A dimensão pedagógica nas avaliações em larga escala: a teoria de Van Hiele como suporte para produção e análise de itens de Matemática

Abstract

This study was developed within the scope of the Master's program in Public Education Management and Evaluation at the Federal University of Juiz de Fora (UFJF/CAEd). It sought to understand how the process of acquiring geometric knowledge occurs and how it is manifested in items applied in large-scale assessments. In this sense, the guiding question was: How do the levels of geometric thinking of the Van Hiele Theory manifest in the Geometry items of large-scale assessments, what is the relationship between this manifestation and the empirical behavior of these items, and how can this integrated analysis support the proposition of an Educational Action Plan to develop items more aligned with students' cognitive development? To answer this, the general objective was to analyze how the geometric thinking levels proposed by the Van Hiele Theory are mobilized in Geometry items present in large-scale assessments, relating this pedagogical structuring to the statistical behavior of the items, in order to propose an Action Plan for developing instruments more suited to the cognitive development of Basic Education students. Specifically, the study aimed to characterize the item development process, its criteria, and the pedagogical considerations that can be employed; investigate the items of the Geometry knowledge axis regarding the development of the proposed tasks and their intrinsic characteristics; and propose criteria for developing items capable of generating information at different points of the scale. Methodologically, this research utilized a mixed-methods approach (qualitative and quantitative) with an exploratory sequential design, conducted in two phases. For the analysis, 94 public items from the Geometry axis (5th and 9th grades of Elementary Education and 3rd grade of High School) were used, developed by the Fundação CAEd based on the 2001 Saeb reference matrix. The pedagogical analysis of the items was based on the Van Hiele Theory and Bloom's Taxonomy and was subsequently cross-referenced with the statistical parameters of discrimination, difficulty, and guessing (a, b, and c) generated by Item Response Theory (IRT). It was concluded that the set of items was too modest to establish strong correlations between the Van Hiele Theory levels and the psychometric parameters, but that the development of items with diagnostic intent allows for the evaluation of students stagnated at a lower level of geometric knowledge. Based on these findings, an Educational Action Plan was developed for the Assessment Instruments Team. The plan proposes the adoption of pedagogical guidelines and a protocol for the construction of items that encompass the geometric learning continuum, thereby enhancing the measurement of proficiency and educational diagnostics.