The appropriate methodology for psychological research depends on whether one is studying mental algorithms or their implementation. Mental algorithms are abstract specifications of the steps taken by procedures that run in the mind. Implementational issues concern the speed and reliability of these procedures. The algorithmic level can be explored only by studying across-task variation. This contrasts with psychology's dominant methodology of looking for within-task generalities, which is appropriate only for studying implementational issues.

The implementation-algorithm distinction is related to a number of other “levels” considered in cognitive science. Its realization in Anderson's ACT theory of cognition is discussed. Research at the algorithmic level is more promising because it is hard to make further fundamental scientific progress at the implementational level with the methodologies available. Protocol data, which are appropriate only for algorithm-level theories, provide a richer source than data at the implementational level. Research at the algorithmic level will also yield more insight into fundamental properties of human knowledge because it is the level at which significant learning transitions are defined.

The best way to study the algorithmic level is to look for differential learning outcomes in pedagogical experiments that manipulate instructional experience. This provides control and prediction in realistically complex learning situations. The intelligent tutoring paradigm provides a particularly fruitful way to implement such experiments.

The implications of this analysis for the issue of modularity of mind, the status of language, research on human/computer interaction, and connectionist models are also examined.