The Psychology of Arithmetic

by Edward L. Thorndike

2. How many pounds of butter-fat did the cow produce in Jan.? 3. In Feb.? 4. In Mar.? 5. In Apr.? 6. In May? 7. In June?

GRADE 5 OR LATER

Using Recipes to Make Larger or Smaller Quantities

I. State how much you would use of each material in the following recipes: (a) To make double the quantity. (b) To make half the quantity. (c) To make 1½ times the quantity. You may use pencil and paper when you cannot find the right amount mentally.

1. Peanut Penuche	2. Molasses Candy
1 tablespoon butter	½ cup butter
2 cups brown sugar	2 cups sugar
1⁄3 cup milk or cream	1 cup molasses
¾ cup chopped peanuts	1½ cups boiling water
1⁄3 teaspoon salt
3. Raisin Opera Caramels	4. Walnut Molasses Squares
2 cups light brown sugar	2 tablespoons butter
7⁄8 cup thin cream	1 cup molasses
½ cup raisins	1⁄3 cup sugar
	½ cup walnut meats
5. Reception Rolls	6. Graham Raised Loaf
1 cup scalded milk	2 cups milk
1½ tablespoons sugar	6 tablespoons molasses
1 teaspoon salt	1½ teaspoons salt
¼ cup lard	1⁄3 yeast cake
1 yeast cake	¼ cup lukewarm water
¼ cup lukewarm water	2 cups sifted Graham flour
White of 1 egg	½ cup Graham bran
3½ cups flour	¾ cup flour (to knead)

II. How much would you use of each material in the following recipes: (a) To make ²⁄₃ as large a quantity? (b) To make 1¹⁄₃ times as much? (c) To make 2½ times as much?

1. English Dumplings	2. White Mountain Angel Cake
½ pound beef suet	1½ cups egg whites
1¼ cups flour	1½ cups sugar
3 teaspoons baking powder	1 teaspoon cream of tartar
1 teaspoon salt	1 cup bread flour
½ teaspoon pepper	¼ teaspoon salt
1 teaspoon minced parsley	1 teaspoon vanilla
¼ cup cold water

In many cases arithmetical facts and principles can be well taught in connection with some problem or project which is not arithmetical, but which has special potency to arouse an intellectual activity in the pupil which by some ingenuity can be directed to arithmetical learning. Playing store is the most fundamental case. Planning for a party, seeing who wins a game of bean bag, understanding the calendar for a month, selecting Christmas presents, planning a picnic, arranging a garden, the clock, the watch with second hand, and drawing very simple maps are situations suggesting problems which may bring a living purpose into arithmetical learning in grade 2. These are all available under ordinary conditions of class instruction. A sample of such problems for a higher grade (6) is shown below.

Estimating Areas

The children in the geography class had a contest in estimating the areas of different surfaces. Each child wrote his estimates for each of these maps, A, B, C, D, and E. (Only C and D are shown here.) In the arithmetic class they learned how to find the exact areas. Then they compared their estimates with the exact areas to find who came nearest.