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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]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

The Process of Problem Solving

• Editor's Choice
• Experimental Psychology
• Problem Solving

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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Careers Up Close: Joel Anderson on Gender and Sexual Prejudices, the Freedoms of Academic Research, and the Importance of Collaboration

Joel Anderson, a senior research fellow at both Australian Catholic University and La Trobe University, researches group processes, with a specific interest on prejudice, stigma, and stereotypes.

Experimental Methods Are Not Neutral Tools

Ana Sofia Morais and Ralph Hertwig explain how experimental psychologists have painted too negative a picture of human rationality, and how their pessimism is rooted in a seemingly mundane detail: methodological choices. 

APS Fellows Elected to SEP

In addition, an APS Rising Star receives the society’s Early Investigator Award.

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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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DOI : https://doi.org/10.1186/s40852-018-0085-4

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Takahashi I , Obara T , Ishikuro M, et al. Screen Time at Age 1 Year and Communication and Problem-Solving Developmental Delay at 2 and 4 Years. JAMA Pediatr. 2023;177(10):1039–1046. doi:10.1001/jamapediatrics.2023.3057

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Screen Time at Age 1 Year and Communication and Problem-Solving Developmental Delay at 2 and 4 Years

• 1 Graduate School of Medicine, Tohoku University, Sendai, Japan
• 2 Tohoku Medical Megabank Organization, Tohoku University, Sendai, Japan
• 3 Department of Pharmaceutical Sciences, Tohoku University Hospital, Sendai, Japan
• 4 United Graduate School of Child Development, Hamamatsu University School of Medicine, Hamamatsu, Japan
• 5 Research Center for Child Mental Development, Hamamatsu University School of Medicine, Hamamatsu, Japan
• 6 International Research Institute of Disaster Science, Tohoku University, Sendai, Japan

Question   Is there a dose-response association between screen time for children aged 1 year and functional development at ages 2 and 4 years?

Findings   In this cohort study including 7097 mother-child pairs, a dose-response association was observed between greater screen time at age 1 year and developmental delays in communication and problem-solving at ages 2 and 4 years.

Meaning   These findings suggest that domains of developmental delay should be considered separately in future discussions on screen time and child development.

Importance   Whether some domains of child development are specifically associated with screen time and whether the association continues with age remain unknown.

Objective   To examine the association between screen time exposure among children aged 1 year and 5 domains of developmental delay (communication, gross motor, fine motor, problem-solving, and personal and social skills) at age 2 and 4 years.

Design, Participants, and Setting   This cohort study was conducted under the Tohoku Medical Megabank Project Birth and Three-Generation Cohort Study. Pregnant women at 50 obstetric clinics and hospitals in the Miyagi and Iwate prefectures in Japan were recruited into the study between July 2013 and March 2017. The information was collected prospectively, and 7097 mother-child pairs were included in the analysis. Data analysis was performed on March 20, 2023.

Exposure   Four categories of screen time exposure were identified for children aged 1 year (<1, 1 to <2, 2 to <4, or ≥4 h/d).

Main Outcomes and Measures   Developmental delays in the 5 domains for children aged 2 and 4 years were assessed using the Japanese version of the Ages & Stages Questionnaires, Third Edition. Each domain ranged from 0 to 60 points. Developmental delay was defined if the total score for each domain was less than 2 SDs from its mean score.

Results   Of the 7097 children in this study, 3674 were boys (51.8%) and 3423 were girls (48.2%). With regard to screen time exposure per day, 3440 children (48.5%) had less than 1 hour, 2095 (29.5%) had 1 to less than 2 hours, 1272 (17.9%) had 2 to less than 4 hours, and 290 (4.1%) had 4 or more hours. Children’s screen time was associated with a higher risk of developmental delay at age 2 years in the communication (odds ratio [OR], 1.61 [95% CI, 1.23-2.10] for 1 to <2 h/d; 2.04 [1.52-2.74] for 2 to <4 h/d; 4.78 [3.24-7.06] for ≥4 vs <1 h/d), fine motor (1.74 [1.09-2.79] for ≥4 vs <1 h/d), problem-solving (1.40 [1.02-1.92] for 2 to <4 h/d; 2.67 [1.72-4.14] for ≥4 vs <1 h/d), and personal and social skills (2.10 [1.39-3.18] for ≥4 vs <1 h/d) domains. Regarding risk of developmental delay at age 4 years, associations were identified in the communication (OR, 1.64 [95% CI, 1.20-2.25] for 2 to <4 h/d; 2.68 [1.68-4.27] for ≥4 vs <1 h/d) and problem-solving (1.91 [1.17-3.14] for ≥4 vs <1 h/d) domains.

Conclusions and Relevance   In this study, greater screen time for children aged 1 year was associated with developmental delays in communication and problem-solving at ages 2 and 4 years. These findings suggest that domains of developmental delay should be considered separately in future discussions on screen time and child development.

Screen time is the amount of time that individuals spend watching television, playing video games, and using mobile phones, tablets, and other electronic devices. To ensure that children engage in physical activity and obtain adequate sleep for healthy growth and well-being, the World Health Organization 1 and the American Academy of Pediatrics 2 have issued guidelines that recommend limiting screen time for children, including a limit of 1 hour per day for children aged 2 to 5 years. 2 However, a recent meta-analysis reported that only a minority of children meet these guidelines. 3 In addition, children’s screen time has increased in recent years because of the rapid proliferation of digital devices and the COVID-19 pandemic. 4 - 6 Therefore, it is essential to consider how screen time affects child development.

