How people learn to skip steps.

Novices often explicitly apply in a domain each necessary operator while solving a problem, whereas experts often skip steps, and as a result, the solution procedures they use are often organized differently from those of novices. Using an algebra analog, the authors examined this change in process. In 2 experiments, people learned the rules of the task and then solved many problems. Their solution procedures were monitored, and concurrent verbal protocols were taken. When participants started overtly skipping steps, they appeared to be performing them mentally but later started to use new transformations, thereby covertly skipping steps as well. An adaptive control of thought—rational model (J. R. Anderson, 1993) of problem-solver behavior within this task was developed and evaluated with respect to existing theories of skill acquisition. As people solve the same type of problem again and again, not only do they get faster at doing that type of problem, but very often the process they use to solve the problems changes as well, often resulting in skipped steps (Koedinger & Anderson, 1990). This reorganization and skipping of steps allow people to solve problems more quickly, efficiently, and easily. One might expect this change in process to result in performance discontinuities in a person's acquisition of a skill because the person is undergoing what may be a radical reorganization of how that skill is performed. However, Newell and Rosenbloom (1981) showed that a variety of skills are acquired at a steady rate, one that follows a power function (an equation of the form y = a + bxc, where a, b, and c are constants). In this article we examine the step-skipping phenomenon and its apparent relationship to the power law of learning. Step skipping is often thought of as a compositional process, in which a person who used to take two or more steps to do a task now takes only one. Intuitively then, if a person does a problem in fewer steps in completing a task, he or she should take less time in performing that task. Research by Charness and Campbell (1988) showed that compositional processes account for about 70% of the speedup associated with acquiring a new skill, with the rest of the speedup accounted for by becoming faster at the operations themselves. Work done by Frensch and Geary (1993; Frensch, 1991) also indicated the importance of compositional processes, as distinct from a general speedup in performance, in learning a task. It is evident from this research that composition is an important component to acquiring a skill.