Slides of lecture at Psycogeometry conference in Prague 2013.

1. The geometry book according
to “Psicogeometria” by
Montessori
Benedetto Scoppola
Universita’ di Roma “Tor Vergata”
Praha, March 16, 2013

2. 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.”

3. 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.

4. The geometry book in the
children’s house
Based on the use of metal insets

5. Points, lines, angles

8. The classification of triangles

10. Decorative drawings

12. The classification of
quadrilaterals

13. Dictionary
List A-
Line - straight
curvilinear
perpendicular
oblique
parallel
convergent
divergent
Angle- right
acute
obtuse
Triangle- equilateral
isosceles
scalene
equiangular
right-angled
obtuse-angled
acute-angled
square
rectangle
rhombus

14. List B
A- acute
alternate
altitude
angle
arc
B- base
bisector
C- centre
chord
circle
circumference
compass
complementary
convergent
curvilinear
D- decagon
degree
diagonal
diameter
divergent

15. Equal, equivalent and similar shapes

16. Equal, equivalent and similar
shapes

18. The square half of a given
square

20. First self-similar structures

22. Problems

25. Hexagons

30. Pythagoras (1)

31. Other self similar structures

33. Isoperimetrical problem

35. 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

36. Fractions

37. Fractions are numbers?

38. Reduction of areas to
rectangles (1)

39. Reduction of areas to
rectangles (2)

40. Reduction of areas to
rectangles (3)

41. Squaring the circle?

43. Pythagoras (2)