342 THE DISCOVERY OF THE CHILD
wooden cube (about 10 cms. edge) to be divided according to the
divisions of the face into two unequal parts, then another into
three unequal parts; and by separating the parts according to these
divisions there resulted small cubes and rectangular prisms of
varied forms. This was the material representation of algebraic
expressions, the cube of a binomial and a trinomial. The solids
which were equal in decimal value had the same colour, and
groups of similar objects had different colours.
So on opening the box there was seen only one object, a cube
painted in many colours, its individual components aligned and
deposed separately in groups; for example, in the trinomial there
were three cubes of different dimensions and of three diverse
colours; similar prisms with a square face of one colour, e.g.
green; three other prisms also having a square face, but of different
shape, coloured perhaps yellow; and three other prisms with a
square face, different from the other two groups, coloured perhaps
blue; and finally six prisms all alike and with the faces rectangular,
coloured black. The rectangular faces of the three groups of
prisms mentioned are also black. These small coloured objects are
fascinating, and it is a question first of all of grouping them together
according to colour; then of disposing them of in various ways and
inventing a kind of story, in which three cubes are three kings,
each king having followers as high respectively as the other two
kings, the guards being black. From the use of this material
many results can be got; one is the order of the algebraic formula:
Finally the cubes are placed in the box in a certain order
and there is constructed the large cube of many colours: (a+b+c)*.
Playing with this material, there is formed the visual image of
the arrangement of the objects and therefore the memory of their
quantity and their order.
This is a sense preparation ojf the mind. No object is more
attractive to children of four years old. But later on, calling the