The performance of Brazilian students in mathematics is a question that deeply troubles both society and the academic community and public policies have tried to develop actions that respond to a demand for better learning. In this context, teacher education is an important variable to consider. The objective of this research is to present a comparative analysis of the competences developed or improved on by participating teachers in two models of teacher education for mathematics teaching: the postgraduate specialization course offered by the Universidade Federal Fluminense (UFF), which represents the dominant university model, and the teacher residence programme at Colégio Pedro II, representative of a new public policy for continuous teacher education. The data were collected in two stages: in the first stage, teachers responded to a closed questionnaire that identifies socio-historical data and their initial perceptions of their competences; in the second stage, interviews were realized with the teachers in order to develop a greater understanding of the teachers competences in relation to the planning and management of the teaching-learning process, ethicalcritical- reflexive competences, and the establishment and mantenance of relationships in the school environment. The different results and approximations between the two models are analysed, emphasizing the importance and challenge of establishing a satisfactory relationship between theory and practice during teacher education; the relevance of a social context that facilitates the choice of a profession by desire and not by the demand of precocious professionalization; the absence of the intervention of teachers in situations of prejudice between students; the predominance of demonstration as a method for teaching mathematical concepts, amongst other aspects that demonstrate the urgent necessity to transcend the model of teacher education based only on the teaching of mathematical content and to promote active methods in order for the students to learn, considering the importance of developing teacher competences that integrate personal and social relations in mathematics classes.