B024376 - DIDACTICS, EPISTEMOLOGY & HISTORY OF MATHEMATICS WITH MATHEMATICS TEACHING METHODOLOGY WORKSHOP

Italian

Ancient number systems and various multiplication algorithms.
The spread of the Hindu-Arabic numeral system through the Latin West during the 13th century.

Different models of mathematical problems: “Problemi a righe” versus “Problemi a quadretti”, “Variation problems”.

Figures of equal area and equal shape. Geometric misconceptions.

BACCAGLINI-FRANK Anna, DI MARTINO Pietro, NATALINI Roberto, ROSOLINI Giuseppe, Didattica della matematica, Mondadori 2017
BARTOLINI BUSSI Mariolina, Una metodologia didattica della scuola cinese: i problemi con variazione,
disponibile alla pagina web
http://math.unipa.it/~grim/bartolini_IMSI2_giugno2009.pdf

ZAN Rosetta, I problemi di matematica, Carocci 2016

Slides and materials prepared by the teacher (made available during the course on Moodle Platform).

Concerning the mathematical subjects addressed in the course, students must show:
- to interpret correctly the emerging innovation processes
- to interpret teaching-learning processes and frame them in their epistemological and didactic context.
- to possess basic knowledge and understanding of mathematical concepts and to know how to u- to possess communicative skills, by using correctly mathematical language, both in peer-to-peer relationships and in simulating teaching-learning sets;
- to show good skills to learn autonomously and personally and to deepen the subjects, developed in the course

Fundamental prerequisites are both basic knowledge and algorithmic skills, useful to deeply understand the arguments developed in the course; these arguments are developed in any pre-academic teaching, which is supposed to be followed with dealt with seriousness and commitment.
Strong motivations towards the teaching, a positive attitude toward mathematics and the awareness of the importance of mathematical education in training to a conscious and active citizenship are indispensable.

Lecture-style instruction. As far as possible, students may be required to expose suggestions and remarks on the various topics and to try to solve exercises and to suggest mathematical models for simple problematic contexts.
Through the student reception, topics chosen by students will be discussed and deepen in individual way and any question can be posed to the teacher

The course is also connected to a mathematics laboratory

Although not mandatory, attendance is strongly recommended, because of the relevance of relational aspects in teaching-learning processes both with other students and with the teacher.
Teaching takes advantage of MOODLE platform, which is obligatory for all students and can be particularly useful for students having motivated difficulties in attending classes with regularity.
During the course, the student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis

Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the two types, it is possible to state that subjects of particular examination of the written exam are all the skills required between the objectives with particular regard to the basic knowledge of the topics addressed and those of the type operational and problem-solving applications and modeling of problem situations, while the subject of particular examination of the oral examination is all the skills required between the objectives with particular regard to linguistic and communicative skills and the ability to structure hierarchically the mathematical knowledge learned by enhancing The originality and autonomy of mathematical thought.
In order to pass the exam, it is necessary at all stages to demonstrate to possess all basic elementary knowledge and basic skills in the execution of standard algorithms, which are taught in primary school.

Constructivist theories in mathematical education. Theory of didactical situations; Semiotic mediation in the mathematics classroom: artifacts and signs after a Vygotskian perspective.

Mistakes, misconceptions and difficulties in mathematics.

The principles of counting (Gelman and Gallistel).
Numeral systems. Bases. Positional and non positional systems. Examples from history of mathematics of positional and non positional systems and various multiplication algorithms (Egyptian multiplication, Lattice or gelusia multiplication, criss-cross multiplication). Egyptian division
Leonardo Pisano, the Liber Abaci (1202, 1228) and the spread of the Hindu-Arabic numeral system through the Latin West during the 13th century. The flourishing of abacus schools and abacus treatises.
Early calculating instruments: Genaille-Lucas rulers and Napier bones.

Theory of figural concepts and geometric misconceptions. Zukei puzzles. The Van Hiele Model for the learning and teaching of geometry.

Figures of equal area and/or equal shapes. Area maze puzzles.

Different models of mathematical problems: “Problemi a righe” versus “Problemi a quadretti”, “Variation problems”. The Singapore maths.

The INVALSI test and problems taken from "Rally matematico transalpino".