Benedetto Scoppola: The geometry book according to "Psicogeometria" by Montessori

The geometry book according to “Psicogeometria” by

Montessori

Benedetto Scoppola

Universita’ di Roma “Tor Vergata”

Praha, March 16, 2013

The main idea

“Our studies thus far have led to the acquisition of many new words, which refer to specific concepts. It is therefore advisable to bring these words together, classifying them on the basis of the ideas they represent, and placing them in alphabetical order. We thus carry out two different tasks: we create a geometry book and a geometry dictionary. The geometry book or album can be used to bring together the drawings and definitions etc. while the dictionary is written in the form of a list.”

Few preliminary observations

• All the works to be put in the geometry book should be related to prior works made with material.

• The dictionary is really a bright intuition: the development of the geometrical ideas is strictly related to the creation of a proper dictionary.

• The works on the geometry book should be as exact as possible.

The geometry book in the children’s house

Based on the use of metal insets

Points, lines, angles

The classification of triangles

Decorative drawings

The classification of quadrilaterals

DictionaryList A-Line - straight

curvilinearperpendicularobliqueparallelconvergentdivergent

Angle- rightacuteobtuse

Triangle- equilateralisoscelesscaleneequiangularright-angledobtuse-angledacute-angled

squarerectanglerhombus

List B

A - acute alternatealtitudeanglearc

B - basebisector

C - centrechordcirclecircumferencecompasscomplementaryconvergentcurvilinear

D - decagondegreediagonaldiameterdivergent

Equal, equivalent and similar shapes

Equal, equivalent and similar shapes

The square half of a given square

First self-similar structures

Problems

Hexagons

Pythagoras (1)

Other self similar structures

Isoperimetrical problem

1 2 3 4 5 6 7 8 9 10

2 4 6 8 10 12 14 16 18 20

3 6 9 12 15 18 21 24 27 30

4 8 12 16 20 24 28 32 36 40

5 10 15 20 25 30 35 40 45 50

6 12 18 24 30 36 42 48 54 60

7 14 21 28 35 42 49 56 63 70

8 16 24 32 40 48 56 64 72 80

9 18 27 36 45 54 63 72 81 90

10 20 30 40 50 60 70 80 90 100

Fractions

Fractions are numbers?

Reduction of areas to rectangles (1)

Reduction of areas to rectangles (2)

Reduction of areas to rectangles (3)

Squaring the circle?

Pythagoras (2)