Benedetto Scoppola: The geometry book according to "Psicogeometria" by Montessori
-
Upload
jirka-pelc -
Category
Documents
-
view
689 -
download
9
Transcript of 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)