Formação docente em escolas do campo: entrelaces da teoria da objetivação e a sequência Fedathi com grupos de simetria mediadas pelo Geogebra

Abstract

Teacher education in rural contexts opens multiple pathways for integrating campesino cultural knowledge into pedagogical practices through Digital Technologies (DT) and disruptive methodologies. This program, <Geometry Teacher Education for Rural Schools in Primary Education=, serves as a space for engaging with pedagogical constructs that arise from Didactic Sessions (DS) designed and enacted in the classroom, grounded in the Fedathi Sequence (FS) and the Theory of Objectivation (TO), for Geometry Teaching (GT) using the GeoGebra software. The present study investigates the ongoing professional development of mathematics teachers in the upper grades of rural primary schools in Quixeramobim, Ceará, focusing on algebraic structures of Symmetry Groups mediated by DT with GeoGebra and informed by TO and FS. From this context emerges the research question: What are the affordances of Symmetry Groups and the contributions of the TO/FS/DT/GT quadrilateral to structuring campesino mathematics teachers9 pedagogical practices in the upper grades for effective symmetry instruction? Accordingly, this study aims to analyze the TO/FS/DT/GT quadrilateral alongside Symmetry Groups to foster critical3reflective awareness among rural mathematics teachers in the upper grades, thereby enriching Campesino Didactic Sessions in the teaching 3 learning process. We hypothesize that intertwining GeoGebra and geometry with TO and FS, combined with digital technologies in rural teacher education, positively impacts mathematics teaching and learning by enhancing critical3reflective and ethical practice through sociocultural artifacts grounded in Symmetry Groups. Methodologically, we adopt a qualitative case‐study approach. We discuss the procedures and instruments used for data collection and analysis via Content Analysis. The research is structured in four main phases: (I) documentary and bibliographic review; (II) dynamic planning of the didactic sessions modules; (III) the Extension Course experience; and (IV) preparation of the dissertation report. Findings reveal that pedagogical practice, in dialogue with TO, FS, geometry teaching, and GeoGebra studies, strengthened the development of Campesino Didactic Sessions as an effective methodological device for mathematics instruction in rural schools. The articulation of the TO/FS/DT/GT quadrilateral enabled participating teachers to develop more critical, creative, and contextualized pedagogical proposals aimed at promoting geometric learning and valuing sociocultural artifacts associated with Symmetry Groups. In conclusion, the study highlights the formative role of collaborative labor and community ethics, which emerge as essential elements for empowering rural mathematics teaching committed to DT-mediated pedagogical practices with Symmetry Groups and GeoGebra, grounded in the quadrilateral framework.