DIDACTICS OF MATHEMATICS I
Academic year and teacher
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- Versione italiana
- Academic year
- 2017/2018
- Teacher
- MARIA TERESA BORGATO
- Credits
- 9
- Didactic period
- Primo Semestre
- SSD
- MAT/04
Training objectives
- The aim of the course is to provide knowledge on foundations and teaching of mathematics and geometry, in particular, non-Euclidean geometries and Hilbert's axioms, teaching theories and software. At the end of the course the student is able to critically analyse these theories and demonstrate their main results. Moreover, he/she can realize practical applications of software tools in various contexts related to the teaching of geometry.
Prerequisites
- Basic knowledge of differential and integral calculus, algebra and geometry.
Course programme
- Euclid's Elements. The Fifth Postulate. The theory of parallels. Hyperbolic and elliptic geometries. Consistency of non-Euclidean geometries. Circle inversion. The Beltrami-Klein and Poincaré models.
Hilbert's system of axioms (40 hours).
High School geometry text book approach. The Van Hiele model of thinking in geometry and Fischbein's theory of figural concepts (8 hours).
Interactive programs for the teaching and learning of mathematics (Cabri-géomètre, Geogebra) (24 hours). Didactic methods
- Frontal lessons. Seminars. Laboratory activities with dynamic software for the teaching of geometry (Cabri-géomètre, etc.)
Learning assessment procedures
- Oral exam. Computer test on Cabri-géomètre.
The course exam (both oral and computer test) has the porpose to verify the level of achievement of the previously indicated training objectives: the theoretical and critical knowledge of the topics of the course and the ability in the use of teaching software. The oral exam counts for two thirds and the computer test for one third of the final garde.
To pass the exam the student must obtain a minimum score of 18 out of 30. Reference texts
- Gli Elementi di Euclide, a cura di A. Frajese e L. Maccioni, Torino, Utet, 1970.
N. Efimov, Géométrie Supérieure, Moscou, MIR,1978.
D. Hilbert, Fondamenti della geomatria, Milano, Feltrinelli, 1970.
Teaching materials available at the course web site.
