This research was developed during the Specialization Course in Educational Management/UFSM, at a State School in Santa Maria, which has pupils identifi ed as having high abilities/giftedness. Its objective is to investigate how a school, through its process of educational administration, organizes its teaching and administrative proposals to promote the development of potential of students with high abilities/giftedness. The research uses a qualitative approach, of the case study type, and the tools of document search, semi-structured interviews with teachers of students identifi ed as having high abilities/giftedness, and a semi-structured interview with a member of the school administration, as well as observation in the classroom.