Previous studies have reported associations between screen time and child development outcomes. These outcomes include communication, 7 , 8 daily living skills, 7 socialization, 7 gross and fine motor skills, 8 problem-solving skills, 8 personal and social skills, 8 developmental screening test total scores, 9 cognitive development, 10 , 11 socioemotional development, 9 language development, 11 - 13 attention problems, 14 behavioral problems, 15 , 16 and developmental disorders such as autism spectrum disorder. 17 , 18

Although several studies have examined the association between screen time and child development outcomes, 2 questions remain. The first is whether screen time is associated with child development domains and, if so, which ones. Because there are several domains of child development, its association with screen time may be domain specific. However, most previous studies examined a single measure as an outcome. 9 - 18 Only 2 studies 7 , 8 focused on multiple child development domains: one that considered several domains was cross-sectional, 8 and the other performed a longitudinal examination. 7 Therefore, further research focusing on several developmental domains is needed to clarify the association between screen time and individual child development domains.

The second question is whether the association between children’s screen time and developmental delay continues with age. To our knowledge, only 2 studies 9 , 16 have examined whether screen time is associated with child development outcomes at several later time points. Both studies used random-intercept cross-lagged panel models: one examined the association between screen time and developmental screening scores at ages 2, 3, and 5 years, 9 and the other examined the association between screen time and externalizing and internalizing behavior at ages 3, 5, 7, and 9 years. 16 The findings of both studies did not support an association between children’s screen time at a single point and child development outcomes at 2 or more later points. 9 , 16 These studies examined developmental and behavioral screening test scores 9 , 16 ; however, there are several phenotypic domains of child development.

Considering these findings, it is essential to examine whether screen time is continuously associated with child development domains at multiple time points and, if so, which ones. Therefore, this study examined the association between screen time exposure at age 1 year and 5 domains of developmental delay (communication, gross motor, fine motor, problem-solving, and personal and social skills) at ages 2 and 4 years among participants in the Tohoku Medical Megabank Project Birth and Three-Generation (TMM BirThree) Cohort Study, a representative population in Japan and one of the largest cohorts for this research area.

Details of the TMM BirThree cohort study are provided elsewhere. 19 - 22 The Tohoku Medical Megabank Organization Institutional Review Board reviewed and approved the study protocol. Pregnant women at 50 obstetric clinics and hospitals in the Miyagi and Iwate prefectures in Japan were recruited into the study between July 2013 and March 2017. 19 , 20 Trained genomic medical research coordinators explained the study details to all potential participants and obtained signed consent. 19 , 20 The study followed the Strengthening the Reporting of Observational Studies in Epidemiology ( STROBE ) reporting guideline.

Of the 23 130 mother-child pairs in the TMM BirThree cohort, 16 033 were excluded as follows: 505 withdrew informed consent, 875 participated in the study survey more than once, 8820 were missing information on screen time at age 1 year, and 2512 and 3321 were missing information on development outcomes at ages 2 and 4 years, respectively. Therefore, 7097 mother-child pairs were included in the analysis ( Figure ).

Children’s screen time at age 1 year was assessed using a questionnaire in which participants were asked the following: “On a typical day, how many hours do you allow your children to watch TV, DVDs, video games, internet games (including mobile phones and tablets), etc?” There were 5 response categories: none, less than 1, 1 to less than 2, 2 to less than 4, or 4 or more hours per day. We merged 2 categories (none and <1), resulting in 4 categories of screen time exposure (<1, 1 to <2, 2 to <4, or ≥4 h/d).

To assess developmental delay among children, we used the Ages & Stages Questionnaires, Third Edition (ASQ-3). 23 , 24 The ASQ-3 assesses child development from ages 1 to 66 months. In this study, parents responded to questions in the Japanese version of the ASQ-3 regarding their children aged 2 and 4 years. 24 The ASQ-3 comprised 6 questions divided into the following 5 domains: communication (babbling, vocalizing, and understanding), gross motor (arm, body, and leg movement), fine motor (hand and finger movement), problem-solving (learning and playing with toys), and personal and social skills (solitary social play and playing with toys and other children). The response options included “yes,” “sometimes,” or “not yet” (10, 5, or 0 points, respectively), and each domain was scored with a range of 0 to 60 points. 23 , 24 If 1 or 2 of the 6 questions were missed, the remaining total score was multiplied by 1.2 or 1.5, adjusted from 0 to 60, respectively. 23 , 24 One question in the gross motor domain for children aged 2 years asked about a possible behavior that they may have had previously but no longer did because they acquired more advanced skills. If parents answered “not yet” or “sometimes” on the easier item and “yes” on the more advanced item, the response on the earlier item was changed to “yes.” 23 , 24 A total score of each domain that was less than −2 SDs relative to the mean in reference indicated developmental delay and the need for further assessment. 23 , 24 A previous study showed that this cutoff point had moderate sensitivity and specificity to estimate any delay, severe delay, motor delay, and cognitive delay, 25 and it has also been used widely in the screening of Japanese children. 26 , 27

We selected covariates that may affect the association between children’s screen time and developmental delay based on previous studies. 7 - 18 Children’s sex was garnered from birth records. Information about maternal age at delivery and parity (nulliparous, or primiparous or multiparous) was gathered from medical records. We divided maternal age into 4 categories (<25, 25-29, 30-35, or >35 years). Information on annual household income (<¥4 000 000 [US <$28 400], ¥4 000 000-5 999 999 [US $28 400-$42 599], or ≥¥6 000 000 [US ≥$42 600]) was gathered from the midpregnancy questionnaire. Data on maternal educational attainment (high school graduate or less, junior college or vocational college graduate, university graduate or above, or other), child living with grandparents or other adults (yes or no), and maternal postpartum depression and maternal bonding disorder were gathered using the questionnaire at 1 year post partum. Maternal postpartum depression was assessed using the Japanese version of the Edinburgh Postnatal Depression Scale (EPDS). 28 - 30 In Japan, an EPDS score of 9 or higher is widely used as the cutoff point for screening of postpartum depression, with previous studies reporting sensitivity of 75% and 82% and specificity of 93% and 95% at 1 month post partum. 29 , 30 Maternal bonding disorder was assessed using the Japanese version of the Mother-to-Infant Bonding Scale 31 - 33 (MIBS-J), and the cutoff point was set at 5. A previous study of Japanese mothers with 1-month-old infants showed that an MIBS-J cutoff point of 4 or 5 correctly classified approximately 90% of pathological maternal bonding disorders. 33

Participant characteristics were described according to the 4 categories of child screen time at age 1 year (<1, 1 to <2, 2 to <4, or ≥4 h/d). Characteristics are presented as frequencies with percentages and as medians with IQRs. Associations between the 4 screen time categories at 1 year and the 5 ASQ-3 domains of developmental delay in children at 2 and 4 years were evaluated using multivariable logistic regression analysis to estimate odds ratios (ORs) and 95% CIs (with <1 h/d as the reference). Missing covariates were imputed through multiple imputations by chained equations using the exposure, outcome, and covariates in the main analysis. 34 Twenty sets of quasi-complete data were analyzed in the multivariable analyses independently and the estimates were integrated. 34 In addition, as a supplemental analysis, a complete case analysis was performed in which participants with at least 1 missing covariate were excluded. All statistical analyses were performed using R, version 4.0.2 (R Project for Statistical Computing), and 95% CIs not crossing 1.00 were considered statistically significant. Data analysis was performed on March 20, 2023.

Of the 7097 children included this study, 3674 were boys (51.8%) and 3423 were girls (48.2%). Table 1 presents participant characteristics according to the 4 categories of children’s screen time. In terms of screen time exposure per day, 3440 children (48.5%) had less than 1 hour, 2095 (29.5%) had 1 to less than 2 hours, 1272 (17.9%) had 2 to less than 4 hours, and 290 (4.1%) had 4 or more hours. At age 2 years, developmental delays were observed in the communication (361 [5.1%]), gross motor (400 [5.6%]), fine motor (329 [4.6%]), problem-solving (301 [4.2%]), and personal and social skills (387 [5.5%]) domains. At age 4 years, developmental delays were also observed in the communication (283 [4.0%]), gross motor (303 [4.3%]), fine motor (349 [4.9%]), problem-solving (269 [3.8%]), and personal and social skills (328 [4.6%]) domains. Mothers of children with high levels of screen time were characterized as being younger, having never given birth, and having a lower household income, lower maternal education level, and having postpartum depression.

Table 2 presents the association between the 4 screen time categories at age 1 year and each domain of developmental delay at ages 2 and 4 years through multivariable logistic regression (with <1 h/d as the reference). After adjusting for covariates, we observed an association between screen time at age 1 year and a higher risk of developmental delay at age 2 years in the communication (OR, 1.61 [95% CI, 1.23-2.10] for 1 to <2 h/d; 2.04 [1.52-2.74] for 2 to <4 h/d; 4.78 [3.24-7.06] for ≥4 vs <1 h/d), fine motor (1.74 [1.09-2.79] for ≥4 vs <1 h/d), problem-solving (1.40 [1.02-1.92] for 2 to <4 h/d; 2.67 [1.72-4.14] for ≥4 vs <1 h/d), and personal and social skills (2.10 [1.39-3.18] for ≥4 vs <1 h/d) domains. We also observed an association between screen time at age 1 year and developmental delay at age 4 years in the communication (OR, 1.64 [95% CI, 1.20-2.25] for 2 to <4 h/d; 2.68 [1.68-4.27] for ≥4 vs <1 h/d) and problem-solving (1.91 [1.17-3.14] for ≥4 vs <1 h/d) domains.

We conducted a supplemental analysis that excluded 19 children whose parents self-reported that their child had been diagnosed with autism spectrum disorder and cerebral palsy by age 4 years as a factor in the association between screen time and developmental delay. We observed that the estimates did not show any meaningful departure from the main results.

The eTable in Supplement 1 presents the results of the complete case analysis. No significant difference in interpretation due to the use of multiple imputations was observed.

The findings of this study support previous research showing an association between screen time among young children and subsequent developmental outcomes. 7 - 18 These results also suggest that there was a dose-response association between longer screen time at age 1 year and developmental delays in communication and problem-solving at ages 2 and 4 years. In particular, more than 4 hours of screen time per day was associated with developmental delays in communication and problem-solving across ages 2 and 4 years.

