Figure 1416

Typical log-log plot for the Power Law of Practice.

Practice makes perfect

Common-sense suggests that one way to become an expert is to practice something. Chase and Simon (1973a) estimated that most grand masters had studied for at least 9 to 10 years to reach their level of expertise. The relationship between practice and performance in perceptual-motor skills has been captured by one of the few "laws" in cognitive psychology; the Power Law of Practice (see Figure 14.16). This law states that if the time per trial and number of trials are graphed on log-log co-ordinate axes, then a straight line results (Fitts & Posner, 1967). It is now generally accepted that the power law also holds for purely cognitive skills, so much so that Logan (1988, p. 495) has said that "the power-function speed-up has been accepted as. a law, a benchmark prediction that theories of skill acquisition must make to be serious contenders". Not surprisingly several researchers have suggested a number of mechanisms to explain these effects of practice and the acquisition of expertise: chunking, proceduralisation, and compression (see Chapter 1; Anderson, 1993, 1996; Newell, 1990; Rosenbloom & Newell, 1986). Most of these techniques have been developed in the context of production system models of cognition (Chapter 1).

Practice makes chunks

One proposal is that a form of chunking underlies practice effects (this is a very specific sense of the term, to be distinguished from Miller's, 1956, memory formulation; see Chapter 6). Rosenbloom and Newell (1986, 1987) have argued that when a series of production rules is applied to solve a particular problem, a new rule can be created that does away with the chain of rules (moves) to get to the solution. For example, suppose an problem solver encounters a problem situation, state-a, and needs to reach a goal state, state-f. In solving the problem a chain of rules might be applied: rule 1 changes state-a to state-b, rule 2 changes state-b to state-e, and rule 3 changes state-e to state-f. Stated simply, chunking would create a new rule that contains the relevant conditions that led to the goal state; a new rule that will change state-a to state-f in one step. An immediate implication of chunking is that the problem is solved in one step rather a succession of steps, allowing the time taken to solve the problem to decrease significantly. The idea of a chunk of knowledge has become a standard in many cognitive architectures (e.g., Anderson, 1996; Newell, 1990) and, as we have seen, proves to be a very useful concept in characterising chess expertise.

A schematic diagram of the major components and interlinking processes used in Anderson's (1983, 1993) ACT models. Reprinted by permission of the author.

Learning from problem-solving attempts and instruction: Proceduralisation

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