The shift with practice from use of generic, multistep problem-solving strategies to fast and relatively effortless memory-based strategies, was explored in 2 experiments using pseudoarithmetic tasks. A complete transition to the memory strategy occurred by about the 60th exposure to each problem. The power law of practice did not hold in the overall data for either the mean or the standard deviation of response latency, but it did hold within each strategy (algorithm or retrieval). Learning was highly specific to the practiced problems. These results constitute the 1st clear demonstration of a skill for which the power law does not apply overall. The results do not support the instance theory of automatization (G. D. Logan, 1988) but are consistent with an alternative component 12ower laws (CMPL) theory that assumes that because of intrinsic attentional limitations, only 1 strategy can be executed at a time.One of the fundamental processes of human skill acquisition is the strategy shift with practice from use of generic, multistep procedures to direct retrieval of answers from memory (Ashcraft, 1992;Lemaire & Siegler, 1995;Logan, 1988;Reder and Ritter, 1992;Rickard & Bourne, 1996;Siegler, 1988). Examples are numerous in both the natural environment and the laboratory. Foreign vocabulary learning (Crntcher, 1989), spelling (Siegler, 1986), acquisition of linguistic rules (Bourne, Healy, Rickard, & Parker, 1997;Healy & Sherrod, 1994), and visual numerosity judgments (Lassaline & Logan, 1993; Palmed, 1997) can all reflect this type of strategy shift. Basic single-digit arithmetic is probably the most familiar example. During initial stages of learning, children often use counting procedures that can require 10 s or longer to execute. With sufficient practice, however, they learn to retrieve answers to individual problems directly from memory. By adulthood, the directretrieval strategy typically yields answers in about a second (Siegler, 1988).This article evaluates two candidate accounts of adult skill acquisition, strategy shifting, and the development of automaticity in these and related skill domains, with a current focus on mental calculation. 1 The models under comparison make diametrically opposing claims about two fundamental properties of human information processing. The instance theory of automatization (Logan, 1988) Special thanks to Lyle Bourne and Alice Healy for their many thoughtful comments. Special appreciation to Gordon Logan for his helpful comments.Correspondence concerning this article should be addressed to Timothy C. Rickard, Department of Psychology, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0109. Electronic mail may be sent via Internet to trickard@ucsd.edu. 288 that direct retrieval from memory is automatic and executable in parallel with a variety of other more complex processes, such as multistep procedures or algorithms. The alternative model developed in this article assumes that memory retrieval is strongly dependent on attention and that o...