Work each of the following problems. The correct answer is given as one of the five answers at the right

Black out the correct answer. Use the margin for scratch work, if you cannot do the problem in your head.

1. Add: 236 1544 1533 ¢ 1565 1567

451 879

2. Subtract: 5764 ¢ 2375 2276 2176 2278

3489

3. Multiply: 258 11,216 12,126 21,126 12,612 11,516

47

Discouraged parents should now hold on to their seats, for only the aptitude tests have been finished. There are also achievement tests to measure precisely what the student has accomplished in reading, writing, and arithmetic during seven or eight grades of elementary school. Here again we find significant only by their absence such subjects as art,, music appreciation, science, nature study (those subjects which we seem to have heard most about). That all-inclusive paragon of all education, learning, and life itself is omitted when your child is examined to see whether or not he qualifies for the college preparatory course in high school or is prepared to enter an independent secondary school. The subject that has taken so much time during elementary school--from cutting out pictures of tomato pickers to field trips to the town incinerator--there is no achievement test in social studies. But the mathematics test stretches every fiber of junior's arithmetical accomplishments, and the English test probes every nook and cranny of spelling, writing, grammar, and comprehension in reading.

The achievement test in mathematics will usually require from one to two hours to take. Some independent schools compose their own distinctive tests; others use the standard type provided by the various testing agencies. The last mentioned are the ones used chiefly to test for qualification for admission to a college preparatory course in the better high schools. The tests examine for skills in handling addition, subtraction, multiplication, and division; also skills in using mixed numbers, fractions, and decimals. There are tests dealing with facts of measurements, weights, geometric areas, and rules and formulae. Terms and concepts are also given extensive space in a recognition part of the test. Practical application and appreciation of mathematical procedures are thoroughly exhausted in most of the achievement tests by a series of word problems. "A big dose of strong medicine for little, and sometimes very weak, boys and girls," said one high school principal, "but if they are still struggling with third grade multiplication when they come to us, the damage has been done. Legally they have to be admitted to a program of college preparation because their parents demand it, but in a few weeks parents and child give up, and the hard courses are exchanged for Shop and Advertising and Home Improvement. Our high schools cannot be strengthened until there is more required of the elementary school. We have to have a foundation upon which to build."

The headmaster of an independent secondary school says: "We have to accept candidates who make a miserable showing in mathematics; to reject them would be terribly unfair. They have average intelligence but they haven't had a chance. In our school we feel that mathematics requires more personal and individual attention, explanation, and drill, than any other subject except perhaps a foreign language. Consequently, we restrict our mathematics classes, as we do our foreign language classes, to about twelve students per class. Many of our students come from classrooms where they have been one of thirty, or even more, for their whole eight years of elementary school. Even if the school devoted the proper amount of the school day to reading, writing, and arithmetic, it is highly improbable that an earnest, hard-working teacher could ever find the time to sit down and go over with a single child a difficult problem or the meaning of common denominator. This same teacher might appreciate fully the importance of practice in arithmetic, but if junior goes home night after night with ten examples to work and hounds his parents for help, eighty per cent of the parents will complain either to the teacher or ignore the child's request for help until he is convinced that work outside of school is unimportant and unnecessary. Even if the homework had the blessing and cooperation of the public, what teacher could find the time necessary to grade that many papers each day? We get children from elementary schools who have never, during the eight years, had the experience of working examples on the blackboard before the class. The teacher's explanation on the blackboard does not educate the child. Education is for the most part a personal thing, the child will develop and improve his innate desire to learn and educate himself, or he will revolt against it to escape responsibility. Which he does depends a great deal upon the help and encouragement or neglect and indifference, he gets at home. Until there is real concern at home for junior's arithmetic homework, and a demand from the home that he have homework, we will continue to spend hours and years doing corrective mathematics to fill the gap left in elementary school. As tragic as the lack of an arithmetical foundation itself is the rank dislike for mathematics which has been fed by misunderstanding and want of accomplishment. In eight years a great many habits and ideas become fixed; to change them is costly in both effort and time."

Methods of making elementary school mathematics more meaningful will be dealt with in a later chapter; meanwhile, there are still tests which are required as a measure of achievement from elementary school. Something of the ability and aptitude in reading and writing has already been noted in the description of the junior scholastic aptitude test, but almost all independent secondary schools require an English examination. Of thirty schools canvassed, the English requirements vary only in minor details and demands. The fundamental requirements for grammar usage, reading comprehension, correct spelling, writing ability, and a sense of neatness are generally the same. Some high schools also require similar tests of pupils applying for college preparatory English courses. The two tests given below are characteristic of hoped-for accomplishment from eight years of elementary school: