A secondary data analysis was conducted using a large dataset from a study related to online professional development for eighth grade teachers of mathematics. Using this data, the paper provides a snapshot of the current state of teachers' knowledge related to proportional reasoning and functions. The paper also considers how teachers' knowledge…

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.…