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I suggest, is the act of breaking out of an impasse. . . . Without the impasse, there is no insight, only smooth progress. (Ohlsson, 1992, p. 4)
According to Ohlsson (1992), restructuringâ€”changing the problem representation in response to impasseâ€”can take several forms.
Creativity: Understanding Innovation
1. The individual may try to find a different way to describe an object or objects in the problem, which might be important in opening a new path that leads to solution. This is called elaboration of the problem representation.
2. The individual may decide that some previously ignored object should be included among the objects in the problem, which can lead to new solution methods. This is called re-encoding of the problem representation, since new information is encoded into the representation.
3. The individual may change the way in which he or she thinks about the goal of the problem, or the method to be used in reaching the goal. This is called relaxing goal constraints.
As a concrete example of how these ideas work, Ohlsson (1984b) analyzes behavior in several insight problems, including the Two-String problem (Figure 6.1G) and the Candle problem (Figure 6.1B). In analyzing the Two-String problem, Ohlsson considers the predicament of an individual who is at impasse, holding one string but unable to reach the second. That person may, though elaboration, examine the other objects in the problem and note that the pliers are heavy. That realization may lead him or her to contemplate uses for heavy things, which can lead to the possible use of the pliers as a weight for a pendulum. In this situation, elaboration of an object in the problem representation leads to new solution possibilities. In the Candle problem, similarly, Ohlsson assumes that the initial attempts to solve the problem result in an impasse, which forces the individual to attempt to restructure the problem. This may lead to an examination of the features of the box, which, again through Ohlssonâ€™s postulated process of elaboration, might lead to the realization that the box is flat and sturdy, which can pave the way to the idea of using it as a shelf. It is also possible that the individual working on the Candle problem might not even have noticed the box initially, so re-encoding the problem in response to impasse might reveal the presence of the box, which also could trigger new solution possibilities.
A Bottom-Up Explanation of Restructuring
In the neo-Gestalt view, the original Gestalt notion of perceptually based restructuring is replaced with the idea of heuristic search for an alternative problem representation. Heuristic methods, such as switch when stuck or restructure when stuck (Kaplan & Simon, 1990; Ohlsson, 1992), are weak methods and are independent of the knowledge of the thinker. One does not have to know much, if anything, about the problem itself to try to change the descriptions of the objects in it or the relations among those objects. One could thus say that, in the neo-Gestalt analysis, restructuring as a re-
The Question of Insight in Problem Solving
suit of heuristically guided search is a bottom-up phenomenon; without any overall plan, the person works up from the information in the problem in the hope of finding a better way of representing the problem. When trying to restructure the Two-String problem, say, by considering the features of the objects lying on the table, the person would not know which objects to examine or how to rethink the description of each. This conclusion follows logically from the notion of impasse: A person at impasse is at a loss. A similar bottom-up process is seen if one tries to find a way to solve the Candle problem, as the neo-Gestalt view proposes (e.g., Ohlsson, 1992), by examining each object in the problem to see if a possible new solution comes to mind. In these examples, the person is not actively doing much to deal with the problem; he or she is simply looking around with no particular purpose in the hope of finding something that might workâ€”again, as the notion of impasse implies. This bottom-up analysis of insight in problem solving can be contrasted with the emphasis on top-down processing in the cognitive-analytic view summarized in Table 6.1.
Studies of Restructuring in Response to Impasse
Knoblich, Ohlsson, and Raney (2001) and Kaplan and Simon (1990) investigated the responses of individuals to impasses during problem solving, looking for restructuring and insight. Knoblich and colleagues used matchstick-arithmetic problems to test Ohlssonâ€™s (1992) analysis of restructuring (see Table 6.2). According to their findings, solution of matchstick-arithmetic problems requires that the person carry out constraint relaxation and chunk decomposition. These are two examples of Ohlssonâ€™s notion of loosening of problem constraints. As noted in Chapter 3, matchstick-arithmetic problems clash with constraints imposed by oneâ€™s experience with equations in ordinary arithmetic. For example, in ordinary arithmetic, individual numerical values cannot be changedâ€”one can only perform the same operations to both sides of any equation. That is, there is a numerical