, because the second
necessary criterion (novelty) is missing. This does not mean, however, that such solutions
are useless.
The hierarchical organization of products shown in Table 1 introduces an important
principle into the discussion of problem solving: Creativity is not an all-or-nothing quality
of a solution, but there are levels and kinds of creativity. It is not something that solutions
either have or do not have. Different solutions can have creativity to greater or lesser
degrees, or they can display different kinds of it. I have already suggested different labels
for different kinds of creative solution (“original,” “elegant,” “innovative”), while the
hierarchical organization of these kinds of creativity means that there are also levels of
creativity (innovative solutions are more creative than elegant ones, while elegant solutions
are more creative than original ones).
Table 1. The hierarchical organization of products
Criterion
Kind of Solution
Routine Original
Elegant Innovative Aesthetic
Effectiveness ++++ ?
Novelty - + + + +
Elegance - - + + ?
Generalizability - - - + ?
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A simple case study gives an idea of the usefulness of this approach for assessing the
creativity of solutions to problems. University students complained about experiencing
discomfort in the classroom because the desks—even the “large” ones—were too small for
some of them.2 On the other hand, simply increasing the desks’ size was not the answer, since
very large desks would be too large for smaller students. A special team was formed to solve
the problem. The team’s members concluded that there were three issues:
1. The desks needed to fit both small and large people;
2. They needed to be able to prevent pencils rolling off onto the floor;
3. A cup holder was needed on the desks.
After a brainstorming session the team designed an expanding desk that could be adjusted
according to the size of the user. The top had grooves for pencils and a hole bored in it as a cup
holder. When the desk was built it was found to work so well that the team began the process of
obtaining a patent.
In discussing this case, Vielot (2001) posed a series of important questions about the
solution to the desk problem. Modified for our purposes, these are:
1. Where did the creativity lie?
2. Just because the desk proved to be useful, can it be said that the ideas involved in
designing it were creative?
3. Are other desks that may well have involved a good idea nonetheless not creative
because they did not get built?
Vielot himself made a number of interesting points. If the desk itself is the creativity, what
is it about it that is creative? The individual parts are not new: Sliding mechanisms are not
new, nor are grooves for pencils or holes for holding cups. The whole desk is not new either,
nor is its function, since we are perfectly familiar with sitting at desks. Unusual is that the
2 This case was posted on the website www.ijee.dit.ie/forum/forum1.html by Jacques Vielot. The site is dedicated
to the “Forum on creativity in engineering education” of the International Journal of Engineering Education.
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desk is adjustable, but the basic idea of adjustability is not new. How then was creativity
involved in the design and construction of the adjustable desk?
The desk was relevant and effective—it did what its designers wanted it to do. However,
effectiveness alone produces only routine solutions. Simply being built and proving useful did
not make the desk creative. Fortunately, it displayed an additional property—it was adjustable.
Adjustable desks are not commonplace. Thus, in addition to effectiveness the design displayed
novelty. The minimum requirements were met, and it is possible to say that the desk was an
“original” solution in the sense of Table 1. An adjustable desk may even possess a certain degree
of elegance—it would probably be “neater” than a device with, let us say, several different seats
and footrests, in some kind of staircase or stepladder arrangement: The desk earns a ? in this
category. The presence of generalizability is highly questionable: Does the design help us to see
desks in a new light? What new lines of attack are offered by the adjustable desk (germinality)?
What new problems or issues did it reveal (seminality)? Does it suggest spin-offs in other areas
(was it foundational)? In my view the solution’s creativity is limited to originality—a low level
of creativity. In analyzing and evaluating their own solution to the desk problem, the students
would be advised to attempt to increase its elegance and generalizability. Thus, it can be seen
that the concept of creativity makes it possible to define the solution to a problem in a novel way,
permitting a differentation of the idea of “solution”.
3. The creative problem-solving process
In my own early work I concentrated on the second element in the list in the first
section—the process of constructing solutions. Guilford had already offered the concept
needed to distinguish between “creative” and “ordinary” problem-solving by distingishing
between “divergent” and “convergent” thinking. The convention was quickly established that
convergent thinking = intelligence, divergent thinking = creativity. These two came to be
treated as competitors or even as mutually exclusive (e.g., Getzels and Jackson, 1962,
Torrance, 1965). In rejecting the incompatibility approach I regarded creativity as a qualitative
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phenomenon that involves the way or style in which people go about working towards a
solution, not whether or not they have more or less of something (Cropley, 1968), thus taking
an approach similar to that of Hudson (1968). If problem solvers concentrate on recalling what
they already know and logically combining elements of information (i.e., if they think
convergently), they will often come up with ideas that may be highly effective in solving the
problem (and thus very intelligent). If they concentrate on speculating, making unexpected
links, finding surprising answers, etc (i.e., if they think divergently), they may open new
perspectives, develop new techniques, arrive at unorthodox conclusions, etc, and thus be
“creative”. This may not lead to high scores on IQ tests, but despite this may solve the problem
and thus be, in a sense, very intelligent. This view means that both convergence and divergence
can lead to useful solutions to problems, and both are intelligent. What then characterizes
“creative” problem solving processes?
One of the enduring conceptualizations of creative thinking is that it involves a process
of association and selection. A striking description of the thinking that leads to production of
effective novelty is found in the writings of Poincaré. He regarded production of novelty as a
process of selection in which knowledge elements from widely separated domains are
selectively combined. He possessed vast knowledge of mathematics, and could in principle
have produced an endless string of combinations, but somehow homed in on the effective ones
(see below) . This idea was well established before the beginning of the modern era: Rossman’s
(1931) study of inventors for instance, concluded that they “manipulate the symbols of … past
experience (p. 82)” [my italics]. He also showed that they combine “known movements (p.
77)” adding or subtracting known elements to a mix of ideas, until a happy combination is
found. In an early modern study of inventors, Olken (1964) argued strongly that creativity is a
trial-and-error process, in which possible solutions are imagined as mental images and
compared with the desired end-result, being discarded when this comparison shows that the
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solution envisaged in the mental image does not match the desired solution or, of course,
retained when it does match.
