16789 - Teaching of Mathematics

Learning outcomes

At the end of the course, the student: -  knows the main results of international research in didactics of mathematics; - is able to handle concrete learning situations in the teaching-learning process of math in secondary school; - is able to use, manage, criticize several different tools for didactics; - is able to use this knowledge to develop effective teaching materials that can be experienced in the classroom.

Course contents

The course integrates a theoretical part,  of critical analysis of the methodologies developed in math education research and in the history of mathematics,  with laboratory activities,  designing and developing mathematics teaching methodologies for building activities and, more generally, a mathematics curriculum consistent with the goals set by national high school guidelines and guidelines for technical and professional institutes..

The first part  has as the aim to contextualize the teaching-learning process  both from the institutional and the research point of view and point out the complexity and the various facets of this process, highlighting the the role of the teacher, conceptual, epistemological, linguistic and didactic nodes in teaching and learning mathematics. In particular, the following issues will be pursued:

1) institutional context: National Guidelines for Secondary School and  Invalsi, OECD-Pisa framework. This  analysis wats  to combine the skills and contents there described with those acquired in the first level degree;

2) basics of didactics of mathematics: the didactic triangle, the didactic contracts and the theory of learning situations, images and models, conflicts and misconceptions, metaphors and language use, semiotics and the theory of representations. This discussion will be used to provide reading lenses for the disciplinary topics that will be deepen in the laboratory activities;

3) study of teaching processes and math learning using technology, with particular attention to new digital technologies, analyzing the potential and criticality of the use of technological tools for teaching and learning math.

In laboratory activities,  some  "disciplinary" path (also in agreement with the students) will be described  in a vertical approach to the secondary school (first and second degree) study-course. The analysis will be dealt with in the design and development of teaching and learning activities of mathematics mainly focused on the use of new technologies. This will also give  the opportunity to experience firsthand  some teaching methods and to  analyze some textbooks. Among the possible laboratories:  geometry of transformations, symbol sense and algebraic thought, role of the proofs, probabilistic thinking.

Readings/Bibliography

During the course, teaching material will be provided through the e-learning platform. The material consist in slides / presentations, research articles, digital textbooks, work materials (tutorials, group work papers, research questionnaires, student protocols, ...).

Teaching methods

The course consists of: ex-cathedra lectures, critical analysis of texts and articles, laboratories or small group activities, cooperative learning  and microteaching activities, co-design, collective discussion and peer-to-peer evaluation.

Assessment methods

Realization of projects (a group one and an individual one), one written and one oral exam.

Projects:  implementation of  two projects, an individual one and  a group one. Subject and tools for projects will be described during the course,  once laboratory topics have been fixed.

Written test: it evaluates the ability to: solve, propose and analyze exercises related to the topics of secondary school deepened in the course, contextualizing them within the didactic practice, the National Guidelines and the theoretical lenses discussed in the lectures.

Oral exam

First part:  presentation of the projects carried out and discussion over them from a didactical point of view.

Second part:   written test examination.  "Disciplinary" and "didactical" discussion on concepts and topics dealt with during the course. In this part the following abilities will be evaluated:  the level of understanding  the concepts and themes discussed in the course, the ability to analyze such a theme or concept from a didactical point of view, recognizing delicate points for understanding; the ability to place such a topic or concept in a broad educational and cultural perspective and within a learning path.

Office hours

See the website of Alessia Cattabriga

See the website of Michele Mulazzani