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TER XXIV.

UPILS WITHDRAW FROM THE
LIC SCHOOLS.1

ARD, Washington University, St. Louis.

wer this question, I desire to call attention to the ct answer. The best planned course of study takes obable duration of a school course and the age of the I this question is seen in the fact that an estimated of pupilage is frequently made the basis of arguments modification of the course of study, or some other detail

draw" in a somewhat restricted sense, and as properly ortality among school children; that is to say, I exclude who can with propriety be said to "withdraw from school," rse is cut short by death. Fortunately, this allowance is at account to be ignored. The propriety of omitting from ho die can not be seriously questioned. The practical inquiry pils leave school to enter upon the active duties of life, or to

calculations are the reports of the superintendents of the public Chicago, and Boston. In these reports the ages of all the chilecorded either at the beginning, or in the middle of the school aber for each year of age is given without any regard to the pupils. For example, we have the number that are between 7 and he number between 8 and 9, the number between 9 and 10, and umbers are given in every annual report, and I have taken them al reports of twelve or thirteen consecutive years. I am bound to ese reports are accurate, although they exhibit certain anomalous ouping these reports as exhibited in Tables I, II, and III, and then he figures in any vertical column, I am able to follow the same group of gh their course in the public schools. I have assumed that no pupils vre the age of 8 years. By following down any vertical column we can ambers increase or diminish from the combined effect of immigration, eath, and withdrawals from school, till the class disappears altogether 20.

and my investigations over as much ground as possible I have entered on II. III sufficient data to enable me to make three independent calculations have named the columns A, B, C in each case, so that in all I sis to nine sets of pupils-three in each city. I will add that to the cities St. Louis, Chicago, and Boston for the reason that ties failed to furnish me with the requisite data.

ademy of Science of St. Louis, April 20, 1896. Published in the Transactions of I, No. 8; issued May 21, 1896.

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2. Much of the pupil's time in the school is spent in contact with immature minds. It is certainly true that while there are advantages to be derived from the freedom of children teaching one another, it is not on the whole to be counted equal in value to an equal amount of time spent with a full-grown and sympathetic teacher. It should be remembered, however, in weighing this objection, that the same amount of time is seldom realized even in schools which are not overcrowded, and that the teachers, as we find them, are not always full-grown and are not invariably sympathetic. Ideal conditions, even with teachers enough to supply all the classes, are seldom found.

3. The time occupied by pupils when teaching is lost to their studies. This objection is entirely invalid, for, as has been shown, the exercise in teaching-in the habits of thought and clearer understanding which it inculcates-more than compensates for any supposed loss of time from the lessons.

means.

4. The monitorial system lessens the number of professional teachers needed, and would therefore diminish the number of persons who gain a livelihood by this While this is not the most ostensible, it is nevertheless the most formidable objection to the establishment of schools on the monitorial plan. Any argument which lessens an individual's chances for employment will not weigh heavily with him. It was this objection, though not outspoken, which rang the knell to mutual instruction in Boston and other American cities. This is strictly a class objection. It weighs not against the system as such, but against the probability of its successful establishment.

5. It would be difficult to find masters with the requisite ability to carry on the monitorial system. It is evident that the management of a monitorial school requires unusual ability. The master must possess the qualities of generalship com bined with great teaching power and unbounded sympathy. Without such a master a monitorial school could not carry on its face even the semblance of success. In schools conducted on the usual plan, where the teacher does all the work, defec s may be covered by superficial show. But this would be impossible on the mutual plan.

As to the number of teachers in this country possessing the requisite characteristics, it would be difficult to furnish any estimate; but I am quite certain that there would be many, were the conditions favorable for their development, if there were a positive demand for such talent.

The considerations which bring us to the answer of the main question in the s bject of this paper have now been briefly and imperfectly pointed out. What is the left in the monitorial or mutual system for the schools of the South?

From the foregoing analysis of the subject we are forced to the following conditional answer: If the schools of the children of the South are supplied with all the modern means of obtaining an education; if they have sanitary school buildings, equipped with apparatus to accommodate all the pupils who ought to attend the school; if these buildings are supplied with first-class teachers with first-class salaries, then any argument that could be urged in favor of the monitorial schools would be futile. But if, on the contrary, there exists to-day in the South a large number of children who, for lack of these provisions, are not being educated, and if for these children monitorial masters could be obtained, then there is certainly something in the monitorial system for the children of the South.

