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
What is math. Mathematical thinking and its meaning
Role of mathematics in the cognitive development of the child
The mathematical language
The number
Natural numbers and numbering systems
Number as an expression of quantity and order
The oriented line
Sets and operations between sets
Set of natural numbers and their algebra
Elementary arithmetic
Set of rational numbers
Set of real numbers
The base 10 positional system.
Numbering systems with a base other than 10
Geometric thought and its historical evolution
Euclidean geometry, a good approximation of reality
Pedagogical role of geometry in the child
Intuitive approach to plane geometry elementary concepts
Geometric quantities, concept of measurement
Geometric figures and their properties
Relation between geometry and algebra
Geometry of the straight line of the plane and of space
Applications of mathematics, models and predictions
Concept of theorem as a frame of reference for mathematical thinking.
The theorem of Pitagora
How to set up an arithmetic lesson in a practical way
How to set up a geometry lesson in a practical way
Experience of play and work in kindergarten
Algebra and geometry in primary school
Understanding mathematics from experience
Problem solving
Reference texts
Pensare in matematica, G. Israel, A. M. Gasca, Zanichelli 2012
Elementi di Matematica, A. Gimigliano, L. Peggion, Utet 2018
Elementi di Matematica, A. Gimigliano, L. Peggion, Utet 2018
Programme
Mathematics Institutions ProgramWhat is math. Mathematical thinking and its meaning
Role of mathematics in the cognitive development of the child
The mathematical language
The number
Natural numbers and numbering systems
Number as an expression of quantity and order
The oriented line
Sets and operations between sets
Set of natural numbers and their algebra
Elementary arithmetic
Set of rational numbers
Set of real numbers
The base 10 positional system.
Numbering systems with a base other than 10
Geometric thought and its historical evolution
Euclidean geometry, a good approximation of reality
Pedagogical role of geometry in the child
Intuitive approach to plane geometry elementary concepts
Geometric quantities, concept of measurement
Geometric figures and their properties
Relation between geometry and algebra
Geometry of the straight line of the plane and of space
Applications of mathematics, models and predictions
Concept of theorem as a frame of reference for mathematical thinking.
The theorem of Pitagora
How to set up an arithmetic lesson in a practical way
How to set up a geometry lesson in a practical way
Experience of play and work in kindergarten
Algebra and geometry in primary school
Understanding mathematics from experience
Problem solving
Reference texts
Pensare in matematica, G. Israel, A. M. Gasca, Zanichelli 2012
Elementi di Matematica, A. Gimigliano, L. Peggion, Utet 2018
Core Documentation
Pensare in matematica, G. Israel, A. M. Gasca, Zanichelli 2012Elementi di Matematica, A. Gimigliano, L. Peggion, Utet 2018
Reference Bibliography
Pensare in matematica, G. Israel, A. M. Gasca, Zanichelli 2012 Elementi di Matematica, A. Gimigliano, L. Peggion, Utet 2018Type of evaluation
. teacher profile teaching materials
2. Integers numbers. Mental calculation and written algorithms.
3. Elementary arithmetic.
4. Ratios and proportions. The mathematical basis of measurement.
5. Elementary Euclidean geometry, geometric constructions and the Cartesian plane.
6. Isometries, symmetries and geometric transformations in the plane.
7. The number system in mathematics: rational numbers.
8. Proportionality and introduction to the concept of function.
9. Introduction to real numbers and the concept of continuum.
10. Didactic nodes of children's initiation into mathematics.
- ANA MILLÁN GASCA, All’inizio fu lo scriba. Piccola storia della matematica come strumento di conoscenza, Milano, Mimesis, 2009 (3° ristampa).
- GIULIO CAIATI, ANGELICA CASTELLANO, In equilibrio su una linea di numeri, Milano, Mimesis, 2007.
Programme
1. Numerals and counting. Symbols: modern and ancient numbering systems2. Integers numbers. Mental calculation and written algorithms.
3. Elementary arithmetic.
4. Ratios and proportions. The mathematical basis of measurement.
5. Elementary Euclidean geometry, geometric constructions and the Cartesian plane.
6. Isometries, symmetries and geometric transformations in the plane.
7. The number system in mathematics: rational numbers.
8. Proportionality and introduction to the concept of function.
9. Introduction to real numbers and the concept of continuum.
10. Didactic nodes of children's initiation into mathematics.
Core Documentation
- GIORGIO ISRAEL, ANA MILLÁN GASCA, Pensare in matematica, Bologna, Zanichelli, 2012.- ANA MILLÁN GASCA, All’inizio fu lo scriba. Piccola storia della matematica come strumento di conoscenza, Milano, Mimesis, 2009 (3° ristampa).
- GIULIO CAIATI, ANGELICA CASTELLANO, In equilibrio su una linea di numeri, Milano, Mimesis, 2007.
Type of delivery of the course
The course will be offered through theoretical lessons and exercises.Type of evaluation
Passing the exam will take place through a written test. The student who deems it necessary can request an oral interview, upon passing the written test.