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H          A          P          T          E          R           XX


COUNTING up to 100 and the exercises connected therewith, which
unite simple reckoning with a rational study of the first numbers,
seemed to us an important matter, especially because the elements
of reasoned arithmetic were given instead of numeration being
entrusted to the memory and to a mnemonic repetition.

For more than twenty years these remained the limits of the
development of the teaching.

I held, like everybody else, the prejudice that arithmetic pre-
sents great difficulty and that it was almost absurd to expect more
than the result already obtained at so early an age.

Experience in fact demonstrated a lack of interest when
compared with the enthusiasm and the surprising results obtained
with written language. The superiority of interest in language
apparently confirmed the prejudice about the difficulty and the
dryness of arithmetic.

Meanwhile I had prepared for the older children in the elemen-
tary schools (where from the beginning the attempt was made to
extend a method which had given such excellent results) material
to represent the numbers under geometrical forms and with movable
objects which would allow of combinations of the numbers being