A framework is described for extending the principles of apprenticeship to teaching such subjects as reading, writing, and mathematics. Such a cognitive apprenticeship is aimed at teaching students the processes experts use to handle complex tasks. Conceptual knowledge and factual knowledge are illustrated within the contexts in which they are used. The proposed framework, comprised of content, method, sequencing, and sociology, is consistent with the goals of compensatory education. The cognitive apprenticeship model is useful for all students, but is particularly effective for disadvantaged, or at-risk, students because learning is embedded in a setting that is more like work, with an authentic connection to students' lives. Examples are given of cognitive apprenticeship programs in an urban middle school in Rochester (New York), and an urban secondary school in Harlem (New York). By giving their students long-term projects that engage them deeply and by constructing an environment embodying the principles of the described framework, these schools have begun fostering cognitive apprenticeship. The two schools' progress should be followed and their methods replicated to move education to a more rational system. One figure and a 25-item list of references are included. The paper's discussant is Herb Rosenfeld in a taining piece entitled "Reflections from a Workplace for Cognitive Apprenticeship." (SLD)