problem solving definition journal

Problems: Definition, Types, and Evidence

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Problem solving

A distinction can be made between “task” and “problem.” Generally, a task is a well-defined piece of work that is usually imposed by another person and may be burdensome. A problem is generally considered to be a task, a situation, or person which is difficult to deal with or control due to complexity and intransparency. In everyday language, a problem is a question proposed for solution, a matter stated for examination or proof. In each case, a problem is considered to be a matter which is difficult to solve or settle, a doubtful case, or a complex task involving doubt and uncertainty.

Theoretical Background

The nature of human problem solving has been studied by psychologists over the past hundred years. Beginning with the early experimental work of the Gestalt psychologists in Germany, and continuing through the 1960s and early 1970s, research on problem solving typically operated with relatively simple laboratory problems, such as Duncker’s...

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Berry, D. C., & Broadbent, D. E. (1995). Implicit learning in the control of complex systems: A reconsideration of some of the earlier claims. In P. A. Frensch & J. Funke (Eds.), Complex problem solving: The European perspective (pp. 131–150). Hillsdale: Lawrence Erlbaum.

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Seel, N.M. (2012). Problems: Definition, Types, and Evidence. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_914

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21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
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This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “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 [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

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PERSPECTIVE article

Problem-solving is embedded in context… so how do we measure it.

• 1 University of California, Irvine, Irvine, United States
• 2 California State University, Fullerton, Fullerton, California, United States

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Problem solving encompasses the broad domain of human, goal-directed behaviors. Though we may attempt to measure problem solving using tightly controlled and decontextualized tasks, it is inextricably embedded in both reasoners’ experiences and their contexts. Without situating problem-solvers, problem contexts, and our own experiential partialities as researchers, we risk intertwining the research of information relevance with our own confirmatory biases about people, environments, and ourselves. We review each of these ecological facets of information relevance in problem-solving, and we suggest a framework to guide its measurement. We ground this framework with concrete examples of ecologically valid, culturally relevant measurement of problem solving.

Keywords: problem-solving, Measurement, Information relevance, Ecological Validity, Cultural relevance

Received: 01 Feb 2024; Accepted: 26 Apr 2024.

Copyright: © 2024 Rhodes, Richland and Alcalá. 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) or licensor 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: Katherine Rhodes, University of California, Irvine, Irvine, United States

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. 

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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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• Open access
• Published: 05 February 2018

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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Ji Young Kim, Dae Soo Choi & Chang-Soo Sung

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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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Received : 12 September 2017

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

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