  Mastery learning, the notion that students learn best if they move on from
studying a topic only after having demonstrated mastery, sits at the foundation
of the theory of intelligent tutoring. This paper is an exploration of how
mastery learning plays out in practice, based on log data from a large
randomized effectiveness trial of the Cognitive Tutor Algebra I (CTAI)
curriculum. We find that students frequently progressed from CTAI sections they
were working on without demonstrating mastery and worked units out of order.
Moreover, these behaviors were substantially more common in the second year of
the study, in which the CTAI effect was significantly larger. We explore the
various ways students departed from the official CTAI curriculum, focusing on
heterogeneity between years, states, schools, and students. The paper concludes
with an observational study of the effect on post-test scores of teachers
reassigning students out of their current sections before they mastered the
requisite skills, finding that reassignment appears to lowers posttest
scores--a finding that is fairly resilient to confounding from omitted
covariates--but that the effect varies substantially between classrooms.
