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Creative Problem Solving

Finding innovative solutions to challenges.

By the Mind Tools Content Team

creative problem solving article

Imagine that you're vacuuming your house in a hurry because you've got friends coming over. Frustratingly, you're working hard but you're not getting very far. You kneel down, open up the vacuum cleaner, and pull out the bag. In a cloud of dust, you realize that it's full... again. Coughing, you empty it and wonder why vacuum cleaners with bags still exist!

James Dyson, inventor and founder of Dyson® vacuum cleaners, had exactly the same problem, and he used creative problem solving to find the answer. While many companies focused on developing a better vacuum cleaner filter, he realized that he had to think differently and find a more creative solution. So, he devised a revolutionary way to separate the dirt from the air, and invented the world's first bagless vacuum cleaner. [1]

Creative problem solving (CPS) is a way of solving problems or identifying opportunities when conventional thinking has failed. It encourages you to find fresh perspectives and come up with innovative solutions, so that you can formulate a plan to overcome obstacles and reach your goals.

In this article, we'll explore what CPS is, and we'll look at its key principles. We'll also provide a model that you can use to generate creative solutions.

About Creative Problem Solving

Alex Osborn, founder of the Creative Education Foundation, first developed creative problem solving in the 1940s, along with the term "brainstorming." And, together with Sid Parnes, he developed the Osborn-Parnes Creative Problem Solving Process. Despite its age, this model remains a valuable approach to problem solving. [2]

The early Osborn-Parnes model inspired a number of other tools. One of these is the 2011 CPS Learner's Model, also from the Creative Education Foundation, developed by Dr Gerard J. Puccio, Marie Mance, and co-workers. In this article, we'll use this modern four-step model to explore how you can use CPS to generate innovative, effective solutions.

Why Use Creative Problem Solving?

Dealing with obstacles and challenges is a regular part of working life, and overcoming them isn't always easy. To improve your products, services, communications, and interpersonal skills, and for you and your organization to excel, you need to encourage creative thinking and find innovative solutions that work.

CPS asks you to separate your "divergent" and "convergent" thinking as a way to do this. Divergent thinking is the process of generating lots of potential solutions and possibilities, otherwise known as brainstorming. And convergent thinking involves evaluating those options and choosing the most promising one. Often, we use a combination of the two to develop new ideas or solutions. However, using them simultaneously can result in unbalanced or biased decisions, and can stifle idea generation.

For more on divergent and convergent thinking, and for a useful diagram, see the book "Facilitator's Guide to Participatory Decision-Making." [3]

Core Principles of Creative Problem Solving

CPS has four core principles. Let's explore each one in more detail:

  • Divergent and convergent thinking must be balanced. The key to creativity is learning how to identify and balance divergent and convergent thinking (done separately), and knowing when to practice each one.
  • Ask problems as questions. When you rephrase problems and challenges as open-ended questions with multiple possibilities, it's easier to come up with solutions. Asking these types of questions generates lots of rich information, while asking closed questions tends to elicit short answers, such as confirmations or disagreements. Problem statements tend to generate limited responses, or none at all.
  • Defer or suspend judgment. As Alex Osborn learned from his work on brainstorming, judging solutions early on tends to shut down idea generation. Instead, there's an appropriate and necessary time to judge ideas during the convergence stage.
  • Focus on "Yes, and," rather than "No, but." Language matters when you're generating information and ideas. "Yes, and" encourages people to expand their thoughts, which is necessary during certain stages of CPS. Using the word "but" – preceded by "yes" or "no" – ends conversation, and often negates what's come before it.

How to Use the Tool

Let's explore how you can use each of the four steps of the CPS Learner's Model (shown in figure 1, below) to generate innovative ideas and solutions.

Figure 1 – CPS Learner's Model

creative problem solving article

Explore the Vision

Identify your goal, desire or challenge. This is a crucial first step because it's easy to assume, incorrectly, that you know what the problem is. However, you may have missed something or have failed to understand the issue fully, and defining your objective can provide clarity. Read our article, 5 Whys , for more on getting to the root of a problem quickly.

Gather Data

Once you've identified and understood the problem, you can collect information about it and develop a clear understanding of it. Make a note of details such as who and what is involved, all the relevant facts, and everyone's feelings and opinions.

Formulate Questions

When you've increased your awareness of the challenge or problem you've identified, ask questions that will generate solutions. Think about the obstacles you might face and the opportunities they could present.

Explore Ideas

Generate ideas that answer the challenge questions you identified in step 1. It can be tempting to consider solutions that you've tried before, as our minds tend to return to habitual thinking patterns that stop us from producing new ideas. However, this is a chance to use your creativity .

Brainstorming and Mind Maps are great ways to explore ideas during this divergent stage of CPS. And our articles, Encouraging Team Creativity , Problem Solving , Rolestorming , Hurson's Productive Thinking Model , and The Four-Step Innovation Process , can also help boost your creativity.

See our Brainstorming resources within our Creativity section for more on this.

Formulate Solutions

This is the convergent stage of CPS, where you begin to focus on evaluating all of your possible options and come up with solutions. Analyze whether potential solutions meet your needs and criteria, and decide whether you can implement them successfully. Next, consider how you can strengthen them and determine which ones are the best "fit." Our articles, Critical Thinking and ORAPAPA , are useful here.

4. Implement

Formulate a plan.

Once you've chosen the best solution, it's time to develop a plan of action. Start by identifying resources and actions that will allow you to implement your chosen solution. Next, communicate your plan and make sure that everyone involved understands and accepts it.

There have been many adaptations of CPS since its inception, because nobody owns the idea.

For example, Scott Isaksen and Donald Treffinger formed The Creative Problem Solving Group Inc . and the Center for Creative Learning , and their model has evolved over many versions. Blair Miller, Jonathan Vehar and Roger L. Firestien also created their own version, and Dr Gerard J. Puccio, Mary C. Murdock, and Marie Mance developed CPS: The Thinking Skills Model. [4] Tim Hurson created The Productive Thinking Model , and Paul Reali developed CPS: Competencies Model. [5]

Sid Parnes continued to adapt the CPS model by adding concepts such as imagery and visualization , and he founded the Creative Studies Project to teach CPS. For more information on the evolution and development of the CPS process, see Creative Problem Solving Version 6.1 by Donald J. Treffinger, Scott G. Isaksen, and K. Brian Dorval. [6]

Creative Problem Solving (CPS) Infographic

See our infographic on Creative Problem Solving .

creative problem solving article

Creative problem solving (CPS) is a way of using your creativity to develop new ideas and solutions to problems. The process is based on separating divergent and convergent thinking styles, so that you can focus your mind on creating at the first stage, and then evaluating at the second stage.

There have been many adaptations of the original Osborn-Parnes model, but they all involve a clear structure of identifying the problem, generating new ideas, evaluating the options, and then formulating a plan for successful implementation.

[1] Entrepreneur (2012). James Dyson on Using Failure to Drive Success [online]. Available here . [Accessed May 27, 2022.]

[2] Creative Education Foundation (2015). The CPS Process [online]. Available here . [Accessed May 26, 2022.]

[3] Kaner, S. et al. (2014). 'Facilitator′s Guide to Participatory Decision–Making,' San Francisco: Jossey-Bass.

[4] Puccio, G., Mance, M., and Murdock, M. (2011). 'Creative Leadership: Skils That Drive Change' (2nd Ed.), Thousand Oaks, CA: Sage.

[5] OmniSkills (2013). Creative Problem Solving [online]. Available here . [Accessed May 26, 2022].

[6] Treffinger, G., Isaksen, S., and Dorval, B. (2010). Creative Problem Solving (CPS Version 6.1). Center for Creative Learning, Inc. & Creative Problem Solving Group, Inc. Available here .

