In this article, elements are presented to problematize the professional development of teachers from the state of the art in a doctoral research project whose purpose is to analyze and understand how the training of teachers who teach mathematics in primary basic education in Colombian education has been, with a look at the Latin American context. It is assumed that in the conceptualization of teacher professional development, the reference to inservice teacher training and the ways in which teacher professionalization is configured is sustained in a systemic and dynamic manner. The analysis has been carried out qualitatively from a methodological adaptation of the grounded theory (Wolfswinkel et al., 2013). From this analysis, it can be seen in broad strokes that in the Latin American region there is a trend of technical training in accordance with the international market agenda; however, from the context of school mathematics, spaces for collaborative, investigative and reflective participation of teachers are glimpsed to question aspects and elements of pedagogical practice and to resolve situations over time that give meaning to their professional development. The increase in discussions and practices around the professional development of teachers has fostered a field of research in which the teacher is recognized as a subject who learns and who, in addition, produces knowledge; These elements provide important questions in the planning and implementation of public teacher training policies.