The problem-solving literature commonly distinguishes between search and pop-out solutions. Search strategies are deliberate and effortful methods for proceeding incrementally from the initial state to the solution. Because these strategies deposit intermediate results in working memory, when solvers use them they report a gradual accumulation of partial information on the way to solution. Sometimes, however, the solution simply pops into mind suddenly without any consciousness awareness of how it was generated, and therefore without the awareness of incremental progress toward the goal that accompanies search solutions.
Probably the most intriguing aspect of the Gestalt view of problem solving is the claim that pop-out (insight) solutions are qualitatively different from search solutions, in particular that they are objectively as well as subjectively sudden. Durso, Rea, and Dayton (1994) obtained results from subjects' similarity ratings for word pairs that would seem to indicate evidence for the nonsudden accumulation of solution-relevant information underlying the phenomenological experience of sudden pop-out. However, this interpretation is not the only possible one because subjects rated the same 12 word pairs (two of which were related to the solution) numerous times prior to solution. It is not unreasonable to think that the repetition of this small number of word pairs might have altered subjects' approach to solving the problem. In particular, it might have caused them to search through the space of word pairs and related conceptual knowledge for information possibly relevant to solving the problem. This strategy might have enabled them to construct the solution incrementally, thereby yielding the increasing similarity ratings for the critical word pairs prior to solution, even though the typical solution to the puzzle pops into mind suddenly.
Therefore, an additional test of the Gestalt hypothesis that pop-out solutions are qualitatively different from search solutions, that avoids the potential problems inherent in Durso et al.'s (1994) methodology, clearly is warranted. Such a test should explicitly compare the accumulation of information underlying pop-out and search solutions, and it should avoid requiring subjects to make the same judgments multiple times for a given problem. For the sake of generality, it also would be advantageous to select a new problem domain, with different characteristics. Jim Sherman, at Indiana University, and I conducted such a test using the domain of anagram solution (Novick & Sherman, 2003). The results of Experiment 1 indicated that pop-out solutions occur for anagrams and that highly skilled anagram solvers, on average, are much more likely to generate pop-out solutions than are less skilled solvers (also see Novick & Sherman, 2008). Thus anagram solution is an appropriate domain for studying the accumulation of information underlying pop-out solutions. By way of an operational definition when retrospective solution-process reports are unavailable, our data indicate that anagram solutions occurring within 2 sec are almost certainly pop-out solutions.
As noted earlier, Durso et al.'s subjects made repeated similarity ratings for concepts related to the required restructuring. In Experiment 2, our subjects made a single solvability judgment for each of numerous letter strings that either could or could not be unscrambled to form an English word (Novick & Sherman, 2003). The solvable and unsolvable letter strings were closely equated so that distinguishing them would require information about the degree of fit of the letters to the constraints of English spelling. Because the letter strings were presented for a very short amount of time (average display times of approximately 470 and 950 msec), and subjects were given a deadline for responding, subjects' responses had to be based on whatever partial information, if any, had accumulated at the time a response was required. Some of the solvable letter strings (i.e., anagrams) in this experiment were ones for which pop-out solutions are preferentially associated with expertise. We referred to these stimuli as differential pop-out anagrams. For these items, a comparison of more and less skilled solvers yields a between-subjects comparison of anagrams that would lead to pop-out versus search solutions. The solvability judgment results for this stimulus set were contrary to the Gestalt view but consistent with the results of Durso et al. (1994) that pop-out solutions depend on the gradual accumulation of partial information. In particular, even for highly skilled solvers, d' increased with increasing display duration.
Durso et al. (1994, p. 98) noted that "if one looks closely, a long fuse warns of the impending reorganization." Our close look into the information underlying pop-out solutions in the anagram domain also revealed a fuse, although its length clearly depends on the amount of time required for solution. Our fuse showed signs of life as early as about 284 msec after presentation of the problem (for two anagram experts), and the explosion occurred within 2 sec.
The Effects of Superficial and Structural Information on On-line Problem Solving as a Function of Expertise
An extensive literature has documented striking differences in the types of problem features on which experts and novices focus their attention. Whereas novices attend preferentially to solution-irrelevant superficial features of problems (e.g., the specific objects and terms mentioned in the problem), experts attend preferentially to underlying solution-relevant structural features (e.g., relations among the objects in the problem). These differences have primarily been documented in off-line tasks such as problem sorting and recall. Jim Sherman and I predicted that these differences also have important consequences for on-line problem solving. In particular, we predicted that superficial features have a greater effect on solution difficulty for novices, whereas structural features have a greater effect on solution difficulty for experts. Surprisingly, only a few studies have addressed this issue, and all involved mathematical problem solving. We tested these predictions in two experiments in the domain of anagram solution (Novick & Sherman, 2008).
In Experiment 1, we orthogonally manipulated the pronounceability of the anagram (a superficial characteristic) and the fit of the solution word to the constraints of English spelling (a structural characteristic). Our structural measure was derived from the summed bigram frequency of the word, which was computed using our type-based norms of bigram frequency (Novick & Sherman, 2004). There were three categories of words, termed strong convergence, weak convergence, and unlikely. The first two categories include well-structured words (e.g., beach, sound, story), whereas the third category includes poorly-structured words (e.g., cargo, grief, haste). In Experiment 2, we orthogonally manipulated two structural characteristics -- fit to spelling constraints and number of syllables (one vs. two). We also conducted multiple regression analyses using the data from both studies combined in which we predicted solution difficulty from these two measures of word structure as well as several other structural and superficial characteristics of words: whether the solution begins with a consonant or a vowel (structural), fit to pronunciation rules (structural), presence of an uncommon letter (structural), and number of orthographic neighbors (superficial).
