This study provides knowledge to understand the complexity associated with the supervision or tutoring that is carried out from the university centers of teacher training. It aims to reveal the conceptions, expectations, beliefs, fears and general attitudes that emerge in the two educational agents involved in research - supervisors and supervised - when confronted with the process of supervision to determine their initial positions, their crossings and the implications that it entails for the educational transformation and the formation of the teacher identity in gestation in the teachers in formation and the re-signification of the own in the experienced teachers in their role of teaching supervisors. In order to approach the study, a qualitative methodology of case studies with selective codification of the information coming from interviews with teachers in training and supervising teachers is designed, based on strictly formative and relational dimensions. The results indicate that the common categories point to the formative-instructional dimension, linked to didactic sub-dimensions, teaching-learning and disciplinary strategies, with the exception of the category of "fears", also common, pointing to the expressive-relational dimension. The implications for the professional identity conformation are addressed to attend to these initial dimensions of the formative device of the practical and how to channel them in the pedagogical process of supervision.