Understanding Excellence Gaps: What Can We Learn From Studying Within-School Variability?

• In Event: Are Excellence Gaps the Unavoidable Consequence of Expanded Opportunity for High-Performing Students?

Abstract

Larry Coleman once said that the goal of education should be that variance in achievement is larger at the end of school than it is at the beginning of school. In other words, if students learn (grow) at different rates, then students’ achievement will be more variable at the end of their educational careers than it is at the beginning – absent artificial ceilings that limit the ability of high performing students to continue learning at the rates that they are capable of. In fact, this is a mathematical necessity. Those who grow faster will ultimately display higher achievement.

For the gap between initially high and low achieving students to decrease over time, the correlation between initial status and growth would have to be negative. Such a pattern seems unlikely. After all, how do we explain why some students have higher achievement at the beginning of school? They must have exhibited higher growth before starting school. If initial status and growth are not negatively related to each other, then the degree to which initial achievement is related to race and poverty is maintained, or perhaps even exacerbated across students’ academic careers. What is the solution? Striving for schools in which the highest achieving students at the beginning of kindergarten grow more slowly than the students who enter school the furthest behind does not seem like a reasonable goal. On the other hand, allowing inequities that exist at the beginning of school to compound across students’ academic careers appears to further entrench existing social inequities. Ideally, it seems to us, if schools are effective, they produce substantial within school variability that cannot be explained by subgroup membership.

This paper explores the relationship between within school variability, school growth, and school mean achievement. First, we model the relationship between within school heterogeneity and school mean achievement, using the mixed effects location scale model (Hedeker & Nordgren, 2013). This model allows the within school (residual) variance to randomly vary across schools, and allows us to model this within group (residual) variance as a function of student and school level predictors. Next, we incorporate demographic variables such as free lunch status and the percentage of free lunch students into the model and estimate the percentage of variance in within school variance that can be explained by these demographic variables. We generate empirical Bayes estimates of the within school variance, after controlling for demographic variables. We examine the relationship between within school residual variance, school growth slopes, and school mean achievement. We hypothesize that schools with larger residual variance (after accounting for school and student demographics) should also have higher school growth rates. Then, at the district level, we examine the relationship between within district achievement gaps as more traditionally defined and within district residual variance in achievement to determine the relationship the degree to which within district achievement gaps can predict differences in within district achievement variance. We discuss the implications and provide recommendations for issues to consider when modeling achievement and excellence gaps.

Authors

• D. Betsy Mccoach, University of Connecticut

• Rashea Hamilton, University of Connecticut - Storrs

• Danielle Rita Bousquet, University of Connecticut