Evaluating Problemsolving Research

Problem-solving research is important to cognitive psychology because it is a testbed for the methodology of cognitive science. Since the advent of information-processing psychology, problem-solving research has been at the forefront in combining the use computational techniques and empirical testing (cf. Newell & Simon, 1972). During this time, the area has made steady progress and is quite unified in embracing a common theoretical stance, based on problem-space theory. To conclude these chapters on problem solving, we consider a number of core issues that are posed by this research. First, we consider what problem-space theory says about what makes problems difficult. Second, we broach the question of the ecological validity of problem-solving research. Finally, we consider the extent to which thinking phenomena can be modelled using connectionist techniques.

Why are problems difficult?

Given 30 or so years of problem-solving research, we should be able to say something about what influences the ease of problem solving. First, problems are made more difficult if people have to memorise and search through a large problem space to find a solution. Stated more simply, problems get difficult when people have to "hold more in their heads" (for "heads" read "working memory"). Second, search difficulties can be alleviated by knowledge of the problem; whole parts of the problem can be chunked and routine strategies used, all of which lightens the load on working memory. In short, the more familiar a problem the easier it becomes. Third, problems can be difficult because they are ill defined; again, the ability to define problems hinges on having the right sort of knowledge available. Problems may be difficult because it is not clear what they are about or how they can be solved.

The constant theme that emerges from this research is that problems are difficult because of two main limitations; resource limitations and limitations of knowledge. The major resource limitations lie in a working memory that can only process a certain quantity of information at a certain rate. Knowledge limitations can give rise to a wide range of difficulties. Furthermore, there is an interaction between these two limitations; the probability of being affected by resource limitations can decrease the more knowledge one has of a problem (because of chunking). In Chapter 14 we saw that the essential difference between expert problem solvers and novice problem solvers hinges on the amount and type of knowledge they have available about a domain; this knowledge may take the form of "facts" about the domain or "rules" about what to do in the domain. Knowledge is the key to unlocking difficult problems.

Indeed, many of the problem-solving methods we have encountered in these two chapters can be classified in terms of the amount and specificity of their domain knowledge (see Carbonell, 1986, and Figure 15.8).

• In knowledge-poor, puzzle situations where we have little useful past experience, the only useful methods are universal, weak methods (e.g., means-ends analysis).

• A problem may be relatively familiar but we may lack specific plans to solve it, in which case general plans may be applied; these plans will break the problem down into subproblems, in a divide-and-conquer fashion, even though these sub-problems will not suggest immediate solutions (cf, in successive problem-solving attempts on the Tower of Hanoi problem).

• With more familiar problems we may have various specific plans or schemata about how to solve them (e.g., the expert physicist or programmer); in these cases, we can instantiate such schemata and solve any sub-problems that arise with other instantiated schemata.

• Finally, if problem solvers have no specific or general schemata, they may choose a specific past experience (e.g., a specific previously encountered problem) and apply it by analogy to solve the problem they face, or they may modify some past instances using structured imagination.

These four situations lay out the main ways in which researchers have proposed that different types of knowledge are used. Clearly, we would not want to maintain that the application of these approaches is mutually exclusive; people may use a combination of all four at different points in solving a particular

Problem solving may involve the following: (a) instantiating specific plans, (b) using analogical transformation to a known solution of a similar problem, (c) applying general plans to reduce the problem, (d) applying weak methods to search heuristically for a possible solution, or using a combination of these approaches. Reproduced with the permission of the publishers from Machine learning: An artificial intelligence approach, Volume 2, edited by R.S.Michalski, J.G.Carbonell, and T.M.Mitchell. Copyright © by Morgan Kaufmann.

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