Are schools becoming more unequal? Insights from exploratory data mining of international large-scale assessment, TIMSS 2003-2019

The aim of this study was to examine how achievement varied within and between schools at different grade levels, and long-term trends in variation within and across multiple countries. We used science achievement data from five cycles of Trends in International Mathematics and Science Study (TIMSS) from 2003 to 2019 involving 10 countries from Asia, Europe, and the United States. Employing exploratory data mining methods of variance decomposition, correlation analysis, and Gaussian mixture modeling of data distributions, we found the following: First, between-school variances generally remained consistent across two decades, suggesting that inequality between schools has not increased over time. Second, between-school variances were relatively small for elementary grade level but increased at secondary grade level, though marginally even for countries with early tracking. Third, higher-achieving schools tended to have more equal student achievement levels than lower-achieving schools, lending within-country support for the “virtuous” efficiency-equality trade-off. We further found that reduced equality within lower-achieving schools was associated with bimodality in achievement distribution. Overall, there is little evidence of inequality across schools changing over time. However, there may be evidence of increased inequalities associated with student subpopulations, particularly within lower-achieving schools, with implications on classroom instruction and school cohesion.