problem solving journal articles

ORIGINAL RESEARCH article

Creative problem solving as overcoming a misunderstanding.

• 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).

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 […].

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.

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 ).

Figure 3. The square and parallelogram problem.

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 ).

Figure 5. The pigs in a pen problem.

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.

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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]

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To Solve a Tough Problem, Reframe It

Five steps to ensure that you don’t jump to solutions by Julia Binder and Michael D. Watkins

Summary .   

Research shows that companies devote too little effort to examining problems before trying to solve them. By jumping immediately into problem-solving, teams limit their ability to design innovative solutions.

The authors recommend that companies spend more time up front on problem-framing, a process for understanding and defining a problem. Exploring different frames is like looking at a scene through various camera lenses while adjusting your angle, aperture, and focus. A wide-angle lens gives you a very different photo from that taken with a telephoto lens, and shifting your angle and depth of focus yields distinct images. Effective problem-framing is similar: Looking at a problem from a variety of perspectives helps you uncover new insights and generate fresh ideas.

This article introduces a five-phase approach to problem-framing: In the expand phase, the team identifies all aspects of a problem; in examine, it dives into root causes; in empathize, it considers key stakeholders’ perspectives; in elevate, it puts the problem into a broader context; and in envision, it creates a road map toward the desired outcome.

When business leaders confront complex problems, there’s a powerful impulse to dive right into “solving” mode: You gather a team and then identify potential solutions. That’s fine for challenges you’ve faced before or when proven methods yield good results. But what happens when a new type of problem arises or aspects of a familiar one shift substantially? Or if you’re not exactly sure what the problem is?

Research conducted by us and others shows that leaders and their teams devote too little effort to examining and defining problems before trying to solve them. A study by Paul Nutt of Ohio State University, for example, looked at 350 decision-making processes at medium to large companies and found that more than half failed to achieve desired results, often because perceived time pressure caused people to pay insufficient attention to examining problems from all angles and exploring their complexities. By jumping immediately into problem-solving, teams limit their ability to design innovative and durable solutions.

When we work with organizations and teams, we encourage them to spend more time up front on problem-framing, a process for understanding and defining a problem. Exploring frames is like looking at a scene through various camera lenses while adjusting your angle, aperture, and focus. A wide-angle lens will give you a very different photo from that taken with a telephoto lens, and shifting your angle and depth of focus yields distinct images. Effective problem-framing is similar: Looking at a problem from a variety of perspectives lets you uncover new insights and generate fresh ideas.

As with all essential processes, it helps to have a methodology and a road map. This article introduces the E5 approach to problem-framing—expand, examine, empathize, elevate, and envision—and offers tools that enable leaders to fully explore the problem space.

Phase 1: Expand

In the first phase, set aside preconceptions and open your mind. We recommend using a tool called frame-storming, which encourages a comprehensive exploration of an issue and its nuances. It is a neglected precursor to brainstorming, which typically focuses on generating many different answers for an already framed challenge. Frame-storming helps teams identify assumptions and blind spots, mitigating the risk of pursuing inadequate or biased solutions. The goal is to spark innovation and creativity as people dig into—or as Tina Seelig from Stanford puts it, “fall in love with”—the problem.

Begin by assembling a diverse team, encompassing a variety of types of expertise and perspectives. Involving outsiders can be helpful, since they’re often coming to the issue cold. A good way to prompt the team to consider alternative scenarios is by asking “What if…?” and “How might we…?” questions. For example, ask your team, “What if we had access to unlimited resources to tackle this issue?” or “How might better collaboration between departments or teams help us tackle this issue?” The primary objective is to generate many alternative problem frames, allowing for a more holistic understanding of the issue. Within an open, nonjudgmental atmosphere, you deliberately challenge established thinking—what we call “breaking” the frame.

It may be easy to eliminate some possibilities, and that’s exactly what you should do. Rather than make assumptions, generate alternative hypotheses and then test them.

Consider the problem-framing process at a company we’ll call Omega Soundscapes, a midsize producer of high-end headphones. (Omega is a composite of several firms we’ve worked with.) Omega’s sales had declined substantially over the past two quarters, and the leadership team’s initial diagnosis, or reference frame, was that recent price hikes to its flagship product made it too expensive for its target market. Before acting on this assumption, the team convened knowledgeable representatives from sales, marketing, R&D, customer service, and external consultants to do some frame-storming. Team members were asked:

• What if we lowered the price of our flagship product? How would that impact sales and profitability?
• How might we identify customers in new target markets who could afford our headphones at the current price?
• What if we offered financing or a subscription-based model for our headphones? How would that change perceptions of affordability?
• How might we optimize our supply chain and production processes to reduce manufacturing costs without compromising quality?

In playing out each of those scenarios, the Omega team generated several problem frames:

• The target market’s preferences have evolved.
• New competitors have entered the market.
• Product quality has decreased.
• Something has damaged perceptions of the brand.
• Something has changed in the priorities of our key distributors.

Each of the frames presented a unique angle from which to approach the problem of declining sales, setting the stage for the development of diverse potential solutions. At this stage, it may be relatively easy to eliminate some possibilities, and that’s exactly what you should do. Rather than make assumptions, generate alternative hypotheses and then test them.

