Modeling the relationship between cognitive artifacts and rationality is the central issue with which this paper is concerned. In the research on cognitive artifacts, two models of the relationship between cognition and artifacts can be identified: the amplification model and the transformation model. It is argued that the amplification model leads to trivial conclusions about the role of artifacts for cognition. The transformation model provides an insightful perspective on cognitive artifacts, but needs to be submitted to careful scrutiny. Research on problem solving is used in order to make the advantages of the transformation model explicit.