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The Journal of Problem Solving • volume 3, no. 2 (Winter 2011) 119
Human Performance on Insight Problem Solving: A Review
Yun Chu^1 and James N. MacGregor^2
Invited
Abstract:
The article provides a review of recent research on insight problem-solving performance. We discuss what insight problems are, the different types of classic and newer insight problems, and how we can classify them. We also explain some of the other aspects that affect insight performance, such as hints, analogs, training, thinking aloud, and individual differences. In addition, we describe some of the main theoretical explanations that have been offered. Finally, we present some measures of insight and relevant neuroscience contributions to the area over the last decade.
Keyword:
insight
(^1) State University of New York, Purchase College; 2 University of Victoria
http://dx.doi.org/10.7771/1932-6246.
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1. Introduction: What Is Insight?
Most people have had the “Aha” experience when they suddenly discover the solution to a problem that, until that point, had left them baffled. Often, the experience is accompa- nied by a feeling of puzzlement about why the solution eluded them for so long. What caused the mental block in the first place? Cognitive scientists refer to this experience as “insight problem solving,” and study the phenomenon using problems that tend to evoke this type of solution experience. It is therefore convenient to refer to such problems as “insight problems” (Smith, 1995), although this usage should not be taken to mean that every insight experience is associated with a so-called “insight problem.” Individual expe- riences of insight may be quite idiosyncratic, and one person’s insight problem may be another’s commonplace task. For example, someone might experience an insight when putting together a new piece of furniture, which initially seemed to present an insurmount- able challenge. To someone else, the task might proceed in a series of obvious steps that move smoothly from start to finish, with no sense of being blocked and no sudden flash of illumination. The latter process is more typical of non-insight problem solving, which typically occurs incrementally, with a conscious experience of moving toward a solution. Modern interest in insight problem solving was stimulated by an influential review that was sympathetic to the earlier Gestalt contributions (Sheerer, 1963). More recently, a seminal book on the topic of insight was The Nature of Insight by Sternberg and Davidson (1995). This review primarily focuses on significant contributions to the area of insight since the publication of that book. Insight is important because it has been linked to creativity and scientific discov- eries (Finke, 1995). It has been recognized that creative thinking aids in the solution of insight problems (Lubart & Mouchiroud, 2003). Creativity involves divergent thinking during the initial stages of problem solving by producing and connecting various ideas, while convergent thinking synthesizes, analyzes, and verifies the ideas to generate the solution. In science, sometimes insights occur when analogical reasoning is employed (Dunbar, 1995). What makes insight problems difficult to solve is that, initially, they often appear to be routine problems. However, a familiar solution process is the wrong approach. Take, for example, the following Matching Socks problem: single black and brown socks are in a drawer in the ratio of 5:4. How many socks do you have to pull out before you are guar- anteed a pair of the same color? Initially, this appears to be a routine ratio problem, but with further thought you realize that the solution has nothing to do with the given ratio of colored socks. Before reaching what may be an insightful solution, problem solvers often get “stuck” while looking for the solution. People try everything they can think of but to no avail. At this point, they feel like they have hit a wall. People encounter impasse and stop working toward the solution, because they do not know what else they can try.
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period. For example, in Experiment 3, the analyses took into account the last 4 ratings out of a potential 50 ratings. Each problem was allotted 5 minutes during which ratings were taken every 10 seconds. The last 4 ratings only included the last 40 seconds of the process. If insight were a gradual process, this experiment would not have been able to identify it. There is a possibility that insight is a gradual process and does not require out-of-the-ordinary processes (Weisberg, 1992). This might be especially the case with multi-step insight problems. The sudden-gradual and special-ordinary controversies are issues to consider. A further implication of the sudden appearance of solutions is that the underlying processes operate outside of conscious awareness. Building on an earlier theoretical position (Ohlsson, 1992), Representational Change Theory (RCT) proposed that the problem solver begins with an erroneous initial represen- tation of the problem (Knöblich et al., 1999). Any attempts in that direction will result in failure. Only when the problem solver is able to see the problem in a new light or with a new representation does the solution become attainable. The initial inappropriate representa- tion is considered to arise because past experience prompts the construction of a problem space that does not contain the solution. The result is an impasse, which can be broken by changing the faulty representation. Two specific mechanisms of representational change were presented and tested with Matchstick Arithmetic Problems, constraint relaxation and chunk decomposition. The Matchstick Arithmetic Problem instructs the participant to move one matchstick to make the equation true. (The solution is in the Appendix.)