The association observed between screen time and developmental delay among young children was domain specific. For example, the associations between screen time of children aged 1 year and the communication and problem-solving domains were consistent across ages, although no association was observed in the gross motor domain at ages 2 and 4 years. Sugiyama et al 7 examined the association between screen time at age 2 years and 3 domains (communication skills, daily living skills, and social skills) at age 4 years. They found that screen time was associated with poorer communication and daily living skills and was not associated with social skills. 7 In terms of domain-specific associations, their results are consistent with ours. Here, associations were consistently observed in the communication and problem-solving domains for children aged 2 and 4 years and not in the personal and social skills domain at age 4 years. In addition, a meta-analysis 12 reported an association between screen time and language development, and a cross-sectional study 8 examining the association between screen time and the 5 domains of the ASQ-3 found associations in the domains of communication, problem-solving, and personal and social skills. The results of these previous studies and our study suggested an association between screen time and communication and problem-solving domains in young children, while results for personal and social skills were inconsistent across studies. Based on 2 longitudinal time points of outcomes for each developmental domain, this study emphasized that screen time was not associated with all developmental domains.

We observed that screen time for children aged 1 year was associated with the fine motor and personal and social skills domains at age 2 years; however, this association was not confirmed at age 4 years. There are 2 possible hypotheses for this finding. One hypothesis is that the developmental delay of fine motor and personal and social skills for children aged 2 years caught up with them at age 4 years. Further follow-up studies would be needed to verify whether this phenomenon is specific to the fine motor and personal and social skills domains or whether the association is not confirmed with age even in the communication and problem-solving domains. Another hypothesis is that reverse causation occurs, in which a developmental delay of fine motor or personal and social skills lengthens screen time. Previous studies have examined the association between screen time and the personal and social skills domain; although a cross-sectional study reported an association, 8 a prospective study found no association. 7 Application of the reverse causality described earlier would explain why the association was confirmed in the cross-sectional study and not in the prospective study. However, our prospective study confirmed an association between screen time at age 1 year and developmental delay of personal and social skills at age 2 years. Although this phenomenon is unknown, applying the reverse causality hypothesis may explain the confirmed association at age 2 years in our study by assuming that developmental delay in the personal and social skills domain at age 1 year leads to longer screen time at age 1 year, and developmental delay in the personal-social domain at age 1 year is reflected in the developmental delay in that domain at age 2 years.

Although screen time has been associated with developmental delay, it may have an educational aspect depending on the programs watched on electronic devices. In fact, a meta-analysis showed that greater screen use was associated with decreased language skills, whereas screen time spent on educational programs was associated with increased language skills. 12 In addition, the American Academy of Pediatrics recommends that high-quality (eg, educational) programs should be selected when introducing digital media to children aged 18 to 24 months. 2 Because it is difficult to limit screen time in general in today’s world of electronic devices, it may be beneficial to identify and limit the screen time aspects that are associated with developmental delays while taking advantage of the educational aspects.

This study has 2 strengths. First, developmental delay was measured using the ASQ-3, which has been validated worldwide and used in a variety of studies. 9 , 35 - 37 Although the ASQ-3 is not a diagnostic tool, it is an appropriate screening tool for examining developmental delays according to several developmental domains. Second, the analysis was conducted with one of the largest prospective cohorts of any study examining the association between screen time and child development outcomes.

A limitation is that the information we collected did not allow us to separate educational screen time from other types of screen time. Doing so may have helped us in examining the association between screen time and child development while considering both positive and negative aspects of screen time.

In this cohort study, greater screen time at age 1 year was associated in a dose-response manner with developmental delays in communication and problem-solving at ages 2 and 4 years. These findings suggest that domains of developmental delay should be considered separately in future discussions on screen time and child development.

Accepted for Publication: June 22, 2023.

Published Online: August 21, 2023. doi:10.1001/jamapediatrics.2023.3057

Open Access: This is an open access article distributed under the terms of the CC-BY License . © 2023 Takahashi I et al. JAMA Pediatrics .

Corresponding Author: Taku Obara, PhD, Tohoku Medical Megabank Organization, Tohoku University, 2-1 Seiryo-machi, Aoba-ku, Sendai 980-8573, Japan ( [email protected] ).

Author Contributions: Mr Takahashi and Dr Obara had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

Concept and design: Takahashi, Obara, Tsuchiya.

Acquisition, analysis, or interpretation of data: All authors.

Drafting of the manuscript: Takahashi, Obara, Tsuchiya.

Critical review of the manuscript for important intellectual content: All authors.

Obtained funding: Obara, Kuriyama.

Administrative, technical, or material support: Takahashi, Obara, Kuriyama.

Supervision: Kuriyama.

Conflict of Interest Disclosures: Dr Kuriyama reported receiving grants from the Japanese government during the conduct of the study. No other disclosures were reported.

Funding/Support: The Tohoku Medical Megabank Project Birth and Three-Generation (TMM BirThree) Cohort Study was supported by grants JP17km0105001, JP21tm0124005, and JP19gk0110039 from the Japan Agency for Medical Research and Development.

Role of the Funder/Sponsor: The funder had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

Data Sharing Statement: See Supplement 2 .

Additional Contributions: We thank the participants in the TMM BirThree Cohort Study and the staff members of the Tohoku Medical Megabank Organization. The list of members is available at https://www.megabank.tohoku.ac.jp/english/a220901/ .

