International and Interstate Gaps in Value- Added Math Achievement: Multilevel Instrumental Variable Analysis of Age Effect and Grade Effect

Merging National Assessment of Educational Progress and Trends in International Math and Science Study math data, this study examines the extent and sources of variation in value-added academic growth patterns among different nations and U.S. states. Applying hierarchical linear models with an instrumental variable method, the study disentangles age effect and grade effect on growth and accounts for both international and interstate variations. Math achievement gains between grades 4 and 8 are significant with positive age and grade effects and negative age-by-grade interaction. The study finds convergence of the age effect and divergence of the grade effect among the nations and states. While the Unites States lags further behind East Asian nations in math achievement during middle school years, a few of the U.S. states match East Asian gains. The initial or widening gap between the U.S. states and East Asian countries is more closely related to school factors, whereas family factors play a greater explanatory role for achievement gaps among the U.S. states.