Enrollment year
2018/2019
Academic discipline
MAT/04 (COMPLEMENTARY MATHEMATICS)
Department
DEPARTMENT OF EARTH AND ENVIRONMENTAL SCIENCES
Curriculum
PERCORSO COMUNE
Period
2nd semester (02/03/2020 - 12/06/2020)
Lesson hours
48 lesson hours
Activity type
WRITTEN AND ORAL TEST
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 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.
Course contents
We will discuss a selection of mathematical topics in Arithmetic, Algebra 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;
Geometry and measure.
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:
Israel – Gasca, Pensare in matematica, Zanichelli, 2012
Prodi, Foà, Berni, Dall’aritmetica all’algebra, Ghisetti e Corvi, 2005
Prodi, Tani, Introduzione all’algebra, Ghisetti e Corvi, 2003
Prodi, Bastianoni, Geometria del piano, Ghisetti e Corvi, 2003
Prodi, Mariotti, Bastianoni, Geometria dello spazio e oltre, Ghisetti e Corvi, 2009
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.
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