See more HBR charts in Data & Visuals

Phase 2: Examine

If the expand phase is about identifying all the facets of a problem, this one is about diving deep to identify root causes. The team investigates the issue thoroughly, peeling back the layers to understand underlying drivers and systemic contributors.

A useful tool for doing this is the iceberg model, which guides the team through layers of causation: surface-level events, the behavioral patterns that drive them, underlying systematic structures, and established mental models. As you probe ever deeper and document your findings, you begin to home in on the problem’s root causes. As is the case in the expand phase, open discussions and collaborative research are crucial for achieving a comprehensive analysis.

Let’s return to our Omega Soundscapes example and use the iceberg model to delve into the issues surrounding the two quarters of declining sales. Starting with the first layer beneath the surface, the behavioral pattern, the team diligently analyzed customer feedback. It discovered a significant drop in brand loyalty. This finding validated the problem frame of a “shifting brand perception,” prompting further investigation into what might have been causing it.

Phase 3: Empathize

In this phase, the focus is on the stakeholders—employees, customers, clients, investors, supply chain partners, and other parties—who are most central to and affected by the problem under investigation. The core objective is to understand how they perceive the issue: what they think and feel, how they’re acting, and what they want.

First list all the people who are directly or indirectly relevant to the problem. It may be helpful to create a visual representation of the network of relationships in the ecosystem. Prioritize the stakeholders according to their level of influence on and interest in the problem, and focus on understanding the roles, demographics, behavior patterns, motivations, and goals of the most important ones.

Now create empathy maps for those critical stakeholders. Make a template divided into four sections: Say, Think, Feel, and Do. Conduct interviews or surveys to gather authentic data. How do various users explain the problem? How do they think about the issue, and how do their beliefs inform that thinking? What emotions are they feeling and expressing? How are they behaving? Populate each section of the map with notes based on your observations and interactions. Finally, analyze the completed empathy maps. Look for pain points, inconsistencies, and patterns in stakeholder perspectives.

Returning to the Omega case study, the team identified its ecosystem of stakeholders: customers (both current and potential); retail partners and distributors; the R&D, marketing, and sales teams; suppliers of headphone components; investors and shareholders; and new and existing competitors. They narrowed the list to a few key stakeholders related to the declining-sales problem: customers, retail partners, and investors/shareholders; Omega created empathy maps for representatives from each.

Here’s what the empathy maps showed about what the stakeholders were saying, thinking, feeling, and doing:

Sarah, the customer, complained on social media about the high price of her favorite headphones. Dave, the retailer, expressed concerns about unsold inventory and the challenge of convincing customers to buy the expensive headphones. Alex, the shareholder, brought up Omega’s declining financial performance during its annual investor day.

Sarah thought that Omega was losing touch with its loyal customer base. Dave was considering whether to continue carrying Omega’s products in his store or explore other brands. Alex was contemplating diversifying his portfolio into other consumer-tech companies.

As a longtime supporter of the brand, Sarah felt frustrated and slightly betrayed. Dave was feeling anxious about the drop in sales and the impact on his store’s profitability. Alex was unhappy with the declining stock value.

Sarah was looking for alternatives to the headphones, even though she loves the product’s quality. Dave was scheduling a call with Omega to negotiate pricing and terms. Alex was planning to attend Omega’s next shareholder meeting to find out more information from the leadership team.

When Omega leaders analyzed the data in the maps, they realized that pricing wasn’t the only reason for declining sales. A more profound issue was customers’ dissatisfaction with the perceived price-to-quality ratio, especially when compared with competitors’ offerings. That insight prompted the team to consider enhancing the headphones with additional features, offering more-affordable alternatives, and possibly switching to a service model.

Phase 4: Elevate

This phase involves exploring how the problem connects to broader organizational issues. It’s like zooming out on a map to understand where a city lies in relation to the whole country or continent. This bird’s-eye view reveals interconnected issues and their implications.

For this analysis, we recommend the four-frame model developed by Lee Bolman and Terrence Deal, which offers distinct lenses through which to view the problem at a higher level. The structural frame helps you explore formal structures (such as hierarchy and reporting relationships); processes (such as workflow); and systems, rules, and policies. This frame examines efficiency, coordination, and alignment of activities.

The human resources frame focuses on people, relationships, and social dynamics. This includes teamwork, leadership, employee motivation, engagement, professional development, and personal growth. In this frame, the organization is seen as a community or a family that recognizes that talent is its most valuable asset. The political frame delves into power dynamics, competing interests, conflicts, coalitions, and negotiations. From this perspective, organizations are arenas where various stakeholders vie for resources and engage in political struggles to influence decisions. It helps you see how power is distributed, used, and contested.

The symbolic frame highlights the importance of symbols, rituals, stories, and shared values in shaping group identity and culture. In it, organizations are depicted as theaters through which its members make meaning.

Using this model, the Omega team generated the following insights in the four frames:

Structural.

A deeper look into the company’s structure revealed siloing and a lack of coordination between the R&D and marketing departments, which had led to misaligned messaging to customers. It also highlighted a lack of collaboration between the two functions and pointed to the need to communicate with the target market about the product’s features and benefits in a coherent and compelling way.

Human resources.

This frame revealed that the declining sales and price hikes had ramped up pressure on the sales team, damaging morale. The demotivated team was struggling to effectively promote the product, making it harder to recover from declining sales. Omega realized it was lacking adequate support, training, and incentives for the team.

