numbers, to memorize nonsense syllables, to mark out all the verbs in a printed page, etc. the surfaces of frequency which we should get when the results were plotted would approximate the normal curve. Examples of such curves of distribution or surfaces of frequency for human abilities are shown in the figures on page 377.

Hence abilities and marks in ordinary classes follow normal curve. Similar normal curves are obtained if the marks made by a sufficient number of students of the same grade in any school subject are tabulated and then plotted, provided these marks represent the real relative achievements. Thus, if a teacher of algebra with five classes of thirty students each would give at the end of the first semester a test which would give all pupils a chance to show just how much and how well they could do in a limited period of time, the one hundred fifty scores which resulted would prove to be distributed according to the normal curve. A special technique must be observed in such testing, which will be discussed in Chapter XXII. The distributions shown in Monroe's table on page 374 give the results of such an algebra test and illustrate the normal distribution of abilities of high-school students.

In view of the fact that reliable tests of the mental abilities of nonselected groups show the normal distribution, the teacher of any subject in high school should form the habit of expecting such a distribution of the term grades or final grades of his students when he has a sufficient number; that is, if he has only five, ten, or even fifteen students in one class in algebra, the distribution might be different, but if he has fifty in two or more classes, the chances are pretty large that the normal distribution will be found, and this is almost certain if he has ninety or more pupils in the same subject and grade. (Compare 13 and 14.) In more concrete terms, this would mean that if the teacher was using a marking system consisting of the letters A, B, C, D, E,

his grades or marks in the long run should be distributed roughly as follows:

3 per cent of the grades should be A 22 per cent of the grades should be B 50 per cent of the grades should be C 22 per cent of the grades should be D 3 per cent of the grades should be E

Typical experiments in adapting instruction to differences in capacity. The statistical proofs of the amount of the differences in capacity to be found in ordinary classes have aroused a general interest in securing a means of modifying the method of simultaneous class instruction in such a way as to vary the pace for the slow, the medium, and the fast pupils. A number of experiments have been tried, and some of these will be discussed under the following headings :

1. Abolishing all class instruction and reverting to the individual method: the Pueblo plan.

2. Self-conducted homogeneous groups: a modified form of the monitorial scheme.

3. Recitations only for students who need them; seat work for others.

4. Required supervised study periods supplementary to recitation periods: the Batavia scheme.

1. Abolishing class instruction and reverting to individual instruction: the Pueblo plan. In 1888 P. W. Search became superintendent of the schools of Pueblo, Colorado. He found the parents of the high-school students complaining of over-pressure in connection with home study. To relieve this situation, all home study was abolished and experiments undertaken to have all studying done during school hours. The final result was a scheme in which studying occupied the greater part of the school day and nearly all recitations were abolished. Each pupil, working at his desk, advanced as rapidly as he could master the assignments. Naturally, some did much more than others.

For example, Mr. Search, in his book entitled "An Ideal School," describes the achievements of the members of a Latin class that was studying Cæsar. During a given length of time the fastest pupil completed 140 chapters, the slowest only 40 chapters. One pupil completed 110 chapters, three completed 95, five completed 90, and one completed only 45. The rest of the members were distributed between these extremes.

These figures show approximately the same relations between students of different degrees of ability as were brought out in the tables given above. Thus the brightest pupil did three and a half times as much as the slowest, and twice as much as the median. Instead of marking time while most of the class accomplished the amount ordinarily done, the brightest forged ahead. Moreover, instead of the slow pupils being dragged over assignments which they had not mastered, they worked diligently as long as was necessary on the amount that they were capable of mastering. There was evidence in the form of individual recitations and quizzes and examinations to show that pupils who covered given assignments did so satisfactorily.

Several favorable reports on Pueblo plan. - The Pueblo plan was tried in a few other places, and in some cases very favorable reports were made concerning its success. Occasionally graduate students in my classes, who have been skilled high-school teachers, have reported that they use the Pueblo scheme regularly in teaching classes in mathematics and have found it works quite satisfactorily. They state that they never have any class discussions even in attacking a new principle. Each pupil begins work on a given principle or new operation when he reaches it, and the teacher, in passing around the room, watches him and makes such suggestions as the student seems to need.

Too difficult for unskilled teacher to keep track of one hun dred fifty individuals.-One of my students (Mr. I. M. Allen),

however, reported an experiment with the Pueblo plan that brought out a serious objection to its being used by any except skilled, resourceful teachers. As principal of a large high school he was interested in finding some method that his teachers could use to meet the needs of pupils of varying capacities. He decided to try the Pueblo plan himself with an algebra class before asking his teachers to use it. He did so, and found that it accomplished all that was claimed for it by its advocates, but that it taxed his ingenuity and resourcefulness to keep track of thirty students in one class, all of whom were progressing at different rates. He decided that if it troubled him to keep track of thirty pupils by the method of pure individual instruction, it would be entirely too much to expect an ordinary mathematics teacher to keep track of one hundred fifty students, assuming that he had five classes with thirty students in each.

Additional objections to the Pueblo plan are based on its elimination of all the social elements that accompany the class method of instruction. The chief value lost is the training in expression that students receive in well-conducted contribution recitations. Another important loss is the training in thinking in a complex social situation such as the group recitation offers. In view of these losses, as well as the difficulty of keeping track of so many individuals at different stages of advancement, most educators would not favor the Pueblo plan with its abolishing of class recitations.

2. Self-conducted homogeneous groups: a modified form of the monitorial system. -A modified form of the monitorial system was used for years in the geometry classes in the high school which I attended. The classes usually numbered from twenty to twenty-five students and met in fairly large rooms with ample blackboard space. Each class was divided into three sections containing from six to eight students each. The brightest students composed the first section, the medium students the second, and the slow students the

third section. The first section had as a permanent monitor, or captain, one of its most capable students; that is, one who possessed executive and teaching ability as well as ability in mathematics. The second section had a similar monitor from among its own numbers, one who might not be as capable or quick in mathematics as the members of the first section, but who was among the best in his own section and had executive and teaching capacity. For the third or slow section, monitors from the other sections were provided from week to week or for slightly longer periods. Each of these monitors for the third section would be absent from the recitations of his own section during his period of service with the third section, but he could easily keep up or catch up with his own section.

Bright section completes plane and solid geometry in one year. - After the teacher had got the class started as a single group on the first book, and some of the fundamental ideas of geometric procedure had been established, the sections were organized on the basis of the students' records in previous work as well as their ability as shown in the new work. Each section was then assigned a corner of the room as its regular recitation place, and henceforth each section proceeded at its own pace through the geometry. The first section commonly completed the plane and solid parts of Wentworth's Geometry in one year. The medium section usually completed the plane geometry only (that is, five books), as is commonly done by classes using the simultaneous method. The slow section usually got through about four books, but most of its members managed to do this much with a fair degree of thoroughness, instead of being dragged over the whole five books in an uncomprehending way, as commonly occurs when the ordinary class method is used.

Three recitations simultaneously without confusion. — At the beginning of each recitation period the monitor of each section assigned each student a proposition or exercise to