Relationships Between the Knowledge of Practices in Mathematics and the Pedagogical Content Knowledge of a Mathematics Lecturer

Currently, studies focusing on mathematics education pay more attention to the study of the lecturer’s knowledge, aiming to understand this knowledge, its development, and how it is reflected in the practice of teaching. Following this line of research, the present study is based in the Mathematics Teacher’s Specialized Knowledge (MTSK) model, which includes two domains of knowledge, namely, mathematical knowledge and pedagogical content knowledge. Through an instrumental case study, classroom observation, and a semi-structured interview, we inquire how the knowledge of practices in mathematics, one of the subdomains of mathematical knowledge, is related to the pedagogical content knowledge of a lecturer in a real analysis course. The results show relationships between these subdomains considering their nature of support or conditioning. In this regard, the lecturer’s knowledge of practices in mathematics conditions his/her knowledge of mathematics teaching (e.g. techniques, metaphors, and analogies). So, a lecturer’s teaching goal is that students, in addition to understanding the mathematical contents, learn how to think mathematically to validate and construct arguments. Additionally, a lecturer’s knowledge of students’ weaknesses in carrying out proofs and working with quantifiers is supported by his/her knowledge of practice in mathematics (e.g. different methods of proofs and statements with quantifiers, as well as their meaning). In this respect, the nature of relationships between two or three subdomains of the MTSK model contributes to understanding how the lecturer’s knowledge is integrated and is a good starting point for investigating the development of lecturers’ mathematical and pedagogical knowledge.