The making of change is a form of numeration so attractive as to hold the attention of the child. I present the one, two, and four centime pieces and the children, in this way learn to count to ten.
No form of instruction is more practical than that tending to make children familiar with the coins in common use, and no exercise is more useful than that of making change. It is so closely related to daily life that it interests all children intensely.
Having taught numeration in this empiric mode, I pass to more methodical exercises, having as didactic material one of the sets of blocks already used in the education of the senses; namely, the series of ten rods heretofore used for the teaching of length. The shortest of these rods corresponds to a decimetre, the longest to a metre, while the intervening rods are divided into sections a decimetre in length. The sections are painted alternately red and blue.
Some day, when a child has arranged the rods, placing them in order of length, we have him count the red and blue signs, beginning with the smallest piece; that is, one; one, two; one, two, three, etc., always going back to one in the counting of each rod, and starting from the side A. We then have him name the single rods from the shortest to the longest, according to the total number of the sections which each contains, touching the rods at the sides B, on which side the stair ascends. This results in the same numeration as when we counted the longest rod—1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Wishing to know the number of rods, we count them from the side A and the same numeration results; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. This correspondence of the three sides of the triangle causes the child to verify his knowledge and as the exercise interests him he repeats it many times.
We now unite to the exercises in numeration the earlier, sensory exercises in which the child recognised the long and short rods. Having mixed the rods upon a carpet, the directress selects one, and showing it to the child, has him count the sections; for example, 5. She then asks him to give her the one next in length. He selects it by his eye, and the directress has him verify his choice by placing the two pieces side by side and by counting their sections. Such exercises may be repeated in great variety and through them the child learns to assign a particular name to each one of the pieces in the long stair. We may now call them piece number one; piece number two, etc., and finally, for brevity, may speak of them in the lessons as one, two, three, etc.
THE NUMBERS AS REPRESENTED BY THE GRAPHIC SIGNS
At this point, if the child already knows how to write, we may present the figures cut in sandpaper and mounted upon cards. In presenting these, the method is the same used in teaching the letters. "This is one." "This is two." "Give me one." "Give me two." "What number is this?" The child traces the number with his finger as he did the letters.
Exercises with Numbers. Association of the graphic sign with the quantity.
I have designed two trays each divided into five little compartments. At the back of each compartment may be placed a card bearing a figure. The figures in the first tray should be 0, 1, 2, 3, 4, and in the second, 5, 6, 7, 8, 9.