On some mathematical concepts / themes to be faced in teaching

Reflections / indications on mathematical themes to be addressed, in a coordinated way, in the various school levels

INDEX
 

[primary - A   primary - B   lower secondary   upper secondary - A   upper secondary - B  school]
[some operative considerations]
 

On some mathematical concepts / themes to be faced in the first years of school
("interwoven" within teaching units)

The same contents present in the document relating to the next school level are more or less faced, with a different slant.
The indications refer to how much should be dealt with in kindergarten and in the first part of primary school.

The concept of model
Statistics (and probability calculus)
Number and arithmetic operations
Diagrams, formulas and functions
Space

On some mathematical concepts / themes to be faced in the 2nd part of primary school
("interwoven" within teaching units)

The same contents present in the document relating to the next school level are more or less faced, with a different slant; however, many topics are also dealt with in the one relating to the previous level.
The indications refer to how much should be faced on average in the 2nd part of primary school. They are presented articulated by thematic areas but, as it is clarified, in the didactic paths the different mathematical concepts must intertwine with each other and with the other disciplines.

The concept of model
The concept of number
Exponentiation
Elementary arithmetic
The concepts of ratio and proportionality
The diagrams
Approximations. Calculators. Computer
Descriptive statistics
Formulas, terms, graphs
The concepts of function and resolution of an equation
Space
Theory of probability

On some mathematical concepts / themes to be faced in the lower secondary school
("interwoven" within teaching units)

The same contents present in the document relating to the previous level and the next school level are more or less faced, with a different slant.
The indications refer to how much should be faced on average in the lower secondary school.  They are presented articulated by thematic areas but, as it is clarified, in the didactic paths the different mathematical concepts must intertwine with each other and with the other disciplines.

The concept of model
The concept of number
Exponentiation
Elementary arithmetic
The concepts of ratio and proportionality
The diagrams
Approximations
Calculators. Computer. Logic
Descriptive statistics
Formulas, terms, graphs
The concepts of function and resolution of an equation
Space
Inverse proportionality
Theory of probability

On some mathematical concepts / themes to be faced in the 1st part of upper secondary school
("interwoven" within teaching units)

The same contents present in the document relating to the previous level are more or less faced, with a different slant.
The indications relate to how much should be dealt with in the upper secondary school.
They are presented articulated by thematic areas but, as it is clarified, in the didactic paths the different mathematical concepts must intertwine with each other and with the other disciplines.
In the last paragraph there are indications on the possible diversification of educational development in the various types of schools.

The concept of model
The concept of real number
Non decimal numbering bases
Exponential notation
Powers
Elementary arithmetic
The concepts of ratio and proportionality
The diagrams
Approximations
Calculators. Computer. Logic
Descriptive statistics
Variation and slope
Formulas, terms, graphs
The concepts of function and resolution of an equation
Space
Circular functions
Inverse proportionality
Continuity
Systems of equations . Inequations
Polynomial functions
Exponential function
Mathematical structures
Combinatorics
Theory of probability
Educational differentiations 

On some mathematical concepts / themes to be faced in the last years of upper secondary school
("interwoven" within teaching units)

In the last years of high school, in addition to in-depth themes already present in the previous school levels, new themes are being launched (differential and integral calculus, but not only).
They are presented articulated by thematic areas but, as it is clarified, in the didactic paths the different mathematical concepts must intertwine with each other and with the other disciplines.
Some of the themes presented in the part relating to the early years of of upper secondary school, although not mentioned here, must be taken up and developed in these final years.
In the last paragraph there are indications on the possible diversification of educational development in the various types of schools.

The concept of model
Ireal (and complex) numbers
Non decimal numbering bases
The concept of limit
Continuity, integration, differentiation, antidifferentiation
Exponentiation and logarithm
Space
Statistics and theory of probability
Relationships between two random variables
Insights on mathematical analysis
More
Educational differentiations, and final considerations