A geometria e o seu ensino na compreensão de professores de Matemática após o Novo Ensino Médio

Abstract

This research aimed to investigate mathematics teachers’ understanding of Geometry and the teaching practices developed in this area after the implementation of the New High School reform. In the theoretical chapter, the study discusses Geometry as a field of knowledge within the contemporary curricular context, addressing the organization of this area in the Brazilian National Common Curricular Base (BNCC), the transformations resulting from the High School reform, and a specific topic devoted to geometric demonstrations as foundation for critical mathematical formation at the high school level. This is a qualitative study grounded in a phenomenological approach, conducted with eight teachers from the state public school system in Riachão do Jacuípe, Bahia, Brazil. Data were produced through semi-structured interviews and analyzed according to the ideographic and nomothetic movements, following the moments of description, reduction, and interpretation, organized into Units of Meaning, Nuclear Ideas, Axes, and Open Categories. The analysis revealed that Geometry is experienced under a constitutive tension: although it remains mandatory knowledge in curricular documents and external assessments, it appears weakened in terms of instructional time, centrality, and content depth within the curricular reorganization promoted by the New High School reform. The emerging phenomenon is not one of absence but of a compressed presence, whose realization largely depends on teachers’ intentionality and on material and pedagogical conditions. At the same time, Geometry is understood as structuring, sensitive, and integrative knowledge, grounded in perceptual experience and capable of articulating relationships both within Mathematics and beyond it. In this context, teacher identity—shaped by formative trajectories, affections, and support networks—proves decisive for sustaining the area. We conclude that the permanence of Geometry in the curriculum is sustained not exclusively by its normative obligatoriness, but by the meaning it assumes in teachers’ lived experience, highlighting the need for continuing teacher education policies and improved structural conditions for its teaching.