**
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**

I**real (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*** **