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Original research article, creative problem solving as overcoming a misunderstanding.

creative problem solving article

  • Department of Psychology, University of Milano-Bicocca, Milan, Italy

Solving or attempting to solve problems is the typical and, hence, general function of thought. A theory of problem solving must first explain how the problem is constituted, and then how the solution happens, but also how it happens that it is not solved; it must explain the correct answer and with the same means the failure. The identification of the way in which the problem is formatted should help to understand how the solution of the problems happens, but even before that, the source of the difficulty. Sometimes the difficulty lies in the calculation, the number of operations to be performed, and the quantity of data to be processed and remembered. There are, however, other problems – the insight problems – in which the difficulty does not lie so much in the complexity of the calculations, but in one or more critical points that are susceptible to misinterpretation , incompatible with the solution. In our view, the way of thinking involved in insight problem solving is very close to the process involved in the understanding of an utterance, when a misunderstanding occurs. In this case, a more appropriate meaning has to be selected to resolve the misunderstanding (the “impasse”), the default interpretation (the “fixation”) has to be dropped in order to “restructure.” to grasp another meaning which appears more relevant to the context and the speaker’s intention (the “aim of the task”). In this article we support our view with experimental evidence, focusing on how a misunderstanding is formed. We have studied a paradigmatic insight problem, an apparent trivial arithmetical task, the Ties problem. We also reviewed other classical insight problems, reconsidering in particular one of the most intriguing one, which at first sight appears impossible to solve, the Study Window problem. By identifying the problem knots that alter the aim of the task, the reformulation technique has made it possible to eliminate misunderstanding, without changing the mathematical nature of the problem. With the experimental versions of the problems exposed we have obtained a significant increase in correct answers. Studying how an insight problem is formed, and not just how it is solved, may well become an important topic in education. We focus on undergraduate students’ strategies and their errors while solving problems, and the specific cognitive processes involved in misunderstanding, which are crucial to better exploit what could be beneficial to reach the solution and to teach how to improve the ability to solve problems.

Introduction

“A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action, then there has to be recourse to thinking. (…) Such thinking has the task of devising some action which may mediate between the existing and the desired situations.” ( Duncker, 1945 , p. 1). We agree with Duncker’s general description of every situation we call a problem: the problem solving activity takes a central role in the general function of thought, if not even identifies with it.

So far, psychologists have been mainly interested in the solution and the solvers. But the formation of the problem remained in the shadows.

Let’s consider for example the two fundamental theoretical approaches to the study of problem solving. “What questions should a theory of problem solving answer? First, it should predict the performance of a problem solver handling specified tasks. It should explain how human problem solving takes place: what processes are used, and what mechanisms perform these processes.” ( Newell et al., 1958 , p. 151). In turn, authors of different orientations indicate as central in their research “How does the solution arise from the problem situation? In what ways is the solution of a problem attained?” ( Duncker, 1945 , p. 1) or that of what happens when you solve a problem, when you suddenly see the point ( Wertheimer, 1959 ). It is obvious, and it was inevitable, that the formation of the problem would remain in the shadows.

A theory of problem solving must first explain how the problem is constituted, and then how the solution happens, but also how it happens that it is not solved; it must explain the correct answer and with the same means the failure. The identification of the way in which the problem is constituted – the formation of the problem – and the awareness that this moment is decisive for everything that follows imply that failures are considered in a new way, the study of which should help to understand how the solution of the problems happens, but even before that, the source of the difficulty.

Sometimes the difficulty lies in the calculation, the number of operations to be performed, and the quantity of data to be processed and remembered. Take the well-known problems studied by Simon, Crypto-arithmetic task, for example, or the Cannibals and Missionaries problem ( Simon, 1979 ). The difficulty in these problems lies in the complexity of the calculation which characterizes them. But, the text and the request of the problem is univocally understood by the experimenter and by the participant in both the explicit ( said )and implicit ( implied ) parts. 1 As Simon says, “Subjects do not initially choose deliberately among problem representations, but almost always adopt the representation suggested by the verbal problem statement” ( Kaplan and Simon, 1990 , p. 376). The verbal problem statement determines a problem representation, implicit presuppositions of which are shared by both.

There are, however, other problems where the usual (generalized) interpretation of the text of the problem (and/or the associated figure) prevents and does not allow a solution to be found, so that we are soon faced with an impasse. We’ll call this kind of problems insight problems . “In these cases, where the complexity of the calculations does not play a relevant part in the difficulty of the problem, a misunderstanding would appear to be a more appropriate abstract model than the labyrinth” ( Mosconi, 2016 , p. 356). Insight problems do not arise from a fortuitous misunderstanding, but from a deliberate violation of Gricean conversational rules, since the implicit layer of the discourse (the implied ) is not shared both by experimenter and participant. Take for example the problem of how to remove a one-hundred dollar bill without causing a pyramid balanced atop the bill to topple: “A giant inverted steel pyramid is perfectly balanced on its point. Any movement of the pyramid will cause it to topple over. Underneath the pyramid is a $100 bill. How would you remove the bill without disturbing the pyramid?” ( Schooler et al., 1993 , p. 183). The solution is burn or tear the dollar bill but people assume that the 100 dollar bill must not be damaged, but contrary to his assumption, this is in fact the solution. Obviously this is not a trivial error of understanding between the two parties, but rather a misunderstanding due to social conventions, and dictated by conversational rules. It is the essential condition for the forming of the problem and the experimenter has played on the very fact that the condition was not explicitly stated (see also Bulbrook, 1932 ).

When insight problems are used in research, it could be said that the researcher sets a trap, more or less intentionally, inducing an interpretation that appears to be pertinent to the data and to the text; this interpretation is adopted more or less automatically because it has been validated by use but the default interpretation does not support understanding, and misunderstanding is inevitable; as a result, sooner or later we come up against an impasse. The theory of misunderstanding is supported by experimental evidence obtained by Mosconi in his research on insight problem solving ( Mosconi, 1990 ), and by Bagassi and Macchi on problem solving, decision making and probabilistic reasoning ( Bagassi and Macchi, 2006 , 2016 ; Macchi and Bagassi, 2012 , 2014 , 2015 , 2020 ; Macchi, 1995 , 2000 ; Mosconi and Macchi, 2001 ; Politzer and Macchi, 2000 ).

The implication of the focus on problem forming for education is remarkable: everything we say generates a communicative and therefore interpretative context, which is given by cultural and social assumptions, default interpretations, and attribution of intention to the speaker. Since the text of the problem is expressed in natural language, it is affected, it shares the characteristics of the language itself. Natural language is ambiguous in itself, differently from specialized languages (i.e., logical and statistical ones), which presuppose a univocal, unambiguous interpretation. The understanding of what a speaker means requires a disambiguation process centered on the intention attribution.

Restructuring as Reinterpreting

Traditionally, according to the Gestaltists, finding the solution to an insight problem is an example of “productive thought.” In addition to the reproductive activities of thought, there are processes which create, “produce” that which does not yet exist. It is characterized by a switch in direction which occurs together with the transformation of the problem or a change in our understanding of an essential relationship. The famous “aha!” experience of genuine insight accompanies this change in representation, or restructuring. As Wertheimer says: “… Solution becomes possible only when the central features of the problem are clearly recognized, and paths to a possible approach emerge. Irrelevant features must be stripped away, core features must become salient, and some representation must be developed that accurately reflects how various parts of the problem fit together; relevant relations among parts, and between parts and whole, must be understood, must make sense” ( Wertheimer, 1985 , p. 23).

The restructuring process circumscribed by the Gestaltists to the representation of the perceptual stimulus is actually a general feature of every human cognitive activity and, in particular, of communicative interaction, which allows the understanding, the attribution of meaning, thus extending to the solution of verbal insight problems. In this sense, restructuring becomes a process of reinterpretation.

