School value-added studies have largely demonstrated the effects of socioeconomic and demographic characteristics of the schools and the pupils on performance in standardised tests. Traditionally, these studies have assessed the variation coming only from the schools and the pupils. However, recent studies have shown that the analysis of academic performance could significantly benefit from additional complexity in the model structure, incorporating non-hierarchical and unexplored levels of variation. Using data on secondary students from the Chilean National Pupil Database (2004-2006), this study shows how the traditional value-added models fall short in addressing the complex phenomenon of academic performance, because they largely overestimate school effects. A 4-level contextualised value-added model for progress in Mathematics was implemented and shown to avoid the masking of classroom and locality effects found in the traditional models. We also analyse the effects of important structural factors in Chile such as family income and school type.