LATER DEVELOPMENTS IN ARITHMETIC 341
made. It is the splendid material to which is given the name of
*' material of the beads ". In it are represented the numbers in
their natural series from 1 to 10 with rods composed of beads
of coloured glass; every number has a different colour. The
number of these objects was so large that the numbers could be
combined into groups. The 10 was repeated ten times, uniting
ten rods in the form of a square, making the square of 10, com-
posed of a hundred beds. Finally, ten squares superposed and
bound together form a cube (the cube of 10, that is 1,000). This
material is described in the book on advanced method for education
in the elementary schools. (The Advanced Montessori Method, II.)
Now it happened that some children of about four years old
were attracted to those things which were so brilliant, so easily
handled and moved about, and to our great surprise, they began
to use them as they had seen the older children doing.
The consequence was a development so enthusiastic about the
work with numbers and specially about the decimal system that
it is true to say that arithmetic became one of the favourite
exercises.
Children four years old composed numbers up to 1,000. And
later, from five to six years, the development became really
wonderful, so much so that today the six years old children can
perform the four operations on numbers with many thousands
of units.
Signor Mario M. Montessori has helped with this develop-
ment, interpreting and materializing many calculations up to the
extraction of the square root of two, three and even four figures;
and the combination of the number-rods has made it possible to
introduce the first operations in algebra.
Urged by the evident pleasure which the children took in these
exercises, and by the skill which they possessed for manipulating
the small geometrical solids (as Froebel also understood when he
prepared his famous " gifts" of cubes and prisms collected in a
•cubical box), I thought of preparing similar objects. Only, instead
of making all the cubes or all the bricks alike, I caused a large