We are able to get out of the impasse by neglecting the default interpretation and looking for another one that is more pertinent to the situation and which helps us grasp the meaning that matches both the context and the speaker’s intention; this requires continuous adjustments until all makes sense.

In our perspective, this interpretative function is a characteristic inherent to all reasoning processes and is an adaptive characteristic of the human cognitive system in general ( Levinson, 1995 , 2013 ; Macchi and Bagassi, 2019 ; Mercier and Sperber, 2011 ; Sperber and Wilson, 1986/1995 ; Tomasello, 2009 ). It guarantees cognitive economy when meanings and relations are familiar, permitting recognition in a “blink of an eye.” This same process becomes much more arduous when meanings and relations are unfamiliar, obliging us to face the novel. When this happens, we have to come to terms with the fact that the usual, default interpretation will not work, and this is a necessary condition for exploring other ways of interpreting the situation. A restless, conscious and unconscious search for other possible relations between the parts and the whole ensues until everything falls into place and nothing is left unexplained, with an interpretative heuristic-type process. Indeed, the solution restructuring – is a re -interpretation of the relationship between the data and the aim of the task, a search for the appropriate meaning carried out at a deeper level, not by automaticity. If this is true, then a disambiguant reformulation of the problem that eliminates the trap into which the subject has fallen, should produce restructuring and the way to the solution.

Insight Problem Solving as the Overcoming of a Misunderstanding: The Effect of Reformulation

In this article we support our view with experimental evidence, focusing on how a misunderstanding is formed, and how a pragmatic reformulation of the problem, more relevant to the aim of the task, allows the text of the problem to be interpreted in accordance with the solution.

We consider two paradigmatic insight problems, the intriguing Study Window problem, which at first sight appears impossible to solve, and an apparent trivial arithmetical task, the Ties problem ( Mosconi and D’Urso, 1974 ).

The Study Window problem

The study window measures 1 m in height and 1 m wide. The owner decides to enlarge it and calls in a workman. He instructs the man to double the area of the window without changing its shape and so that it still measures 1 m by 1 m. The workman carried out the commission. How did he do it?

This problem was investigated in a previous study ( Macchi and Bagassi, 2015 ). For all the participants the problem appeared impossible to solve, and nobody actually solved it. The explanation we gave for the difficulty was the following: “The information provided regarding the dimensions brings a square form to mind. The problem solver interprets the window to be a square 1 m high by 1 m wide, resting on one side. Furthermore, the problem states “without changing its shape,” intending geometric shape of the two windows (square, independently of the orientation of the window), while the problem solver interprets this as meaning the phenomenic shape of the two windows (two squares with the same orthogonal orientation)” ( Macchi and Bagassi, 2015 , p. 156). And this is where the difficulty of the problem lies, in the mental representation of the window and the concurrent interpretation of the text of the problem. Actually, spatial orientation is a decisive factor in the perception of forms. “Two identical shapes seen from different orientations take on a different phenomenic identity” ( Mach, 1914 ).

The solution is to be found in a square (geometric form) that “rests” on one of its angles, thus becoming a rhombus (phenomenic form). Now the dimensions given are those of the two diagonals of the represented rhombus (ABCD).

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Figure 1. The study window problem solution.

The “inverted” version of the problem gave less trouble:

[…] The owner decides to make it smaller and calls in a workman. He instructs the man to halve the area of the window […].

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Figure 2. The inverted version.

With this version, 30% of the participants solved the problem ( n = 30). They started from the representation of the orthogonal square (ABCD) and looked for the solution within the square, trying to respect the required height and width of the window, and inevitably changing the orientation of the internal square. This time the height and width are the diagonals, rather than the side (base and height) of the square.

Eventually, in another version (the “orientation” version) it was explicit that orientation was not a mandatory attribute of the shape, and this time 66% of the participants found the solution immediately ( n = 30). This confirms the hypothesis that an inappropriate representation of the relation between the orthogonal orientation of the square and its geometric shape is the origin of the misunderstanding .

The “orientation” version:

A study window measures 1 m in height and 1 m wide. The owner decides to make it smaller and calls in a workman. He instructs the man to halve the area of the window: the workman can change the orientation of the window, but not its shape and in such a way that it still measures one meter by one meter. The workman carries out the commission. How did he do it?

While with the Study window problem the subjects who do not arrive at the solution, and who are the totality, know they are wrong, with the problem we are now going to examine, the Ties problem, those who are wrong do not realize it at all and the solution they propose is experienced as the correct solution.

The Ties Problem ( Mosconi and D’Urso, 1974 )

Peter and John have the same number of ties.

Peter gives John five of his ties.

How many ties does John have now more than Peter?

We believe that the seemingly trivial problem is actually the result of the simultaneous activation and mutual interference of complex cognitive processes that prevent its solution.

The problem has been submitted to 50 undergraduate students of the Humanities Faculty of the University of Milano-Bicocca. The participants were tested individually and were randomly assigned to three groups: control version ( n = 50), experimental version 2 ( n = 20), and experimental version 3 ( n = 23). All groups were tested in Italian. Each participant was randomly assigned to one of the conditions and received a form containing only one version of the two assigned problems. There was no time limit. They were invited to think aloud and their spontaneous justifications were recorded and then transcribed.

The correct answer is obviously “ten,” but it must not be so obvious if it is given by only one third of the subjects (32%), while the remaining two thirds give the wrong answer “five,” which is so dominant.

If we consider the text of the problem from the point of view of the information explicitly transmitted ( said ), we have that it only theoretically provides the necessary information to reach the solution and precisely that: (a) the number of ties initially owned by P. and J. is equal, (b) P. gives J. five of his ties. However, the subjects are wrong. What emerges, however, from the spontaneous justifications given by the subjects who give the wrong answer is that they see only the increase of J. and not the consequent loss of P. by five ties. We report two typical justifications: “P. gives five of his to J., J. has five more ties than P., the five P. gave him” and also “They started from the same number of ties, so if P. gives J. five ties, J. should have five more than P.”

Slightly different from the previous ones is the following recurrent answer, in which the participants also consider the decrease of P. as well as the increase of J.: “I see five ties at stake, which are the ones that move,” or also “There are these five ties that go from one to the other, so one has five ties less and the other has five more,” reaching however the conclusion similar to the previous one that “J. has five ties more, because the other gave them to him.” 2

Almost always the participants who answer “five” use a numerical example to justify the answer given or to find a solution to the problem, after some unsuccessful attempts. It is paradoxical how many of these participants accept that the problem has two solutions, one “five ties” obtained by reasoning without considering a concrete number of initial ties, owned by P. and J., the other “ten ties” obtained by using a numerical example. So, for example, we read in the protocol of a participant who, after having answered “five more ties,” using a numerical example, finds “ten” of difference between the ties of P. and those of J.: “Well! I think the “five” is still more and more exact; for me this one has five more, period and that’s it.” “Making the concrete example: “ten” – he chases another subject on an abstract level. I would be more inclined to another formula, to five.”

About half of the subjects who give the answer “five,” in fact, at first refuse to answer because “we don’t know the initial number and therefore we can’t know how many ties J. has more than P.,” or at the most they answer: “J. has five ties more, P. five less, more we can’t know, because a data is missing.”

Even before this difficulty, so to speak, operational, the text of the problem is difficult because in it the quantity relative to the decrease of P. remains implicit (−5). The resulting misunderstanding is that if the quantity transferred is five ties, the resulting difference is only five ties: if the ties that P. gives to J. are five, how can J. have 10 ties more than P.?

So the difficulty of the problem lies in the discrepancy between the quantity transferred and the bidirectional effect that this quantity determines with its displacement. Resolving implies a restructuring of the sentence: “Peter gives John five of his ties (and therefore he loses five).” And this is precisely the reasoning carried out by those subjects who give the right answer “ten.”

