Reinterpreting The Gestalt Findings

We began this chapter by considering the perceptual theories of problem solving proposed by the Gestalt school of psychology. The information-processing approach has inherited the burden of re-interpretation or explanation of the findings of Gestalt research in information-processing terms (see Chapter 1). This reconception of things past has been carried out since the 1970s (see e.g., Holyoak, 1991; Keane, 1985a, 1989; Knoblich, Ohlsson, Haider, & Rhenius, 2000; Knoblich & Wartenberg, 1998; Metcalfe, 1986a; Newell, 1980; Ohlsson, 1984a, 1985, 1992; Simon, 1986; Weisberg, 1980; Weisberg & Alba, 1981; Weisberg & Suls, 1973).

Problem-space models of water-jug problems

We saw earlier that water-jug problems were intensively investigated by Gestalt researchers (see Luchins & Luchins, 1959, 1991). These problems are very amenable to a treatment in terms of problem-space theory. In the 8-8, 5-0, and 3-0 problem we encountered earlier (see Table 14.1), the initial state consists of the largest jug being full of water and the other two jugs empty, and the goal state has four pints of water in the largest- and middle-sized jugs with nothing in the smallest. The operators consist of pouring various amounts of water from one jug to another and the operator restrictions are that the water cannot be added to or flung away while solving the problem.

Atwood and Polson (1976) produced a state-space analysis of these problems in the context of a full process model for explaining subjects' behaviour on water-jug problems. They specified the various heuristic methods used by subjects and included assumptions about the limitations on human information processing (i.e., working memory limitations). Their model had the following main points:

• In planning moves, subjects only look ahead to a depth of one move.

• Moves are evaluated using a means-ends analysis method, where subjects look at the difference between the actual and goal quantities in the two largest jugs and see which of the next alternative states will bring them closer to the goal state.

• Subjects tend to avoid moves that return them to immediately preceding states (an anti-looping heuristic).

• There are limitations on the number of possible alternative moves that can be stored in working memory.

• This limitation can be somewhat alleviated by transferring information into long-term memory.

This model makes predictions about the difficulties that people should encounter in solving water-jug problems, which Atwood and Polson (1976) tested. They were particularly interested in two problems: one involving jugs of 8, 5, and 3 units, and one involving jugs of 24, 21, and 3 units. In both cases, the largest jug is filled and the other jugs are empty, and the goal is to distribute the largest jug's contents evenly between the largest and middle jugs. Both problems are isomorphic in the number of moves one needs to consider to solve the problem. Their model predicted that the 8-8, 5-0, 3-0 problem should be harder than the 24-24, 21-0, 3-0, because the latter could be solved by simply applying the means-ends heuristic whereas the former required a violation of this heuristic. Their results showed that the mean number of moves to solve either problem confirmed this prediction.

Atwood, Masson, and Polson (1980) also tested the proposal that subjects only planned one move ahead to avoid overloading working memory. They assumed that any reduction of the memory load should have the effect of freeing up the problem solver for more long-term planning. To achieve this manipulation they provided subjects with information about all the different moves available from any state in the problem. One group of subjects received even more information in the form of a record of the previous states they had visited. However, although Atwood et al. discovered that the more information subjects received the fewer the number of moves they needed to consider in solving the problem, they did not find the big "planning improvement" they expected. It seems that when the information load is lifted subjects do not use the extra capacity to plan ahead, but rather become more efficient at avoiding states that lead them back to the initial state of the problem.

On the whole, this sort of model has been shown to be very useful. Jeffries, Polson, Razan, and Atwood (1977) and Polson and Jeffries (1982) have extended it to apply to versions of the missionaries-cannibals and Tower of Hanoi problems. So, the model combines predictive specificity with some generality in its applicability.

Problem-space accounts of insight and restructuring

Weisberg and Alba (1981) re-examined the nine-dot problem (see Figure 14.4). In Scheerer's (1963) original paper on the nine-dot problem, he had argued that subjects failed to solve the problem because they assumed that the lines drawn had to stay within the square shape formed by the dots; they were "fixated" on the Gestalt of the nine dots. To test this Weisberg and Alba gave subjects a hint that they could draw lines outside the square. However, with this hint, only 20% solved the problem. They, therefore, concluded that fixation on the square of dots was not the only factor responsible for subjects' failures. In further experiments, Weisberg and Alba used simpler versions of the problem (a four-dot task) and explored the use of specific hints (e.g., drawing some of the lines that lead to the solution). From these experiments they concluded that in order to solve the problem subjects required highly

PANEL 14.2:

OHLSSON'S (1992) INSIGHT THEORY

• The representation of insight problems is a matter of interpretation; so there may be many different mental representations of the same problem (i.e. the problems are ill-defined).

