The course has two objectives: to analyze the main models for Mathematics teaching and learning, and those "theories" which provide the classical conceptual background for research in Mathematics Education; and to study innovative didactical methodologies.

Frontal lessons, collaborative activity and discussions. Students will be asked to read articles which will be collectively discussed during the course.

The achievement of the learning objectives will be ascertained through a written and an oral examination.

Mathematical knowledge and compentencies developed in the "laurea triennale" in mathematics. The course is not recommended for students of the "laurea triennale".

The course is divided into two parts.

First Part
Teaching-learning Mathematics models:
the traditional model of knowledge transmission (empirism);
the radical constructivism (Von Glasersfeld);
the social constructivism (P. Ernest and others);
the theory of didactic situations (G. Brousseau);
the "Inquiry" model (R. Borasi);
the cooperative learning model.
Examples of constructivist didactical transpositions
Analysis of Ministry of education documents on Mathematics teaching at the pre-university level. Study of specific research subjects.

Second Part
We will analyse the main tenets of "theories" which provide the classical conceptual background for research in Mathematics Education, and investigate how some of the ideas developed within these theories have informed research studies in Mathematics Education.
More specifically, we will focus on:
- Piaget's studies on the development of the cognitive development
- Vygotsky's studies and the cultural-historical approach;
- the studies on embodied cognition.

-"I suggerimenti della ricerca in didattica della matematica per la pratica scolastica", A. Pesci, available online at the web page of A. Pesci.
- Documentation available online on the website of the Italian Ministry of
Education (Ministero della Pubblica Istruzione).
- Articles from scientific journals and other materials made available on the course website.