28409 - DIDATTICA DELLA MATEMATICA 1

Academic Year 2018/2019

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Physics (cod. 9245)

    Also valid for Second cycle degree programme (LM) in Mathematics (cod. 8208)

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 guidelines.

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, 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. 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: non-euclidean geometries, mathematics and arts, 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, ...).

 

SUGGESTED READINGS

Baccaglini Frank, Di Martino, Natalini, Rosolini, Didattica della matematica, Mondadori Università (2018)
Bolondi, Fandino Pinilla, Metodi e strumenti per l’insegnamento e l’apprendimento della matematica, EdiSES, 2012
Israel, Millan Gasca, Pensare in matematica, Zanichelli 2015

Dedò, Alla ricerca della geometria perduta 1, Alice e Bob 46 (2016)
Di Sieno, Alla ricerca della geometria perduta 2, Alice e Bob 53 (2018)
Dedò, Di Sieno, Laboratorio di matematica: una sintesi di contenuti e metodologie

Castelnuovo, Pentole, ombre, formiche, Utet 2017
Castelnuovo, Didattica della matematica, Utet 2017

Benvenuti, Natalini, Comunicare la matematica: chi, come, dove, quando e, soprattutto, perché?!, Rivista Umi - Matematica, cultura e società, agosto 2017.

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 (two group ones and an individual one) and one oral exam.

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

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 Silvia Benvenuti