(11) _Needless linguistic difficulties._--It should be unnecessary to add that bonds should not be formed between the pupil's general attitude toward arithmetic and needless, useless difficulty in language or needless, useless, wrong reasoning. Our teaching is, however, still tainted by both of these unfortunate connections, which dispose the pupil to think of arithmetic as a mystery and folly. Consider, for example, the profitless linguistic difficulty of problems 1-6, whose quantitative difficulties are simply those of:-- 1. 5 + 8 + 3 + 7 2. 64 ÷ 8, and knowledge that 1 peck = 8 quarts 3. 12 ÷ 4 4. 6 ÷ 2 5. 3 × 2 6. 4 × 4 1. What amount should you obtain by putting together 5 cents, 8 cents, 3 cents, and 7 cents? Did you find this result by adding or multiplying? 2. How many times must you empty a peck measure to fill a basket holding 64 quarts of beans? 3. If a girl commits to memory 4 pages of history in one day, in how many days will she commit to memory 12 pages? 4. If Fred had 6 chickens how many times could he give away 2 chickens to his companions? 5. If a croquet-player drove a ball through 2 arches at each stroke, through how many arches will he drive it by 3 strokes? 6. If mamma cut the pie into 4 pieces and gave each person a piece, how many persons did she have for dinner if she used 4 whole pies for dessert? Arithmetically this work belongs in the first or second years of learning. But children of grades 2 and 3, save a few, would be utterly at a loss to understand the language. We are not yet free from the follies illustrated in the lessons of pages 96 to 99, which mystified our parents. LESSON I [Illustration: FIG. 5.] 1. In this picture, how many girls are in the swing? 2. How many girls are pulling the swing? 3. If you count both girls together, how many are they? _One_ girl and _one_ other girl are how many? 4. How many kittens do you see on the stump? 5. How many on the ground? 6. How many kittens are in the picture? One kitten and one other kitten are how many? 7. If you should ask me how many girls are in the swing, or how many kittens are on the stump, I could answer aloud, _One_; or I could write _One_; or thus, _1_. 8. If I write _One_, this is called the _word One_. 9. This, _1_, is named a _figure One_, because it means the same as the word _One_, and stands for _One_. 10. Write 1. What is this named? Why? 11. A figure 1 may stand for _one_ girl, _one_ kitten, or _one_ anything. 12. When children first attend school, what do they begin to learn? _Ans._ Letters and words. 13. Could you read or write before you had learned either letters or words? 14. If we have all the _letters_ together, they are named the Alphabet. 15. If we write or speak _words_, they are named Language.