Module page
Didattica della Matematica
| academic year: | 2013/2014 |
| instructor: | Mario Barra |
| degree course: | Mathematics (magistrale), I year |
| type of training activity: | caratterizzante |
| credits: | 6 (48 class hours) |
| scientific sector: | MAT/04 Matematiche complementari |
| teaching language: | italiano |
| period: | II sem (03/03/2014 - 13/06/2014) |
Presence: highly recommended
Module subject:
Fusionism of Felix Klein and Bruno de Finetti (connections between Geometry and other fields of the mathematics). The didactic philosophy of Piaget, Dewey, Hadamard, Laplace and Polya. The "constructivism", the "mental images"and the didactic aspects of the visualization. Examples of Problem Solving and Problem Posing. The problem of the inductive reasoning and its connection with the deductive one. Dynamic aspects in the instruction of the mathematics. Teaching mathematics through the dynamic geometry software. Traditional geometric transformations. and a new geometric, not linear, transformation, the radiality. Determination of the area of the sinusoid, the cardioid, the Archimedes' spiral, the cycloid, the "geometric flowers" and other curves, through the radiality. Hyper-tetrahedrons and hyper-cubes, their portions and projections, in order to determine in more ways the sum of the powers of natural numbers, some aspects connected with the "third Hilbert's problem", space's tessellatios, the Euler's Characteristic in any dimensions, the Little Fermat's Theorem,
. Importance of the connection between the history of the mathematics and its didactics. Analysis in historical and didactic key of some fundamental problems and some frequent errors. The programs of the school. Some aspects of international didactic research. Didactic experimentations and connected aspects.
Suggested reading:
Castelnuovo E, Barra M., 2000 (1976). Matematica nella realtà, Boringhieri, Torino.
Verranno distribuite dispense e indicazioni bibliografiche di alcuni articoli.
Castelnuovo E, Barra M., 2000 (1976). Matematica nella realtà, Boringhieri, Torino.
Type of course: standard
Knowledge and understanding: successful students will be able to deal with arguments concerning the teaching of the mathematics, having caught up a good familiarity with fundamental aspects, as the connection between the various fields of the mathematics, between the various dimensions of the space and between discreet and the continuous space and will be able to use a dynamic geometry software.
Skills and attributes: successful students will be able to prepare lessons to teach mathematics holding present some solutions to several didactic problems and taking advantage themselves also of cards of "auto-learning" and of dynamic geometry software.
Personal study: the percentage of personal study required by this course is the 65% of the total.