The key insight from this frame was that the finance team’s reluctance to approve promotions in the sales group to maintain margins was exacerbating the morale problem. Omega understood that investing in sales leadership development while still generating profits was crucial for long-term success and that frank discussions about the issue were needed.

This frame highlighted an important misalignment in perception: The company believed that its headphones were of “top quality,” while customers reported in surveys that they were “overpriced.” This divergence raised alarm that branding, marketing, and pricing strategies, which were all predicated on the central corporate value of superior quality, were no longer resonating with customers. Omega realized that it had been paying too little attention to quality assurance and functionality.

Phase 5: Envision

In this phase, you transition from framing the problem to actively imagining and designing solutions. This involves synthesizing the insights gained from earlier phases and crafting a shared vision of the desired future state.

Here we recommend using a technique known as backcasting. First, clearly define your desired goal. For example, a team struggling with missed deadlines and declining productivity might aim to achieve on-time completion rates of 98% for its projects and increase its volume of projects by 5% over the next year. Next, reverse engineer the path to achieving your goal. Outline key milestones required over both the short term and the long term. For each one, pinpoint specific interventions, strategies, and initiatives that will propel you closer to your goal. These may encompass changes in processes, policies, technologies, and behaviors. Synthesize the activities into a sequenced, chronological, prioritized road map or action plan, and allocate the resources, including time, budget, and personnel, necessary to implement your plan. Finally, monitor progress toward your goal and be prepared to adjust the plan in response to outcomes, feedback, or changing circumstances. This approach ensures that the team’s efforts in implementing the insights from the previous phases are strategically and purposefully directed toward a concrete destination.

Applying the Approach

Albert Einstein once said, “If I had one hour to solve a problem, I would spend 55 minutes thinking about the problem and five minutes thinking about the solution.” That philosophy underpins our E5 framework, which provides a structured approach for conscientiously engaging with complex problems before leaping to solutions.

As teams use the methodology, they must understand that problem-framing in today’s intricate business landscape is rarely a linear process. While we’re attempting to provide a structured path, we also recognize the dynamic nature of problems and the need for adaptability. Invariably, as teams begin to implement solutions, new facets of a problem may come to light, unforeseen challenges may arise, or external circumstances may evolve. Your team should be ready to loop back to previous phases—for instance, revisiting the expand phase to reassess the problem’s frame, delving deeper into an overlooked root cause in another examine phase, or gathering fresh insights from stakeholders in a new empathize phase. Ultimately, the E5 framework is intended to foster a culture of continuous improvement and innovation.

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Cognition ; Problem typology ; Problem-based learning ; Problems ; Reasoning

Problem solving is the process of constructing and applying mental representations of problems to finding solutions to those problems that are encountered in nearly every context.

Theoretical Background

Problem solving is the process of articulating solutions to problems. Problems have two critical attributes. First, a problem is an unknown in some context. That is, there is a situation in which there is something that is unknown (the difference between a goal state and a current state). Those situations vary from algorithmic math problems to vexing and complex social problems, such as violence in society (see Problem Typology ). Second, finding or solving for the unknown must have some social, cultural, or intellectual value. That is, someone believes that it is worth finding the unknown. If no one perceives an unknown or a need to determine an unknown, there is no perceived problem. Finding...

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The role of problem solving ability on innovative behavior and opportunity recognition in university students

• Ji Young Kim 1 ,
• Dae Soo Choi 1 ,
• Chang-Soo Sung 1 &
• Joo Y. Park 2  

Journal of Open Innovation: Technology, Market, and Complexity volume  4 , Article number:  4 ( 2018 ) Cite this article

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Universities engage in entrepreneurship education to increase social value creation, through students’ new opportunities recognition. However, there are not enough of empirical researches on whether the current entrepreneurship education can be differentiated from other curriculum to improve the opportunity recognition process. This study argues that it is very important for cognitive abilities to be manifested as behavior when students in university are new opportunities recognition. For this purpose, the relationship between problem solving ability, innovation behavior, and opportunity perception was verified empirically. This study was conducted on 203 students who took entrepreneurship education courses at Korean universities. The results of this study showed that problem solving ability positively influenced innovation behavior and opportunity perception. Innovation behavior was identified as a key parameter that partially mediated the relationship between problem solving ability and innovation behavior. The implication of this study is to prove the relationship between individual ‘s problem - solving ability considering the characteristics of education in Korea and the opportunity through innovative behavior and various learning strategies to help entrepreneurship education to design better courses for the future It has important implications for strategic pedagogy that can enhance behavioral elements in development.

