Resumen

The main objective of this theoretical essay is to present suggestions for competencies that should be cultivated by mathematics teachers. We present a possibility of creative insubordination and responsible subversive pedagogical action, which can be critical in the development of teachers, in both teacher education programs and professional development courses. We also introduce the definitions that will help to understand how teachers can act, do it differently and, hopefully, make a difference. We also present aspects of responsible subversion in mathematics teacher education programs rooted in ethnomathematical perspectives. Our theoretical references are Ubiratan D’Ambrosio, Beatriz D’Ambrosio, Celi Espasandin Lopes, Philippe Perrenoud e Paulo Freire.