However, the mental images are not produced, combined and tested randomly. According
to Miller (1992), in creative thinking nearly all of the theoretically possible combinations are
“filtered out”, leaving only the ones that are “harmonious” and “beautiful”. In Miller’s view, it is
“sensible intuition” that makes it possible to eliminate from the beginning the large number of
dead-end combinations. Olken also believed that promising lines of attack are selected from
among the large number of possibilities on the basis of “hunches”, or what are now called
“heuristics”.
Although some contemporary authors have gone so far as to argue that creativity results
from random processes of association (e.g., Simonton’s, 1988, “chance configuration” model,
according to which elements of knowledge are blindly combined until a lucky hit occurs), I take
the view that information processing leading to effective novelty cannot proceed by what Simon
(1989) called “brute force”, in a process of perceiving, blindly associating, and occasionally
recognizing, perhaps by good fortune, that a new combination happens to offer the required
solution. This would lead to a “combinatorial explosion” (Simon, 1989) involving huge numbers
of “empty” trials (Altshuller, 1984), and leading to “cognitive strain” (Bruner, 1962). Thus,
combinatorial processes must be guided in some systematic way if they are to produce effective
novelty. This is presumably done by “editing out” the high proportion of alternatives that lead
nowhere.
Some writers emphasize the role of “intuition” in directing attention to promising lines of
attack (for a relevant discussion, see Policastro, 1995). The basic idea is that, early in the process
of production of variability, people sometimes see the novelty for which they are striving in the
form of a rough, “intuitive” outline of the solution. Their task is then that of defining and refining
this into effective novelty. The outline may be acquired via implicit learning, i.e., learning that
occurs without the learner being aware of it, for instance in the course of everyday life. To take a
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simple example, during the course of riding to work every day by bus and sitting just behind the
driver, a person might learn a great deal about the work of a busdriver, without ever having
thought of the ride to work as a learning experience. Such learning leads to tacit knowledge that
people do not know they possess, and this can prestructure thinking about an issue. For instance,
engineers exposed to the situation above might already have acquired information about
redesigning buses and have stored this in the form of tacit knowledge. Upon being hired to
design a new bus, they would already possess a preliminary framework that could suggest where
the required answer might be found or approximately what the eventual solution might look like.
When this leads to production of effective novelty it is experienced as intuition. When it
narrowly focuses information processing and leads to production of singularity it is experienced
as a set or corset that blocks ideas (see below).
Olken (1964) was one of the earlier writers to focus attention of the problem of avoiding
dead ends. In an examination of the development of innovative ideas in engineering such as the
triode vacuum tube, the Astron machine (a reactor for producing power by controlled nuclear
fusion), or a device for the simultaneous production of multiple photocopies, he identified the
“wrong approach barrier”. He pointed out how starting along a wrong approach is very
dangerous, because the difficulty of getting out of the cul de sac increases as the problem solver
invests more and more resources (money, time, ego-commitment, prestige, etc) in the dead end.
In effect, a barrier builds up, that blocks finding a productive approach. Thus, the first step in
generating effective novelty is to produce variability, to be sure, but to confine this to promising
alternatives, and avoid the barrier. Olken identified three ways of breaking the barrier: a lucky
break, “letting the work lie fallow” (incubating), or continuing along the fruitless line of attack,
but gradually “veering around” to find a new direction.
Although some writers (e.g., Hausman, 1984) argued that “true” creativity is always so
novel that it is unprecedented, and thus has no connection to anything that went before, others
such as Bailin (1988) have concluded that creative products are always conceived by both the
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creative person and external observers in terms of existing knowledge, and Weisberg (2003)
showed that even an extraordinarily radical product such as Picasso’s Les demoiselles
d’Avignon arose out of what Picasso had experienced up until the time he painted it. Sternberg
(1999) turned attention to the way the known is used to introduce effective novelty in problem-
solving with the help of the idea of “propelling a field”. He suggested a number of ways in
which this can occur: conceptual replication (the known is transferred to a news setting),
redefinition (the known is seen in a new way), forward incrementation (the known is extended
in an existing direction), advance forward incrementation (the known is extended in an existing
direction but goes beyond what is currently tolerable), redirection (the known is extended in a
new direction), reconstruction and redirection (new life is breathed into an approach previously
abandoned), and reinitiation (thinking begins at a radically different point from the current one
and takes off in a new direction).
Savransky (2000) turned specifically to “inventive problems”, which always involve “a
conflict between new requirements and an old system”, i.e., they necessitate a change in what
already exists. He discerned six ways in which this can occur. Slightly modified for present
purposes, creative problem-solving according to Savransky involves one or more of
improvement (improvement or perfection of both quality and quantity of what already exists),
diagnostics (search for and elimination of shortcomings in what already exists), trimming
(reduction of costs associated with existing solutions), analogy (new use of known processes
and systems), synthesis (generation of new mixtures of existing elements), and genesis
(generation of fundamentally new solutions). As was the case with Sternberg’s list, only the last
of these involves something fundamentally new.
What this means is that even creative problem-solving does not necessarily involve
calling into existence something that never existed before, although in saying this I do not mean
to deny the possibility of fundamentally new solutions. The point is that effective, elegant,
generalizable novelty is mainly produced through re-application of the already known. This
18
means that in order to solve problems a great deal of knowledge about the domain in question is
required. This idea has been put in modern terms by Boden (1994), using the language of
artifical intelligence. What I call “knowledge”, she calls “representation of structural features” of
a domain. The more structural features of a domain are represented in a person’s mind (the more
the person knows), the more creative the person can be. Boden gave the example of Mozart and
what it was that made him capable of musical creativity: According to her, the the crucial
property of Mozart was his possession of rich, deep, and detailed “cognitive maps of musical
space”. Mozart’s creativity lay in his exploitation of existing musical knowledge, and it was the
vastness of his knowledge (plus the quality of the use he made of it) that made him a great
composer. In general (e.g., Elshout, 1990, Walberg and Stariha, 1992), an “apprenticeship” of 10-
15 years seems to be necessary for acquiring the fund of knowledge and skills necessary for
creativity, even in the case of people like Mozart, who produced creative music in his teens, it is
true, but who started his musical education by playing at the age of four!
