When a child has learned to count through the use of such objects as I have mentioned he may be taught what is called the addition table. This table can be learned by heart easily enough, but when we reach the multiplication table we come upon one of the tortures of childhood. Would it not be simpler and easier to make the children construct these tables, instead of making them learn them? [Illustration: FIG. 1.] Let us first take the addition table, and suppose that we trace ten columns on suitably ruled paper, at the top of which we write the first ten numbers, for example, and then write them again at the beginning of a certain number of horizontal lines (Fig. 1). Let us suppose, too, that we have a box divided into compartments arranged like the squares in our table, into which we put heaps of balls, beans, or dice corresponding to the numbers indicated in the table. The child will take, for example, two balls from one compartment and three from another, will put them together and place his five balls in the case corresponding with the point where the lines of two and three will meet, and will thus gradually accustom himself to the idea that two added to three are equal to five, four and two to six, etc., before he knows how to write the corresponding figures. As soon as he has learned how to write them he can himself make the table with figures (Fig. 2), showing that one and one make two, one and three four, etc. [Illustration: FIG. 2.] This will be all the easier for him because he will only have to write the figures in their order in the lines and the columns. This furnishes an excellent writing exercise after the children have begun to write figures, and affords besides a certain method of teaching them the addition table up to nineteen at least. I insist that all this can be done even before the child knows how to write the figures by means of an arrangement like a printer's case, and that it will be as a play, rather than a study, to the child. Hardly anything more will be required than to bring the toy to the child's notice and leave him to himself after he has been started with it, and he will get along the faster the less he is bothered. A similar process may be adopted with the multiplication table. With a case like the other, it is only necessary to tell the child that if he wants to know how much are three times four he has only to make heaps of four things each, take three of them and put them in the box at the intersection of the line three and the column four. If he can write the figures he will write 12, instead of gathering up the twelve objects that represent the product. When he has played at this for some time he may become acquainted with all the products up to ten times ten or beyond without having to make any abnormal effort of memory.