Figure 1. A Matchstick Arithmetic Problem.
Constraint relaxation refers to the releasing of unnecessarily constraining assump- tions. In the above problem, if the problem solver assumes that she can only move the matchsticks making up the roman numerals and not the operators (+, -, =), she would not be able to solve the above problem. Once she realizes that the matchsticks making up the operators can also be moved, constraint relaxation occurs and she is open to finding the solution. Chunk decomposition refers to the deconstruction of perceptual chunks into smaller features, which may be recombined into potentially more produc- tive representations. There are different levels of chunk decomposition. For example, in Matchstick Arithmetic, the easiest level of chunk decomposition is for roman numerals containing parts that have meaning on their own (I, II, and III). It is easy to separate a I from III, leaving II and I, because the separated pieces, on their own, still have meaning as roman numerals. It is a bit harder to separate the two matchsticks making up X, because
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\ and / do not have meaning on their own. Since this is the case, it does not seem useful to dechunk roman numerals such as V and X. However, if V and X were dechunked, then X could form a V, and vice versa. Fewer problem solvers are willing to dechunk a V and X than a I, II, and III. Yet an even harder chunk decomposition is that of the operators, as it is called for in the problem above. Generally, problem solvers will not even consider moving a matchstick that is part of an operator, because operators seem unchangeable. The participant mistakenly assumes she can only move the matchsticks making up the numbers. RCT considers that both constraint relaxation and chunk decomposition occur beyond conscious, voluntary control. A second recent theory of insight is the Criterion for Satisfactory Progress theory (CSP, formerly known as PMT—Progress Monitoring Theory) (MacGregor, Ormerod, & Chronicle, 2001). The theory proposes that a problem solver consciously monitors progress toward a solution against a “criterion of progress” that arises from the problem requirements. The difficulty in reaching a solution lies in the fact that, initially, the participant appears to be making sufficient progress toward the goal state. For example, take the 9-dot problem, which requires the participant to connect all 9 dots with 4 straight lines without lifting his pencil or retracing any lines. (The solution is in the Appendix.)
Figure 2. The 9-dot Problem.
There appears to be sufficient progress toward the solution as long as each line covers 2.25 dots, because 9 dots/4 lines = 2.25 dots covered per line. Following along the edge of the perceived “square” made by the 9 dots, the first line connects 3 dots (suf- ficient progress) making up one side of the square. The second line connects another 3 dots (sufficient progress) on the other side of the square, even though one of the 3 dots on the second side is actually a dot that has already been covered by the first line. However, participants do not seem to count their dot coverage that way. So far, “6” dots have been covered by only 2 lines. At this point, the participant thinks she is making suf- ficient progress, because she still has 2 more lines to go and only 4 more dots to cover. Not until she draws the third line does she realize that the remaining fourth straight line cannot possibly cover the remaining 2 dots. The lack of lookahead ability (being able to see several moves down from the current state) leads the problem solver to think she is making sufficient progress.
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might profitably be merged, since they are effective in explaining different phases of the insight process (Jones, 2003).
3. Types of Insight Problems Used in Research
3.1. Classic Problems
A varied selection of insight problems is found in a number of published sources (Ansburg & Dominowski, 2000; Dow & Mayer, 2004; Gilhooly & Murphy, 2005; Metcalfe & Wiebe, 1987; Weisberg, 1996). Dow and Mayer (2004) categorized insight problems into verbal, mathematical, and spatial.
