The objective of this study is to evaluate the effect of Brazilian elementary schools on the chances of their students achieving at different levels of mathematics proficiency. Since student proficiency is classified at three levels--Insufficient, Basic and Proficient--the chosen model of analysis was the hierarchical multinomial model. The explicit use of proficiency levels, which have a clear normative and pedagogical interpretation, allows the findings to be expressed in language more relevant to schools and educational policy. The main findings are: the infrastructure factor (quality of the school buildings, library, computers, etc.) is related mainly to the effect of the school on the chances of their students being at the Basic level; only one pedagogical factor (homework) is related to the chances of students being at the Proficient level. The findings suggest that Brazilian schools need to undergo interventions of a different kind for their students to succeed.