Abstract
National educational systems are not usefully described by a single rank in mathematics achievement.
•Empirical subscores obtained through IRT factor analysis show different countries have different profiles of mathematics achievement.
•Asian countries have generally strong performance across empirically-distinct content areas.
•In Factions and Decimals, the USA did well in fractions in 2007 and 2011 at Grade 4, and two participating states (Massachusetts, Minnesota) in 2007 had superior performance.
•A number of post-Soviet states did well in algebra in 2007 and 2011.
National profiles in mathematics achievement were obtained from a multidimensional analysis of item response data from the Trends in Mathematics and Science Study (TIMSS) for 2011 and 2015 by means of IRT factor analysis. Empirical subscores were then obtained at Grade 4 Grade 8. These subscores were less correlated than TIMSS-reported subscores, and revealed previously unknown information for some countries. The empirical subscores also resulted in ranks that differed from TIMSS- reported unidimensional ranks. In general, the analysis demonstrates that educational systems are not usefully described by a single mathematics score, or in terms of traditional subscores.