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The influencing factors of clinical nurses’ problem solving dilemma: a qualitative study

a Department of Nursing, Shanghai Pulmonary Hospital, Tongji University, Shanghai, China

b Tongji University School of Medicine, Shanghai, China

c Beijing Tiantan Hospital, Capital Medical University, Beijing, China

Problem solving has been defined as “a goal-directed sequence of cognitive and affective operations as well as behavioural responses to adapting to internal or external demands or challenges. Studies have shown that some nurses lack rational thinking and decision-making ability to identify patients’ health problems and make clinical judgements, and have poor cognition and response to some clinical problems, easy to fall into problem-solving dilemma. This study aimed to understand the influencing factors of clinical nurses’ problem solving dilemma, to provide a basis for developing training strategies and improving the ability of clinical nurses in problem solving.

A qualitative research was conducted using in-depth interviews from August 2020 to December 2020. A total of 14 participants from a tertiary hospital in Shanghai, China were recruited through purposive sampling combined with a maximum variation strategy. Data were analysed with the conventional content analysis method.

Three themes and seven subthemes were extracted: nurse’s own factors (differences in knowledge structure and thinking, differences in professional values, poor strain capacity); improper nursing management (low sense of organizational support, contradiction between large workload and insufficient manpower allocation); patient factors (the concept of emphasizing medicine and neglecting to nurse, individual differences of patients).

The influencing factors of clinical nurses’ problem-solving dilemma are diverse. Hospital managers and nursing educators should pay attention to the problem-solving of clinical nurses, carry out a series of training and counselling of nurses by using the method of situational simulation, optimize the nursing management mode, learn to use new media technology to improve the credibility of nurses to provide guarantee for effective problem-solving of clinical nurses.

Introduction

Nursing education in China can be divided into two main levels: vocational education and higher education. Vocational education includes technical secondary schools and junior colleges, while higher education includes undergraduate, master’s and doctoral education. Vocational education aims at training students to master basic nursing service skills and to be able to take the post to engage in daily nursing work (Sun & Zong, 2017 ). Higher nursing education started late, and undergraduate education has always followed the “three-stage” education model of clinical medicine (basic medical courses, specialized courses and clinical practice). Most courses are centred on subject knowledge, and all clinical practice takes the form of centralized practice (Li, 2012 ). The training goal of nursing postgraduates is gradually expanding from academic master to professional master. The curriculum mainly includes classroom teaching and clinical practice. The classroom teaching contents include public courses (political theory, foreign languages, etc.), professional basic courses (advanced health assessment, pharmacotherapy, pathophysiology, evidence-based nursing, medical statistics or clinical epidemiology), specialized courses (advanced nursing practice theory) and Academic activities . The goal of nursing doctoral training is to cultivate high-level nursing research talents, focusing on the cultivation of scientific research ability rather than clinical practice ability. The curriculum includes ideology and politics, basic theory, research methods, specialized courses, development frontier, scientific writing, etc (Luo et al., 2018 ). There are some problems in the training mode and curriculum, such as theory and practice are out of touch, traditional lecture-based classroom teaching makes students passively accept knowledge, students attach importance to theory over practice, knowledge input to ability output, professional study to humanities knowledge. Nursing students receive no theoretical and/or practical training in problem solving before entering the clinical setting, so there is not a starting point for these nurses to clinical dilemmas in their professional life.

With the development of medicine, people pay more attention to health and have higher requirements for nursing service ability (Yang, Ning, et al., 2018). The National Nursing Development Plan (National Development and Reform Commission, 2017 ) points out that it is necessary to strengthen the construction of nurse teams, establish nurse training mechanisms and improve the professional quality and service ability of nurses. However, in the face of increasingly complex and changeable clinical environment, nurses are still lacking in problem-solving thinking and ability, and often fall into the dilemma of problem solving (Li et al., 2020 ).

Typical decision theory approaches to the identification of problem solving in nursing have viewed the process as a series of decision formulations that include: decisions about what observations should be made in the patient situation; decisions about deriving meaning from the data observed (clinical inferences); and decisions regarding the selection of action to be taken that will be of optimal benefit to the patient (McGuire, 1985 ). Information processing theory describes problem solving as an interaction between the information processing system (the problem-solver) and a task environment, which can be analysed as two simultaneously occurring sub-processes of “understanding” and “search” (VanLehn, 1989 ). Individuals collect the stimulus that poses the problem in the understanding process, forming the internal representation of the problem, transforming the problem stimulus into the initial information needed in the search process, and then producing mental information structures for the understanding of the problem, which making individuals distinguish the nature of the problem and clarify the goal of the problem. The mental information structures drive the search process that enables the individual to find or calculate the solution to the problem. This process starts with the nurse identifying the clinical problem and continues until the decision is made to resolve the problem (Taylor, 2000 ). Clinical problem solving requires nurses to have a variety of cognitive strategies, which involves nurses’ knowledge, experience, and memory process. Nurses must recognize the current problem and use all available knowledge and experience to transform the problem into their internal problem representation, and then set goals and search for strategies that can achieve the goal (Mayer & Wittrock, 1992 ). In today’s complex clinical environment, nurses need to be able to solve problems accurately, thoroughly, and quickly. Nurses who can solve problems efficiently have fewer medical errors (Babaei et al., 2018 ), and the level of nursing skills and empathy are higher (Ay et al., 2020 ; Bayindir Çevik & Olgun, 2015 ). To cultivate nurses’ problem solving thinking and ability, it is necessary to better understand the influencing factors of problem solving dilemma. However, these cannot be obtained by observing nurses’ behaviour in their work, and cannot be obtained through quantitative research either. Exploring the thinking process involved in nurses’ work through qualitative interviews is an effective way to understand the influencing factors of nurses’ problem solving. Given this, this study used qualitative research methods to deeply analyse the influencing factors of clinical front-line nurses’ problem solving dilemma, to provide a basis for making relevant strategies to cultivate nurses’ thinking and ability of problem solving.

