The City Has Abandoned Geometry: The Countryside Has Not! Reflections on Geometry and Its Teaching from the Perspective of Countryside Education

Background: On the one hand, the history of mathematics teaching in Brazil is marked by the gradual abandonment of Geometry teaching; on the other hand, the countryside has always assumed it as an essential ally in the political and identity affirmation of its populations. Objectives: This paper discusses how Geometry and its teaching can emerge, in the paradigm of Countryside Education, as a possibility of political-epistemic disobedience to a Mathematics Education referenced in the knowledge, procedures, attitudes, and values of urban, industrial, and market forms of life. Design: The research uses qualitative methodology with a focus on Countryside Education. Setting and participants: The investigation was developed in the context of an Undergraduate Teaching Degree in Countryside Education, based on records of students' activities. Data collection and analysis: The text mobilizes formative experiences of a degree in Countryside Education with emphasis on Mathematics to reflect on how Geometry can be articulated to rural peoples' territories and territorialities, aiming to contribute to pedagogical guidelines for teaching K-12 Mathematics. Results: The paper contributes to evaluating epistemological and educational positions regarding Geometry and geometric knowledge commonly established by school cultures, not necessarily limited to schooling in rural regions. Conclusions: Geometry in school cultures can be used to understand the social reality in which subjects, communities and collectives are inserted, mapping inequality relations, and proposing ways to overcome them.