Università di Pavia - Offerta formativa

ELEMENTS OF MATHEMATICS FOR TEACHING

Enrollment year

2019/2020

Academic year

2021/2022

Regulations

DM270

Academic discipline

MAT/04 (COMPLEMENTARY MATHEMATICS)

Department

DEPARTMENT OF BIOLOGY AND BIOTECHNOLOGY "LAZZARO SPALLANZANI"

Course

BIOLOGICAL SCIENCES

Curriculum

PERCORSO COMUNE

Year of study

3°

Period

2nd semester (01/03/2022 - 14/06/2022)

ECTS

6

Lesson hours

48 lesson hours

Language

Italian

Activity type

WRITTEN AND ORAL TEST

Teacher

MAFFIA ANDREA (titolare) - 6 ECTS

Prerequisites

Mathematical knowledge and compentencies developed in the upper secondary schools

Learning outcomes

The course addresses mainly those students who intend to become mathematics teachers at the lower secondary school. It provides theoretically grounded elements for designing didactical activities in Arithmetic, Algebra, Probability, and Geometry, consistent with the national curricula, and for interpreting students' possible difficulties.

To this end, it will be needed to revise and consolidate theoretical knowledge concerning the matematical contents at stake.

To this end, it will be needed to revise and consolidate theoretical knowledge concerning the matematical contents at stake.

Course contents

We will discuss a selection of mathematical topics in Arithmetic, Algebra, Probability, and Geometry, consistent with the Italian national curricula both from the mathematical and from the didactical point of view. We will introduce and discuss specific theoretical notions helpful for designing and interpreting didactical activities: the idea of mathematical laboratory and the use of artefacts, elements of a socio-constructivist approach to teaching, the notion of didactical contract, the notion of figural concept, Van Hiele's theory of the levels of development geometrical thinking, the early algebra.

As for mathematical topics, the course will deal with the following themes:

Number systems;

Representation of numbers;

Divisibility;

Algorithms;

Standard operation algorithms;

Functions and their representation;

Fundamental entities and axioms of Plane and Space Geometry;

Definitions and properties of the main geometrical figures;

Introduction to classical probability.

As for mathematical topics, the course will deal with the following themes:

Number systems;

Representation of numbers;

Divisibility;

Algorithms;

Standard operation algorithms;

Functions and their representation;

Fundamental entities and axioms of Plane and Space Geometry;

Definitions and properties of the main geometrical figures;

Introduction to classical probability.

Teaching methods

Lectures, interactive lessons and group discussions aimed at making possible errors and misunderstanding come to light, and experiencing innovative teaching modalities.

Reccomended or required readings

Didactical material will be made available online by the teacher.

Material consists in texts elaborated starting from scientific journal articles and from the following bibliography:

Villani, Cominciamo dal punto, Pitagora, 2006

Villani - Berni, Cominciamo dallo zero, Pitagora, 2014

Material consists in texts elaborated starting from scientific journal articles and from the following bibliography:

Villani, Cominciamo dal punto, Pitagora, 2006

Villani - Berni, Cominciamo dallo zero, Pitagora, 2014

Assessment methods

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

mathematical tasks and open questions. The examinations will aim at assessing the level of knowledge of the contents of the course and the

ability to autonomously re-elaborate these contents.

mathematical tasks and open questions. The examinations will aim at assessing the level of knowledge of the contents of the course and the

ability to autonomously re-elaborate these contents.

Further information

Sustainable development goals - Agenda 2030