It is the new opportunity recognition that all firms focus on for a new economic paradigm (Ancona and Caldwell, 1992 ). Recognizing high opportunities can significantly improve profit, growth, and / or competitive positioning. And this new opportunity leads to innovation. From a conceptual point of view, research is continuing on the question of ‘what is opportunity’ and ‘where is opportunity’ (Gartner and Carter, 2003 ; Venkataraman & Sarasvathy, 2001 ). Research on the discovery and realization of new opportunities is a very important research area that suggests how to discover and utilize creative opportunities that create new value and profit for pre-service workers, and is the ultimate goal of entrepreneurship education. (Kim et al., 2016 ). Particularly, there is a lot of debate about the relationship between opportunity perception and personal characteristics. Despite many arguments, however, research on individual characteristics and opportunity perceptions is still insufficient, and a unified opinion has not been created due to differences between cognitive and behavioral theories (Ko & Butler, 2003 ). In particular, there is much controversy over the relationship between opportunity recognition and personal traits, and research has been continuing to demonstrate that organizational learning in organizations can influence opportunity recognition (Shane & Venkataraman, 2000 ). In particular, learning enhances cognitive ability, which is an opportunity that leads to opportunity recognition through the manifestation of behavior (Lumpkin and Dess, 2004 ). Many studies have also demonstrated the difference in behavior that successful entrepreneurs see as contributing to their ability to recognize opportunities and create innovative business ideas (Dyer et al., 2008 ; Kim et al., 2017 ). For example, Alvarez and Barney ( 2005 ) argue for mountain climbing and mountain building to understand the implications of entrepreneurial behavior in relation to these theories. In other words, a new opportunity for entrepreneurs is not a passive case that is generally found and climbed by climbers such as mountains, but rather by the actions of entrepreneurs, creating competition for the market, creating another market, Is the same. Therefore, in order for a person’s cognitive ability to recognize a new opportunity, it must focus on manifesting an action that can realize an innovative idea. In this regard, Kanter ( 1988 ) proved the relationship between new opportunity recognition and those with innovative tendencies and regarded this new opportunity recognition as innovation activity through organizational education. Scott and Bruce ( 1994 ) have integrated a number of research flows into innovation pioneers to develop and test individual innovative behavioral models. In particular, they argued that individual problem-solving styles are very important to induce innovative behavior. Although there are a number of studies on problem solving ability, innovation behavior, and new opportunities, most of the opportunistic researches have been conducted in organizational units of companies. Is still insufficient. Furthermore, unified opinions were not created due to differences between cognitive theory and behavioral theory (Ko & Butler, 2003 ). It is also true that the effects of entrepreneurship education in university have not been studied empirically because they are mainly focused on promoting cognitive ability and applied to various kinds of teaching methods.

This study argues that it is very important for cognitive abilities to be manifested as behavior that. “Through” courses, In other words, it is very important to induce students to act through ‘learning through process’ learning through behavioral learning by providing students with some (virtual or real) business to start doing some of the actions of the entrepreneur. When students in university are new opportunity recognition. Especially, entrepreneurship education, which ultimately focuses on whether it is a new opportunity, is very important to induce behavior through behavior learning beyond the cognitive ability as the general education curriculum. Particularly, innovative behaviors that create and realize innovative ideas are very important for new opportunity recognition (Paine & Organ, 2000 ).In order to achieve this, various kinds of teaching methods are being pursued in the university, but studies on the effectiveness of behavioral learning have not been studied yet. In this study, we are based on team-based learning among various teaching methods for behavior learning that leads to innovative behaviors. Team learning instructional activity sequence designed by Michaelsen and Sweet ( 2008 ), the most well known team-based learning in entrepreneurship education as in class-primarily group work and outside class-primarily individual work. In this way, we demonstrate empirically the relationship between individual problem solving ability and opportunity through innovative behavior, and develop a variety of learning strategies that help entrepreneurship education to design better courses for the future. I would like to point out some implications for strategic pedagogy to increase the element.

The paper proceeds as follows: Initially we present the theory of innovative behavior with individual problem-solving ability, innovative behavior and opportunity recognition. We develop hypotheses to confirm its basic predictions in the student context. Finally, we link the findings with the wider social effect of entrepreneurship literature and highlight the theoretical contributions and practical implications.

Theoretical background

‘opportunity recognition’ as entrepreneurship education unit of analysis.

A commonly focused analysis in entrepreneurship research over the last 30 years has been the ‘opportunity’, most simply defined as any situation in which new products or services can be development of production (Casson, 1982 ; Shane & Venkataraman, 2000 ; Venkataraman, 1997 ). The definition of opportunity recognition is defined in many ways, but opportunity is defined as a perceived means of generating economic value (ie, profit) that has not been exploited previously and is not currently exploited by others. If opportunity is defined in this way, opportunity recognition can be defined as a cognitive process (or process) that concludes that an individual has identified an opportunity (Baron and Ensley, 2006 ). Kirzner ( 1997 ) pointed out that the distribution of information in society affects the discovery of entrepreneurial opportunities and that only a few individuals can identify and recognize specific opportunities in the market. The process of finding opportunities also depends on the individual’s ability and discovery (Stevenson & Gumpert, 1985 ). For example, people may miss opportunities due to a lack of cognitive ability to change external environments (Stevenson & Gumpert, 1985 ). Only those who recognize and value the existence of opportunity can benefit from new opportunities (Ardichvili et al., 2003a , b ; Shane & Venkataraman, 2000 ). Opportunity recognition is an early step in transforming value into a business concept that creates value and generates revenue and distinguishes it from the aggressive stages of detailed assessment and development of recognized opportunities and potential economic value. The focus of the new venture business is also an innovative opportunity to create new opportunities rather than merely expanding or repeating existing business models (Gaglio & Katz, 2001 ). As a result, universities need to make use of a variety of initiatives to educate students to recognize innovative opportunities. Therefore, entrepreneurship education aimed at a new opportunity recognition should be able to provide learning opportunities based on various theories of favorable conditions for new business creation and the types of traits required for new ventures (Garavan & O’Cinne’ide, 1994 ).