A verbal insight problem might be:
Marsha and Marjorie were born on the same day of the same month of the same year to the same mother and the same father yet they are not twins. How is that possible?
A mathematical insight problem might be:
There are 10 bags, each containing 10 gold coins, all of which look identical. In 9 of the bags, each coin is 16 ounces, but in one of the bags, the coins are actually 17 ounces each. How is it possible, in a single weighing on an accurate weighing scale, to determine which bag contains the 17-ounce coins?
(The solutions to both problems are in the Appendix.) A spatial problem might be the 9-dot problem in Figure 2 above. These “classic” insight problems represent the primary stimuli in insight research. Yet their availability has been limited to a small collection of spatial puzzles and verbal riddles, such as the 9-dot problem, the triangle of coins, the CNP (above), six matchsticks, and so on (Isaak & Just, 1996), which vary widely in form, content, and level of difficulty. Typically, the relationships among them are unknown and their status as “insight problems” has, in some cases, been questioned (Weisberg, 1996). The absence of large numbers of homogenous stimuli has limited the psychological methods that can be applied in study- ing insight. For example, because of the lack of alternate forms of stimuli, procedures as fundamental as establishing test/retest reliability and transfer of training effects become difficult or impossible. The same stimulus limitations have restricted the applicability of neuroimaging techniques (Luo & Knöblich, 2007). The foregoing discussion has illustrated three limitations with the problems available for studying insight. First, for most clas- sic insight problems, it has not been established that solutions actually require insight.
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Frequently the only rationale for using a problem in an insight study is that it was used previously (Weisberg, 1996). Second, the relationships between problems are unknown. Are all insight problems members of a single class, are there identifiable subsets, or is each one unique? Without knowing the answer, it is impossible to compare results across stud- ies that used different problems. For example, concurrent verbalization has been found to disrupt problem solving with some insight problems (Schooler, Ohlsson, & Brooks, 1993) but not with others (Fleck & Weisberg, 2004). This could be due to differences in the insight status of the problems used, or because they involved different types of insight problem. The current state of knowledge does not allow us to rule out either possibility. Third, even if all “classic” problems do involve insight, they are few in number and they vary widely in content, materials, mode of presentation, and level of difficulty (Luo & Knöblich, 2007; MacGregor & Cunningham, 2008). Until relatively recently, the field has lacked large sets of homogenous stimuli. This, in turn, has limited the kinds of research procedures that can be applied (Bowden et al., 2005). These issues will be discussed below.
3.2. Recent Problems
In contrast to the classic type of insight problem, several more recent sources of insight problem have been identified that promise to provide essentially unbounded sources of relatively homogenous problem. These include Matchstick Arithmetic explained above (Knöblich et al., 1999), Compound Remote Associates (CRAs) (Bowden & Jung-Beeman, 2003a), and Rebus Puzzles (MacGregor & Cunningham, 2008). A CRA requires the problem solver to find the solution word associated with all words of the triad forming three compound words. For example: Age/Mile/Sand. Rebus Puzzles combine verbal and visual or spatial cues that must be deciphered to give a common phrase or saying: i i i i oooo
(All insight problem solutions are in the Appendix.) In addition to providing a large repertoire of potential insight problems, these three types of problems have several useful properties. They require little or no domain-specific knowledge to solve and they are easily explained in a few minutes. More important, and in contrast to most classic problems, the experimenter can manipulate the level of dif- ficulty of the problems. For example, for Rebus Puzzles, the more implicit assumptions that are involved, the more difficult the problem. A rebus that requires only a spatial rela- tion principle (you just me—“just between you and me”) is easier to solve than a rebus that requires two principles (SOMething—spatial relation and font property—“the start of something big”). The hardest rebuses tested have up to four principles present in one problem. Similarly, the difficulty of Matchstick Arithmetic Problems can be manipulated