We have therefore formulated a new version in which a pair of verbs should make explicit the loss of P.:

Peter loses five of his ties and John takes them.

However, the results obtained with this version, submitted to 20 other subjects, substantially confirm the results obtained with the original version: the correct answers are 17% (3/20) and the wrong ones 75% (15/20). From a Chi-square test (χ 2 = 2,088 p = 0.148) it results no significant difference between the two versions.

If we go to read the spontaneous justifications, we find that the subjects who give the answer “five” motivate it in a similar way to the subjects of the original version. So, for example: “P. loses five, J. gets them, so J. has five ties more than P.”

The decrease of P. is still not perceived, and the discrepancy between the lost amount of ties and the double effect that this quantity determines with its displacement persists.

Therefore, a new version has been realized in which the amount of ties lost by P. has nothing to do with J’s acquisition of five ties, the two amounts of ties are different and then they are perceived as decoupled, so as to neutralize the perceptual-conceptual factor underlying it.

Peter loses five of his ties and John buys five new ones.

It was submitted to 23 participants. Of them, 17 (74%) gave the answer “ten” and only 3 (13%) the answer “five.” There was a significant difference (χ 2 = 16,104 p = 0.000) between the results obtained using the present experimental version and the results from the control version. The participants who give the correct solution “ten” mostly motivate their answer as follows: “P. loses five and therefore J. has also those five that P. lost; he buys another five, there are ten,” declaring that he “added to the five that P. had lost the five that J. had bought.” The effectiveness of the experimental manipulation adopted is confirmed. 3

The satisfactory results obtained with this version cannot be attributed to the use of two different verbs, which proved to be ineffective (see version 2), but to the splitting, and consequent differentiation (J. has in addition five new ties), of the two quantities.

This time, the increase of J. and the decrease of P. are grasped as simultaneous and distinct and their combined effect is not identified with one or the other, but is equal to the sum of +5 and −5 in absolute terms.

The hypothesis regarding the effect of reformulation has also been confirmed in classical insight problems such as the Square and the Parallelogram ( Wertheimer, 1925 ), the Pigs in a Pen ( Schooler et al., 1993 ), the Bat & Ball ( Frederick, 2005 ) in recent studies ( Macchi and Bagassi, 2012 , 2015 ) which showed a dramatic increase in the number of solutions.

In their original version these problems are true brain teasers, and the majority of participants in these studies needed them to be reformulated in order to reach the solution. In Appendix B we present in detail the results obtained (see Table 1 ). Below we report, for each problem, the text of the original version in comparison with the reformulated experimental version.

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Table 1. Percentages of correct solutions with reformulated experimental versions.

Square and Parallelogram Problem ( Wertheimer, 1925 )

Given that AB = a and AG = b, find the sum of the areas of square ABCD and parallelogram EBGD ( Figures 3 , 4 ).

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Figure 3. The square and parallelogram problem.

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Figure 4. Solution.

Experimental Version

Given that AB = a and AG = b , find the sum of the areas of the two partially overlapping figures .

Pigs in a Pen Problem ( Schooler et al., 1993 )

Nine pigs are kept in a square pen . Build two more square enclosures that would put each pig in a pen by itself ( Figures 5 , 6 ).

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Figure 5. The pigs in a pen problem.

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Figure 6. Solution.

Nine pigs are kept in a square pen. Build two more squares that would put each pig in a by itself .

Bat and Ball Problem ( Frederick, 2005 )

A bat and a ball cost $1.10 in total. The bat costs $ 1.00 more than the ball. How much does the ball cost? ___cents.

A bat and a ball cost $1.10 in total. The bat costs $ 1.00 more than the ball. Find the cost of the bat and of the ball .

Once the problem knots that alter the aim of the task have been identified, the reformulation technique can be a valid didactic tool, as it allows to reveal the misunderstanding and to eliminate it without changing the mathematical nature of the problem. The training to creativity would consist in this sense in training to have interpretative keys different from the usual, when the difficulty cannot be addressed through computational techniques.

Closing Thoughts

By identifying the misunderstanding in problem solving, the reformulation technique has made it possible to eliminate the problem knots, without changing the mathematical nature of the problem. With the experimental reformulated versions of paradigmatic problems, both apparent trivial tasks or brain teasers have obtained a significant increase in correct answers.

Studying how an insight problem is formed, and not just how it is solved, may well become an important topic in education. We focus on undergraduate students’ strategies and their errors while solving problems, and the specific cognitive processes involved in misunderstanding, which are crucial to better exploit what could be beneficial to reach the solution and to teach how to improve the ability to solve problems.

Without violating the need for the necessary rigor of a demonstration, for example, it is possible to organize the problem-demonstration discourse according to a different criterion, precisely by favoring the psychological needs of the subject to whom the explanation discourse is addressed, taking care to organize the explanation with regard to the way his mind works, to what can favor its comprehension and facilitate its memory.

On the other hand, one of the criteria traditionally followed by mathematicians in constructing, for example, demonstrations, or at least in explaining them, is to never make any statement that is not supported by the elements provided above. In essence, in the course of the demonstration nothing is anticipated, and indeed it happens frequently that the propositions directly relevant and relevant to the development of the reasoning (for example, the steps of a geometric demonstration) are preceded by digressions intended to introduce and deal with the elements that legitimize them. As a consequence of such an expositive formalism, the recipient of the speech (the student) often finds himself in the situation of being led to the final conclusion a bit like a blind man who, even though he knows the goal, does not see the way, but can only control step by step the road he is walking along and with difficulty becomes aware of the itinerary.

The text of every problem, if formulated in natural language, has a psychorhetoric dimension, in the sense that in every speech, that is in the production and reception of every speech, there are aspects related to the way the mind works – and therefore psychological and rhetorical – that are decisive for comprehensibility, expressive adequacy and communicative effectiveness. It is precisely to these aspects that we refer to when we talk about the psychorhetoric dimension. Rhetoric, from the point of view of the broadcaster, has studied discourse in relation to the recipient, and therefore to its acceptability, comprehensibility and effectiveness, so that we can say that rhetoric has studied discourse “psychologically.”

Adopting this perspective, the commonplace that the rhetorical dimension only concerns the common discourse, i.e., the discourse that concerns debatable issues, and not the scientific discourse (logical-mathematical-demonstrative), which would be exempt from it, is falling away. The matter dealt with, the truth of what is actually said, is not sufficient to guarantee comprehension.

Data Availability Statement

The datasets generated for this study are available on request to the corresponding author.

Ethics Statement

Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.

Author Contributions

LM and MB devised the project, developed the theory, carried out the experiment and wrote the manuscript. Both authors contributed to the article and approved the submitted version.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

  • ^ The theoretical framework assumed here is Paul Grice’s theory of communication (1975) based on the existence in communication of the explicit layer ( said ) and of the implicit ( implied ), so that the recognition of the communicative intention of the speaker by the interlocutor is crucial for comprehension.
  • ^ A participant who after having given the solution “five” corrects himself in “ten” explains the first answer as follows: “it is more immediate, in my opinion, to see the real five ties that are moved, because they are five things that are moved; then as a more immediate answer is ‘five,’ because it is something more real, less mathematical.”
  • ^ The factor indicated is certainly the main responsible for the answer “five,” but not the only one (see the Appendix for a pragmatic analysis of the text).
  • ^ Versions and results of the problems exposed are already published in Macchi e Bagassi 2012, 2014, 2015.

Bagassi, M., and Macchi, L. (2006). Pragmatic approach to decision making under uncertainty: the case of the disjunction effect. Think. Reason. 12, 329–350. doi: 10.1080/13546780500375663

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Pragmatic analysis of the problematic loci of the Ties problem, which emerged from the spontaneous verbalizations of the participants:

- “the same number of ties”

This expression is understood as a neutral information, a kind of base or sliding plane on which the transfer of the five ties takes place and, in fact, these subjects motivate their answer “five” with: “there is this transfer of five ties from P. to J. ….”

