DIDATTICA DELLA MATEMATICA 1

To know the main theoretical frameworks in mathematics education.

To know the main methodologies developed in mathematics education.

To know how to manage concrete classroom situations in the process of teaching-learning mathematics in secondary school.

To be able to use technologies for the teaching of mathematics.

In particular, the course has the following objectives:

Knowledge and understanding:

- to understand a text related to the didactics of mathematics, both institutional and research nature

- report on teaching issues and design teaching activities

- know and understand the main theories about teaching and learning mathematics

- to frame from a historical point of view the epistemological references of mathematics topics useful for teaching

- know the basics of the main theoretical lines of research in didactics of mathematics.

Applying knowledge and understanding:

- solve activities for students at secondary school level highlighting conceptual nodes, objectives, prerequisites, methodologies

- to face problems of didactics of mathematics such as the design of innovative didactic pathways

- use the technologies for the teaching of mathematics to enhance the teaching and learning of the discipline

Making judgments:

- analyze students' processes during math activities by analyzing movies or protocols

- to draw up reports of didactic activities using materials in Italian and English

- work autonomously and in groups, in attendance and remotely via a synchronous and asynchronous platform

- produce textual or multimedia teaching objects independently

Communication skills:

- Ability to expose the results of historical-epistemological and theoretical-experimental studies, even to a non-expert audience. Being able to support the importance of the results achieved and highlight the fallout in different environments (school, etc..).

Learning skills:

- Ability to update with the consultation of scientific publications in the field of Didactics of Mathematics. Ability to follow, using the knowledge acquired during the course, both second-level masters, as well as in-depth courses and specialized seminars in the field of Didactics of Mathematics and their theoretical-experimental systematization.

The course aims to provide theoretical and practical tools for professional growth as a teacher of mathematics.

Each lesson, therefore, consists of two parts:

I) In the first part of the lesson, knowledge of pedagogical theories and didactical methodologies is conveyed through participatory frontal lessons;

II) in the second part of the lesson in general these theories and methodologies are put into practice in

laboratory activities (usually already tested at school), often in a collaborative or cooperative way.

If logistically possible, a visit to a science museum is planned.

The course includes activities related to teacher training.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Learning assessment may also be carried out online, should the conditions require it.

• Theoretical frameworks and basic elements of mathematics education;
• Institutional context: National guidelines for high schools and guidelines for technical and professional institutes;
• Classical models of mathematical learning and specific studies on the development of mathematical thought;
• The didactical methodology of the mathematics laboratory;
• History of mathematics in mathematics education;
• Presentation and discussion of the main cognitive and didactic aspects (strategies and methodologies, the role and management of error, misconceptions, registers of representation, ...);
• Reflection on some transversal skills such as argumentation, conjecture and proof through guided analysis of teaching materials supported by experiments (UMI, m@t.abel, ...) and INVALSI tests of mathematics for possible educational uses;
• Study of the teaching and learning processes of mathematics mediated by the use of technologies, with particular attention to new digital technologies;
• Examples of national and international research in mathematics education.

1. Materiale didattico fornito dal docente
2. B. D’Amore, S. Sbaragli. (2011). Principi di base di Didattica della matematica. Bologna: Pitagora.
3. R. Zan. (2007). Difficoltà in matematica. Osservare, interpretare, intervenire. Milano: Springer.
4. Villani, V. (2003). Cominciamo da zero: domande, risposte e commenti per saperne di più sui perchè della matematica: aritmetica e algebra. Bologna: Pitagora.
5. Villani, V. (2006). Cominciamo dal punto: domande, risposte e commenti per saperne di più sui perché della matematica (geometria). Bologna: Pitagora.
6. INDIRE – Risorse per docenti dai progetti nazionali: Il progetto M@t.abel: http://www.scuolavalore.indire.it/?s=search&keyword=&taxo[0][name]=ordine_di_scuole&taxo[0][term]=primaria&taxo[1][name]=discipline&taxo[1][term]=matematica
7. U.M.I. Matematica 2001 – Materiali per un nuovo curricolo di matematica con suggerimenti per attività e prove di verifica: http://www.umi-ciim.it/materiali-umi-ciim/primo-ciclo/