ABSTRACT
There is a mathematical model of learning and expertise development that appears to cover a range of measures and a wide range of domains. This is the Power Law of Practice (Newell & Rosenbloom, 1981). Newell and Rosenbloom referenced a number of studies (mirror tracing, cigar manufacturing, learning to read inverted texts, scanning for targets in a display and so on), all of which showed the same learning pattern that could be displayed as a version of the one in Figure 6.1 which gives an abstract version of the graphs based on the law. In the graph on the left, as practice continues (x-axis), measures such as the number of errors or reaction times (RTs) drop but the rate at which this happens changes over time. So, for example, RTs might be very slow to begin (a in the figure) but speed up rapidly with relatively little practice
INFORMATION BOX 6.1 DEVELOPMENT OF EXPERTISE
Cognitive stage
Associative stage
(b), but this speed up slows so that a lot of practice is needed to make a small difference in RT (c). The same effect is shown in the right-hand graph, but this time the spacing in the x-axis is logarithmic. For example a might be 1 hour, b 10 hours, c 100 hours, d 1,000 hours and e 10,000 hours. The law is in the form RT = aP−b + c, where
RT = Trial completion time P = Trial number, starting from 1 (for exponential functions the P − 1 argument is used) a, b and c are constants
Other models of the acquisition of expertise include stages of development leading to expertise beginning with a stage where one’s knowledge is declarative and verbalisable and where general knowledge becomes more and more specialised. Fitts and Posner (1967) provided an early list of the phases of learning and expertise development and these have often been incorporated in various guises into other learning models (e.g., Anderson, 1982, 1983; Schneider & Shiffrin, 1977; Tenison & Anderson, 2015). These are listed in Information Box 6.1.