However, despite its importance, research has shown that high expertise does not
always facilitate novelty production. A very high level of familiarity with a field and with
existing solution strategies can preorganize thinking so effectively that it leads only to
production of tried and trusted, “correct” answers. Working successfully in an area over a long
period of time (i.e., becoming an expert) can provide a knowledge base that can be manipulated
to yield effective novelty, but it can also produce a kind of tunnel vision that narrows thinking
and restricts it to the conventional. Indeed, experts may have a vested interest in maintaining
the status quo. Radical new solutions to old and intractable problems may threaten to render
irrelevant the lifetime’s work of experts who have laboured long on a particular problem.
Knowledge thus seems to be a two edged sword when it comes to creative problem-
solving. In fact, the advantage that experts enjoy may lie less in the area of finding solutions
and more in in the area of problem finding and definition, or problem recognition and
reformulation. Experts seem to spend more time than beginners on (re)formulating problems
19
(Rostan, 1994), and less on searching for solution strategies. Experts reformulate problems on
the basis of recognition of their definitive patterns. Once they have done this, the solution is
often at hand, since it is obvious once you know what the problem is. Thus, in a sense, experts
already know the solution, and the task is to find the problem. This is done by means of
identifying its deep structure (its systematic and metasystematic properties). Beginners, on the
other hand, believe that they already know the problem, which they define on the basis of its
surface structure (its immediate, concrete, unique properties), and spend their time searching
for an unknown solution. Martinson (1995) suggested a solution to the problem of defining the
relationship between knowledge and problem solving by arguing that the relationship is U-
shaped: Both very high (great experise) and very low (ignorance) levels of pre-existing
knowledge inhibit creative problem-solving.
In an empirical study of almost 1000 employees and managers, van der Heijden (2000)
showed that expertise has five dimensions, including special knowledge and specific skills as
would be expected, as well as two further important dimensions: “meta-cognitive knowledge”
and “growth and flexibility”. The former involves self-insights the latter the combining of
fields. Fields that are combined may be adjacent, with the result that combining them produces
only orthodox solutions or, more interesting for present purposes, they may be radically
different or remote, in which case combining them leads to novelt solutions. In other words,
deep knowledge is only favourable for creativity when it is accompanied by insight, flexibility
and similar properties. Resnick (1987) made a similar point in a more general way in an
analysis of metacognitive processes and creativity. According to her, thinking favourable for
production of effective novelty would be nonalgorithmic (no fixed pathway is specified in
advance) and complex (oriented towards achieving multiple solutions, and guided by multiple
criteria). Exploration would have to be self-regulatory, tolerant of uncertainty, and based on
nuanced judgment (i.e., subjective interpretation by the thinker would play an important role).
20
Despite their expertise, highly creative experts often show a freshness and openness that
is more typical of beginners. This has been referred to by Root-Bernstein, Bernstein and Garnier
(1993) as the “novice effect”. I once attended a lecture by the then 70 year old Hans Selye,
discoverer among other things of the stress syndrome, who apologized for being in plaster from
his toes to his hip—a few days before he had fallen out of a tree after he saw something that
seemed odd and interesting in its branches and climbed it in order to have a better look! A less
creative senior researcher would have been too busy with current research problems to bother
with something in a tree or would have sent a junior staff member to investigate!
4. Defining the solution
The traditional model of problem-solving sketched out above presupposes that the solution
is known and can be recognized by a knowledgeable observer—in my experience, this is
precisely the situation that teachers and, above all, students like best. However, where problems
are loosely defined and the solution pathway involves branching out, making unexpected
connections, trying unlikely possibilities, taking a risk, being tolerant of uncertainty, using
nuanced judgment, and the like, it may be difficult to say just what constitutes a solution or to
recognize a solution when one is at hand. Indeed, Ghiselin (1955) argued that recognizing
solutions is the key to creativity.
A striking example of failure to recognize a solution involves the German-Latvian
microbiologist and pathologist, Eugen Semmer, who worked in the Institute of Veterinary
Medicine in Riga. In 1870 Semmer published a paper in the widely-read German-language
scientific journal, Virchows Archiv3, reporting on the strange recovery of two horses that he was
treating for what we would now call “infections”. At the Veterinary Clinic the horses were
accidentally exposed to spores of the mushroom penicillium notatum and inexplicably got better,
despite a grave prognosis. This was seen by Semmer as a problem that impeded his research on
3 This journal still exists.
21
the pathology of disease: How can you conduct microbiological studies in pathology if the
patients regain their health? Both Semmer himself, as well as the distinguished readers of the
journal, which still specializes in pathology today, failed to recognize that the curing of infection
by a living organism (mushroom spores) had introduced a novel (and as we now know,
extremely effective) approach to fighting infection (i.e., antibiotics). Biology and medicine had
to wait another 8 years for Pasteur to discover bacteria, and another 70 years for Fleming to
discover penicillin. A simple example from the business world is seen in the report that Victor
Kayam declined the opportunity to purchase the rights to Velcro, because he could not see any
practical application for it! Both Semmer and Victor Kayam had extremely important, novel and
effective, elegant and generalizable solution in their hands, but did not see this.
The effect of the problem on creativity
One way of showing the relationship of creativity to problem-solving is to focus, not on
creativity, but on the problems themselves. Sticking to the three dimensions introduced at the
beginning, problems can be divided according to:
their degree of definition;
the degree to which the solution pathway has already been defined;
the clarity of the criteria for recognizing a solution.
