Knowing Mathematics of primary schools within the framework of the current discipline, and along its historical development; being aware of the value, the need, and the nature of mathematical reasoning and of it symbolism.
Knowledge and understanding:
- know the elementary mathematics of pre-primary and primary schools, making use of disciplinary, epistemological and historical elements, reflecting on primordial and basic mathematical concepts, on the nature of mathematical reasoning and its argumentative techniques, on the extension of the theoretical field of mathematics and mathematical symbolism;
- integrate mathematics in the field of culture, as a gateway to scientific thought in its philosophical matrix and its links with techniques and arts.
Ability to apply knowledge and understanding:
- promote the ability to consider mathematical and scientific literacy in pre-primary and primary school from a superior point of view.
Making judgements:
- encourage the opening to renewal of teaching practices through the combination of historical, epistemological and didactic research on the basic concepts of mathematics.
Communication skills:
- develop a superior vision on mathematical language, on symbolism, on representation, on the network structure of mathematical concepts and on approaching reality by setting and solving problems.
Learning skills:
- promote skills and interest in the constant study and tireless updating in the field of elementary mathematics, history and the epistemology of mathematics, through books and articles, conferences, courses and conferences, with discernment and depth.
Knowledge and understanding:
- know the elementary mathematics of pre-primary and primary schools, making use of disciplinary, epistemological and historical elements, reflecting on primordial and basic mathematical concepts, on the nature of mathematical reasoning and its argumentative techniques, on the extension of the theoretical field of mathematics and mathematical symbolism;
- integrate mathematics in the field of culture, as a gateway to scientific thought in its philosophical matrix and its links with techniques and arts.
Ability to apply knowledge and understanding:
- promote the ability to consider mathematical and scientific literacy in pre-primary and primary school from a superior point of view.
Making judgements:
- encourage the opening to renewal of teaching practices through the combination of historical, epistemological and didactic research on the basic concepts of mathematics.
Communication skills:
- develop a superior vision on mathematical language, on symbolism, on representation, on the network structure of mathematical concepts and on approaching reality by setting and solving problems.
Learning skills:
- promote skills and interest in the constant study and tireless updating in the field of elementary mathematics, history and the epistemology of mathematics, through books and articles, conferences, courses and conferences, with discernment and depth.
scheda docente
materiale didattico
1. Primordial mathematical conceptions: form, order, measure
2. Elementary Euclidean geometry.
3. Problems, investigations, proofs in mathematics as part of human culture. Mathematics at school and its educational role.
4. Counting numbers and early extensions of the number system: number words, number symbols, zero, integers.
5. Elementary arithmetic: divisibility and numerical congruence.
6. The quantification of reality. The geometrical continuum, magnitudes, ratios. The mathematical foundation of measure.
7. The number system of mathematics and the number line. Rational numbers. What are “real numbers”Il sistema dei numeri nella matematica e la retta numerica. I numeri razionali. Cosa sono i numeri “reali”?
8. Dynamical geometry: isometries and similarities in the plane.
9. Examples of mathematics in science. The concept of function.
Ana Millán Gasca, All’inizio fu lo scriba. Piccola storia della matematica come strumento di conoscenza, Milano, Mimesis.
Programma
In this course selected issues in elementary mathematics are considered, from a higher viewpoint, to reach greater awareness in view of professional work with children from preschool to the final year of primary school; moreover, a cultural outlook on mathematics is outlined, by connecting mathematical knowledge with history and epistemology of mathematics; some aspects of modern challenges in children's mathematics education are considered. Further educational aspects are considered in the course Mathematics and mathematics education.1. Primordial mathematical conceptions: form, order, measure
2. Elementary Euclidean geometry.
3. Problems, investigations, proofs in mathematics as part of human culture. Mathematics at school and its educational role.
4. Counting numbers and early extensions of the number system: number words, number symbols, zero, integers.
5. Elementary arithmetic: divisibility and numerical congruence.
6. The quantification of reality. The geometrical continuum, magnitudes, ratios. The mathematical foundation of measure.
7. The number system of mathematics and the number line. Rational numbers. What are “real numbers”Il sistema dei numeri nella matematica e la retta numerica. I numeri razionali. Cosa sono i numeri “reali”?
8. Dynamical geometry: isometries and similarities in the plane.
9. Examples of mathematics in science. The concept of function.
Testi Adottati
Giorgio Israel, Ana Millán Gasca, Pensare in matematica, Bologna, Zanichelli.Ana Millán Gasca, All’inizio fu lo scriba. Piccola storia della matematica come strumento di conoscenza, Milano, Mimesis.
Bibliografia Di Riferimento
GIULIO CAIATI, ANGELICA CASTELLANO, In equilibrio su una linea di numeri, Milano, mimesis, 2007. RICHARD COURANT, HERBERT ROBBINS, Che cos’è la matematica, Torino, Bollati Boringhieri, Torino, varie edizioni FEDERIGO ENRIQUES, Le matematiche nella storia e nella cultura, Bologna, Zanichelli, 1982. FRANCIS SU, Matematica per il fiorire dell'essere umano, Roma, Carocci, 2023. ANA MILLÁN GASCA, Numeri e forme. Didattica della matematica con i bambini, Bologna, Zanichelli, 2016. HANS MAGNUS ENZELSBERGER, Il mago dei numeri, Torino Einaudi, varie edizioni. STELLA BARUK, Dizionario di matematica elementare, Bologna, Zanichelli, 1998.Modalità Erogazione
Theoretical lessons are combined with exercises, including teamwork. Together with usual methodologies in mathematics courses (first year undergraduate students), text reading and analysis and audiovisual materials are introduced.Modalità Frequenza
Theoretical lessons are combined with exercises, including teamwork. Together with usual methodologies in mathematics courses (first year undergraduate students), text reading and analysis and audiovisual materials are introduced.Modalità Valutazione
Written exam