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a number of different principles to encrypt a phrase or saying. For example, the rebus “thought an” (an afterthought), is solved by interpreting the relative positions of compo- nents spatially, rather than grammatically as in normal reading. In “PUNISHMENT” (“capital punishment”), the visual characteristic of the font has to be interpreted verbally, which again is not something that is done in normal reading. Thus, solving rebuses may involve relaxing one or more of the constraints that apply in processing normal text. Constraint relaxation has been considered to be an important component of insight problem solv- ing (Ohlsson, 1992). Because the same rebus can often be represented in multiple forms, the puzzles have the potential to allow for systematic variation of one or more problem parameters. MacGregor and Cunningham (2008) used alternate forms of the same set of Rebus Puzzles to independently vary the number of constraints to be relaxed and the linguistic level at which the constraints operated (sub-word, word, or supra-word). The results indicated that both factors influence problem difficulty. As mentioned above in Section 3.2, recent developments have uncovered three categories of problems that are candidates to satisfy the need for a pool of homogenous stimuli. These are Matchstick Arithmetic Problems (Knöblich et al., 1999), CRAs (Bowden & Jung-Beeman, 2003a), and Rebus Puzzles (MacGregor & Cunningham, 2008). In each case, there is evidence that some examples of the problem types are associated with insight solution, but there is also evidence that some examples are not (Knöblich et al., 1999; Bowden & Jung-Beeman, 2003b). It is important to have either a theoretical or an empirical basis for identifying which are which. In the case of Matchstick Arithmetic Prob- lems and Rebus Puzzles, there is also evidence that there are subcategories of problems (Knöblich et al., 1999; MacGregor & Cunningham, 2008). Rebus Puzzles tend to be solved fairly quickly, when they are solved at all. Typically, participants are allowed 30 seconds per problem (MacGregor & Cunningham, 2008), compared to 5 minutes or longer for the classic insight problems (Chronicle, MacGregor, & Ormerod, 2004). The short solution du- rations of Rebus Puzzles may present challenges to the use of FOW ratings and protocols. If so, new or modified procedures may need to be developed. In contrast, some studies have categorized insight problems post hoc. Dow and Mayer (2004) categorized a collection of 67 spatial, verbal, and mathematical insight problems based on participant feedback that suggested that participants viewed insight problems as being domain specific. To do so, participants were instructed to sort a number of insight problems into as many groups as they found necessary based on perceived similarities among the problems (Study 1). All possible pairs of problems were scored on the basis of how often the members of a pair were grouped together, and the scores submitted to a cluster analysis. The results indicated four main problem clusters: a spatial cluster, a verbal cluster, a mathematical cluster, and a mixed spatial-verbal cluster. Gilhooly and Murphy (2005) presented participants with 24 insight problems and 10 non-insight problems to solve. Time to solution was measured and a cluster analysis was run after dropping a few
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problems that had very low solution rates (9-dot problem, the mutilated checkerboard problem, 4 trees, and the farm problem). The analysis yielded nine clusters of problems based on performance. Some clusters belonged in the insight category and some belonged in the non-insight category. For example, cluster 1 contained insight problems such as Murples, Matching Socks, and Hole in the Earth, among others. These problems share the characteristics that they seem to be mathematical problems, but the quantities provided in the problems are useless in attaining the solution. The solution for such problems lies in visualizing the potential outcome of the situations. In summary, there are numerous types of insight problems. Some researchers first categorize problems into insight and non-insight problems. Within the insight category, different types of insight problems have been determined using a priori and post hoc procedures. Some classic insight problems are discussed along with their drawbacks as far as the limited number of problems available and lack of problem homogeneity leading to the inability to compare insight problem performance across experiments. However, some new insight problems have come to the forefront due to their versatility. These in- clude Rebus Puzzles, Matchstick Arithmetic Problems, and CRAs. Their advantages over classic insight problems include a large pool of problems from which to draw from and the ability to vary the level of difficulty of the problem.
