Cálculo das proficiências dos alunos de MG na prova de matemática do ENEM de 2011 através de um modelo da Teoria de Resposta ao Item

Abstract

This study in the area of educational assessment discusses the calculation of proficiencies of students from Minas Gerais who made the Mathematics exam of ENEM/2011 using a model of Item Response Theory (IRT). IRT is a set of mathematical models which expects that theperformance of a rated on a test can be predicted (or explained) by proficiency (skill) and the characteristics of the test items. The IRT has contributed to models that represent the relationship between the probability of an individual to respond correctly to an item and its skills inthe area that has been evaluated. A 3-parameter logistic model that describes the relationship between the ability of the examined individual and the probability of a correct answer with three parameters: difficulty, discrimination and causality, was adopted in this study. This monographypresents a study of Item Response Theory applied to microdata from 438,974 students who have made the inscription in 853 municipalities of Minas Gerais. The results showed that the estimated proficiencies for males were higher than for females. Relating to administrative schoolsystem, the best performances were observed in students of the Federal network, followed by those of private, and finally public network. It was also observed that higher proficiencies were registered in larger municipalities. The SPSS software was used for the reading and formatting of the database, while the analysis of modeling by IRT was performed by BILOG, and the data visualization through tables, graphics and maps was obtained using the computing environment R.