CHAPTER XXIV.

AT WHAT AGE DO PUPILS WITHDRAW FROM THE PUBLIC SCHOOLS.1

By Prof. C. M. WOODWARD, Washington University, St. Louis.

1. Before attempting to answer this question, I desire to call attention to the obvious importance of a correct answer. The best planned course of study takes into consideration both the probable duration of a school course and the age of the pupils. The direct bearing of this question is seen in the fact that an estimated average length of the period of pupilage is frequently made the basis of arguments for or against some proposed modification of the course of study, or some other detail of school management.

2. I use the word "withdraw" in a somewhat restricted sense, and as properly excluding the effect of mortality among school children; that is to say, I exclude from the number of those who can with propriety be said to "withdraw from school,” those whose school course is cut short by death. Fortunately, this allowance is small, but it is not on that account to be ignored. The propriety of omitting from my calculations those who die can not be seriously questioned. The practical inquiry is: At what age do pupils leave school to enter upon the active duties of life, or to enter private schools?

3. The data for my calculations are the reports of the superintendents of the public schools of St. Louis, Chicago, and Boston. In these reports the ages of all the children enrolled are recorded either at the beginning, or in the middle of the school year, and the number for each year of age is given without any regard to the grading of those pupils. For example, we have the number that are between 7 and 8 years old, and the number between 8 and 9, the number between 9 and 10, and so on. These numbers are given in every annual report, and I have taken them from the annual reports of twelve or thirteen consecutive years. I am bound to assume that these reports are accurate, although they exhibit certain anomalous results. By grouping these reports as exhibited in Tables I, II, and III, and then considering the figures in any vertical column, I am able to follow the same group of children through their course in the public schools. I have assumed that no pupils withdraw before the age of 8 years. By following down any vertical column we can see how the numbers increase or diminish from the combined effect of immigration, emigration, death, and withdrawals from school, till the class disappears altogether at the age of 20.

4. To extend my investigations over as much ground as possible I have entered on Tables I, II, III sufficient data to enable me to make three independent calculations from each table. I have ́named the columns A, B, C in each case, so that in all I have applied my analysis to nine sets of pupils—three in each city. I will add that I limited my study to the cities St. Louis, Chicago, and Boston for the reason that all the other large cities failed to furnish me with the requisite data.

Read before the Academy of Science of St. Louis, April 20, 1896. Published in the Transactions of the Academy, Vol. VII, No. 8; issued May 21, 1896.

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5. It is a source of regret that the data furnished by the three cities are not uniform in character. In the Boston schools the reports give the number "16 years old," "17 years old," "18 years old," "19 years old and over." In the Chicago reports all pupils "17 years old and over" are lumped together. In the St. Louis reports all pupils "16 years old and over" are lumped together. It has been necessary to distribute the pupils thus lumped together, according to their ages, as accurately as possible.

It was useless to refer to the unpublished records in St. Louis and Chicago for the exact details of such distribution, as they could give no additional information. In this emergency I adopted the following method, based upon an examination of the distribution in the Boston schools and of the ratio which the 16-year-old pupils bore to those "17 and over" in the city of Chicago. I will not give the details of my investigation, but will plainly state that I assumed in the case of St. Louis that 52 per cent of those who were reported to me as "16 years old and over" were 16 years old; 30 per cent were 17 years old; 13 per cent were 18 years old; 5 per cent were "19 years old and over." This distribution is made for each of the numbers at the bottoms of several columns in Table I.

In the case of the Chicago schools I assumed that 63 per cent of those who were enrolled as "17 years old and over" were 17 years old; 27 per cent were 18 years old; 10 per cent were "19 years old and over." This, I may say in parenthesis, corre. sponds to the distribution in the St. Louis schools for those three years. This method of distribution is applied to the last numbers in several columns in Table II. The fact that nearly all of these tables show the withdrawal of the 20-year-old pupils in the years 1895-96, and even later, was an inevitable consequence, but the results are not on that account to be called in question. All my results are based upon averages, and are the consequence of laws which vary very slightly from year to year in any given city.