4. Theories Facilitating Insight
A significant amount of research and theory has investigated the following aspects of insight problem solving. These include (but are not limited to) hints (Burke, Maier, & Hoffman, 1966; Chronicle, Ormerod, & MacGregor, 2001; Kokinov, Hadjiilieva, & Yoveva, 1997; Ormerod, MacGregor & Chronicle, 2002); problem analogs (Gick & Holyoak, 1980; MacGregor, Ormerod, & Chronicle, 2001); number of moves available (Ash & Wiley, 2006; MacGregor, Ormerod, & Chronicle, 2001); types of training (Ahmed & Patrick, 2006; Ans- burg & Dominowski, 2000; Chrysikou, 2006; Cunningham & MacGregor, 2008; Dow & Mayer, 2004); and concurrent verbalization (Fleck & Weisberg, 2004; Schooler, Ohlsson, & Brooks, 1993).
4.1. Hints Derived from Theories The type of hint provided for an insight problem depends on what the researcher thinks the obstacle to solution is. Chronicle, Ormerod, and MacGregor (2001) found that visual and visual-procedural hints did not help the solution to the 9-dot problem. The authors believed that the difficulty lay in the mismatch between the shape of the initial problem and the shape of the solution. Hints included shading outside of the perceived “square” formed by the nine dots. Even when the shading was in the shape of the solution lines, it did not increase solution rates significantly. Verbal hints instructing participants to pay
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three individually opened links used as connectors in the solution. However, when both the verbal and visual hints were combined in one condition, this significantly increased the solution rate. This points to the fact that perhaps many constraints need to be broken in order to solve a multi-step insight problem like the CNP. Limiting the number of moves available helps solution (verbal hint). Having too many erroneous options available leads to an increased time to solution (MacGregor, Ormerod, & Chronicle, 2001). Thomas and Lleras (2010) gave an implicit hint by having one group swing their arms in a manner related to the solution in the two strings problem. This group was more likely to find the solution than a control group that was instructed to stretch their arms in a manner inconsistent with the solution. The authors concluded that subtly directing people’s actions can aid in guiding their thoughts toward the solution. Apparently, this cue was enough to lead to higher solution rates.
4.2. Analogical Transfer
Sometimes providing a problem analogy improves solution rates, but often when ac- companied by an explicit hint to use the analogy. Welling (2007) identified analogy as one of the main processes involved in creative thinking. There are three types of analo- gies. A local analogy is when an analogy is drawn based on a single characteristic that is similar between the base and the target problems. A regional analogy is mapping a set of similarities between two such problems in similar domains. A long-distance analogy is when a set of similarities is mapped between problems in completely different domains (Dunbar, 1995). Gick and Holyoak (1980) presented participants with a long-distance analogy to Duncker’s Radiation Problem in the form of the Attack Dispersion story, in which a general must capture a fortress in the middle of the country. There are several roads leading to the fortress that contain mines that will detonate when a large army passes over them, but a small group of soldiers can pass over them safely. The general must think of a way to launch a full-force attack in order to capture the fortress. The so- lution is to send in small groups over each of the roads and have them converge at the fortress simultaneously. The participants were then presented with Duncker’s Radiation Problem and instructed to use the first story to help them solve it. Although solution rates for the Radiation Problem increased significantly, the hint to use the analogy appears to have been critical to the increased success rate. Using a different base insight problem, Ormerod, Chronicle, and MacGregor (2006) reported successful spontaneous transfer from a more difficult version of the problem to a structurally similar but simpler analog. However, no corresponding transfer was observed from the simpler version to the more difficult, similar to asymmetrical transfer effects that have been observed with non-insight problems. In sum, analogical transfer occurs, but only under certain conditions. The level of similarity between the problems in an analogy plays a significant role in whether the transfer will take place.