Clearly-defined problems that are solvable by means of standard techniques and for which there
are obvious and well-known criteria identifying the solution constitute “routine” problems. They
can often be solved without the need to generate novelty, although when existing knowledge is
applied in settings where it has previously been treated as irrelevant, a certain technical or
inventive creativity occurs. Nonetheless, creativity is not absolutely necessary, and is probably
not usual. By contrast some problems require in the first instance becoming aware that there is a
problem at all and finding a way of defining it, secondly working out techniques for solving the
problem and thirdly developing criteria for recognizing a solution. Such “loosely-defined”
problems often demand a high level of creativity.
22
This raises the possibility that certain kinds of problem (routine problems) may actually
inhibit creativity (see also earlier discussions of high expertise and creativity). It is also
conceivable that the reverse could occur: Creativity could inhibit the solving of routine problem,
for instance by making the solver overlook perfectly effective and obvious (but not novel)
solutions and look for obscure (novel) ones, or by encouraging the solver to go beyond the actual
problem at hand and define it in an excessively complex fashion. In the case of loosely-defined
problems, on the other hand, creativity may be indispensable.
It also seems that a too highly defined definition of the solution may hinder problem-
solving. An example is to be seen in the now almost infamous Australian “submarine project”.
The Department of Defence budgeted six billion Dollars (although it has spent much more) on
designing and building a new class of submarine (the Collins class). Unfortunately despite the
protests of the apologists the submarine is said to be as loud as a rock band, to have a weapons
system that cannot hit anything, and a propulsion system that cannot guarantee to move the
submarine. Although they were asked to build something effectively novel, the designers and
engineers were given excessively narrow specifications of the nature of the end product. Not
only did it have to be a submarine, but even the material of which the screw was to be
constructed was specified, i.e., the solution was over-defined. A truly open task statement would
have been something like: “Design and build an effective device for defending Australia’s coastal
waters at a cost of no more than six billion Dollars.”
Practical implications
What does all this mean for practice? Although it would be possible to tease out from these
thoughts practical suggestions for, for instance, business, I will concentrate here on education,
and in particular on classroom teaching. This link has a substantial history in modern thinking:
From the very beginning, the modern creativity discussion focused on education. Immediately
following the Sputnik shock of 1957, the perceived defeat of American engineers in the first
event of the space race was attributed to defects in their education, and the now familiar call for
23
education to foster creativity arose. This culminated in the United States of America in the
almost bizarrely named National Defense Education Act, which called for schools and
universities to foster creativity, especially in areas relevant to national defence.
Setting assignments
I have discussed creativity-facilitating classroom instruction in other places (e.g., Cropley
and Urban, 2000; Cropley, 2001), as well as out-of-school measures for fostering creativity
(Cropley and Gribov, 2003). For the purposes of the present paper, I will concentrate on
assessment. The first issue, to which I will devote only a few sentences in this paper, is that of
setting tasks that permit, facilitate, or even provoke creative solutions. The key difficulty here, in
my opinion, is the one I have already referred to: Not only do teachers like overdefined
problems, or even have difficulty breaking away from them, but students like them too, because
they are so clearcut. Both parties know how to prepare themselves and what is expected of them,
even students who do not make any particular effort to prepare well. As a university student I
was a master at predicting what questions would be on the final (through an analysis of past
papers), and focused on preparing only for what I knew was coming! Overdefined examinations
were vital to my ability to pass.
A case study of the reactions of teachers and pupils to grading practice at the University
of Adelaide in South Australia at two points 100 years apart is informative here. In the nineteenth
and early twentieth centuries Western Australia had no university. Consequently, students in that
state often attended the University of Adelaide and, as a result, had to take that university’s
entrance examination. In 1904 there was an unusually high failure rate among Western Australian
students, and this led to an intense public discussion (e.g., Morning Herald, 1904). The
complaint was straightforward: The university had changed its assessment criteria and made the
exams too difficult. The problem was that the university had suddenly set assignments such as
“To what extent can Sir Walter Scott’s novels be classified as ‘historically accurate’?” whereas
what the parents and protesting teachers wanted was “List three examples of historical errors in
24
the novel Ivanhoe.” The complainants specifically criticized the fact that it would not be possible
to learn the answer to the “To what extent …” example by heart, and that students would have to
use their own judgment, with all the risks associated with this, including the possibility of being
wrong! The new approach had negated all the hours of learning by heart that many students had
carried out, with the result that earnest and hardworking people had failed. Protesting parents and
educators made it plain that they were not demanding an easy examination, but one that they saw
as predictable, objective and fair. The demand was for (a) assignments that were, in our terms,
overdefined, (b) highly defined solutions, and (c) a clearly defined pathway to the solution (learn
by heart).
Almost 100 years later, in 1996, the same university changed the criteria for admission to
medical school—as a rule, students in Australia enter medical school directly from high school,
and the number of applications exceeds by far the number of places available. The new criteria
involved a combination of high school grades, scores on an aptitude test, and results of an
interview. Among other things, the latter two procedures assess problem-solving ability,
communication skills and ability to work in teams. There was a public outcry. Some candidates
with extraordinarily good high school grades did not obtain a place, and the university was
depicted as being anti-academic. Some parents even went to the South Australian ombudsman
(without success), although the procedure had been judged by educational theorists to be “based
on cogent reasoning”. Once again, the thrust of the argument was that (a) problem-solving ability
and the like are subjective, (b) what students need to know cannot be reduced to pre-defined
factual knowledge that teachers know in advance and can pass on to students, and (c) the
necessary knowledge cannot be acquired by (possibly) long hours of honest toil over textbooks,
whereas the facts of physics, chemistry, and biology can.
Table 2 offers some guidelines for setting assignments that would have defeated me, but
probably have caused fury in Perth in 1904 or Adelaide in 1996! The rows in the table are
derived from earlier sections of this paper, the columns represent a progression from more
25
general, abstract statements to increasingly specific and concrete specifications, and the entries in
the cells of the tables are derived from ideas developed in the body of this paper.
