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. What is mathematics?
2. Natural numbers and numbering systems
3. The integers
4. Elementary arithmetic
5. Rational numbers
6. The real numbers and the continuum
7. Geometric thought and Euclidean geometry
8. Algebra, geometry and the concept of space
9. Mathematical analysis
10. Axiomatic mathematics
11. Probability
12. Applied mathematics and modeling
13. Returning mathematics to culture
- Alessandro Gimigliano e Leonardo Peggion “Elementi di matematica” UTET
Programme
The course integrates with exercises and insights the activities planned by the co-teacher titular colleague, with whom the lessons will be coordinated. In particular, arguments from the following list:1. What is mathematics?
2. Natural numbers and numbering systems
3. The integers
4. Elementary arithmetic
5. Rational numbers
6. The real numbers and the continuum
7. Geometric thought and Euclidean geometry
8. Algebra, geometry and the concept of space
9. Mathematical analysis
10. Axiomatic mathematics
11. Probability
12. Applied mathematics and modeling
13. Returning mathematics to culture
Core Documentation
- Giorgio Israel e Ana Millán Gasca "Pensare in matematica Edizioni" Zanichelli 2012- Alessandro Gimigliano e Leonardo Peggion “Elementi di matematica” UTET
Reference Bibliography
- Alessandro Gimigliano e Leonardo Peggion "Elementi di matematica" UTET 2018Type of delivery of the course
Traditional lessons in presence, classroom according to institutional places. In case of COVID Emergency, the indications of the University concerning on line lessons will be applied.Type of evaluation
Written exam and short oral discussion. teacher profile teaching materials
History of the concept of number: The origins, counting, positional system, in Roman, Egyptian, Greek, Sumerian numerals, ...
Natural Numbers: Peano's Axioms, Operations on naturals, divisibility criteria, prime numbers, GCD and lcm, row and column calculations, sequences and progressions
Integers: Divisions with remainder, congruence classes and different arithmetic
Rational Numbers: Operations on rationals, fractions as operators, ordering of rational numbers, decimal representation, percentages and proportions
Real and Complex numbers: what are real numbers, algebraic and literal calculus, complex numbers
Calculation of probability: naive probability and properties of probability
Euclidean geometry: angles, polygons, triangles, regular polygons, circle, Pythagorean theorem, Polyhedra, Prisms and Pyramids
Analytical geometry: of the plane and of space
Programme
Naive set theory: Elements of set theory, Operations between sets, sets of numbers, functions, Operations and algebraic structuresHistory of the concept of number: The origins, counting, positional system, in Roman, Egyptian, Greek, Sumerian numerals, ...
Natural Numbers: Peano's Axioms, Operations on naturals, divisibility criteria, prime numbers, GCD and lcm, row and column calculations, sequences and progressions
Integers: Divisions with remainder, congruence classes and different arithmetic
Rational Numbers: Operations on rationals, fractions as operators, ordering of rational numbers, decimal representation, percentages and proportions
Real and Complex numbers: what are real numbers, algebraic and literal calculus, complex numbers
Calculation of probability: naive probability and properties of probability
Euclidean geometry: angles, polygons, triangles, regular polygons, circle, Pythagorean theorem, Polyhedra, Prisms and Pyramids
Analytical geometry: of the plane and of space
Core Documentation
Alessandro Gimigliano e Leonardo Peggion "Elementi di matematica" UTET 2018Reference Bibliography
Giorgio Israel e Ana Millán Gasca "Pensare in matematica Edizioni" Zanichelli 2012Type of delivery of the course
One hour in attendance and three hours away each weekType of evaluation
Written exam and short oral discussion. Students who pass the ongoing tests are exempted from the written test. teacher profile teaching materials
1. What is mathematics?
2. Natural numbers and numbering systems
3. The integers
4. Elementary arithmetic
5. Rational numbers
6. The real numbers and the continuum
7. Geometric thought and Euclidean geometry
8. Algebra, geometry and the concept of space
9. Mathematical analysis
10. Axiomatic mathematics
11. Probability
12. Applied mathematics and modeling
13. Returning mathematics to culture
- Alessandro Gimigliano e Leonardo Peggion “Elementi di matematica” UTET
Programme
The course integrates with exercises and insights the activities planned by the co-teacher titular colleague, with whom the lessons will be coordinated. In particular, arguments from the following list:1. What is mathematics?
2. Natural numbers and numbering systems
3. The integers
4. Elementary arithmetic
5. Rational numbers
6. The real numbers and the continuum
7. Geometric thought and Euclidean geometry
8. Algebra, geometry and the concept of space
9. Mathematical analysis
10. Axiomatic mathematics
11. Probability
12. Applied mathematics and modeling
13. Returning mathematics to culture
Core Documentation
- Giorgio Israel e Ana Millán Gasca "Pensare in matematica Edizioni" Zanichelli 2012- Alessandro Gimigliano e Leonardo Peggion “Elementi di matematica” UTET
Reference Bibliography
- Alessandro Gimigliano e Leonardo Peggion "Elementi di matematica" UTET 2018Type of delivery of the course
Traditional lessons in presence, classroom according to institutional places. In case of COVID Emergency, the indications of the University concerning on line lessons will be applied.Type of evaluation
Written exam and short oral discussion. teacher profile teaching materials
History of the concept of number: The origins, counting, positional system, in Roman, Egyptian, Greek, Sumerian numerals, ...
Natural Numbers: Peano's Axioms, Operations on naturals, divisibility criteria, prime numbers, GCD and lcm, row and column calculations, sequences and progressions
Integers: Divisions with remainder, congruence classes and different arithmetic
Rational Numbers: Operations on rationals, fractions as operators, ordering of rational numbers, decimal representation, percentages and proportions
Real and Complex numbers: what are real numbers, algebraic and literal calculus, complex numbers
Calculation of probability: naive probability and properties of probability
Euclidean geometry: angles, polygons, triangles, regular polygons, circle, Pythagorean theorem, Polyhedra, Prisms and Pyramids
Analytical geometry: of the plane and of space
Programme
Naive set theory: Elements of set theory, Operations between sets, sets of numbers, functions, Operations and algebraic structuresHistory of the concept of number: The origins, counting, positional system, in Roman, Egyptian, Greek, Sumerian numerals, ...
Natural Numbers: Peano's Axioms, Operations on naturals, divisibility criteria, prime numbers, GCD and lcm, row and column calculations, sequences and progressions
Integers: Divisions with remainder, congruence classes and different arithmetic
Rational Numbers: Operations on rationals, fractions as operators, ordering of rational numbers, decimal representation, percentages and proportions
Real and Complex numbers: what are real numbers, algebraic and literal calculus, complex numbers
Calculation of probability: naive probability and properties of probability
Euclidean geometry: angles, polygons, triangles, regular polygons, circle, Pythagorean theorem, Polyhedra, Prisms and Pyramids
Analytical geometry: of the plane and of space
Core Documentation
Alessandro Gimigliano e Leonardo Peggion "Elementi di matematica" UTET 2018Reference Bibliography
Giorgio Israel e Ana Millán Gasca "Pensare in matematica Edizioni" Zanichelli 2012Type of delivery of the course
One hour in attendance and three hours away each weekType of evaluation
Written exam and short oral discussion. Students who pass the ongoing tests are exempted from the written test.