Figure 158

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.

problem. The key point, however, is that different methods of problem solving can be distinguished by the amount and types of knowledge they use.

Is problem-solving research ecologically valid?

Earlier we encountered the criticism that problem-solving research was not ecologically valid because it only considered well defined, puzzle-like problems. This criticism certainly held water in the early history of the area, but is less true now.

We have seen that the research on expertise and mental models has broadened research to consider problem solving in the classroom and other everyday, real-world situations. Investigations of physics expertise have important implications for the teaching of this discipline in schools. Research on programming expertise tackles a very important ability for technological development and suggests better ways to design programming languages and the computers that use such languages. Some expert-novice research, which we have not reviewed here, has been applied to everyday tasks in other domains. For example, Lesgold and his associates (Lesgold et al., 1988; see also Lesgold, 1988) have examined expertise in the reading of X-rays by radiologists. Patel and his associates (Patel & Groen, 1986, 1993; Patel, Groen, & Arocha, 1993) have examined the expertise underlying medical diagnosis. This work has taken cognitive psychology out into the world and indeed, has led some to argue that the everyday world is the most important context in which to test cognitive theories (see Anderson, 1987b; Anderson & Lebiere, 1998).

Connectionism and thinking

The rise of the modelling techniques associated with connectionism appears to be at variance with the character of thinking and the classical, symbolic models that have tended to be used in this area. The argument that theorists often make is that thinking is inherently serial and therefore is not amenable to a parallel processing treatment. Intuitively, this looks like a reasonable proposal, but it does not stand up to much scrutiny. If one examines carefully the models of thinking in the literature, connectionist techniques are used repeatedly.

Consider Anderson's (1983, 1993, 1996; Anderson & Lebiere, 1998) ACT models. Even though they use a production-rule system, the models also have a declarative memory, that is a network of concepts through which activation passes in parallel (indeed, it is a precursor of localist, connectionist nets; see Chapters 1 and 9). More recently, we have seen that connectionist models have been produced to model aspects of skill (see e.g., Lamberts, 1990). Indeed, Holyoak (1991) has suggested that the next generation of expertise models will all have a connectionist character. In analogical thinking, parallel constraint satisfaction has been used with some success; such methods seem central to analogue retrieval (see Thagard et al. 1990) and are an elegant solution to some aspects of analogical mapping (Holyoak & Thagard, 1989, 1995). Holyoak and Spellman (1993) have argued that these techniques have a wider applicability in a range of problemsolving situations. Finally, Shastri and Ajjanagadde's (1993) work on dynamic binding suggests a general solution to modelling problems of seriality in many thinking phenomena. They have been used with some success in modelling analogical thinking (Hummel & Holyoak, 1997) and have the added benefit that they are explicitly designed with neurological constraints in mind.

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