Our indicator of solution difficulty was time spent working on the anagrams, which we measured for both highly skilled and less skilled anagram solvers. The results of our experiments supported both hypotheses. In Experiment 1, skill level interacted with both pronounceability and spelling constraint category, but in opposite directions: Pronounceability had a larger effect on solution time for less skilled solvers, whereas spelling constraint category had a larger effect on solution time for highly skilled solvers. In Experiment 2, word type, a composite structural variable that took into account both fit to spelling constraints and number of syllables, interacted with expertise. As in Experiment 1, word structure mattered more for highly skilled solvers. In the regression analyses, which were based on the data from both experiments, all four structural variables -- word type, fit to pronunciation rules, begins with a vowel or a consonant, contains an uncommon letter -- made reliable independent contributions to predicting time for highly skilled solvers, whereas only vowel first and uncommon letter affected time for less skilled solvers. In contrast, the superficial variable -- number of orthographic neighbors -- was a reliable predictor of time for less skilled solvers but not for highly skilled solvers.
These results indicate that the effects of superficial and structural information on solution difficulty for expert and novice anagram solvers are consistent with what one would expect based on the literature on expertise differences in the types of problem features to which experts and novices preferentially attend during off-line tasks. Moreover, our results support a view of expertise/skill that posits that such differences are a critical part of the reason why experts and novices differ in their problem solving success.
The Time Course of Access to Structural Information
According to Keil, Smith, Simons, and Levin (1998), it has generally been assumed that in the real-time use of concepts, the similarity-based component of reasoning is processed first, followed by the explanation-based component. In contrast, they proposed that abstract conceptual information is available and used from the earliest stages of processing. They reviewed some evidence consistent with their view with respect to category judgments. Novick and Sherman's (2008) results provide further evidence against the similarity-first assumption with respect to problem solving. We conducted a multiple regression analysis of the proportion of pop-out solutions (i.e., solutions occurring within 2 sec) for highly skilled solvers using the same predictors as for the time analyses. All four of the structural variables made reliable or marginally reliable contributions to predicting pop-out solutions. Clearly, highly skilled anagram solvers are sensitive to structural factors from the earliest stages of processing.
Qualitative Differences in Anagram Solution Processes as a Function of Expertise
Novick and Sherman (2003) used two sets of anagrams in their solvability judgment study, which differed in the strength of the relation between solution time and expertise. They found that highly skilled solvers had more or better partial information than did less skilled solvers for both sets of anagrams, that is, regardless of whether they ultimately would solve the anagrams more quickly. We argued that these results suggest that expertise differences in solution time cannot be explained by positing purely quantitative differences (e.g., in speed of processing or knowledge of bigram frequencies) as a function of expertise. Rather, it seems necessary to posit qualitative differences in the processes used by highly skilled and less skilled solvers. If the two groups often follow different paths to solution, then the pattern of expertise differences with complete information need not predict the pattern of such differences for partial information.
Because we have found that highly skilled solvers are much more likely to produce pop-out solutions (Novick & Sherman, 2003, 2008), we hypothesized that the qualitative difference between the expertise groups is a consequence of a qualitative difference between the processes that generate pop-out versus search solutions. In particular, we hypothesized that pop-out solutions result from parallel processing of the constraints on the rearranged order of the anagram letters, whereas search solutions result from a serial hypothesis testing process. One implication of this hypothesis is that there may be a transition from primarily serial to greater parallel processing with increasing expertise in the domain of anagram solution. Such a transition has been documented in other domains as well (e.g., reading, transcription typing). A second implication is that although both pop-out and search solutions to anagrams rely on the gradual accumulation of partial information (Novick & Sherman, 2003), there nevertheless may be some merit to the Gestalt claim that the two types of solutions are qualitatively different.
The results of our experiments investigating the factors that affect solution difficulty as a function of expertise (Novick & Sherman, 2008) also are consistent with the hypothesis that pop-out and search solutions are generated by different types of processes. Novick and Sherman (2008) discuss in some detail the nature of anagram solution for highly skilled versus less skilled solvers, considering both the pop-out process and the search process. An interesting suggestion derived from their analysis is that expert anagram solvers may, in part, co-opt the mechanism they use for reading.
Novick, L. R., & Sherman, S. J. (2008). The effects of superficial and structural information on on-line problem solving for good versus poor problem solvers. The Quarterly Journal of Experimental Psychology, 61, 1098-1120.
Novick, L. R., & Sherman, S. J. (2004). Type-based bigram frequencies for five-letter words. Behavior Research Methods, Instruments, & Computers, 36, 397-401.
Novick, L. R., & Sherman, S. J. (2003). On the nature of insight solutions: Evidence from skill differences in anagram solution. The Quarterly Journal of Experimental Psychology, 56A, 351-382.