9
None.
MAT/04 Complementary Mathematics.
Group report and oral exam.
The aim of the course is to rework basic mathematical knowledge in the light of the issues involved in teaching and learning the subject at school. Interpretation of students’ work on mathematical problems. Building new and stimulating teaching pathways for learning mathematics in secondary school (or at other levels).
Analysis of national and international guidelines on the “mathematics to be taught”. Main theoretical frameworks developed in mathematics education for the design and development of teaching activities. Study of the semiotic mediation model and of the role of signs in mathematical learning (Vygotskij, Duval, Radford). The role of mathematical discussion, technologies and languages, and their management by the teacher in the dynamics of teaching and learning mathematics (Sfard, Ferrari). Teaching elementary algebra: the notion of symbol sense (Arcavi); operational and structural conceptions in mathematics (Sfard); the arithmetic-algebra gap (Mason-Radford). Teaching elementary analysis: history and epistemology of the concept of function; its nature as process and object (Sfard); the cognitive roots of some concepts of analysis and their relationship with definitions (Vinner and Tall). Design and development of teaching methodologies, construction of activities and of a mathematics curriculum. Study of learning processes through the use of technologies: potential and critical issues.
At the end of the course, students must demonstrate that they
Quality of group work. Ability to analyse protocols produced in real teaching/learning situations. Reference to the literature and theories studied in order to argue relevantly on topics in mathematics education and to explore new problems independently.
