ABSTRACT
In order to understand how knowledge and beliefs are used as personal resources and guidance in practice, we study the specialized knowledge of two lecturers of linear algebra at university level and the possible relationships with their beliefs on teaching and learning mathematics, when they teach the subject of matrices, determinants and systems of linear equations. Qualitative research was conducted under an instrumental case study design. The data were collected through video recordings and semi-structured interviews, and after the transcription, they were analysed for evidence of both the lecturers’ knowledge and beliefs. The elements of content knowledge, pedagogical content knowledge and beliefs evidenced appear to be consistent with one another, and their relationships have made it possible to identify key issues in their practice, such as the use of examples and the use of error. The preliminary results of the study could be a starting point for structuring teacher education and development, where the role of examples in helping students overcome difficulties in linear algebra is considered.
