Análise multivariada para dados quantitativos discretos: estudo de caso do desempenho dos alunos na Prova Paraná

Abstract

The present work exposes an investigation of the performance of students in the first edition of the Paraná-2018 Test, through the analysis of a school in the municipality of Toledo-PR, belonging to the Regional Center for Education of Toledo. The objective was to apply discrete quantitative multivariate statistical method to study and compare student performance. The data were collected at the NRE-Toledo and school. The grades evaluated were 6th and 9th years of elementary school and 1st and 3rd years of high school. The information collected was digitalized and organized according to the descriptors, structuring contents, and the SEED Paraná website was made available. From the initial analysis, a multivariate statistical method of Grouping Analysis (conglomerate or Cluster Analysis) was applied, using the Euclidean distance and hierarchical grouping as the grouping method. Three connection methods were considered: Simple connection method or the closest neighbor (Single linkage); Complete linkage method or the farthest neighbor (Complete linkage); Average Linkage method (Average Linkage). The Coefficient of Cofenetic Correlation was used to evaluate the quality of the groups formed. The analyses were implemented using free and open source software, Oksanen et al. (2016). The overall result obtained by the classes shows that the hit rate of high school students is lower than that of elementary school students. Of the 20 questions evaluated, on average, the percentage of correct answers in primary education was 52.35%, while secondary education presented only 32.30%. This indicates that with the passage of time students showed greater difficulties with mathematics. Thus, the Paraná Test needs to be strengthened, improved and expanded and it is necessary that SEED, the NRE and the schools establish actions for the improvement of teaching, in order to overcome the difficulties related to the skills not developed by the students.