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There are two main schools of thought on how analogical transfer happens. Reeves and Weisberg (1994) describe exemplar theories that postulate that analogical solutions come from content domain as well as the specific problems and experiences in the do- main. For example, when a problem solver uses an analogy, she recalls the specific base problem that is similar to the target problem. On the other hand, both structure-mapping and pragmatic schema theories posit that deeper structural similarities are accessed when processing an analogy. That is, abstract knowledge about the problems is used to make an analogy. There is only a handful of research on the use of analogy in insight problem solving in cognitive psychology. However, there are a few more relevant articles on analogy and insight in creativity in the fields of marketing and management. Gassmann and Zeschky (2008) found that analogical thinking is necessary for the development of breakthrough innovations. Identifying a deep level of structural similarities was the key to finding solutions through analogies. Dahl and Moreau (2002) had teams of professional product designers generate ideas for a new product to facilitate eating in the car while driving. Through verbal protocol, it was found that analogy played an important role in the idea generation phase of product development. The more analogies were used, the more original the ideas when there was no external prime for a new line of products. Hints and problem analogies are two methods that have been used to influence insight solution rates.
4.3. Theories on the Effectiveness of Training Insight
A third method has been training, and a number of different types of training emphasizing certain aspects of problem solving have found significant results. However, despite these positive findings, questions remain as to the generalizability of training effects (Ahmed & Patrick, 2006; Ansburg & Dominowski, 2000; Chrysikou, 2006; Cunningham & MacGregor, 2008; Dow & Mayer, 2004). Ansburg and Dominowski reported five experiments testing the effects of training and/or brief instructions. Training involved practice problems that required Ohlsson’s (1992) proposed elaboration mechanism to solve, while instructions stressed looking for different interpretations of a problem. The dependent variable was performance on a set of 15 verbal problems identified as requiring either elaboration or constraint relaxation to solve. In all five experiments, participants in training/instructional conditions significantly outperformed those in control conditions. Although training focused on the mechanism of elaboration, it is equally effective on problems that suppos- edly required constraint relaxation. Ansburg and Dominowski concluded that insightful problem solving can be construed as a general strategic thinking skill that is susceptible to training. Consistent with this conclusion are the results of Chrysikou (2006), who found that insight problem solving could be enhanced by more general training not specifically directed at solving insight problems. In this case, participants were given prior experience in placing common objects in alternative categories (the Alternative Categories Task, a
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process when asked to do so. Some studies have found that generating a solution results in better solution memory than being shown the solution, but Dominowski and Dallob have suggested that the critical factor in enhancing solution memory is not generating the solution per se, but having an understanding of the complete problem structure (which generating a solution may or may not require). This proposal is consistent with that of Ormerod et al., that the difficulty in replicating a solution lies in the multi-step aspect of some insight solutions preventing the solution from being encoded as a single gestalt. Some insight problems may have multiple sources of difficulty (Kershaw & Ohlsson, 2004), and for multi-step problems, the solution may not involve just one insight or the breaking of one constraint, but the recall of many steps and the correct order and combination in which to employ them. This begs the question of what exactly is learned when solving an insight problem if you cannot recall the solution at a later time. Is a sudden leap of insight necessary, yet not sufficient, to find the solution? What conditions are necessary to transfer knowledge from one insight problem to another similar problem? When are the solution components learned well enough to be mapped onto a similar problem? (Pretz, Naples, & Sternberg, 2003). A very vague concept about the solution is learned when a problem solver sees the solution for the first time. She might only have understanding of some surface features of the problem. She might not yet comprehend any underlying patterns behind why the solution is such. A sudden leap of insight might be sufficient for one-step problems, such as certain matchstick problems (e.g., a matchstick solution that involves changing one of the operators). If the impasse occurred because the problem solver thought she could not change the operators, that insight alone might be sufficient to remember the solution upon future encounters. However, in multi-step problems like the 9-dot, the insight of “the lines must go outside of the ‘square’” might not be sufficient to attain solution, because the problem solver still needs to remember where the drawing of the lines starts, where the lines turn, and in what order she must draw the lines. As for transferring knowledge from one insight problem to another similar problem, it depends on what makes the problems similar, as well as how deeply the problem solver understands the solution of the base problem. For example, there are no surface similarities between Duncker’s Radiation Problem and the Attack Dispersion Problem. The first one is a medical problem, while the second one is a military problem. However, if the problem solver gathers the concept that the reason why the Radiation Problem was solved is because of the deeper understanding that weaker components may converge at a single point making a much more powerful impact at the point of convergence, she reflects the deeper structural understanding needed to apply that very same concept to the Attack Dispersion Problem. Overall, the effects of training have yielded mixed results. Some research has found that training and instructions using elaboration and constraint relaxation have improved
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performance. Other research has found that training a general ability to consider solutions outside of the normal set of options comes from a flexibility that aids insight. However, there have been other studies that found that training people in one type of insight prob- lem (e.g., spatial) does not improve performance in a different type of insight problem. One reason could be that the different types of insight problems draw from different cog- nitive abilities, thus, training in one area does not affect solutions in another area. Some issues concerning training involve the generalizability of the training results. It is difficult to talk about training insight problems as a whole due to their lack of homogeneity. For example, a one-move solution for a Matchstick Arithmetic Problem is quite different than a multi-move problem such as the Cheap Necklace Problem. Especially for multi-move problems, they may require several insights to solve. In addition, memory of a solution decays. Training that requires the exactly recall of a previous problem might not be as beneficial to future problems as intended.