Table 2. Guidelines for setting assignments
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26
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Evaluating asssignments
An aspect of practice that is of considerable concern to many teachers is that of evaluation or
grading. In litigious countries teachers are nowadays expected to be able to state in advance in
(!
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,*
Although the call for clear criteria is linked by some teachers with a general, undesirable
climate of dissatisfaction and unwillingness to accept authority, the idea that assessors should
state what they are looking for and show where students’ performances have failed to meet
expectations is not simply a political/legal issue, and is not necessarily a bad thing, even in the
context of fostering creativity, despite the fact that Amabile (e.g., 1996) is generally taken to
have established that extrinsic rewards inhibit creativity and thus to have shown that grades
(since they are given by the teacher, not by students themselves, and are thus extrinsic), are bad
for creativity.
27
In real life, even people in aesthetically “creative” areas (such as literature, music or fine
art), where I have argued above that pressure for concrete effectiveness may be less than in
medicine, business, engineering, and the like, are usually subject to external evaluation of their
work. I suspect that the idea of completely intrinsically motivated creators, who produce novelty
for no-one but themselves and care nothing for other people’s opinions, is not an accurate
representation of the majority of creative people. Indeed, Csikszentmihalyi (e.g., 1988) argued
that creativity is actually in the eye of the beholder (i.e., the external assessor), and that a product
is only creative when knowledgeable people apply this label. I myself (Cropley, 1997) have
argued that Wallas’s (1926) phase model of creativity needs to be expanded to include, among
other things, phases of communication to other people and external evaluation by those people.
Eisenberger and Armeli (1997) showed that the giving of grades can promote creativity,
even in such intrinsically “creative” areas as music, provided that (a) instructors know what it is
that they are trying to promote and (b) students know what it is that they are expected to do
differently in order to be creative, although it must be admitted that the area is beset by
differences of opinion (e.g., Joussemet and Koestner, 1999). Thus, it seems to me to be important
for teachers that they are familiar with what it is that they want students to do in assignments and
that they can (a) show students how to evaluate their own work from the point of creativity, (b)
recognize aspects of students’ work that can be said to be “creative,” (c) show students where
they have fallen down, and (d) give guidelines on how to do better.
In Table 3 (see next page) I have derived from earlier sections of this paper guidelines for
recognizing creativity in students’ reactions to assignments, i.e., for grading assignments. The
rows in the tables (novelty, elegance, generalizability) are derived from the criteria of a creative
product summarized in Table 1. As in Table 2, the columns represent a progression from more
general, abstract criteria to increasingly specific and concrete indicators, and the entries in the
cells of the tables are derived from ideas developed in the body of the paper. It might be thought
28
that judging such properties is so subjective as to become arbitrary, thus defeating the very
purpose of constructing the table. However, Hennessey (1994) reported
inter-rater agreement ranging up to .93 even among untrained undergraduates who rated aspects
of creativity simply applying their own subjective understanding of these qualities. Other
studies also suggest that judging properties connected with the creativity of products such as
novelty, effectiveness, or understandability is not as difficult as might be supposed. Vosburg
(1998) reported that untrained judges who rated products on 7-point scales such as “Very
understandable”—“Not at all understandable” achieved inter-rater reliabilities of about.90.
These guidelines and criteria are not meant to be treated as exhaustive, but only as an
indication of what is needed and a first step towards establishing concrete criteria. What is
Table 3. Guidelines for grading assignments
Principle
Criterion
Indicator
Generation of
Novelty
(i.e, aspects of the
process of generating
something new)
Possession and
use of knowledge
• traditional indicators (does the solution
reveal good knowledge of the facts and
insightful understanding?) See, for
instance, Biggs and Collis (1982) and Biggs
(1996).
Problematization
diagnosis (shortcomings in what already
exists are revealed)
prescription (points at which what already
exists could be improved are indicated)
prognosis (broad suggestions are made for
how to carry out improvements )
Adding to existing knowledge
replication (the known is transferred to a
new setting)
redefinition (the known is seen or used in a
new way)
combination (generation of new mixtures of
existing elements);
incrementation (the known is extended in an
existing direction)
reconstruction (an approach previously
abandoned is shown to be useful)
Developing new knowledge
redirection (the known is extended in a new
direction)
reinitiation (thinking begins at a radically
different point from the current one and takes
off in a new direction that is shown to be
helpful)
29
generation (construction of fundamentally
new—but at least potentially effective—
solutions)
Elegance
(i.e., properties of the
solution)
External elegance: Effect on
other people
surprisingness (the beholder is “surprised”
by the solution)
convincingness (the beholder is convinced
by the solution)
pleasingness (the beholder finds the solution
“beautiful”)
Internal elegance: Ideas are
well worked out and hang
together
completeness (the solution is well worked
out and “rounded”, not just fragmentary)
harmoniousness (the elements of the
solution fit together in an internally
consistent way)
Generalizability
(i.e., properties of the
solution)
Ideas go beyond the
immediate problem
foundationality (the solution lays down a
general basis for further work)
transferability (ideas are offered for other,
apparently unrelated problems)
• germinality (the solution suggests new ways
of looking at existing issues or problems)
seminality (the solution demonstrates the
existence of previously unnoticed additional
problems and/or suggests how they might be
solved)
needed now are practical examples or miniature case studies showing what the criteria look like in
specific assignments. A single example will be given here in abbreviated form.
A brief case study
As part of their assessment, students in an engineering class were required to design and
build “a wheeled vehicle powered by the energy stored in a mousetrap.” Although a passing
grade was guaranteed if the vehicle proved to be capable of moving at least 1m under its own
power, assessment emphasized the importance of novelty, elegance and generalizibility (all of
which had been explained to the students in class) for obtaining a high mark. If students asked
for an elaboration of the assignment, they were told that from the point of the instructor the
problem was sufficiently defined by the words, “Build a wheeled vehicle powered by the energy
stored in a mousetrap.” Some students expressed annoyance at this, in essence demanding what I
have called “overdefinition” of the problem, and the instructor was regarded by some as hard or
unreasonable or unhelpful. Such is students’ love for overdefined problems!
