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
Counting at the beginning: first ideas about numbers. How to write numbers in history: Summers, Babylonians, Egyptians, Greeks, and Romans the positional notation, the axiom of induction and Peano axioms. Cardinality, Cantor diagonal argument. Addition and multiplication. The ordering of natural numbers. Divisibility. The integers. The Euclidean division theorem, basis representation theorem for numbers. The GCD and Euclid algorithm. Prime numbers, their infinity, Eratosthenes, unique factorization theorem, Congruences, and modular arithmetics. Rational numbers. The representation of rationals. Operations on rationals. Order and density of rationals. The cardinality of rationals. The decimal representation of rationals, base 10 and base 3 numbers representation. The irrationality of the square root of 2, and of a prime. Continuity and the set of real numbers.
EUCLIDEAN GEOMETRY
The origin, Euclid and the axioms. Hilbert's observations. The first book of Euclid: Triangles and Pitaghoras Theorem. The geometric algebra and the second book of Elements. The sixth book of Elements and Thales. Polygons. Convex subsets and polygons, regular polygons. Equivalence in geometry: isoperimetry and equi-extension problems. Solid shapes in space. Analytic geometry: the cartesian plane, the equation of a straight line, the distance of two points and the equation of a circumference.
Materials, discussions, forum, video chat on moodle platform http://formonline.uniroma3.it/
Ana Millán Gasca Numeri e Forme , 2016, ed Zanichelli.
morevover Simonetta Di Sieno - Sandro Levi, Aritmetica di base, Mcgraw-Hill ed.,
The student can choose any accredited source according to his or her taste and previous skills.
Programme
NUMBERSCounting at the beginning: first ideas about numbers. How to write numbers in history: Summers, Babylonians, Egyptians, Greeks, and Romans the positional notation, the axiom of induction and Peano axioms. Cardinality, Cantor diagonal argument. Addition and multiplication. The ordering of natural numbers. Divisibility. The integers. The Euclidean division theorem, basis representation theorem for numbers. The GCD and Euclid algorithm. Prime numbers, their infinity, Eratosthenes, unique factorization theorem, Congruences, and modular arithmetics. Rational numbers. The representation of rationals. Operations on rationals. Order and density of rationals. The cardinality of rationals. The decimal representation of rationals, base 10 and base 3 numbers representation. The irrationality of the square root of 2, and of a prime. Continuity and the set of real numbers.
EUCLIDEAN GEOMETRY
The origin, Euclid and the axioms. Hilbert's observations. The first book of Euclid: Triangles and Pitaghoras Theorem. The geometric algebra and the second book of Elements. The sixth book of Elements and Thales. Polygons. Convex subsets and polygons, regular polygons. Equivalence in geometry: isoperimetry and equi-extension problems. Solid shapes in space. Analytic geometry: the cartesian plane, the equation of a straight line, the distance of two points and the equation of a circumference.
Materials, discussions, forum, video chat on moodle platform http://formonline.uniroma3.it/
Core Documentation
Giorgio Israel, Ana Millán Gasca Pensare in matematica, 2012, ed Zanichelli.Ana Millán Gasca Numeri e Forme , 2016, ed Zanichelli.
morevover Simonetta Di Sieno - Sandro Levi, Aritmetica di base, Mcgraw-Hill ed.,
The student can choose any accredited source according to his or her taste and previous skills.
Type of delivery of the course
lessons will require the active participation of students and homework. Constant personal study and review at home of the arguments presented in class are necessary in order to understand the forthcoming lessons. Materials, discussions, forum, video chat on moodle platform http://formonline.uniroma3.it/Attendance
attending lessons is strongly recommended, as usual for any math classType of evaluation
Written test with 4-6 questions, concerning exercises, computations, definitions, statements with proof, theoretical arguments. Eventually, an oral discussion can be asked by the teacher. By COVID emergency, summer exams will go through an oral colloquium plus a cognitive test via Teams official platform teacher profile teaching materials
1. Number words and counting. Numerals and numbering systems.
2. The integers. Mental calculation and written algorithms.
3. Elementary arithmetic.
4. Reports and proportions. The mathematical bases of measurement.
5. Elementary Euclidean geometry, geometric constructions and the Cartesian plane.
6. Isometries, symmetries and geometric transformations in the plane.
7. The system of numbers in mathematics: rational numbers.
8. Proportionality and introduction to the concept of function.
We also want to build a cultural vision of mathematics by integrating disciplinary knowledge with a historical perspective (remote origins of mathematics, the Greek idea of mathematics and its educational value, mathematics in modern science and technology) and epistemological (induction principle and reasoning by recurrence, geometric continuum, problem solving, the question of error).
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.
Programme
In this course we want to retrace the following topics of elementary mathematics from a higher standpoint in order to reach an awareness of their meaning and internal links:1. Number words and counting. Numerals and numbering systems.
2. The integers. Mental calculation and written algorithms.
3. Elementary arithmetic.
4. Reports and proportions. The mathematical bases of measurement.
5. Elementary Euclidean geometry, geometric constructions and the Cartesian plane.
6. Isometries, symmetries and geometric transformations in the plane.
7. The system of numbers in mathematics: rational numbers.
8. Proportionality and introduction to the concept of function.
We also want to build a cultural vision of mathematics by integrating disciplinary knowledge with a historical perspective (remote origins of mathematics, the Greek idea of mathematics and its educational value, mathematics in modern science and technology) and epistemological (induction principle and reasoning by recurrence, geometric continuum, problem solving, the question of error).
Core Documentation
Reference textsGIORGIO 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
Traditional, in the classroom. Small group activities are also planned.Type of evaluation
Written test.