While the child is doing these operations he is writing down the results. For this purpose there is specially prepared paper with an attractive heading which the child can place at the right of his multiplication board. There are ten sets of this paper in a series and ten series in a set, making a hundred sheets with each set of multiplication material. The accompanying cut shows a sheet prepared for the multiplication of number 3.

Everything is ready on the printed sheet; the child has only to write the results which he obtains by adding the beads in columns of three each. If he makes no error he will write: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

In this way he will work out and write down the whole series from 1 to 10; and as there are ten copies of each sheet, he can repeat each exercise ten times.

Thus the child learns by memory each of these multiplications. And we find that he helps himself to memorize even in other ways. He walks up and down holding the multiplication sheet, which he looks at from time to time. It is a sheet which he himself has filled, and he may be memorizing seven times six, forty-two; seven times seven, forty-nine; seven times eight, fifty-six, etc.

This material for the multiplication table is one of the most interesting to the children. They fill six or seven sets, one after the other, and work for days and weeks on this one exercise. Almost all of them ask to take it home with them. With us, the first time the material was presented a small uprising took place, for they all wished to carry it away with them. As this was not permitted the children implored their mothers to buy it for them, and it was with difficulty that we made them understand that it was not on the market and therefore could not be purchased. But the children could not give up the idea. One older girl headed the rebellion. "The Dottoressa wants to try an experiment with us," she said. "Well, let's tell her that unless she gives us the material for the multiplication table we won't come to school any more."

This threat in itself was impolite, and yet it was interesting; for the multiplication table, the bug-bear of all children, had become so attractive and tempting a thing that it had made wolves out of my lambs!

When the children have repeatedly filled a whole series of these blanks, with the aid of the material, they are given a test-card by means of which they may compare their work for verification, and see whether they have made any errors in their multiplication. Table by table, number by number, they do the work of comparing each result with the number which corresponds to it in each one of the ten columns. When this has been done carefully, the children possess their own series, the accuracy of which they are able to guarantee themselves.

Multiplication Table
PRESENTING THE COMBINATIONS OF NUMBERS IN THE
PROGRESSIVE SERIES FROM 1 TO 10

1 × 1 = 12 × 1 = 23 × 1 = 34 × 1 = 45 × 1 = 5
1 × 2 = 22 × 2 = 43 × 2 = 64 × 2 = 85 × 2 = 10
1 × 3 = 32 × 3 = 63 × 3 = 94 × 3 = 125 × 3 = 15
1 × 4 = 42 × 4 = 83 × 4 = 124 × 4 = 165 × 4 = 20
1 × 5 = 52 × 5 = 103 × 5 = 154 × 5 = 205 × 5 = 25
1 × 6 = 62 × 6 = 123 × 6 = 184 × 6 = 245 × 6 = 30
1 × 7 = 72 × 7 = 143 × 7 = 214 × 7 = 285 × 7 = 35
1 × 8 = 82 × 8 = 163 × 8 = 244 × 8 = 325 × 8 = 40
1 × 9 = 92 × 9 = 183 × 9 = 274 × 9 = 365 × 9 = 45
1 × 10 = 102 × 10 = 203 × 10 = 304 × 10 = 405 × 10 = 50