Study design

A qualitative study based on in-depth interviews was conducted to obtain influencing factors of nurses’ problem-solving dilemma.

Settings and participants

Purposive sampling combined with a maximum variation strategy was used to identify and select information-rich participants related to the research phenomenon. Maximum variation was achieved in terms of participants’ gender, education level, professional title, marital status, seniority, and administrative office, respectively. The study was conducted between August 2020 to December 2020 in a tertiary hospital in Shanghai, China. The inclusion criteria were a nurse practicing certificate of the People’s Republic of China and within the valid registration period; having been engaged in clinical nursing work for at least 1 year and still engaged in clinical nursing work; clear language expression, able to clearly describe the solution and feelings of clinical problem solving; informed consent to this study and voluntary participation. The exclusion criterion were on leave during the study period (personal leave, maternity leave, sick leave, etc.); out for further study or came to the hospital for further study; confirmed or suspected mental illness and psychotropic medicine users. Purposive sampling continued until thematic saturation was reached during data analysis.

Data collection

Face-to-face, a semi-structured interview was used to collect information. All interviews were conducted in the lounge to ensure quiet and undisturbed by a female postgraduate nursing student with the guidance of her master tutor. Initially, an interview guide was developed based on literature review and expert consultation including about five predetermined questions: What thorny problems have you encountered in clinical work or have a great impact on you? How did you solve it? Why take such a solution? What is the biggest difficulty encountered in the process of problem solving? How does it affect you? How do you feel in the process of problem solving? Before the interview, the consent of the interviewee was obtained and then the researcher fully explains to the interviewees and starts with a friendly chat to allay the interviewees’ worries. During the interview, the researcher listened carefully and responded in time, always maintaining a neutral attitude, without any inducement or hint, if necessary, giving encouragement and praise to support the expression of the interviewees, and to record the interviewees’ facial expressions, physical movements and emotional responses in time. At the same time, a recording pen was used to ensure that the interview content was recorded accurately and without omission. The interview time for each person was 30 to 40 minutes.

Data analysis

After each interview, the researcher wrote an interview diary in time to reflect on the interview process and transcribed the interview content into words within 24 hours, then the researcher made a return visit by phone the next day to confirm that the information is correct. The seven-step method of Colaizzi’s phenomenological analysis method ( Table I ) was adopted to analyse the collected data(Colaizzi, 1978 ). Two researchers collated the original data, independently coded, summarized this information as themes, and organized a research group meeting once a week to discuss and reach a consensus.

7 steps of Colaizzi’s phenomenological analysis method.

Ethical considerations

This study was approved by the Ethics Committee of the Shanghai Pulmonary Hospital, Affiliated to Tongji University, project number: K16-252. Before the interview, the researcher explained the purpose and significance of the study to each interviewee in detail and obtained the informed consent of them on a voluntary basis and all of the interviewees signed informed consent forms. To protect the privacy of each interviewee, their names are replaced by numbers (e.g., N1, N2), and the original materials and transcribed text materials involved are kept by the first author himself, and all materials are destroyed after the completion of the study.

There was no new point of view when the 13th nurse was interviewed, and there was still no new point of view when one more nurse was interviewed, the interview was over, 14 nurses were interviewed. Three themes and seven subthemes were extracted. The characteristics of the participants ( N = 14) are provided in Table II .

Participant characteristics (N = 14).

Nurses’ own factors

Differences in knowledge structure and thinking.

Differences in the structure of prior knowledge and way of thinking will affect nurses’ processing of clinical data, thus affecting their clinical decision-making. The nurses made a wrong judgement of the condition because of the solidified thinking that postoperative nausea and vomiting symptoms were side effects of narcotic drugs and the lack of overall control and understanding of the patient’s condition.

There was a patient who came back after surgery with nausea and vomiting, the first thing that went through my mind, is the drug side effects, so I didn’t pay much attention, as is often the case, the most common cause of postoperative nausea and vomiting is anesthetic drug side effects, but later found to be cerebral infarction, this kind of situation I find it hard to recognize.

Differences in professional values

Professional values of nurses are accepted codes of conduct internalized by nursing professionals through training and learning (Pan, 2016 ). Negative professional values are easy to lead to problem solving dilemma. Some nurses think nursing is just a service.

The work is difficult to do, everything is the nurse’s fault, the nurse must apologize and put up with the patient’s scolding, nursing is a service industry, sometimes I am really wronged.” There are also nurses who believe that nursing work can reflect their personal value, and solving problems successfully will bring them a sense of achievement.

Although the nursing work is very intense, I live a full life every day. I feel a sense of accomplishment and pride that I can solve the problems of patients and discharge them smoothly through my work.

