The use of Professional Learning Tasks (TAP): collaborative work in the context of the professional development of a Mathematics teacher trainer
This research is the result of a collaborative work process between a teacher educator from a Brazilian university and a researcher. Its aim is to understand how a Collaborative Work involving the design of a Professional Learning Task (PLT) for teaching Linear Systems in a Linear Algebra subject provides opportunities for professional development for a teacher trainer and a researcher. The theoretical-methodological foundation discusses the aspects of the study and understandings of teachers' professional development, mainly in relation to mathematics teacher educators, collaborative work, Professional Learning Tasks (PLT), professional learning and Critical Mathematics Education (CME). This research follows a qualitative approach anchored in the interpretive paradigm, involving collaborative work between a mathematics teacher educator and a researcher. The results of the study show that the literature has pointed out the difficulties students have with the curricular topics of Linear Algebra, due to its formalized, symbolic and abstract context. They also highlight the need to study the roles and identities of mathematics teacher educators in relation to teaching practice and the mathematics taught in academia and the lack of articulation with school mathematics, as well as the need for solid training for teacher educators based on knowledge that enables solutions and alternatives to emerge within collective work, covering all pedagogical action. In this sense, it is important to have math teacher trainers in a context of continuing education aimed at professional development. Collaborative work was a favorable environment for the development of support, mutual respect and reciprocal learning in which, through successive challenges and shared co-responsibilities, collaborative relationships and in-depth reflections on one's own practice were developed, enhancing interaction, bringing university and school closer together through the participation of a researcher and a mathematics teacher trainer.