Alocação dos alunos nas escolas: uma abordagem de algoritmos de pareamento para análise do efeito do cadastro escolar de Belo Horizonte na proficiência dos estudantes

Abstract

This thesis conducts a study of the school registration system in Belo Horizonte, Brazil, this system completed, in 2013, 20 years since its inception. The system performs a registration procedure and suggests enrollment places for public elementary schools for students living in Belo Horizonte. This thesis aims to investigate how the registration system allocates students in schools and what effects this suggested allocation has on student learning, measured by their proficiency in PROEB-MG (Programa de Avaliação da Rede Pública de Educação Básica), a Portuguese language test for students in the 5th year of the elementary education system, in the term of 2010. To achieve this goal, three main references in the literature were employed: the literature of marriages of Becker (1991), extended to pairing between students and schools, the matching algorithms literature initiated by Gale & Shapley (1962) and presented in detail by Roth & Sotomayor (1990), and the one of school effectiveness, school choice and effect of territory on learning. The data from PROEB, School Census and schools, provided by the Municipal Education (SME/ PBH) and the State Secretariat for Education (SEE/MG) was merged and structured into a georeferenced database of students and schools with Euclidean distance of each student to actual schools. The final database obtained 16,354 students and 296 schools, with several information characteristics of the student, school and location: city districts, groups of districts and administrative regions. This database allowed obtaining information on student mobility and building indicators for students changing districts and regions to study in different places of the capital. Matching algorithms and parameters obtained in the exploratory analysis set out new allocations for students. These effects could be added to the proposed allocations average proficiency. Simulations showed that the final proficiency effects could be increased by 10 points on the average. Other simulations suggest that that it is possible to aggregate more 9 points of proficiency if other types of allocations that further shorten the distances of students to schools are used.