Based on these considerations, we also define opportunity recognition as the formation of beliefs that can be translated into actions in order to understand the signals of change (new information on new conditions) and respond to these changes.

Problem-solving ability and innovative behavior of education for students

Problem-solving abilities have been proven to be one of the key factors for success in organizations and personal careers (Anderson & Anderson 1995 ). Through decades of research data, organizations and schools have studied factors that affect improvement. Problem-solving abilities are defined in a number of prior studies, and problem-solving abilities in a volatile and sophisticated knowledge- and technology-based industry are an important ability to drive innovation and sustainable growth and development in the industry. Table  1 show the concept of problem solving ability defined in previous research.

There have been a number of previous studies, emphasis has been placed on the importance and meaning of rational problem-solving processes in order to improve problem-solving abilities, and research has focused on individual problem solving styles (Woodman et al., 1993 ; Scott & Bruce, 1994 ). According to the personal innovation behavior model of Scott and Bruce ( 1994 ), climate has shown individual innovative behavior as a result of individuals signaling the organization’s expectations of behavior and the potential consequences of action. Innovative organizations are, last but not least, equipment, facilities and time, including the direction of creativity and innovative change (Kanter, 1983 ; Siegel & Kaemmerer, 1978 ) Proper supply of such resources is important to innovation (Amabile, 1988 ; Van de Ven & Angle, 1989 ; Dubickis & Gaile-Sarkane, 2017 ). Based on a study of Koestler’s ( 1964 ) creative thinking, Jabri conceptualized a problem-solving style consisting of two independent thinking styles. He uses a structured problem-solving styles that is based on associative thinking, follows a set of rules, resolves reasonably logically, and uses an intuitive problem-solving ability that focuses on problem-solving, not tied to existing rules with multiple ideas. Intuitive problem solving styles tend to process information from different paradigms simultaneously. It is therefore more likely to create new problem solutions as possible (Isaksen, 1987 ; Kirton, 1976 ). However, style assessment is not desirable because the style of problem solving affects style differently depending on the individual problem-solving situations (Scott & Bruce, 1994 ). We are proposing a role for the University to encourage innovative behavior based on the individuality of our students in order to recognize new opportunities through education about Scott and Bruce’s innovative behavioral models and diverse entrepreneurship education approaches. And involvement of resources, such as entrepreneurship awareness programs, ultimately leads to the identification of individual characteristics and innovation. In addition, current Korean entrepreneurship education is mainly focused on cognitive learning to improve problem solving ability, and one aspect of cognitive learning plays an important role in learning process of new venture firms. This study has a more direct focus on behavior learning such as team-based learning.

Hypothesis development

Problem-solving ability and innovative behavior.

Problem solving is to discover knowledge and skills that reach the target country by interfering with a set of processes and goals where the solution is unknown, unfamiliar, or reaching a new state of goal (Jonassen, 2004 ; Inkinen, 2015 ). There are various approaches to solve this problem. To solve problems and improve problem solving with a successful solution experience, you should adopt the method that best suits your problem solution. You need to select the appropriate inputs for the solution elements and a flexible process structure. Problem solving ability has been recognized as a key element of innovative behavior in responding to rapid changes with the ability to find various alternatives and predict outcomes from these alternatives to maximize positive results, minimize negative consequences, and select solutions to problems (Barron & Harrington, 1981 ; Jabri, 1991 ; Kirton, 1976 ). We pose the following hypotheses:

Hypothesis 1: Individual problem-solving ability has an effect on the innovative behavior of students.

Innovative behavior and opportunity recognition

Innovation involves introducing ideas from outside the organization, through creative processes, and linking these ideas to products or processes. Many scholars studying innovation recognize that designing ideas is only one step in the innovation process (Kanter, 1988 ). Innovation is changing at the organizational or individual level. Kanter, Scott and Bruce defined personal innovation. In other words, an innovation act starts with recognition of a problem, adoption of a new idea, or creation of a solution, and an individual with an innovative tendency wants to create a realistically realizable group with the sympathy of such an idea. Innovative individuals create prototypes for innovations that enable ideas to be realized specifically with goods or services and become productive use and social day merchandising. According to previous studies, opportunity perception can be seen as an individual’s corporate strategy that focuses on the perception and exploitation of individuals about potential business ideas and opportunities and finds resources to create innovative outcomes (Manev et al., 2005 ). New Venture Ideas (NVI) are imaginary combinations of product/service offerings; potential markets or users, and means of bringing these offerings into existence (Davidsson, 2015 ). From the viewpoint of a potential entrepreneur like a university student, entrepreneurship starts with an idea. This process continues with a range of practices including attractiveness and feasibility of an idea, gathering information to minimize value-related uncertainty and possibility and perhaps the main idea’s conformity ratio in terms of newly discovered needs (Hayton & Cholakova, 2012 ). Earlier we proposed that the program as a whole increases the students’ innovative behavior and that innovative performance is the new venture ideas. Since it is logical to assume that the relationship between innovative behavior and opportunity recognition. We pose the following hypotheses:

Hypothesis 2: Innovative behavior will be a more potent inducer of opportunity recognition.