4.5. Theories on Metacognition and Verbal Protocol
One way to understand the problem solver’s process is to collect a verbal protocol. The experimenter can simply ask the participant what she is thinking as she is working on the solution. Instructions are to think aloud without filters. A potential drawback of verbal protocol is verbal overshadowing. If the participant is required to explain what she is doing, this is likely to disrupt the very problem-solving process we are attempting to measure. As long as the participant focuses on the problem first and keeps verbalization as a secondary task, verbal protocol is a viable way to investigate the problem-solving process (Ericsson, 2003). Berardi-Coletta et al. (1995, p. 205) have found positive effects of verbal protocol due to the necessary metacognition that occurs with thinking aloud. Metacognition aids in the representation of the problem through reflection and the reassessment of the problem when one encounters obstacles (Davidson & Sternberg, 1998). Problem solving can even benefit from appropriate probes that help people understand their own thought process (Dominowski, 1998). Fleck and Weisberg (2004) found that verbal overshadowing was not a problem in Duncker’s candle problem. On the other hand, Schooler, Ohlsson, and Brooks (1993) found that verbalization hinders insight problem solving. Perhaps verbal overshadowing depends on the specific type of insight problem. Ball and Stevens (2009) presented simple and complex compound remote associates to their participants and found better performance in complex problems when they were allowed to think aloud than when they were asked to suppress talking about their thought processes. Gilhooly, Fioratou, and Henretty (2010) found more negative performance in spatial problems than verbal insight problems when participants were instructed to verbalize. There was no difference in performance between insight and non-insight problems as far as verbaliza- tion. In general, it appears that the metacognitive aspect of verbal protocol is beneficial
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concept to extend three of the lines beyond the dots was employed to increase solution rates on the 9-dot problem. The training and hint worked, yielding a solution rate nearing 50%. In this second experiment, solution rate for the 9-dot was significantly predicted by spatial WM, but not verbal WM. Solvers were significantly more likely to be in the high- spatial WM group than in the low-spatial WM group. In addition, when the analyses only included solvers, individuals with higher spatial WM scores had faster solution times. One limitation of Experiment 2 is that all the training and hints might have changed the 9-dot problem so it is no longer comparable to the standard presentation of the problem (i.e., it is no longer an insight problem). Experiment 3 recorded FOW ratings for the 9-dot to ensure that it still retained its sudden solution pattern as is typical of an insight problem. The FOW pattern for the last 90 seconds for non-solvers remained flat, while the FOW pat- tern for solvers shot up in the last 30 seconds prior to solution attainment. This provides evidence that even with the training and hints, the 9-dot problem retained its insight characteristics. In conclusion, it appears that spatial WM capacity plays an essential role in solution attainment. Solvers were significantly more likely to have high scores in spatial WM. Individuals with high-spatial WM were also faster at solving the problem. DeYoung, Flanders, and Peterson (2008) identified three predictors of insight perfor- mance: convergent thinking (verbal intelligence and working memory) ability, divergent thinking ability (Torrance Tests of Creative Thinking), and ability to break frame (Bruner and Postman’s anomalous card task). They used nine verbal insight problems. For example, “Our basketball team won 72-49, and yet not one man scored a single point. How is that possible?” (Women’s team). These types of problems are considered to be “pure” insight problems. They found that each of the three components predicted performance inde- pendently from the other two. Possessing these abilities predicts insight problem-solving performance. To sum up all the theoretical factors facilitating insight problem solving, hints to the