4. She made sure that all children understood what they were to do.

5. She then said, "Ready, go!"

6. She flashed the first card, for example, , by bringing it from the back of the pack to the front. The first child gave the answer as quickly as he could say it.

7. (a) If his answer was correct, she flashed the next card to the front of the pack. (b) If his answer was incorrect, the next child gave the answer, the card was dropped on the desk for future use, and the next card flashed.

8. This process continued around the class until the whole pack of cards was used.

9. She then picked up from the desk the cards to which incorrect answers had been given, and flashed them again, calling on the pupils who had missed them if she could remember without hesitation who they were.

10. She then asked the timekeeper for the time consumed and wrote it on the board, for example, "3 min. 30 sec.," under the record of the previous day for the same pack of cards, and opposite the record of "3 min. 25 sec." made by another group of children.

II. She concluded with remarks intended to arouse interest in improving the record until it equaled a standard score, such as three minutes for this pack.

Six minutes, fifty problems, zeal and attention, application. The total amount of time consumed in this drill in getting the class ready, flashing the cards, writing the record on the board, and making remarks about it was about six minutes. During this period nearly every child in the group of twenty-two was called on three times, and the total number of problems correctly worked was about fifty. Practically every child was attentive to each of these because of the intense interest in improving the score. After this drill, problems of areas, requiring the use of fractions in square measure, were assigned.

From group practice to individual practice. — Both of the examples of drill method given above illustrate group recitations in which the whole class gives attention to a common center. We shall now give two examples in which the children work as individuals.

Addition combinations to 9 + 9 to be said in thirty seconds.

Our first example of individual drill occurs in the third grade where children memorize for rapid oral reproduction all the forty-five addition combinations up to 9+9. These are all printed or mimeographed on a sheet of paper, in mixed order, making five rows similar to the following :

A copy of the sheet is given to each child after the teacher is sure that the combinations are generally understood. The technique in this case is also somewhat complex. The ultimate achievement expected of each child is ability to give orally the answers to all the combinations in any order on the chart, up or down, from left to right or right to left, in thirty seconds. Every day some children are given trials and their records kept; for example, a child may in the beginning require forty-five seconds, decrease rapidly in a few days to thirty-seven seconds, but not reach the desired goal of thirty seconds for many days. Practice is given by concert drills and individual drills in school, and the children are urged to repeat the answers to someone at home who will time them and correct them.

Systematic and thorough; saves time from useless responses; analyzes and corrects wrong inner responses. The outcome of the device is automatic skill in using rapidly these combinations in problems involving addition. The device is systematic and thorough in achieving this end, since it gives drill on all these combinations. It saves time in many ways. For example, it eliminates the time consumed in the old-fashioned drills by the teacher's saying,

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What is 9 and 6, Johnny?" and waiting for Johnny to wake up and reply. It saves Johnny the time of saying "9 and 6 are." He merely says "fifteen" as quickly as he can when he sees 6 on the paper. Moreover, in Johnny's after life it saves him from saying "9 and 6" thousands of times; instead, when he encounters in an addition 6

problem he merely thinks "fifteen," just as he thinks "cat" when he sees the word, instead of thinking "c-a-t." In order to make sure that each child does read off each answer in this automatic way, without going through some roundabout process, the teacher has to make a careful study of the children who are slow in learning to repeat the combinations in the desired time. For example, one such child was found who, when adding, instead of merely recalling the answer, 7' 16, thought of it as follows: 9+2+2+2+1=16. The teacher had to break up this habit and get the child to

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think automatically 7.

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Printed sheets of problems for fundamental processes; timed tests, individual practice, self-correction, individual advancement. The second example of individual drills is an elaborate extension of the above type of device to the working of all kinds of problems in adding, subtracting, multiplying, and dividing; the problems being printed on sheets or cards ready to be distributed to the pupils. For example, each pupil may be given a sheet or card printed full of such problems in addition as the following:

All he has to do is to write the answers as rapidly as he can on transparent paper or through holes which are perforated in the problem card. He does not begin to write until the teacher gives the signal for the whole class to begin. At the end of seven minutes the signal may be given to stop. All pupils then cease work. They may turn the problem cards over to compare their answers with the correct ones, which may be printed on the back of the cards, or they may use some other device for self-correction. Each pupil makes a record of the number of problems which he has right. If he has completed all the problems correctly, in the allotted time, he is given a different card of problems to work next time. The children who do not have satisfactory scores on the first card may practice on it during study periods until the next timed test on it is given, when they are tested on it again, at the same time that other pupils are tested on the lessons to which they have progressed.

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Elaborate systems organized by authors and publishers ; elaborate routine instituted by teacher. It is obvious that this scheme which provides many sheets of printed problems and permits different pupils to progress at different rates and work with different sheets is much more elaborate than the other examples of drill devices which we described. It involves, in the first place, elaborate printed materials, printed sheets or cards of problems which have been carefully devised so as to give drill on all combinations and operations. This, however, is not a task that confronts the teacher, as it has already been performed by the authors and textbook companies. The teacher's task is to accustom herself and the pupils to the routine which is completely described in the teacher's manual that accompanies the drill materials. As indicated in the chapter on economy in classroom management, however, this need present no special difficulties, since the most elaborate routine can easily be taught to children if the teacher will take the trouble. This

type of drill exercise calls, however, not only for elaborate routine organization but also for careful attention to the individual needs of pupils. Thus it saves much time in two ways: first, by having printed problems at hand, so that pupils spend most of their time in arithmetical thinking instead of fooling it away in copying problems; and, second, by permitting pupils to cease drill on processes which they have already made perfectly automatic and to spend their time on other assignments.

Examples introduce to principles of drill. The four examples of modern drill methods which we have described namely, first-grade drill with vocabulary cards in reading, fifth-grade drill with fraction cards, third-grade oral drill with a chart of addition combinations, and systematic written drill in the middle grades with ready-made printed sheets of problems serve to familiarize us sufficiently with concrete schoolroom drill situations to enable us to understand easily the general principles of teaching to be followed in organizing effective drill lessons. These principles we shall now consider systematically.

1. Only correct practice makes perfect. Our first principle of drill is that "only correct practice makes perfect"; therefore "make haste slowly" and try to make sure that children are making the correct inner responses in their practice. This principle may be formulated in two rules: namely,

a. Repetitions should be delayed until a correct start is assured.

b. Always subordinate speed to accuracy.

These rules may be explained as follows:

a. Correct start should precede repetitions. — In our chapter on apperception we gave examples of the observation and violation of the rule concerning a correct start. One example concerned the children who could recite a rigmarole of number names but could not count objects. They had