Problem-solving ability and opportunity recognition

Among the many factors influencing opportunity perception, the problems that arise in the fourth industry, the knowledge-based industry of the twenty-first century, are unpredictable and unstructured; they cannot be solved with existing solutions and require creative problem-solving skills. In order to determine how to solve problem situations that are different from the current situation and have unknown results, problems are solved through the process of adjusting previous experience, knowledge, and intuition (Charles & Lester, 1982 ). Experience, knowledge, and intuition are applied simultaneously to a single problem, not individually or collectively, and the intellectual and creative results that can be quickly and effectively solved in problem solving are seen as problem solving abilities (Ardichvili et al., 2003a , b ). Empirical studies of problem-solving abilities and opportunity perceptions have provided strong evidence that there is a positive relationship between theoretical integrative processes and corporate opportunity recognition (Ucbasaran et al., 2009 ). Therefore, we hypothesized that:

Hypothesis 3: Problem solving ability has an effect on the opportunity recognition.

The respondents for this study were randomly selected from three universities in Korea. Most of the respondents in this study were Korean university students who experienced team-based learning during behavioral learning through entrepreneurship education. Since then, we have been guided by two main criteria when choosing these universities. First, students who take entrepreneurship courses are critical to their innovation behavior. This led us to realize that innovative behavior is an important factor in an individual’s survival and growth. The second is that the parallel process of theoretical and behavioral learning is highly satisfied. A pilot study was conducted to verify the reliability and validity of the research measurements with 28 students at a university. The results of the pilot study showed high clarity and reliability (Cronbach ‘s alphas were all above 0.70) ​​of the research measurements. The sample of the pilot study was not incorporated in the present study.

This study was conducted in a four - year undergraduate course (various majors) that took entrepreneurship courses in Korea university programs. Students in this course have a mix of students who have previously experienced entrepreneurship and those who have not. During the course, students were taught the theoretical lessons for 8 weeks and the team for the 8 weeks. The questionnaire was administered during the last week of the course.

The data were analyzed from 203 participants, out of a total of 209, of which 7 were not appropriate. Of the 203 participants, 27% were female and 73% were male and the grade distribution was 3% for freshmen, 12% for grade 2, 26% for grade 2, and 59% for grade 2. The main distribution is 26% in social science, 16% in business and economics, 39% in engineering, 11% in music and athletics and 7% in others (see Table  2 ).

Measurement

The structure of the model was measured by questionnaires (problem-solving ability, innovation behavior and opportunity recognition questionnaire) consisting of the scale taken from questionnaires verified in previous studies. Tool selection was performed on two criteria. First, the selected tool should measure the same structure (ie, the original measured structure had to be conceptually identical to the way the structure was defined in this study model). Secondly, the psychometric qualities of the instrument for the student had to be high.

Assessment of the factors was carried out through principal component analyses (varimax rotation with eigenvalues of 1.0 or above) of the scales connected to the same level of the model to confirm the uniqueness of the scales with respect to each other. This was supplemented by the computation of the internal consistency reliability of the scales (Cronbach’s α). These analyses were executed using the individual participants’ responses (Nunnally & Bernstein, 1994 ).

Problem- solving ability was measured on a 7-point Likert-scale (1 = ‘completely disagree’; 7 = ‘completely agree’). Jabri ( 1991 ) used a measurement tool to measure individual problem solving ability.

Innovative behavior was measured on a 7-point Likert-scale (1 = ‘completely disagree’; 7 = ‘completely agree’). In order to measure innovation behavior, we modified the questionnaire items to fit the intention of this study among the questionnaire items used by Scott and Bruce ( 1994 ) and Kim and Rho ( 2010 ).

Opportunity recognition was measured on a 7-point Likert-scale (1 = ‘completely disagree’; 7 = ‘completely agree’). In order to measure opportunity recognition, we modified the questionnaire items to fit the intention of this study among the questionnaire items used by Kim and Rho ( 2010 ).

Methods of analysis

The first two parts of the analysis were primarily based on (multiple) regression analyses. The last part of the analysis was informed through the path analyses. The adequacy of the models was assessed by AMOS 18(Arbuckle & Wothke, 2003 ). Models were all tested with standardized coefficients obtained from the Principal Component Analysis. To ascertain the model fit, we analyzed the comparative fit index (CFI), the normed fit index (NFI), the Root Mean Square Err of Approximation (RMSEA), the standardized root mean square residual (SRMR) and the chi-square test statistic.

Reliability and validity are essential psychometrics to be reported. The first step to evaluate those aspects was to use the Cronbach’s alpha and the composite reliability to test reliability of the proposed scales. The usual threshold level is 0.7 for newly developed measures (Fornell and Larcker, 1981 ). Values range from 0.69 to 0.79 in the case of Cronbach’s alpha, and from 0.85 to 0.92 in the case of composite reliability (see Table  3 ). Therefore, these scales may be considered as reliable. Next, we estimated the research model, displayed in Fig.  1 , using structural equation modeling (SEM) and AMOS 18 (Arbuckle & Wothke, 2003 ). Our analysis revealed an adequate measurement model with high factor loadings for all the items on the expected factors and communalities of each item exceeding 0.50. We discuss three fit indices that are generally considered as important (Hu & Bentler, 1998 ). First, the CFI-value represents the overall difference between observed and predicted correlations. A value of 0.04 which is situated well below the cut-off value of 0.08, suggests that the hypothesized model resembles the actual correlations. Secondly, Bentler’s CFI (comparative fit index) greater than 0.90 and 0.95 which is above the cut-off of 0.90 (Schumacker & Lomax, 1996 ). Thirdly, NFI greater greater than 0.90 and 0.95 which is above the cut-off of 0.90 (Schumacker & Lomax, 1996 ). Fourthly, the standardized root mean square residual (SRMR) value of 0.0392 which is situated well below the cut-off value of 0.05(Hu & Bentler, 1998 ), and the chi-square value of 3581.622 which is situated well below the cut-off value of 0.0005. Finally, the RMSEA (root mean square error of approximation) equals 0.04 with a 90% confidence interval between 0.03 and 0.05.

