Purpose: A growing trend in instructional improvement efforts is the use of formative assessment informed by research-based developmental trajectories of how students gain deeper understanding of subject matter content over time. This article reports the findings of a large-scale experimental study of an innovative mathematics professional…

Background: Cluster-randomized experiments that assign intact groups such as schools or school districts to treatment conditions are increasingly common in educational research. Such experiments are inherently multilevel designs whose sensitivity (statistical power and precision of estimates) depends on the variance decomposition across levels.…