Licenciatura em matemática e o percurso de estudo e pesquisa: uma proposta do modelo epistemológico de referência para o ensino e aprendizagem do conceito de função

This work is about the Study and Research Course (PEP) as a didactic device that can be used as a methodology for teaching and learning mathematical concepts in the Mathematics Degree. The PEP has as theoretical basis the Anthropological Theory of Didactics (TAD), with Yves Chevallard as its main representative, as well as Guy Brousseau's Notion of Didactic Contract (CD), which contains important elements of PEP referral analysis, Highlighting the ruptures in the process. The proposal to apply the PEP will be through the content of Function, an important content of Basic Education and Higher Education. The paper presents some points of connection between the CD and the PEP, which can identify some difficulties in the implementation of the didactic device, mainly in the change of didactic contract already established for a new contract, making it difficult the possible ruptures and causing other difficulties. Another point is to use the PEP to present another way of working mathematical concepts in mathematics degrees.