Avaliações de diagnóstico cognitivo em escolas públicas do Estado do Ceará: Um estudo comparativo

Abstract

Cognitive Diagnostic Models (CDMs) are statistical models used to estimate students’ latent abilities in solving items or questions in a given test. Using the Q matrix as input, which represents the skills required to correctly solve each item, CDMs are fitted to student response data to estimate their abilities to successfully resolve the items and classify them into attribute/skill groups. As a quantitative analysis tool, CDMs have been increasingly utilized in education to identify the mastery levels of the skills required for correct item resolution, thus aiding teaching and learning in the classroom. Bearing this in mind, this master’s thesis aims to conduct a cognitive diagnostic analysis of school data from the Coordenadoria Regional de Desenvolvimento da Educação- CREDE 1, covering the city of Maracanaú and its metropolitan region. More specifically, it will analyze the results of the 3rd year high school Mathematics exam. The test consists of 25 items, for which 4 skills were previously defined by experts as necessary for adequate resolution of the test items. A total of 12,850 students form the sample of test respondents. The cognitive diagnostic analysis was performed using R software with the assistance of the GDINA package (generalized deterministic inputs, noisy “and” gate) which implements the eponymous CDM and specific models like DINA, DINO, A-CDM, LLM, and R RUM. Initially, given the innovative nature of the task, an exploratory data analysis is conducted to present descriptive statistics and a qualitative overview of student performance on the test. Following this, a comparative analysis of the aforementioned CDMs is carried out to infer the individual abilities of the sample students and their groupings by skill classes. The results are promising and support the premise of using CDMs in the evaluation of school performance.