The Institutional Scholarship Program for Teaching Initiation (PIBID) is one of CAPES s initiatives to enhance teacher education in Brazil. In its guidelines, the Program establishes a link between higher education institutions (IES) and public basic education schools through the integration of teacher candidates into the daily environment of their future workplace, envisioning these candidates as the main beneficiaries of the policy. However, the implementation of the Program depends on specific practices and interactions, leading to consequences not anticipated in its formulation. In this regard, this dissertation, under the bottom-up model of policy analysis, investigates whether the students at the field school where a PIBID is implemented can also be considered beneficiaries of the policy. For this purpose, the Mathematics Subproject of the PIBID at the Federal Fluminense University in the Geraldo Reis University College (COLUNI-UFF), regulated by Public Notice No. 23/2022, was selected. The objectives were to map perceptions of practices and interactions in the implementation of this Subproject and to determine whether there are benefits or sanctions for the students at the school. This involved documentary analyses, observations, and interviews. From the content analysis, due to the specificities of COLUNI-UFF, the interpretation of the contribution of the Teaching Initiation Scholars to the students learning and school experiences, as well as the identification of new agents not anticipated by the Program, were derived. Ultimately, it is concluded that the Pibidians, within the context of COLUNI, share benefits from the Program with the students of the school.