Using an HLM Growth Curve Analysis to Determine the Impact of the Milwaukee Mathematics Partnership on Increasing Student Achievement in Mathematics
The data that was used in the analysis consisted of student achievement data from the fall of 2005, 2006, and 2007, as well as responses to an online survey, collected from the spring of 2007. Altogether, a total of 2,341 respondents from 125 schools participated in data collection activities in the spring of 2006.
Hierarchical Linear Modeling analyses were conducted using student achievement in mathematics (as measured by the state mandated test) as the dependent variable. Since three years of student achievement data existed, a three level linear growth model was fit to the data and only two cohorts of MPS students were considered. The first cohort consisted of students that were in third grade in the fall of 2005 and in fifth grade in the fall of 2007. The second cohort consisted of students that were in sixth grade in the fall of 2005 and in eighth grade in the fall of 2007. Only those students that remained in the same school for all three years were considered in this set of analyses, since the primary focus of the analyses was to determine what, if any, school level variable related to the work of the MMP helped to predict differences in student achievement growth.
In the models that were fit to the data the three scale scores comprised the first level (i.e. individual observations within a student). Since this level reflects repeated measures within a student it can be thought of as an individual growth model for a particular student that reflects the mathematics achievement for student i at time t in school j. The second level consisted of student level variables (i.e. SES, race, etc.), and the third level consisted of school level variables (i.e., variables created from the online survey). These variables can either be modeled such that they are related to the initial mathematics achievement or the learning rate of student i. In our case, all of the school level variables obtained from the online MMP Survey administered in the spring of 2007 were hypothesized to be possible predictors of an individual student's growth curve.
These analyses were undertaken to determine if variability in MMP implementation (as indicated by variability in school level variables created from the MMP Survey) could help explain variability in student growth in mathematics achievement.