Almost all participants succeeded in constructing a vehicle that met the minimum formal
requirements (it had wheels and was capable of moving itself, and was thus relevant and
effective). Several of the resulting models were elegantly designed and well finished. However,
30
most students assumed that the vehicle had to be four wheeled and had to run on the ground like
a car or truck. In addition, most focused on the energy stored in the trap’s spring as the source of
power, as well as consciously opting for a vehicle that was effective in the sense that it could
cover well over a metre, and was socially acceptable in that it looked like existing vehicles. An
example of a well constructed conventional vehicle that illustrates the points made above is the
“Ferrari” model I will now show you.
Only a few groups were able to break away from conventional thinking. One used the
mouse trap’s spring to operate a pump which inflated a balloon attached to the car. When the
balloon blew out the air it propelled the car by means of a jet effect. The power source was not
part of the vehicle, although the thruster (the balloon) was.
31
32
Another also used a novel means of propulsion by launching a model car using a catapault
powered by the mousetrap’s spring. Neither power source nor thruster was part of the vehicle.
33
More novelty was introduced by groups that broke away from the idea that all “wheeled
vehicles” must resemble conventional motor cars. One group built a large hollow wheel set
rolling by a weight mounted in its interior and wound into position by the trap’s spring, thus
expanding the meaning of “wheeled vehicle” and using gravity as the actual driver.
Even more novelty was produced by group that set fire to the mousetrap and used the
heat generated by the flames to fire up the boiler of a steam locomotive, thus using the
chemical energy stored in the wood, whereas almost all others focused on the mechanical
energy of the spring. Another group offered what was in some ways the most radical solution: a
wheeled cart attached to the mousetrap by a string. When the mousetrap was thrown off the
table on which the vehicle stood, its weight pulled the cart along as the trap fell to the floor,
thus using the gravitational force acting on the mousetrap’s mass as the source of energy, not
the spring. The only limit on the distance this method could propel the vehicle was the height
of the surface from which the mousetrap was thrown.
34
The final example I will give involved a redefinition of “wheeled vehicle” and a novel
means of propulsion, although it retained the potential energy stored in the mouse trap’s spring
as the source of power. The spring was used to drive a fan and the wind created by the action of
the fan was used to propel an ultralight cylinder (a large “wheel”).
What is now needed is to analyze these solutions using the system presented in Table 3. I
will do this by comparing the Ferrari model with the fan driven vehicle.4 The Ferrari was a
wheeled vehicle, and moved at least a metre. Thus, it successfully took the first hurdle of
relevance and effectiveness, and could be evaluated for creativity. It displayed knowledge of
existing principles and facts (conventional indicator), but did not in any way show concern about
problems with existing approaches or improve them in any way (no points for Problematization).
It displayed a certain degree of novelty in that Lego is not usually used in classroom
assignments, although the use of Lego to make models is commonplace. Thus, it scored a point
4 For simplicity’s sake I will award points only on a “Yes,” or “No” basis: If a criterion is satisfied, one point, of it
is not, zero points. In practice, it would be possible to grade on, let us say, a five point basis such as: “Very
markedly present,: “pronounced,” “obvious,” “observable,” “weakly present,” “absent,” thus providing more
differentiated feedback.
35
for replication (see Table 3). The mouse trap was also used in a new way (redefinition) and there
was a combination of existing elements (model building with Lego and mouse trap), while there
was perhaps incrementation (use of the mouse trap spring was extended, but in an existing way,
since the well known “snapping shut” action of the mouse trap was retained). Thus, the Ferrari
scored five points in all for Generation of Novelty. In the area of “Elegance” this model scored
well: It is convincing, pleasing, complete and harmonious—four points. In the area of
Generalizability, however, it scored zero, yielding a total score of 9, largely obtained via elegant
use of the known. The Ferrari group would be praised for their workmanship, but advised to
introduce more novelty
In some ways the fan driven “vehicle” suffers by contrast with the Ferrari, but overall it
obtained substantially more points. It was a wheeled vehicle and moved one metre, and was thus
relevant and effective. It also showed knowledge of the basic facts (one point). It received points
for diagnosis, prescription and prognosis, since it draws attention to the need to change from
vehicles with a power source that travels with the vehicle, indicates a possible line of
improvement (ultralight vehicle) and shows roughly how these two ideas might be combined:
three points for Problematization. The lever action of the trap’s spring was used to drive a fan
(replication), “wheeled vehicle” was defined in an unusual way (redefinition), the combination
of mousetrap, fan and wheeled vehicle was uncommon (combination), and the already known
ability of fans to impart movement to light objects was extended from air or smoke to a wheel
(incrementation). The known fan action was used in a new way by using it to drive a vehicle
(redirection), “propelled by” and “wheeled vehicle” are existing concepts, but were taken in a
new direction (reinitiation), and the whole resulted in a solution that suggests a new line of
attack: an ultralight vehicle that does not carry the power source with it (generation). Thus the
fan car receives seven points for Generation of Novelty.
In the case of Elegance, the fan vehicle was surprising and elicited a feeling that it was
clever (pleasingness), but was perhaps not convincing. It was, also, only fragmentary and rather
36
crude and scored zero for internal elegance: Two points only for Elegance. Finally, the fan
vehicle suggested where further work could be done (ultralight vehicles, stationary power source,
use of moving air as a driver) (germinality): a point for Generalizability. Thus the fan car
received a total of 14 points, losing points to the Ferrari for its roughness and lack of detail, but
gaining more for its new ideas and generalizability. The fan car group would be praised for their
introduction of effective novelty, but advised try to work out their ideas more fully and build a
more finished prototype.
What is needed now are case studies from disparate fields such as mathematics or
physics, but also mother tongue, foreign languages, history, and the like, that provide concrete
examples of the application of these indicators to the assessment of real assignments. I would
be grateful to any colleagues who provided such studies.