solution work under certain circumstances although some insight problems might require more than one hint to attain insight. Analogies may also help the solution, but it depends on the level of similarity between the base problem and the target problem. Training could improve performance, but different types of training often lead to different results. For example, training on a problem can be very specific to that problem or it can be a general ability to think in a flexible manner. Verbalization can foster successful problem solving, because it taps into metacognition that helps better understand the underlying aspects of the problem and the required mental efforts to solve the problem. However, verbaliza- tion has not helped other types of problems (e.g., spatial). Finally, individual differences in working memory capacity, specifically spatial WM span and the ability to break frame and inhibit an initial perception and switch from that perception, have been found to be related to insight performance.
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5. Performance Measurement in Research
The most frequently used measures are whether or not a problem is solved and the time required for solution. FOW ratings are often used to classify problems into insight/non- insight categories as mentioned above. However, FOW ratings can also be a dependent variable (Metcalfe & Wiebe, 1987). In Experiment 4, Chu (2009) recorded FOW ratings for the CNP, the 9-dot problem, and the 8-ball problem. She also found that the better the participant’s lookahead ability, the lower the FOW ratings when she approached a dead- end in the Cheap Necklace Problem. Cushen and Wiley (2007) found an incremental pattern of importance ratings for important items in the problem as they approached solution and a decrease of importance ratings for items that were unimportant. Other dependent measures are insight ratings (Bowden & Jung-Beeman, 2003b; MacGregor & Cunningham,
- and neuroimaging (Bowden et al., 2005; Luo & Niki, 2003). There are several existing behavioral approaches to establishing the insight status of a solution, including FOW ratings mentioned above, protocol analysis (Fleck & Weisberg, 2004), and two different methods of insight solution ratings (Bowden & Jung-Beeman, 2003b; MacGregor & Cunningham, 2008). FOW ratings and protocols are collected dur- ing the solution process up to the point of solution, whereas insight solution ratings are obtained after solution. This allows more than one method to be applied during a single problem-solving session. Because there may be limitations with each of these methods, it is beneficial to combine all of them in a single empirical procedure. A typical design might involve asking participants to solve a series of potential insight problems. During the so- lution stage, one-third of the participants provide FOW ratings, one-third, protocols, and one-third, neither. The latter condition allows a check on whether collecting FOW ratings or protocols affects solution rates or subsequent insight ratings, which the literature sug- gests could occur (Schooler, Ohlsson, & Brooks, 1993; Weisberg, 1992). Following solution, participants are asked to provide ratings of the insightfulness of the solution, using existing rating methods. Participants who fail to find a solution within the time limit are shown the solution and asked to rate its insightfulness. It is expected that two or three iterations are required to test the array of potential insight problems. The results provide, for a wide range of problems, information on insight status and solution norms. They also identify the comparative usefulness of FOW, protocol analysis, and insight ratings for identifying instances where insight solutions occurred. In addition, the results indicate the problems and conditions where collecting FOW ratings and protocols interfere with solution pro- cesses. Finally, the performance data, ratings, and protocol analysis are used to assess the usefulness of current classifications of problems and to suggest improvements. Grant and Spivey (2003) recorded participants’ saccades while they solved the Radia- tion Problem. They found that solvers and non-solvers focused their attention on different parts of the radiation diagram. For instance, solvers spent more time looking at the skin