- “5 more, 5 less”

We frequently resort to similar expressions in situations where, if I have five units more than another, the other has five less than me and the difference between us is five.

Consider, for example, the case of the years: say that J. is five years older than P. means to say that P. is five years younger than J. and that the difference in years between the two is five, not ten.

In comparisons, we evaluate the difference with something used as a term of reference, for example the age of P., which serves as a basis, the benchmark, precisely.

- “he gives”

The verb “to give” conveys the concept of the growth of the recipient, not the decrease of the giver, therefore, contributes to the crystallization of the “same number,” preventing to grasp the decrease of P.

Appendix B 4

Given that AB = a and AG = b, find the sum of the areas of square ABCD and parallelogram EBGD .

Typically, problem solvers find the problem difficult and fail to see that a is also the altitude of parallelogram EBGD. They tend to calculate its area with onerous and futile methods, while the solution can be reached with a smart method, consisting of restructuring the entire given shape into two partially overlapping triangles ABG and ECD. The sum of their areas is 2 x a b /2 = a b . Moreover, by shifting one of the triangles so that DE coincides with GB, the answer is “ a b ,” which is the area of the resultant rectangle. Referring to a square and a parallelogram fixes a favored interpretation of the perceptive stimuli, according to those principles of perceptive organization thoroughly studied by the Gestalt Theory. It firmly sets the calculation of the area on the sum of the two specific shapes dealt with in the text, while, the problem actually requires calculation of the area of the shape, however organized, as the sum of two triangles rectangles, or the area of only one rectangle, as well as the sum of square and parallelogram. Hence, the process of restructuring is quite difficult.

To test our hypotheses we formulated an experimental version:

In this formulation of the problem, the text does not impose constraints on the interpretation/organization of the figure, and the spontaneous, default interpretation is no longer fixed. Instead of asking for “the areas of square and parallelogram,” the problem asks for the areas of “the two partially overlapping figures.” We predicted that the experimental version would allow the subjects to see and consider the two triangles also.

Actually, we found that 80% of the participants (28 out of 35) gave a correct answer, and most of them (21 out of 28) gave the smart “two triangles” solution. In the control version, on the other hand, only 19% (9 out of 47) gave the correct response, and of these only two gave the “two triangles” solution.

The findings were replicated in the “Pigs in a pen” problem:

Nine pigs are kept in a square pen . Build two more square enclosures that would put each pig in a pen by itself.

The difficulty of this problem lies in the interpretation of the request, nine pigs each individually enclosed in a square pen, having only two more square enclosures. This interpretation is supported by the favored, orthogonal reference scheme, with which we represent the square. This privileged organization, according to our hypothesis, is fixed by the text which transmits the implicature that the pens in which the piglets are individually isolated must be square in shape too. The function of enclosure wrongfully implies the concept of a square. The task, on the contrary, only requires to pen each pig.

Once again, we created an experimental version by reformulating the problem, eliminating the word “enclosure” and the phrase “in a pen.” The implicit inference that the pen is necessarily square is not drawn.

The experimental version yielded 87% correct answers (20 out of 23), while the control version yielded only 38% correct answers (8 out of 25).

The formulation of the experimental versions was more relevant to the aim of the task, and allowed the perceptual stimuli to be interpreted in accordance with the solution.

The relevance of text and the re-interpretation of perceptual stimuli, goal oriented to the aim of the task, were worked out in unison in an interrelated interpretative “game.”

We further investigated the interpretative activity of thinking, by studying the “Bat and ball” problem, which is part of the CRT. Correct performance is usually considered to be evidence of reflective cognitive ability (correlated with high IQ scores), versus intuitive, erroneous answers to the problem ( Frederick, 2005 ).

Bat and Ball problem

A bat and a ball cost $1.10 in total. The bat costs $ 1.00 more than the ball. How much does the ball cost?___cents

Of course the answer which immediately comes to mind is 10 cents, which is incorrect as, in this case, the difference between $ 1.00 and 10 cents is only 90 cents, not $1.00 as the problem stipulates. The correct response is 5 cents.

Number physiognomics and the plausibility of the cost are traditionally considered responsible for this kind of error ( Frederick, 2005 ; Kahneman, 2003 ).

These factors aside, we argue that if the rhetoric structure of the text is analyzed, the question as formulated concerns only the ball, implying that the cost of the bat is already known. The question gives the key to the interpretation of what has been said in each problem and, generally speaking, in every discourse. Given data, therefore, is interpreted in the light of the question. Hence, “The bat costs $ 1.00 more than” becomes “The bat costs $ 1.00,” by leaving out “more than.”

According to our hypothesis, independently of the different cognitive styles, erroneous responses could be the effect of the rhetorical structure of the text, where the question is not adequate to the aim of the task. Consequently, we predicted that if the question were to be reformulated to become more relevant, the subjects would find it easier to grasp the correct response. In the light of our perspective, the cognitive abilities involved in the correct response were also reinterpreted. Consequently, we reformulated the text as follows in order to eliminate this misleading inference:

This time we predicted an increase in the number of correct answers. The difference in the percentages of correct solutions was significant: in the experimental version 90% of the participants gave a correct answer (28 out of 31), and only 10% (2 out of 20) answered correctly in the control condition.

The simple reformulation of the question, which expresses the real aim of the task (to find the cost of both items), does not favor the “short circuit” of considering the cost of the bat as already known (“$1,” by leaving out part of the phrase “more than”).

It still remains to be verified if those subjects who gave the correct response in the control version have a higher level of cognitive reflexive ability compared to the “intuitive” respondents. This has been the general interpretation given in the literature to the difference in performance.

We think it is a matter of a particular kind of reflexive ability, due to which the task is interpreted in the light of the context and not abstracting from it. The difficulty which the problem implicates does not so much involve a high level of abstract reasoning ability as high levels of pragmatic competence, which disambiguates the text. So much so that, intervening only on the pragmatic level, keeping numbers physiognomics and maintaining the plausible costs identical, the problem becomes a trivial arithmetical task.

Keywords : creative problem solving, insight, misunderstanding, pragmatics, language and thought

Citation: Bagassi M and Macchi L (2020) Creative Problem Solving as Overcoming a Misunderstanding. Front. Educ. 5:538202. doi: 10.3389/feduc.2020.538202

Received: 26 February 2020; Accepted: 29 October 2020; Published: 03 December 2020.

Reviewed by:

Copyright © 2020 Bagassi and Macchi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Laura Macchi, [email protected]

This article is part of the Research Topic

Psychology and Mathematics Education

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A Cognitive Trick for Solving Problems Creatively

  • Theodore Scaltsas

creative problem solving article

Mental biases can actually help.

Many experts argue that creative thinking requires people to challenge their preconceptions and assumptions about the way the world works. One common claim, for example, is that the mental shortcuts we all rely on to solve problems get in the way of creative thinking. How can you innovate if your thinking is anchored in past experience?

  • TS Theodore Scaltsas is a Chaired Professor in Classical Philosophy at the University of Edinburgh in Scotland.

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How to Be a More Creative Problem-Solver at Work: 8 Tips

Business professionals using creative problem-solving at work

  • 01 Mar 2022

The importance of creativity in the workplace—particularly when problem-solving—is undeniable. Business leaders can’t approach new problems with old solutions and expect the same result.

This is where innovation-based processes need to guide problem-solving. Here’s an overview of what creative problem-solving is, along with tips on how to use it in conjunction with design thinking.

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What Is Creative Problem-Solving?