Poor strain capacity

Nursing work is patient-centred holistic nursing, the current clinical situation is complex and changeable, requiring nurses must have good strain capacity, and can “be anxious about what the patient needs, think what the patient thinks, and solve the patient’s difficulties.”

All patients are self-centered, and they don’t care whether you (the nurse) are busy or not. For example, once I gave oral medicine to a patient, a patient in the same ward was in a hurry and asked me to help him call his son. I was busy handing out the medicine and did not help. As a result, the patient was very dissatisfied and complained to the head nurse.

The 20-bed patient went through the discharge formalities but was still lying in the hospital bed. when the new patient arrived and she didn’t leave, I went to urge her to leave the hospital, she suddenly got angry and scolded me, I don’t know what to do.

Improper nursing management

Low sense of organizational support.

Organizational support is an important resource for clinical nurses in the process of problem solving (Poghosyan et al., 2020 ). Low sense of organizational support will hinder nurses’ problem solving.

The style of leadership and the atmosphere of the department are very important. in a department I rotated before, the leader was too strict to listen to your explanation, and the atmosphere of the department was not good. I couldn’t find help when I encountered problems. When I have a conflict with a patient, the leader will only criticize me, which makes me feel helpless.

Sometimes there will be a conflict with patients due to the bed turnover problem, and the patient will not listen to your explanation and turn around to complain, the nurse will be responsible for such things. In severe cases, even violent incidents will be encountered and the personal safety can not be guaranteed.

Insufficient allocation of manpower

Although the total number of nurses has increased substantially, there is still a shortage of human resources under the rapidly increasing workload (Guo et al., 2021 ).

When I was on the night shift and I encountered the critical moment of rescuing patients, I had to call an anesthesiologist, a doctor on duty, a nurse on duty simultaneously, an observation of the patient’s condition to prevent accidents was needed, I also have to race against time to give the patient ECG monitoring and oxygen inhalation. When the doctor came, he also criticized me that the first-aid equipment was not in place (crying).

According to the normal nurse-patient ratio, each nurse takes care of eight patients, and now there are not only eight patients, but also with extra beds and a fast turnover, and sometimes a nurse is responsible for more than 12 patients

Patient factors

The concept of emphasizing medicine and neglecting to nurse.

There is a deviation in society’s cognition of the profession of nurses, which believes that nurses are the “legs” of doctors, and nurses’ work is to help doctors run errands, give injections and give fluids. This concept not only leads to nurses’ lack of due respect, but also hinders nurses’ professional identity, and has a great negative impact on nurses’ problem-solving (Gao et al., 2015 ).

The patient did not dare to tell the doctor something he was not satisfied with, but complained directly to the nurse. For example, if the patient did not want to do some tests, he would scold the nurse. The nurse explained to him that he would not listen. But when the doctor came, he smiled and refused to admit that he cursed nurses, and he would frame the nurse. 90% of the patients would be willing to listen to the doctor.

Sometimes the patient says he was not feeling well, and I know the patient’s condition. I will give her some reasonable explanations, but the patient does not accept it. She is satisfied only when the doctor come to see her. In the final analysis, the patient just don’t believe us. No matter how much I explain to her, it is not as effective as the doctor’s glance at her.

Individual differences of patients

There are differences in patients’ personality characteristics, cultural background, views on nurses and state of an illness, these individual differences are also the reasons for nurses’ problem-solving dilemma (Chan et al., 2018 ).

Some cancer patients are in a period of anger, and it is very difficult to communicate with him. When I see him angry and lose his temper, I will not talk to him and just leave.”

Patients have different cultural levels and different social backgrounds. Sometimes I can’t talk too deeply. If patients are a little more educated, it will be easier for us to communicate with them, and some patients can’t understand anything we say.”

Multiple factors affecting clinical nurses’ problem-solving dilemma

The reasons for nurses’ failure in problem solving are mainly in the process of understanding the problem, the search process driven by the psychological information structure, and the problem or loss of balance in the process of implementing the plan. In the process, the three factors of nurses, management and patients all played an important role. Nurses’ knowledge structure and thinking loopholes led to the deviation of nurses’ internal representation of the problem (Jonassen, 2005 ). Poor professional values and low sense of organizational support can lead to nurses’ negative orientation and attitude towards problems (Poghosyan et al., 2020 ; X. Wang et al., 2018 ). The manpower allocation of nurses, patients’ emphasis on medical treatment over nursing care, and individual differences mainly increase the complexity and difficulty of nurses’ problem-solving task environment as external factors. The three factors work together on the problem-solving of clinical nurses, which leads to the dilemma of problem-solving.

Implementing situational simulation training to improve the comprehensive quality of nurses

At present, the overall quality and ability of nurses cannot meet the requirements of systematic, effective and rapid problem-solving. It is necessary to strengthen the construction of nurses to improve nurses’ problem-solving ability. Some studies have shown that situational simulation class can improve students’ knowledge, experience, psychological quality and other abilities (Mohammad, 2020 ). It is suggested that nursing educators should explore targeted situational simulation teaching and strengthen the relationship between classroom teaching and clinical practice through situational simulation, and to build a novel, perfect and clinical knowledge network for nurses. Secondly, emergency situational simulation teaching should be carried out to enable nurses to experience emergency situations from different angles, so as to improve their thinking, skills and timeliness in dealing with emergencies (Zhang et al., 2019 ). The content of professional values training should also be added to the situational simulation class in order to cultivate nurses’ positive, accessible and stable professional values and promote their positive orientation and attitude when facing problems (Skeriene, 2019 ).

