Understanding complex systems requires reasoning about causal relationships that behave or appear to behave probabilistically. Features such as distributed agency, large spatial scales, and time delays obscure co-variation relationships and complex interactions can result in non-deterministic relationships between causes and effects that are best…

The authors propose a strategy for studying the effects of time-varying instructional treatments on repeatedly observed student achievement. This approach responds to three challenges: (a) The yearly reallocation of students to classrooms and teachers creates a complex structure of dependence among responses; (b) a child's learning outcome under a…