Interconnections between Content Knowledge and Pedagogical Content Knowledge of a University Lecturer in Linear Algebra

The aim of this study is to deepen our understanding of the practice of a lecturer in linear algebra by exploring the connections he makes between his content knowledge and his pedagogical content knowledge while working on the topic of matrices. Data were collected through video recordings of his classes and semi-structured interviews, and were analysed with the Mathematics Teacher’s Specialised Knowledge model. Instances of classroom performance, supported by the teacher’s own affirmations, provided evidence relating to the categories comprising the model, and enabled us to establish connections between the lecturer’s knowledge, his understanding of his students’ learning capabilities, and his knowledge of teaching mathematics, which together account for his classroom practice: the use of varied examples to introduce new content, the highlighting of the most salient aspects of the topic, and alerts about potential errors and difficulties. The contribution that these results could make to the training of university teachers, which would be done with the knowledge of the areas of difficulty shown by the teacher in mind, could be used to deepen other elements of their pedagogical content knowledge. The interconnections between areas of knowledge identified by the study also serve to validate the usefulness of a theoretical model for studying teachers’ knowledge.