Optimize nursing management and improve nurses’ working experience

Through interviews, it is found that nursing management factors have caused nurses’ problem-solving dilemma to a certain extent, which needs to be optimized according to the specific problems existing in nursing management to help nurses deal with the problems and solve the dilemma effectively. The total number of registered nurses in China exceeded 4.7 million in 2021, an increase of 1.46 million from 3.24 million in 2015, an increase of 45% (Deng et al., 2019 ]. However, there is still a large workload and underallocation of manpower, which may be due to the unreasonable distribution of human resources between time periods and departments. Hospitals and nursing managers can use the hospital information system to evaluate the nursing workload, and allocate nursing human resources reasonably according to the evaluation results (H. Yang et al., 2019 ), so as to avoid nurses falling into the dilemma of problem solving due to long-term overloaded work. In addition, it is necessary to create a harmonious departmental atmosphere for nurses, create a supportive departmental environment (Aghaei et al., 2020 ), and strictly ensure the safety of nurses’ practice and put an end to the occurrence of violence. Timely and strong organizational support can reduce the painful feelings of nurses caused by adverse events (Stone, 2020 ). and help them to solve problems actively.

Using new media to improve the image and credibility of nurses

There is a bias in social cognition of the profession of nurses, and some negative media reports mislead patients, resulting in social stereotypes of nurses (L. Q. Wang et al., 2021 ). It is necessary to make full use of new media to objectively introduce the nursing profession to the public, publicize outstanding nursing figures and typical deeds, make the public realize the important role of nurses in health care, and create an atmosphere of understanding and supporting nurses in the whole society to enhance the image and credibility of nurses and help nurses deal with problems and solve difficulties effectively (Falkenstrom, 2017 ).

Limitations and strengths of the study

The limitation is that the transferability of this study’s results may be limited as a result of including a small number of participants and the participants all worked in the same hospital in Shanghai. More participants in different cities and hospitals could have increased the variety of the descriptions and experiences. The strength is that the use of purposive sampling facilitated inclusion of participants from a range of demographic groups. The use of maximum variation strategy facilitated that the participants covered different gender, education level, professional title, marital status, seniority and department, which helped to increase the representativeness of sample.

Implications for practice

This study provides an in-depth exploration of the problem solving dilemmas of clinical nurses in China and provides valuable insights into the continuing education of nurses. These insights shine a light on areas that warrant further investigation and need to be improved in continuing education of nurses. It is of great significance to improve nurses’ problem-solving ability, improve nurses’ professional quality, effectively solve patients’ medical treatment and health problems, and improve patients’ experience of seeking medical treatment.

Through the semi-structured interview, it is found that the problem-solving dilemma of clinical nurses is affected by many factors. Nurses themselves should be confident, self-improvement, constantly learning and enterprising to improve their own ability, and be good at using new media to improve nurses’ image and credibility. Hospitals, nursing administrators and nursing educators should take corresponding measures to improve the knowledge structure of nurses, cultivate nurses’ positive professional values and adaptability, and give full organizational support to nurses. optimize the allocation of nursing human resources to provide a strong guarantee for nurses to deal with problems solving dilemma.

Biographies

Yu Mei Li : associate chief nurse, master degree, master supervisor, engaged in nursing of tumor patients.

Yifan Luo : nurse, master degree, engaged in clinical nursing.

Funding Statement

This work was supported by the Graduate Education Research and Reform Education Management program of Tongji University [2021YXGL09].

Disclosure statement

No potential conflict of interest was reported by the author(s).

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Global Optimization for Heilbronn Problem of Convex Polygons Based on Bilinear Matrix Inequalities Solving

• Published: 07 September 2024

Cite this article

• Niuniu Qi 1 ,
• Lydia Dehbi 1 ,
• Banglong Liu 1 ,
• Zhengfeng Yang 1 &
• Zhenbing Zeng 2  

This paper primarily focuses on solving the Heilbronn problem of convex polygons, which involves minimizing the area of a convex polygon P 1 P 2 … P n while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to \(1\over 2\) . The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints. A new method is presented to verify the upper and lower bounds for the optimization problem. The upper bound is obtained by the affine regular decagon. Then Bilinear Matrix Inequalities (BMI) theory and the branch-and-bound technique are used to verify the lower bound of the problem. The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548. The relative error compared to the global optimum is 0.104%.

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Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200241, China

Niuniu Qi, Lydia Dehbi, Banglong Liu & Zhengfeng Yang

Department of Mathematics, Shanghai University, Shanghai, 200444, China

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This research was supported by the National Natural Science Foundation of China under Grant No. 12171159, and the National Natural Science Fund of China Research Fund for International Scientists under Grant No. 12350410363.

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Qi, N., Dehbi, L., Liu, B. et al. Global Optimization for Heilbronn Problem of Convex Polygons Based on Bilinear Matrix Inequalities Solving. J Syst Sci Complex (2024). https://doi.org/10.1007/s11424-024-3366-y

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Received : 10 September 2023

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DOI : https://doi.org/10.1007/s11424-024-3366-y

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