Encountering problems with no clear cause can be frustrating. This occurs when there’s disagreement around a defined problem or research yields unclear results. In such situations, creative problem-solving helps develop solutions, despite a lack of clarity.

While creative problem-solving is less structured than other forms of innovation, it encourages exploring open-ended ideas and shifting perspectives—thereby fostering innovation and easier adaptation in the workplace. It also works best when paired with other innovation-based processes, such as design thinking .

Creative Problem-Solving and Design Thinking

Design thinking is a solutions-based mentality that encourages innovation and problem-solving. It’s guided by an iterative process that Harvard Business School Dean Srikant Datar outlines in four stages in the online course Design Thinking and Innovation :

The four stages of design thinking: clarify, ideate, develop, and implement

  • Clarify: This stage involves researching a problem through empathic observation and insights.
  • Ideate: This stage focuses on generating ideas and asking open-ended questions based on observations made during the clarification stage.
  • Develop: The development stage involves exploring possible solutions based on the ideas you generate. Experimentation and prototyping are both encouraged.
  • Implement: The final stage is a culmination of the previous three. It involves finalizing a solution’s development and communicating its value to stakeholders.

Although user research is an essential first step in the design thinking process, there are times when it can’t identify a problem’s root cause. Creative problem-solving addresses this challenge by promoting the development of new perspectives.

Leveraging tools like design thinking and creativity at work can further your problem-solving abilities. Here are eight tips for doing so.

Design Thinking and Innovation | Uncover creative solutions to your business problems | Learn More

8 Creative Problem-Solving Tips

1. empathize with your audience.

A fundamental practice of design thinking’s clarify stage is empathy. Understanding your target audience can help you find creative and relevant solutions for their pain points through observing them and asking questions.

Practice empathy by paying attention to others’ needs and avoiding personal comparisons. The more you understand your audience, the more effective your solutions will be.

2. Reframe Problems as Questions

If a problem is difficult to define, reframe it as a question rather than a statement. For example, instead of saying, "The problem is," try framing around a question like, "How might we?" Think creatively by shifting your focus from the problem to potential solutions.

Consider this hypothetical case study: You’re the owner of a local coffee shop trying to fill your tip jar. Approaching the situation with a problem-focused mindset frames this as: "We need to find a way to get customers to tip more." If you reframe this as a question, however, you can explore: "How might we make it easier for customers to tip?" When you shift your focus from the shop to the customer, you empathize with your audience. You can take this train of thought one step further and consider questions such as: "How might we provide a tipping method for customers who don't carry cash?"

Whether you work at a coffee shop, a startup, or a Fortune 500 company, reframing can help surface creative solutions to problems that are difficult to define.

3. Defer Judgment of Ideas

If you encounter an idea that seems outlandish or unreasonable, a natural response would be to reject it. This instant judgment impedes creativity. Even if ideas seem implausible, they can play a huge part in ideation. It's important to permit the exploration of original ideas.

While judgment can be perceived as negative, it’s crucial to avoid accepting ideas too quickly. If you love an idea, don’t immediately pursue it. Give equal consideration to each proposal and build on different concepts instead of acting on them immediately.

4. Overcome Cognitive Fixedness

Cognitive fixedness is a state of mind that prevents you from recognizing a situation’s alternative solutions or interpretations instead of considering every situation through the lens of past experiences.

Although it's efficient in the short-term, cognitive fixedness interferes with creative thinking because it prevents you from approaching situations unbiased. It's important to be aware of this tendency so you can avoid it.

5. Balance Divergent and Convergent Thinking

One of the key principles of creative problem-solving is the balance of divergent and convergent thinking. Divergent thinking is the process of brainstorming multiple ideas without limitation; open-ended creativity is encouraged. It’s an effective tool for generating ideas, but not every idea can be explored. Divergent thinking eventually needs to be grounded in reality.

Convergent thinking, on the other hand, is the process of narrowing ideas down into a few options. While converging ideas too quickly stifles creativity, it’s an important step that bridges the gap between ideation and development. It's important to strike a healthy balance between both to allow for the ideation and exploration of creative ideas.

6. Use Creative Tools

Using creative tools is another way to foster innovation. Without a clear cause for a problem, such tools can help you avoid cognitive fixedness and abrupt decision-making. Here are several examples:

Problem Stories

Creating a problem story requires identifying undesired phenomena (UDP) and taking note of events that precede and result from them. The goal is to reframe the situations to visualize their cause and effect.

To start, identify a UDP. Then, discover what events led to it. Observe and ask questions of your consumer base to determine the UDP’s cause.

Next, identify why the UDP is a problem. What effect does the UDP have that necessitates changing the status quo? It's helpful to visualize each event in boxes adjacent to one another when answering such questions.

The problem story can be extended in either direction, as long as there are additional cause-and-effect relationships. Once complete, focus on breaking the chains connecting two subsequent events by disrupting the cause-and-effect relationship between them.

Alternate Worlds

The alternate worlds tool encourages you to consider how people from different backgrounds would approach similar situations. For instance, how would someone in hospitality versus manufacturing approach the same problem? This tool isn't intended to instantly solve problems but, rather, to encourage idea generation and creativity.

7. Use Positive Language

It's vital to maintain a positive mindset when problem-solving and avoid negative words that interfere with creativity. Positive language prevents quick judgments and overcomes cognitive fixedness. Instead of "no, but," use words like "yes, and."

Positive language makes others feel heard and valued rather than shut down. This practice doesn’t necessitate agreeing with every idea but instead approaching each from a positive perspective.

Using “yes, and” as a tool for further idea exploration is also effective. If someone presents an idea, build upon it using “yes, and.” What additional features could improve it? How could it benefit consumers beyond its intended purpose?

While it may not seem essential, this small adjustment can make a big difference in encouraging creativity.

8. Practice Design Thinking

Practicing design thinking can make you a more creative problem-solver. While commonly associated with the workplace, adopting a design thinking mentality can also improve your everyday life. Here are several ways you can practice design thinking:

  • Learn from others: There are many examples of design thinking in business . Review case studies to learn from others’ successes, research problems companies haven't addressed, and consider alternative solutions using the design thinking process.
  • Approach everyday problems with a design thinking mentality: One of the best ways to practice design thinking is to apply it to your daily life. Approach everyday problems using design thinking’s four-stage framework to uncover what solutions it yields.
  • Study design thinking: While learning design thinking independently is a great place to start, taking an online course can offer more insight and practical experience. The right course can teach you important skills , increase your marketability, and provide valuable networking opportunities.

Which HBS Online Entrepreneurship and Innovation Course is Right for You? | Download Your Free Flowchart

Ready to Become a Creative Problem-Solver?

Though creativity comes naturally to some, it's an acquired skill for many. Regardless of which category you're in, improving your ability to innovate is a valuable endeavor. Whether you want to bolster your creativity or expand your professional skill set, taking an innovation-based course can enhance your problem-solving.

If you're ready to become a more creative problem-solver, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses . If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

creative problem solving article

About the Author

Principles of Creative Problem Solving in AI Systems

Ana-Maria Oltețeanu: Cognition and Creative Machine: Cognitive AI for Creative Problem Solving. Freie Universität Berlin, Berlin, Germany, Springer, Cham, 2020 (Online ISBN: 978–3-030–30322-8), 282 pages, price: €117.69 (eBook), DOI: https://doi.org/10.1007/978–3-030–30322-8

  • Book Review
  • Published: 24 August 2021
  • Volume 31 , pages 555–557, ( 2022 )

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  • Zhihui Chen 1 &
  • Ruixing Ye 1  

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The utilization of Artificial Intelligence (AI) is springing up through all spheres of human activities due to the current global pandemic (COVID-19), which has limited human interactions in our societies and the corporate world. Undoubtedly, AI has innovatively transformed our ways of living and understanding how mechanical systems work on problem solving as or even beyond human beings. The core issues of this book include the following issues: (1) understanding the working mechanism of the human mind on problem solving, and (2) exploring what it means to be computationally creative and how it can be evaluated. By having an overview of the development of AI and Cognitive Science and rebranding the strands of creativity and problem solving, Dr. Ana-Maria Oltețeanu attempts to build cognitive systems, which propose a type of knowledge organization and a small set of processes aimed at solving a diverse number of creative problems. Furthermore, with the help of the defined framework, the relevant computational system is implemented and evaluated by investigating the classical and insight problem solving performance.

