This paper focuses on understanding and exploring how a group of university engineering and science tutor educators learn and assimilate new conceptions about their role in the face of the forces of globalisation that are transforming the system of higher education. This research paper adopts the notion of the Teacher Support Team (TST) as developed by Daniels and grounded in Vygotsky's sociocultural account of the social formation of mind. These structures of meaning provide insight into the role played by the context, the interactions, the needs and the demands of actual activities, agreements and learning processes that this group of STEM lecturers undertook as they sought to transform their usual teaching methods that were focused on individual and isolated work in order to create more innovative practices and impact on their students' performance. The analysis of this experience, which was based on the epistemological principles of the sociocultural approach, focused on the educational model that emerges from needs that are perceived and shared through the group's interactions, as well as the transitions that such a team undergoes in its actions and decisions.