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The geometry book according to “Psicogeometria” by
Montessori
Benedetto Scoppola
Universita’ di Roma “Tor Vergata”
Praha, March 16, 2013
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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.”
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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.
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The geometry book in the children’s house
Based on the use of metal insets
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Points, lines, angles
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The classification of triangles
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Decorative drawings
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The classification of quadrilaterals
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DictionaryList A-Line - straight
curvilinearperpendicularobliqueparallelconvergentdivergent
Angle- rightacuteobtuse
Triangle- equilateralisoscelesscaleneequiangularright-angledobtuse-angledacute-angled
squarerectanglerhombus
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List B
A - acute alternatealtitudeanglearc
B - basebisector
C - centrechordcirclecircumferencecompasscomplementaryconvergentcurvilinear
D - decagondegreediagonaldiameterdivergent
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Equal, equivalent and similar shapes
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Equal, equivalent and similar shapes
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The square half of a given square
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First self-similar structures
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Problems
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Hexagons
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Pythagoras (1)
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Other self similar structures
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Isoperimetrical problem
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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
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Fractions
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Fractions are numbers?
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Reduction of areas to rectangles (1)
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Reduction of areas to rectangles (2)
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Reduction of areas to rectangles (3)
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Squaring the circle?
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Pythagoras (2)