Part I of this book includes the previous four chapters, which introduces a series of theories such as creativity (p.11), insight (p.16), and visuospatial intelligence (p.20) to illustrate the necessary process and structure of creative problem solving. The author concludes from the relevant literature that the interplay between knowledge representations and organization processes would play an important role in searching for solutions. For better illustration and understanding, a selection of computational creativity systems is presented, such as AM, HR, Aaron, the Painting fool, Poetry systems, and BACON (p.34–37). Subsequently, from a methodological perspective, Dr. Oltețeanu introduces two different creativity evaluations for human beings and computational machines respectively. On the one hand, when measuring creativity of human, the thinking characteristics of the participants such as divergent thinking (the ability to diverge from subjectively familiar uses and think of other uses) and creative thinking are the primary objective for measurement in some of the most important empirical models. On the other hand, when assessing the creativity in the computational systems, various models of evaluating the behaviors or programs of creative systems are proposed mainly in terms of typicality, quality, and novelty.

In the second part, which comprises chapter 5 th to 8 th , the author develops a cognitive framework to explore how a diverse set of creative problem solving tasks can be solved computationally using a unified set of principles. To facilitate the understanding of insight and creative problem solving, Dr. Oltețeanu puts forward a metaphor, in which representations are seen as cogs in a creative machine and problem solving processes are regarded as clockwork, to view the relationship between creative processes and knowledge (p.69). Building on this idea, a theoretical framework (named as CreaCogs) is proposed based on encoding knowledge, which permits processes of fast and informed search and construction, for creative problem solving. These processes take place conceptually at three levels involving Feature Spaces, Concepts, and Problem Templates (p.91–94). Firstly, whenever an object encoded symbolically is observed, its sensors will be enrolled in the sub-symbolical level of feature maps and spaces. Then, in the following level, various known concepts are grounded in a distributed manner in organized feature spaces, and their names are encoded in a different name tag mapped for functionally constituting another feature. Lastly in the highest level, problem templates are structured representations, which are encoded over multiple concepts, their relations, and the affordance they provide. On the basis of the steps above, an integration of a wide set of principles in the framework would be accessible.

Part III, which forms chapter 9 th to 12 th , mainly focuses on applying the CreaCogs in a set of practical cognitive system cases, and developing a set of tools through which the performance of such systems could be evaluated. It is worth noticing that several evaluation tests of creativity are introduced to illustrate about how to apply implementation of the framework built above. In the preamble of this part, the CreaCogs mechanism of Remote Associates creativity Test (RAT) and Alternative Uses Test (AUT) are explored to develop the corresponding computational systems to solve these test tasks. Based on the practice of implementation and investigation, Dr. Oltețeanu analyzes how to evaluate the performance of the artificial cognitive prototype systems by solving different creativity tasks via inference mechanism or matching algorithm from CreaCogs. The book ends with an overview of the journey of exploring the creative problem solving and an outlook of the relevant experimental work.

Overall, the author provides a revolutionary academic framework to understand the theoretical and empirical cognitive processes involved in creative problem solving by computational systems. Various evaluation of creativity tests and tasks are drawn to illustrate how the cognitive framework works to find solutions of classical or even insight problems, which are stressed in the 2012 paper by Batchelder and Alexander (Insight problem solving: A critical examination of the possibility of formal theory, in The Journal of Problem Solving ), as the alternative productive representations are necessary to overcome the failures of discovering solutions. Besides, it is deep insight when the author describes the cognitive models of creativity through using a variety of schematic diagrams and pictures in this book. That is rather helpful to illustrate how insight and creative problem solving can be viewed as processes of memory management, with both associationist and gestaltic (template pattern-filling) underpinnings, and with processes of recasting and restructuring using from the memory and the environment. From the theoretical matters to the variate practical domains, Dr. Oltețeanu constructs the cognitive systems on the basis of the CreaCogs and develops a set of tools through which the performance of such systems can be evaluated similarly to that of human participants. In short, the theoretical framework and empirical computational exploration contribute to creating the imagination of the efficacy of AI in the area of creative problem solving.

However, the critical issue of the possibility of developing self-adaptive learning by the creative systems has not been further discussed yet. To quote the annotation in the fields of behavioral psychology and cognitive psychology, self-adaptive learning in AI refers to human’s self-adapted learning methods and the habitual condition information processing systems, which forms a method that AI can solve theories and problems independently through discovering and summarizing in operations. Due to emphasizing to develop a framework for analyzing the creative problem solving, the author focuses on introducing the value, mechanism, application, and evaluation of the computational system based on the CreaCogs that is why the issue of self-adaptive learning has rarely been taken into account for now. In summary, this book enhances our understanding of the principles of problem solving in the epoch of AI and deserves to be widely read in this age of intelligent machines. The CreaCogs cognitive framework proposed here could be served as an applicable guide for graduate students and researchers in the sphere of Cognitive Science, AI, and Education.

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Chen, Z., Ye, R. Principles of Creative Problem Solving in AI Systems. Sci & Educ 31 , 555–557 (2022). https://doi.org/10.1007/s11191-021-00270-7

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Principles of Creative Problem Solving in AI Systems

Zhihui chen.

School of Education, South China Normal University, 55 E Zhongshan Ave, Guangzhou, 510631 China

The utilization of Artificial Intelligence (AI) is springing up through all spheres of human activities due to the current global pandemic (COVID-19), which has limited human interactions in our societies and the corporate world. Undoubtedly, AI has innovatively transformed our ways of living and understanding how mechanical systems work on problem solving as or even beyond human beings. The core issues of this book include the following issues: (1) understanding the working mechanism of the human mind on problem solving, and (2) exploring what it means to be computationally creative and how it can be evaluated. By having an overview of the development of AI and Cognitive Science and rebranding the strands of creativity and problem solving, Dr. Ana-Maria Oltețeanu attempts to build cognitive systems, which propose a type of knowledge organization and a small set of processes aimed at solving a diverse number of creative problems. Furthermore, with the help of the defined framework, the relevant computational system is implemented and evaluated by investigating the classical and insight problem solving performance.

Part I of this book includes the previous four chapters, which introduces a series of theories such as creativity (p.11), insight (p.16), and visuospatial intelligence (p.20) to illustrate the necessary process and structure of creative problem solving. The author concludes from the relevant literature that the interplay between knowledge representations and organization processes would play an important role in searching for solutions. For better illustration and understanding, a selection of computational creativity systems is presented, such as AM, HR, Aaron, the Painting fool, Poetry systems, and BACON (p.34–37). Subsequently, from a methodological perspective, Dr. Oltețeanu introduces two different creativity evaluations for human beings and computational machines respectively. On the one hand, when measuring creativity of human, the thinking characteristics of the participants such as divergent thinking (the ability to diverge from subjectively familiar uses and think of other uses) and creative thinking are the primary objective for measurement in some of the most important empirical models. On the other hand, when assessing the creativity in the computational systems, various models of evaluating the behaviors or programs of creative systems are proposed mainly in terms of typicality, quality, and novelty.

