THE TEACHING OF NUMERATION 329
separate units, and initiates the child's mind into the idea of
numerical groups, at the same time fixing before his eyes the suc-
cession of the signs 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This material, called
the tray of spindles, is divided into compartments each named with
one of the ten figures, arranged in sequence. Within these com-
partments, the child accumulates in group separate objects
corresponding to the figures; that is, he groups the units. In our
case these objects are represented by long, spindle-shaped sticks.
The other material which has been mentioned consists of a
group of cards in a box containing certain objects (coloured
markers); the cards are separate (mixed) and on them are written
the ten numbers from zero to nine. The child must first of
all arrange the cards in a row, by himself, showing by this that he
has learned the numerical series, and recognizes the figures which
represent the numbers. Under each figure he then places an appro-
priate quantity of markers, arranging them two by two, that is
one pair under the other; in this way there is made plain the
difference between odd and even numbers.
This is all the material which we have considered necessary
for laying the foundations of number-teaching and some arith-
metical, operations.
What follows here is a more detailed description which may
be of practical assistance to the teacher.
The rods having been arranged together in juxtaposition ac-
cording to length, the red and blue marks have to be counted,
beginning with the smallest piece, that is: one; one and two; one,
two and three, etc. always beginning again with the one for every
piece, commencing from side A. After that, the separate rods have
to be named from the shortest to the longest, according to the
number of sections which they contain, touching the extremities
of them with the finger, starting from the side £ where they go
up in staircase style; there results from this the numbering of the
longest piece: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. This correspondence
of the 10 on the three sides is verified by the child, who repeats the
exercise many times of his own accord because it interests him.