Examining Relationships Between Where Students Start and how Rapidly they Progress: Using New Developments in Growth Modeling to Gain Insight into the Distribution of Achievement Within Schools

Studying change in student achievement is of central importance in numerous areas of educational research, including efforts to monitor school performance, investigations of the effects of educational interventions over time, and school effects studies focusing on how differences in school policies and practices relate to differences in student progress. In this article, we argue that in studying patterns of change, it is often important to consider the relationship between where students start (i.e., their initial status) and how rapidly they progress (i.e., their rates of change). Drawing on recent advances in growth modeling methodology, we illustrate the potential value of such an approach in the context of monitoring school performance. In particular, we highlight the ways in which attending to initial status in analyses of student progress can help draw attention to possible concerns regarding the distribution of achievement within schools. To convey the logic of our approach and illustrate various analysis possibilities, we fit a series of growth models to the time series data for students in several schools in the Longitudinal Study of American Youth (LSAY) sample. In a final section, we discuss some of the possibilities that arise in employing a modeling approach of this kind in evaluating educational programs and in conducting school effects research.