37
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... Similarly, good manipulation skills may be characterized by a flexible and original use of skills, also a feature of creative use (Haylock, 1997). Thus, mathematics instruction should not only teach problem solving and manipulation skills, but do so in a way that develops creativity (Cropley, 2005;Nadjafikhah, Yaftian, & Bakhshalizadeh, 2012;Schoenfeld, 1988). ...
... In such instruction, creative approaches are under-emphasized because they go beyond the scope of to-be-learned solutions, and may lead to errors (Beghetto & Sriraman, 2016;Cropley, 2010;Gralewski & Karwowski, 2013;Runco, Acar, & Cayirdaga, 2017). Of course, good teachers may naturally highlight critical features of problems and discuss alternative solutions, but students are rarely given the opportunities to be creative (Cropley, 2005;Nadjafikhah et al., 2012;Sriraman, 2005). One way to develop creativity and flexibility is to provide students with the opportunity to solve problems on their own, and generate their own examples, problems and solutions (Kapur, 2016;Watson & Mason, 2002). ...
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Typical mathematics instruction starts with a teacher explaining a worked example, followed by students’ practicing isomorphic problems. Because such instruction may not optimally help students notice the critical features of the concept, an alternative way is to have them generate their own examples across a range of contexts. One hundred and sixty four students participated in three algebra-learning studies, where they completed several worksheets, each targeting a specific algebraic manipulation principle. Each worksheet started with worked examples presenting the targeted principle, after which the students had to generate their own examples. Student-generated examples varied from being only superficially different from the worked-examples, to creative ones that differed on a structural level. Path analyses revealed significant indirect and direct effects of structural creativity. The indirect effect revealed that structural creativity was associated with a higher error rate, which, in turn, negatively influenced immediate learning. Interestingly, in spite of the indirect effect, and what was a relatively simple and short intervention embedded in a longer instructional program, the direct effect of structural creativity on delayed posttest outcomes was positive and significant. We situate our findings in the extant literature on the role of failure in mathematical creativity and learning.
... Creativity in learning is the ability to come up with new ideas, develop ideas, find solutions to problems, and find new opportunities (A. Cropley, 2005). According to Okpara (2007), creativity is the capacity to create something new with preexisting elements. ...
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Independence and creativity are considered important aspects of learning in the COVID-19 pandemic era. This study aimed to analyze the independence and creativity profile of elementary school teacher education students in online lectures viewed from learning motivation in the COVID-19 pandemic era. The study used mixed methods with a sequential explanatory design. Snowball sampling technique was used to select the study subjects. Questionnaires and in-depth interviews were used as the data collection tools, using Google Forms software. Miles and Huberman’s (1994) interactive model was used as the data analysis model. The findings of the study showed that: (1) students were less able to work independently and confidently but had high learning discipline and were responsible; and (2) students lack indicators of flexibility and originality but have high curiosity, resilience, and persistence in learning creativity. The findings of the research revealed that independence and creativity in learning were included in the medium category. This study can be used as a reference for further research. Keywords: learning independence, learning creativity, online lecture, application media, learning motivation;
... Although it did not refer to CFTF, an earlier paper (Cropley, 2011) discussed general principles of teacher behavior which can be applied in two-dimensional education. I have also discussed a more specific aspect of classroom instruction in some detail, namely setting and evaluating assignments (Cropley, 2005). Tools exist for checking the creativity focus of teaching behavior and the learning behavior of students and diagnosing and improving them (formative assessment). ...
Article
Increasing digitization and robotization and the resulting cyber-physical systems (CPSs) are leading to an era in which artificial intelligence (AI) is becoming increasingly prominent in our lives. Making the best use of AI in engineering and technology will require not just practical and technical knowledge and skills but “creatively-focused technology fluency” (CFTF), in order to go beyond algorithmic thinking. The creativity focus involves creativity-facilitating competencies such as managing complexity, thinking critically, envisaging possibilities, tolerating uncertainty, displaying self-efficacy, and communicating skillfully; fostering these is now an important element in technology education. Emphasizing the need for a creativity focus (the “CF” in “CFTF”) does not involve neglecting or abolishing traditional knowledge and skills but supplementing them by strengthening creativity-focused competencies.
... The generic nature of the "habits" involved in transferable creativity also means that a unified index of creativity-fostering teacher behaviors, such as the CFTIndex, can be applied to myth-busting in all disciplines, including those regarded as not involving creativity: Cropley (2015aCropley ( , 2015b gave the example of engineering, while Cropley (2012) briefly discussed mathematics. Cropley (2005) also discussed the implications of transferable creativity not for a discipline but for an area of curriculum not normally regarded as creativity-facilitating -evaluation/assessment/testing. This would be facilitated by making the "Judgment" sub-scale of the CFTIndex refer quite specifically to formal school assessment. ...
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[This is a pre-publication summary of a chapter to be published in an edited volume by Kaycheng Soh. The chapter can be cited as Cropley, A. J. (2018). The Creativity-Facilitating Teacher Index: Early thinking, and some recent reflections. in Kaycheng Soh (Ed.), Creativity fostering teacher behavior: Measurement and research (pp. ). Singapore: World Scientific Publishing. The Creativity-Facilitating Teacher Index: Early thinking, and some recent reflections Arthur Cropley University of Hamburg, Germany Summary When I responded to a request from Mark Runco to make a contribution to his Creativity Research Handbook (Cropley, 1997) I prepared an overview of what I regarded as important issues from the preceding 20-25 years, such as, among other things, the psychological dimensions of creativity, creativity tests, and existing formal programs for promoting creativity in the classroom (which I referred to as “creativity technology”). I had no inkling that in Singapore Soh Kaycheng (Soh, 2000, 2015) would see the practical implications of one topic I introduced in the chapter (the role of the teacher) and would move on from my relatively superficial presentation to develop a clearer idea of this role and to design a practical instrument for raising teachers’ awareness of the effects of their behaviour and giving them concrete insights into desirable ways of behaving (the CFTIndex). Soh’s analysis has set me thinking, and in the second half of this contribution I will make some suggestions for further developing his work. These will relate, in the first instance, to further differentiating the structure and content of the scale and giving it a stronger theoretical (but still strongly practice-linked) foundation by showing how its contents can be related to a phase model of creativity. I will also suggest a broadening of its areas of application by emphasizing its value as a tool for teacher education.