Analysis of mediation effect

The value and confidence interval are situated over but below the cut-off value of 0.1 which suggests not a great but a good fit. Factor analysis was verified by factor analysis using principal component analysis and only factors with an eigenvalue of 1 or more by orthogonal rotation method were selected. Factor loading was considered to be significant at 0.5 or more (Hair et al., 2006a , b ). As a result of the analysis, cumulative explanation for 72.4% of the total variance. Confirmatory factor analysis thus supported the differentiation of the three components Also we tested the confirmatory validity of the construct by testing whether the structural linkage of each square is greater than the mean variance extraction (AVE) of each structure. The AVE ranged from 0.52 to 0.53, reaching the recommended level of .50 for both Fornell and Larcker ( 1981 ). Therefore, all constructs showed sufficient convergent validity (see Table 3 ).

As shown in Table  4 , the AVE value of each variable has a higher value than that of other factors. Therefore, the discriminant validity of the proposed model can be judged as appropriate.

Means, standard deviations, and correlations among the study variables are shown in Table  5 .

The mean scores for the conceptual model were as follows for problem-solving ability (MD. 5.20, SD.1.08), innovative behavior (MD.5.20, SD.1.03), and opportunity recognition (MD. 5.14, SD. 1.06) conditions. The means of problem-solving ability, innovative behavior, and opportunity recognition were high. Furthermore, those variables correlated positively with each other.

Figure  1 showed that all paths and their significance levels are presented in Table  6 . The path between the latent variables problem-solving ability and innovative behavior was significant (p, 0.001), consistent with Hypotheses 1. In addition, there was innovative behavior and opportunity recognition (p, 0.01), this result provide empirical support for Hypothesis 2.

H3 proposed that Problem-solving ability is positively related to opportunity recognition. The results of the correlation analysis: The coefficient of problem solving and opportunity perception weakened from .717 to .444, but it is still partly mediated because it is still significant (C. R  = 7.604 ***). This supports H3 (see Table 6 ).

In order to verify the significance of the indirect effect, the bootstrapping must be performed in AMOS, and the actual significance test should be identified using two-tailed significance. As a result, the significance of indirect effect is 0.04 ( p  < 0.05), which is statistically significant (see Table  7 ).

Discussion and conclusion

We have tried to demonstrate the effects of behavior and its significance by differentiating from the general curriculum emphasizing cognitive effects as a model of problem solving ability emerging as innovative behavior through opportunity of university entrepreneurship education.. This supports the premise that entrepreneurship education can improve opportunities or processes through behavioral learning. The results of this study support the role of entrepreneurship education in creating opportunities for innovative behavior and problem solving abilities. Entrepreneurship education should provide different types of learning for new opportunities and focus on what is manifested in behavior.

In addition, based on previous research, we propose whether the following contents are well followed and whether it is effective. First, the emergence of innovative behavior in problem-solving abilities increases as the cognitive diversity of students with diverse majors and diverse backgrounds increases. Second, the more entrepreneurial learning experiences, the greater the chance of new opportunities. Third, it is necessary to investigate students’ problem solving style and problem-solving ability first, and then a teaching strategy based on this combination of systematic and effective theory and practice is needed. Of course, as demonstrated by many studies, it may be easier to enhance the effectiveness of opportunity recognition through cognitive learning. This is because it emphasizes the achievement of knowledge and understanding with acquiring skills and competence. This process, however, is not enough for entrepreneurship education. However, we do not support full team-based behavioral learning in the class designed by Michaelsen and Sweet ( 2008 ). As with the results of this study, problem solving ability is positively related to opportunity perception directly. As previously demonstrated in previous studies, problem solving ability can be enhanced by cognitive learning (Anderson et al., 2001 ; Charles & Lester, 1982 ).

Therefore, it has been demonstrated that it is more efficient to balance a certain level of cognitive learning and behavior learning in consideration of the level of students in a course. Also this study satisfies the need for empirical research by Lumpkin and Lichtenstein ( 2005 ) and Robinson et al. ( 2016 ) and others. This will help to improve understanding of how entrepreneurship training is linked to various learning models and their effectiveness and to design better courses for the future. Finally, this study sought to provide an awareness of entrepreneurship education as the best curriculum for solutions that evolved into innovative behaviors that create new values and ultimately represent new opportunities. This study shows that it can positively influence the social effect of creating new value, that is, not only the cognitive effect of general pedagogy, but also the innovation behavior. By providing this awareness, we have laid the groundwork for empirical research on entrepreneurship education in order to create more opportunities for prospective students in education through education and to expand their capabilities.