• People have many knowledge operators for solving problems, and therefore operators may have to be retrieved from memory; the retrieval mechanism is spreading activation.

• The current representation of the problem acts as a memory probe for relevant operators in memory.

• Impasses occur because the initial representation of the problem is a bad memory probe for retrieving the operators needed to solve the problem.

• Impasses are broken when the representation of the problem is changed (is re-interpreted, re-represented, or restructured) thus forming a new memory probe that allows the retrieval of the relevant operators.

• This re-representation can occur through (i) elaboration, adding new information about the problem from inference Of the environment (e.g. hints), (ii) constraint relaxation, changing some of the constraints on the goal, (iii) re-encoding, changing aspects of the problem representation through re-categorisation or deleting some information (e.g., re-categorising the pliers in the two-string problem as a building material rather than a tool).

• After an impasse is broken a full or partial insight may occur; a full insight occurs if the retrieved operators bridge the gap between the impasse state and the goal state.

problem-specific knowledge. In their eyes, this undercut the Gestalt concepts of "insight" and "fixation", which they argued were of dubious explanatory value (see also Weisberg, 1986).

However, several other researchers have argued and shown that the notion of "insight" is a key part of problem-solving theory (see Dominowski, 1981; Ellen, 1982; Lung & Dominowski, 1985; Metcalfe, 1986a; Ohlsson, 1992; Simon, 1986). For example, Metcalfe (1986a, 1986b; Metcalfe & Weibe, 1987) asked subjects for their metacognitions—their assessment of their feeling-of-knowing a solution or feelings-of-closeness to a solution—on insight problems and trivia questions they were unable to answer. She found that although people had reasonably accurate metacognitions for the memory/ trivia questions they had no predictive metacognitions for the insight problems. This indicates that the insight problems were not solved by an incremental accumulation of information from memory, but by a sudden illumination, which is best described as "insight".

Other theorists, like Ohlsson (1984a, b, 1985, 1992), have tried to re-assess the Gestalt constructs of insight and restructuring in problem-space terms, rather than rejecting them (for related ideas see Keane, 1985b, 1989; Langley & Jones, 1988). Ohlsson's (1992) position is that "insight occurs in the context of an impasse, which is unmerited in the sense that the thinker is, in fact, competent to solve the problem" (p. 4). The impasse is unmerited because the thinker has the knowledge to solve the problem, but for some reason or another cannot use it. Given this definition, Ohlsson maintains that a theory of insight has to explain three things: (i) why the impasse is encountered, (ii) how the impasse is broken, (iii) what happens after it is broken. Ohlsson's theory is summarised in Panel 14.2

This account is consistent with the known evidence on insight problems and is supported by more recent research (Isaac & Just, 1995; Kaplan & Simon, 1990; Richard, Poitrenaud, & Tijus, 1993; Yaniv & Meyer, 1987). Yaniv and Meyer (1987) have demonstrated in another feeling-of-knowing experiment that unsuccessful attempts to retrieve inaccessible stored information can prime the recognition of later information by a process of spreading activation. Here initial retrieval attempts lead to a spread of activation from some concepts to other concepts in memory. This spread of activation then sensitises the problem solver to other, new information in the environment needed for an insightful solution (e.g., hints, or noticing that the swinging string in the two-string problem provides a solution).

The constraint relaxation proposals of the theory have been more directly tested by Knoblich et al. (1999) using matchstick algebra problems (see Figure 14.12). In these problems, the goal is to move a single stick in such a way that the initial false statement is transformed into a true statement, without discarding any sticks. Therefore, a move consists of moving rotating or sliding a single stick. For example, the false equation shown as Type A in Figure 14.12 can be changed into a true equation:

by moving the rightmost stick from III and putting it immediately to the right of V. Knoblich et al. (1999) argued that these problems are solved by relaxing the normal constraints of arithmetic; constraints we implicitly adopt about values, functions, and equality signs not usually considered to be arbitrarily

Two of the matchstick problems used by Knoblich et al. (1999), and the cumulative solution rates produced to these types of problems in their study. Copyright © 1999 by the American Psychological Association. Reprinted with permission.

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