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.
Canali
teacher profile teaching materials
1. The long history of mathematics, from the remote origins to the Scientific and Technological Revolution
2. Primordial mathematical conceptions: form, order, measure. Conceptual universes in mathematics: decomposition, operations, relations. Quantification: discrete and continuum.
3. Elementary Euclidean geometry.
4. Problems, investigations, proofs in mathematics as part of human culture. Mathematics at school and its educational role.
5. Counting numbers and early extensions of the number system: number words, number symbols, zero, integers.
6. Elementary arithmetic: divisibility and numerical congruence.
7. Dynamical geometry: isometries and similarities in the plane.
9. The number system of mathematics and the number line. Rational numbers.
A. Millán Gasca, All'inizio fu lo scriba (Mimesis)
Programme
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. The long history of mathematics, from the remote origins to the Scientific and Technological Revolution
2. Primordial mathematical conceptions: form, order, measure. Conceptual universes in mathematics: decomposition, operations, relations. Quantification: discrete and continuum.
3. Elementary Euclidean geometry.
4. Problems, investigations, proofs in mathematics as part of human culture. Mathematics at school and its educational role.
5. Counting numbers and early extensions of the number system: number words, number symbols, zero, integers.
6. Elementary arithmetic: divisibility and numerical congruence.
7. Dynamical geometry: isometries and similarities in the plane.
9. The number system of mathematics and the number line. Rational numbers.
Core Documentation
G. Israel, A. Millán Gasca, Pensare in matematica (Zanichelli)A. Millán Gasca, All'inizio fu lo scriba (Mimesis)
Attendance
Regular class attendance is strongly recommendedType of evaluation
The questions included in the written exam regard the subjects considered in the course, including mathematics exercises teacher profile teaching materials
2. Elementary Euclidean geometry.
3. Problems, inquiries, and proofs in mathematics as part of human culture. Mathematics in schools and its educational value.
4. Natural numbers. Words for counting. The writing of numbers: numeral systems. The extension of the number system: zero; the integers.
5. Elementary arithmetic: the theory of divisibility and numerical congruences.
6. The quantification of reality. The geometric continuum, magnitudes, and ratios. The mathematical foundations of measurement.
7. The number system in mathematics and the number line. Rational numbers. What are “real” numbers?
8. Dynamic 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.
Programme
1. The primordial mathematical concepts: form, order, measure.2. Elementary Euclidean geometry.
3. Problems, inquiries, and proofs in mathematics as part of human culture. Mathematics in schools and its educational value.
4. Natural numbers. Words for counting. The writing of numbers: numeral systems. The extension of the number system: zero; the integers.
5. Elementary arithmetic: the theory of divisibility and numerical congruences.
6. The quantification of reality. The geometric continuum, magnitudes, and ratios. The mathematical foundations of measurement.
7. The number system in mathematics and the number line. Rational numbers. What are “real” numbers?
8. Dynamic geometry: isometries and similarities in the plane.
9. Examples of mathematics in science. The concept of function.
Core Documentation
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.
Attendance
Students are strongly encouraged to attend classes in person.Type of evaluation
The examination consists of a written test, including open questions as well as exercises and problems related to the topics covered during the course.