A focus of early mathematics education is to build fluency through practice. Several models of skill acquisition have sought to explain the increase in fluency because of practice by modeling both the learning mechanisms driving this speedup and the changes in cognitive processes involved in executing the skill (such as transitioning from…

Two stages of skill development are: declarative (facts are interpreted) and procedural (knowledge is embodied in skill procedures). Knowledge compilation moves skills from the declarative to procedural stage in subprocesses of composition, which collapses sequences of productions into single productions, and proceduralization, which embeds…

This article has three goals: to set forth some general claims about the course of skill acquisition; to discuss a series of counter intuitive predictions derived from the ACT theory; and to review the state of empirical evidence relevant to these predictions. (LMO)

According to the ACT theory of skill acquisition, cognitive skills are encoded by a set of productions, which are organized according to a hierarchical goal structure. People solve problems in new domains by applying weak problem-solving procedures to declarative knowledge they have about this domain. From these initial problem solutions,…