In the second part, which comprises chapter 5 th to 8 th , the author develops a cognitive framework to explore how a diverse set of creative problem solving tasks can be solved computationally using a unified set of principles. To facilitate the understanding of insight and creative problem solving, Dr. Oltețeanu puts forward a metaphor, in which representations are seen as cogs in a creative machine and problem solving processes are regarded as clockwork, to view the relationship between creative processes and knowledge (p.69). Building on this idea, a theoretical framework (named as CreaCogs) is proposed based on encoding knowledge, which permits processes of fast and informed search and construction, for creative problem solving. These processes take place conceptually at three levels involving Feature Spaces, Concepts, and Problem Templates (p.91–94). Firstly, whenever an object encoded symbolically is observed, its sensors will be enrolled in the sub-symbolical level of feature maps and spaces. Then, in the following level, various known concepts are grounded in a distributed manner in organized feature spaces, and their names are encoded in a different name tag mapped for functionally constituting another feature. Lastly in the highest level, problem templates are structured representations, which are encoded over multiple concepts, their relations, and the affordance they provide. On the basis of the steps above, an integration of a wide set of principles in the framework would be accessible.

Part III, which forms chapter 9 th to 12 th , mainly focuses on applying the CreaCogs in a set of practical cognitive system cases, and developing a set of tools through which the performance of such systems could be evaluated. It is worth noticing that several evaluation tests of creativity are introduced to illustrate about how to apply implementation of the framework built above. In the preamble of this part, the CreaCogs mechanism of Remote Associates creativity Test (RAT) and Alternative Uses Test (AUT) are explored to develop the corresponding computational systems to solve these test tasks. Based on the practice of implementation and investigation, Dr. Oltețeanu analyzes how to evaluate the performance of the artificial cognitive prototype systems by solving different creativity tasks via inference mechanism or matching algorithm from CreaCogs. The book ends with an overview of the journey of exploring the creative problem solving and an outlook of the relevant experimental work.

Overall, the author provides a revolutionary academic framework to understand the theoretical and empirical cognitive processes involved in creative problem solving by computational systems. Various evaluation of creativity tests and tasks are drawn to illustrate how the cognitive framework works to find solutions of classical or even insight problems, which are stressed in the 2012 paper by Batchelder and Alexander (Insight problem solving: A critical examination of the possibility of formal theory, in The Journal of Problem Solving ), as the alternative productive representations are necessary to overcome the failures of discovering solutions. Besides, it is deep insight when the author describes the cognitive models of creativity through using a variety of schematic diagrams and pictures in this book. That is rather helpful to illustrate how insight and creative problem solving can be viewed as processes of memory management, with both associationist and gestaltic (template pattern-filling) underpinnings, and with processes of recasting and restructuring using from the memory and the environment. From the theoretical matters to the variate practical domains, Dr. Oltețeanu constructs the cognitive systems on the basis of the CreaCogs and develops a set of tools through which the performance of such systems can be evaluated similarly to that of human participants. In short, the theoretical framework and empirical computational exploration contribute to creating the imagination of the efficacy of AI in the area of creative problem solving.

However, the critical issue of the possibility of developing self-adaptive learning by the creative systems has not been further discussed yet. To quote the annotation in the fields of behavioral psychology and cognitive psychology, self-adaptive learning in AI refers to human’s self-adapted learning methods and the habitual condition information processing systems, which forms a method that AI can solve theories and problems independently through discovering and summarizing in operations. Due to emphasizing to develop a framework for analyzing the creative problem solving, the author focuses on introducing the value, mechanism, application, and evaluation of the computational system based on the CreaCogs that is why the issue of self-adaptive learning has rarely been taken into account for now. In summary, this book enhances our understanding of the principles of problem solving in the epoch of AI and deserves to be widely read in this age of intelligent machines. The CreaCogs cognitive framework proposed here could be served as an applicable guide for graduate students and researchers in the sphere of Cognitive Science, AI, and Education.

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There is no conflict of interest.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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  1. What Is Creative Problem-Solving & Why Is It Important?

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    Specifically, creativity often involves coordination between the cognitive control network, which is involved in executive functions such as planning and problem-solving, and the default mode network, which is most active during mind-wandering or daydreaming (Beaty, R. E., et al., Cerebral Cortex, Vol. 31, No. 10, 2021).

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    CPS is a comprehensive system built on our own natural thinking processes that deliberately ignites creative thinking and produces innovative solutions. Through alternating phases of divergent and convergent thinking, CPS provides a process for managing thinking and action, while avoiding premature or inappropriate judgment. It is built upon a ...

  5. Developing Creative Potential: The Power of Process, People, and Place

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  6. Design Thinking: A Creative Approach to Problem Solving

    Abstract. Design thinking—understanding the human needs related to a problem, reframing the problem in human-centric ways, creating many ideas in brainstorming sessions, and adopting a hands-on approach to prototyping and testing—offers a complementary approach to the rational problem-solving methods typically emphasized in business schools.

  7. Creative Problem Solving as Overcoming a Misunderstanding

    Solving or attempting to solve problems is the typical and, hence, general function of thought. A theory of problem solving must first explain how the problem is constituted, and then how the solution happens, but also how it happens that it is not solved; it must explain the correct answer and with the same means the failure. The identification of the way in which the problem is formatted ...

  8. Creative Problem-Solving

    Humans are innate creative problem-solvers. Since early humans developed the first stone tools to crack open fruit and nuts more than 2 million years ago, the application of creative thinking to solve problems has been a distinct competitive advantage for our species (Puccio 2017).Originally used to solve problems related to survival, the tendency toward the use of creative problem-solving to ...

  9. A Cognitive Trick for Solving Problems Creatively

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  11. Creative Problem Solving: Out-of-the-box Solutions to Everyday Problems

    Udemy Editor. Creative problem solving is a technique to approach a problem or address a challenge in an imaginative way; it helps us flex our minds, find path-breaking ideas and take suitable actions thereafter. Often we come across a dead-end while trying to solve a problem at workplace or home; either our understanding of the issue is wrong ...

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    In addition to strategy use, the motivational component of perceived self-efficacy was the strongest predictor of students' creative problem-solving. To conclude these seven excellent and worth reading research articles, we can say that there are two general ways to promote learning and problem solving.

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    Working on a creative science project may help developing students' creative abilities, and the interaction between teacher and students during the work on defining a problem and solving the problem, is an ideal forum for supporting students' creativity. Purpose .

  15. Enhancement of Creative Thinking Skills Using a Cognitive-Based

    Impact of the Training on Creative Performance. The effectiveness of the training was scientifically tested by means of a pre- and post-test, employing creativity measures that relied on divergent thinking (the "Divergent Thinking: the AUT" section), convergent thinking (the "Convergent Thinking: the RAT" section), and creative problem solving skills (the "Creative Problem Solving ...

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  18. How To Kickstart Creative Problem Solving

    My research focuses on how anxiety harms performance, but it can also kill your creativity. As the saying goes, work smarter - not harder. Instead of mentally preparing yourself to endure a ...

  19. Principles of Creative Problem Solving in AI Systems

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  20. Mind wandering in creative problem-solving: Relationships with

    Mind wandering may improve creative problem solving; however, it could also lead to negative moods and poor mental health. It has also been shown that some forms of mental illness are positively related to creativity. However, the three factors of mind wandering, divergent thinking, and mental health have not been examined simultaneously, so it ...

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  24. Boost Creative Problem Solving with Team Collaboration

    Creative problem solving is an invaluable skill that thrives on diverse perspectives and knowledge. If you're looking to enhance this skill through interdisciplinary collaboration, you're on the ...

  25. The Alexander Company: Resourceful, creative spirit

    In the property development and historic renovation business, innovation and complex problem-solving skills are prized, and The Alexander Company meets the challenge by giving its employees freedom to make decisions. ... "Overcoming these obstacles requires an environment that naturally cultivates and nourishes new ideas and creative ...