Limitation and future research

Indeed, the concepts presented here and the limitations of this study have important implications that can fruitfully be addressed in future research. First, we selected a sample of college students taking entrepreneurship training. However, since it is not the whole of Korean university students, it is difficult to extend the research results to all college students in Korea. Second, there is no precedent research on the role of innovation behavior as intermedia in college students. Therefore, we were forced to proceed as an exploratory study.

The ability to recognize opportunities can provide significant benefits that can remain firm and competitive in an ever-changing environment. Future research should therefore expand these insights and try to empirically test more ways in which entrepreneurship pedagogy teaches how learning methods can be integrated into venture creation and growth processes to help new process opportunities. By providing this study, we will help entrepreneurship education in the university to create more opportunities and expand the capacity of prospective members.

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Kim, J.Y., Choi, D.S., Sung, CS. et al. The role of problem solving ability on innovative behavior and opportunity recognition in university students. J. open innov. 4 , 4 (2018). https://doi.org/10.1186/s40852-018-0085-4

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The Journal of Problem Solving (JPS) was a multidisciplinary journal that published empirical and theoretical papers on mental mechanisms involved in problem solving. This journal is no longer accepting submissions.

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The Process of Problem Solving

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In a 2013 article published in the Journal of Cognitive Psychology , Ngar Yin Louis Lee (Chinese University of Hong Kong) and APS William James Fellow Philip N. Johnson-Laird (Princeton University) examined the ways people develop strategies to solve related problems. In a series of three experiments, the researchers asked participants to solve series of matchstick problems.

In matchstick problems, participants are presented with an array of joined squares. Each square in the array is comprised of separate pieces. Participants are asked to remove a certain number of pieces from the array while still maintaining a specific number of intact squares. Matchstick problems are considered to be fairly sophisticated, as there is generally more than one solution, several different tactics can be used to complete the task, and the types of tactics that are appropriate can change depending on the configuration of the array.

Louis Lee and Johnson-Laird began by examining what influences the tactics people use when they are first confronted with the matchstick problem. They found that initial problem-solving tactics were constrained by perceptual features of the array, with participants solving symmetrical problems and problems with salient solutions faster. Participants frequently used tactics that involved symmetry and salience even when other solutions that did not involve these features existed.

To examine how problem solving develops over time, the researchers had participants solve a series of matchstick problems while verbalizing their problem-solving thought process. The findings from this second experiment showed that people tend to go through two different stages when solving a series of problems.

People begin their problem-solving process in a generative manner during which they explore various tactics — some successful and some not. Then they use their experience to narrow down their choices of tactics, focusing on those that are the most successful. The point at which people begin to rely on this newfound tactical knowledge to create their strategic moves indicates a shift into a more evaluative stage of problem solving.

In the third and last experiment, participants completed a set of matchstick problems that could be solved using similar tactics and then solved several problems that required the use of novel tactics.  The researchers found that participants often had trouble leaving their set of successful tactics behind and shifting to new strategies.

From the three studies, the researchers concluded that when people tackle a problem, their initial moves may be constrained by perceptual components of the problem. As they try out different tactics, they hone in and settle on the ones that are most efficient; however, this deduced knowledge can in turn come to constrain players’ generation of moves — something that can make it difficult to switch to new tactics when required.

These findings help expand our understanding of the role of reasoning and deduction in problem solving and of the processes involved in the shift from less to more effective problem-solving strategies.

Reference Louis Lee, N. Y., Johnson-Laird, P. N. (2013). Strategic changes in problem solving. Journal of Cognitive Psychology, 25 , 165–173. doi: 10.1080/20445911.2012.719021

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In-person and online studies examining the influence of problem solving on the fading affect bias.

1. Introduction

1.1. problem solving and emotions, 1.2. the fading affect bias (fab), 2. the current study, 2.1. study 1: in person, 2.1.1. method, participants, materials and measures, analytic strategy, 2.1.2. results, discrete two-way interactions, continuous two-way interactions, continuous three-way interactions, examining rehearsals as mediators of the three-way interactions, 2.1.3. discussion, 2.2. study 2: online replication, 2.2.1. method, procedure and analytic strategy, 2.2.2. results, only thinking rehearsals mediated two three-way interactions, 2.2.3. discussion, 3. general discussion, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

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Gibbons, J.A.; Vandevender, S.; Langhorne, K.; Peterson, E.; Buchanan, A. In-Person and Online Studies Examining the Influence of Problem Solving on the Fading Affect Bias. Behav. Sci. 2024 , 14 , 806. https://doi.org/10.3390/bs14090806

Gibbons JA, Vandevender S, Langhorne K, Peterson E, Buchanan A. In-Person and Online Studies Examining the Influence of Problem Solving on the Fading Affect Bias. Behavioral Sciences . 2024; 14(9):806. https://doi.org/10.3390/bs14090806

Gibbons, Jeffrey Alan, Sevrin Vandevender, Krystal Langhorne, Emily Peterson, and Aimee Buchanan. 2024. "In-Person and Online Studies Examining the Influence of Problem Solving on the Fading Affect Bias" Behavioral Sciences 14, no. 9: 806. https://doi.org/10.3390/bs14090806

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