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Talking about creative productions seems to be a common activity in both everyday language and the language used by researchers. The use of the term creative implies the existence of a creativity variable that allows for comparisons between different productions. According to the standard definition of creativity (Runco & Jaeger, 2012), to be creative, a production must have both value and novelty. So far, empirical psychometric studies looking for a creativity variable with these two dimensions have shown that value and novelty are not only independent, but are also only weakly correlated. This empirical evidence, which has been widely replicated in the literature, indicates that, according to psychometric rules, it is impossible and indeed paradoxical to talk about the creativity of a production. In the present study, we sought to replicate these results by including a new dimension that has mostly been omitted in psychometric studies of creativity dimensions, namely feasibility. Results (N = 662 ideas) tended to show that this new dimension, negatively correlated with novelty and positively correlated with value, led to a second-order general factor of creativity. We named the axis formed by these three dimensions disruptiveness in order to underline the subtle difference from what would be an axis of creativity. The theoretical and applied implications of these results are discussed.
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Tanzen bildet?! Kulturelle Bildungsangebote im Bereich von Tanz gewinnen an Bedeutung. Dabei wird davon ausgegangen, dass sich Kreativer Tanz positiv auf die Entwicklung motorisch-kreativer Fähigkeiten auswirkt. Allerdings liegen weder zur Einflussnahme des Kreativen Tanzes auf die Kreativitätsentwicklung noch zur methodisch-didaktischen Unterrichtsgestaltung empirische Erkenntnisse vor. An diesem Forschungsdefizit setzt Esther Pürgstaller an und geht erstens der Frage nach, ob die Teilnahme an einem Kreativen Tanzangebot zu einer Steigerung der motorischen Kreativitätsentwicklung von Grundschulkindern führen kann. Zweitens beantwortet die Autorin die Frage, wie das Tanzangebot methodisch-didaktisch gestaltet ist und die Kreativitätsentwicklung beeinflussen kann. Der Inhalt • Kulturelle Bildung • Kreativitätsförderung durch Tanz • Methodisch-didaktische Unterrichtsgestaltung • Empirische Längsschnitt-Studie und videobasierte Unterrichtsstudie Die Zielgruppen • Lehrende und Studierende sowie Wissenschaftlerinnen und Wissenschaftler aus Sportwissenschaft, Erziehungswissenschaft und Tanzwissenschaft, • Lehrkräfte im Bereich des Tanzes und der Kulturellen Bildung, Grundschullehrkräfte Die Autorin Dr. Esther Pürgstaller ist Wissenschaftliche Mitarbeiterin am Institut für Sportwissenschaft der Westfälischen Wilhelms-Universität Münster. Ihre Arbeitsschwerpunkte liegen in der empirischen Unterrichtsforschung der Tanz- und Sportdidaktik, -pädagogik, Kreativität und Kulturellen Bildung.
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Nachdem im Bereich der Kulturellen Bildung über Jahre hinweg wenige Projekte, Konzepte und Forschung durchgeführt und gefördert wurden, erlebte das Feld in den vergangenen zehn Jahren einen Aufschwung. So wird mittlerweile eine Vielzahl an neuen Modellen und Konzepten (z. B. „Tanz in Schulen“), Preisen (z. B. „BKM-Preis Kulturelle Bildung“), Wettbewerben (z. B. „Komposition“), Fonds (z. B. „Tanzfonds Partner“) und Förderprogrammen (z. B. „Jedem Kind Instrumente/Tanz/Stimme“) finanziert, um zur Professionalisierung und fachlichen Weiterentwicklung im Feld der Kulturellen Bildung beizutragen (Bockhorst, 2012, S. 348–355). Insbesondere an Schulen wird versucht kulturelle Bildungsangebote zu implementieren, um allen Heranwachsenden eine Teilhabe an Kultureller Bildung, dem „catalyst for change“, zu ermöglichen (Arts Council England, 2010, S. 1).
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Kreativität ist in den vergangenen Jahrzehnten zu einem hoffnungstragenden Begriff geworden, der nicht mehr aus den unterschiedlichen ästhetischen, kulturellen, politischen, pädagogischen und wirtschaftlichen Diskursen wegzudenken ist. Aufgrund des sich verschärfenden ökonomischen Wettbewerbs erhoffen sich Politiker mit neuen Produkten und Dienstleistungen neue Ressourcen und Arbeitsplätze zu schaffen, um den Wirtschaftsstandort zu sichern, dem ökologischen Standard zu entsprechen und gegenüber anderen Ländern wettbewerbsfähig zu bleiben (Giesler, 2003, S. 13). Gleichzeitig vollzieht sich ein gesellschaftlich-sozialer Wandel, der einen Umbruch in Bildung und Gesellschaft mit sich bringt.
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Einher mit dem Anstieg an kulturellen Bildungsangeboten in den vergangenen Jahren (vgl. Kapitel 2.2) zeichnet sich auch im Tanz eine zunehmende Förderung und Etablierung von Tanzangeboten im schulischen wie außerschulischen Kontext auf nationaler Ebene ab. Im Zuge dessen rückt der Kreative Tanz vermehrt als Anknüpfungspunkt zur Welt des Tanzes in den Mittelpunkt, in dessen Fokus die Entdeckung individueller Ausdrucksund Bewegungsmöglichkeiten liegt und weniger die Vermittlung von Tanztechniken und -fertigkeiten. Der Unterricht in Kreativem Tanz bietet Gelegenheit, den eigenen Körper als bespielbares Instrument kennen und manipulieren zu lernen sowie Stimmungen, Gefühle und (Körper-)Bilder durch den Körper transparent zu machen.