Geometry history and education

A.Y. 2018/2019
9
Max ECTS
86
Overall hours
SSD
MAT/04
Language
Italian
Learning objectives
This class will deal with some basic questions on the learning and teaching of middle and high school mathematics, setting the historical and laboratory perspectives in the appropriate theoretical math education frameworks.
In the optional second part the focus will be on some specific topics, the goal being the production of teaching items.
Expected learning outcomes
Basic elements of methodologies and technologies for the teaching of geometry useful for the exercise of the teaching profession.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Storia e Didattica dellla Geometria (prima parte)
Course syllabus
Geometry history and education
This class will deal with some basic questions on the learning and teaching of middle and high school mathematics, setting the historical and laboratory perspectives in the appropriate theoretical math education frameworks.
Part A
I. Topics on math education: Theories of learning and teaching in math; mistakes, misconceptions and remedial actions; debating and proving in math.
II. Math history as a teaching methodology: Euclid and the foundations of Geometry. Euclid's Elements, Books I-VI; Circular inversion and circles determined by three conditions. The problem of Apollonius; Hilbert and the foundations of Geometry. Geometry over fields. The real Cartesian plane and the Hilbert plane. The Poincaré model and the consistency of non-Euclidean geometry. Complex numbers and the regular 17-sided Polygon (Gauss). Construction problems and field extensions. Constructions with the marked ruler. Classical construction problems of antiquity. Euclid's Elements, Books XI-XII. Euclid's theory of volume. Hilbert's third problem.
III. Ruler and compass constructions as a teaching methodology: Introduction to GeoGebra; its applications to advanced problems in elementary geometry.
Storia e Didattica della Geometria (mod/02)
Course syllabus
Part B
The exploration of geometric shapes and their properties in 2D and in 3D; geometrical reasoning to solve problems and find new relationships; misconceptions and difficulties; what is wrong with this proof?; the communication of mathematical reasoning; virtual and practical artefacts.
Storia e Didattica della Geometria (mod/02)
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 3
Laboratories: 36 hours
Professor: Gario Paola
Storia e Didattica dellla Geometria (prima parte)
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Practicals: 10 hours
Laboratories: 12 hours
Lessons: 28 hours