Perceptions of indigenous mathematics teachers regarding the historical resource of Archimedes' balance

This study, aims to analyze the perceptions of seven indigenous Mathematics teachers from the Pataxó ethnic group regarding the production, observation, and manipulation of the historical resource Archimedes' balance for the purpose of constituting mathematical expressions for calculating the spherical surface and volumes of a right cone and a sphere, based on the right equilateral cylinder. The balance and the three solids involved were made of wood (cedar) by a Pataxó artisan at the request of the participants. This is a qualitative research, in the midst of a didactic sequence, organized in two face-to-face meetings that totaled six hours (two in the first and four in the second), in November 2024, with a theoretical basis based on the History of Mathematics from the perspective of Ethnomathematics. The perceptions of the indigenous teachers indicate that they understood the constitution of these expressions, and that they intend to replicate the dynamics in their classes with indigenous students.