Symmetries of the equilateral triangle mediated by geogebra: a proposal for training rural mathematics teachers

Background: The equilateral triangle is a fundamental object in geometry, notable for its symmetrical properties, which are best understood through dynamic visualization. Traditional methods often fall short in making these concepts accessible, especially in rural educational contexts with limited resources. Aims: This study aimed to explore the effectiveness of GeoGebra software as a mediating tool to enhance rural mathematics teacher training, particularly in understanding the symmetries of equilateral triangles. Methods: Employing a qualitative and descriptive methodology, the research collected data through classroom observations, analysis of participants’ digital constructions using GeoGebra, and reflective interviews. These methods were chosen to capture how pre-service teachers engage with geometric concepts via dynamic tools. Results: The results demonstrated that GeoGebra significantly improves the visualization of geometric transformations such as rotations and reflections. Participants reported increased comprehension and engagement due to the interactive nature of the software. The teaching approach also encouraged deeper geometric reasoning and fostered the ability to connect abstract group theory with concrete visual representations. Conclusion: The use of GeoGebra in rural teacher training is not only feasible but transformative. As a free, accessible platform, it bridges gaps caused by resource limitations and aligns well with local educational realities. The software empowers future educators to adopt student-centered approaches that make geometry both meaningful and contextually relevant. This proposal supports the integration of digital tools in teacher education and provides a replicable model for similar contexts globally. Future research should investigate broader applications of GeoGebra across other geometric topics and assess its long-term impact on classroom practice in rural environments.