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THE PLAY OF LEARNING. 127

fixed in the memory. The class is now weary; a little change will rest them. The teacher leads in a merry song, and then all are ready for fresh work.

The whole school is now called up. Their lesson will combine grammar and arithmetic, and at the same time exercise their imaginative faculties. The teacher writes a number of simple sums on the blackboard. The pupils are to match and explain each one of these sums with a story. A dozen eager hands are up. " Well, Leona ? " Leona rises and says, " I was walking in the lane and I found two butterflies and then I saw two more, and that made four butterflies." "Very well." The teacher puts the answer under the proper example and then calls another child. " I had two red. apples and my brother gave me five yellow ones, and then I had seven." The whole school is interested. Each one is eager to tell a story and win one of the sums.

SUGGESTIVE WHISPERS are freely allowed.

The little inventive brains soon capture the entire board with exactly fitting stories. Now the exercise is changed to work in subtraction and the answers are in stories as before. The children form their answers from their own range of experience, in the house, the field or the street. They are encouraged to name the properties of the objects which they use to make the answers. They do not merely say " apples " but " red apples " or " yellow apples."

Let us try a class in fractions. They deal with dividing objects. And the first thing must be to let them see the division take place. The class is seated around a table, and before each is a lump of clay. Each one pats his lump down to a square cake.

The cake is now divided into two equal parts and these are again divided and their size and weight compared. They see the meaning of wholes and halves and fourths, and they state these distinctions in words.

In the same way they study the addition of fractions. One child's cake is divided into eight parts, then four are taken away and half a cake is added from another cake. They see at once that putting together one-half and four-eighths make one whole thing. They have learned a real fact, not a string of words in a book. Now they are ready for a diagram. They draw four white bands on the blackboard, then they divide these by cross-lines in red and subdivide them by lines in green. Tracing the colors through each band, the pupil sees the exact relation of halves and fourths to the whole.

The modern method of writing down a fraction is deceptive and not ingenious. The child looks at 2,3 and he thinks that each of these figures, in some way stands for a number; yet only the upper figure represents a number. The lower figure only tells what kind of a number it is. Just as when we write 2 lbs. The lbs. is not a number, it only tells what is the denomination of the number 2 in this case. It is pounds. You cannot multiply or divide or subtract pounds, but you can reduce pounds to ounces, another denomination. And so you can reduce the denominator of a fraction, but you cannot multiply or add or subtract it. Yet the text books of arithmetic tell the student to do this absurd and impossible thing. Fractions should be written as we do other denominate numbers.

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