Fatores institucionais associados ao desempenho em matemática por meio da análise de componentes principais (PCA) e da decomposição em fatores paralelos (PARAFAC)

• Autor(a) principal: Hippolyto, Luzia de Queiroz
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Texto Completo: http://www.repositorio.ufc.br/handle/riufc/31636
• topic: Avaliação; Matemática; Análise de Componentes Principais (PCA); Decomposição em Fatores Paralelos (PARAFAC); Evaluation; Mathematics; Principal Component Analysis (PCA); Decomposition in Parallel Factors (PARAFAC).

The results of academic performance in the discipline of Mathematics in Basic Education in Brazil, according to the benchmarking cycles of the Basic Education Assessment System (SAEB), point to a scenario that is not motivating. The negative results of Ceará revealed by SAEB, together with the national and international trend of large-scale evaluations, culminated, in 1992, when the first cycle of large-scale educational assessment of Ceará was carried out, with the aim of providing more accurate and timely information on local education and to monitor policies aimed at advancing the quality, equity, and efficiency of the state education system. However, several factors contribute to the fact that learning does not consolidate as expected. In this sense, the present thesis proposal has as general objective the accomplishment of a study that addresses two techniques of analysis, one bilinear and another trilinear, with the purpose of identifying socioeconomic factors and of institutional school climate, in conventional and professional schools, which are associated to the academic performance, especially in the Mathematics discipline, of high school students, in the city of Fortaleza-CE. The quantitative paradigm is used to measure and establish correlations, trying to identify patterns. Multivariate Analysis, in particular the Principal Component Analysis (PCA) and Multilinear Algebra technique, will be used through the tensor analysis focusing on the Decomposition in Parallel Factors (PARAFAC). The results show that: (i) that the Analysis of Variance (ANOVA) test pointed to a significant difference between students in conventional and professional schools for mathematics; (ii) the efficiency of multilinear algebra for data processing in the field of educational evaluation, since the findings in PARAFAC are directed toward the PCA, a tool readily validated by the academic community for this type of analysis.