6. Other data essential to my calculation are: First, the rate at which the population is increasing on account of the excess of the number of births over the number of deaths. Secondly, the rate at which the population is increasing, or diminishing, from all causes, whether by accession of new territory, the moving in or the moving out of children, or from births or deaths. The internal growth (by which I mean that arising from the excess of births over deaths) I calculate from data furnished by the city officials. The growth from excess of immigration over emigration and death, added to the growth from the accession of new territory (as in the case of Chicago in the year 1889) I call the "external growth." The total growth is, of course, the sum of the "internal" and "external" growths. I may here remark that the growth in school population shown by the enrollment in the public schools may differ from that shown by a general census. There may be a general movement toward private schools, or from private schools. When a pupil leaves a public school and enters a private one, he practically "emigrates;" when he enters the public schools in one of the higher grades, he practically "immigrates."

7. The rate of internal growth.-As the number of children of school age in a city bears a very nearly fixed ratio to the total population, the increase in the number of school children from year to year is the same as the rate at which the total population increases. This is true of both the "external" and the "internal" growth. Now the internal growth of a city is exactly measured by the increase of births over deaths. Hence I calculate the rate from the official reports of births and deaths. All cities give accurate reports of deaths; the reports of births are incomplete. In Boston they are more nearly complete than in Chicago, and in Chicago they appear to be better than in St. Louis. In Boston, as would be expected, the internal growth is least, viz, 7-1000, or 0.7 per cent. In St. Louis it is, as nearly as I can learn, 16-1000, or 1.6 per cent. In Chicago it is greatest, viz, 20-1000, or 2 per cent. While these rates are not uniform they are approximately so. In fact these results are averages of several years. In a former discussion of this problem in May, 1879, I did not distinguish the two kinds of growth, but allowed for the death rate of school children directly.

8. The total rate of growth in school population.-This rate is readily found by comparing the enrollment of any one year by the enrollment for the same ages for the preceding year. For example, take the two years 1889-90 and 1890-91 in the table of the Chicago schools. The attendance of children above 7 years of age in 1889–30 was 115,366. The next year the enrollment was 124,144, a growth of 7.6 per cent. This approximately represents the growth of the city. In the last column but one on Tables I, II, and III, representing the attendance in St. Louis, Chicago, and Boston, this total rate of growth of school population for each year is given. It will be seen that in some cases it is small, in others very large. Thus in Chicago schools the increase from 1882 to 1883 was 5.7 per cent; from 1883 to 1884, 4.5 per cent; from 1884 to 1885, 5.8 per cent; from 1886 to 1887, 2.5 per cent, and so on. In the year 1888 to 1839 I find the enormous increase of 41.5 per cent; this signalizes, of course, an immense accession of territory with a school population two-fifths as large as that of the former city itself. This explains the unexpected showing made by the city of Chicago in the census of 1890. The growth since 1890 has been all the while rapid, reaching in the year 1892 to 1893, 9 per cent.

It is probable that the increase in the school population as shown by the public school report was relatively greater than the increase in the population of the city, for two reasons: (a) The ratio of children to population was greater in surburban than in urban districts; and (b) the proportion of children in the public schools was greater in the suburbs than within the old city limits.

It is evident that both the rate of internal growth and the total rate of growth are affected by the mortality rate of school children, so that element needs no further consideration.

9. Now it is evident that the increase with which we are concerned when we are considering any group of pupils is that which arises from "external" growth alone. No increase in the number of births over deaths can add to the number of those who were 10 years old last year and who are 11 years old this year; though such increase does help to explain why the number who were 10 years old this year is greater than the number who were 10 years old last year. Consequently, in order to find the possible increase (which may be shown as we read down any vertical column) we must, from the total rate at which the school population increases, subtract the rate of internal growth, and then apply the remaining rate to the number enrolled the previous year. For example: I found that in 1890-91 the rate of increase of school attendance in Chicago was 7.6 per cent. I had already found that the internal rate of growth was 2 per cent; the difference is 5.6 per cent. This is the rate at which the number of pupils of certain ages in 1889-90 would have been increased during the next twelve months had there been no withdrawals. In the year 1889-90 there were 7,029 pupils in the Chicago schools who were between 14 and 15 years old. Five and six-tenths per cent of that number is 394; hence the "possible number" of pupils between 15 and 16 years old at the registration in 1890-91 was 7,423, as given in Table VII. By means of the final rates, which I have in the same way calculated for each and every year in the series, I have calculated the possible attendance for each year.

10. Now turn to Tables IV-XII. I have here in every case in the third column one of the columns from Tables I, II, and III. In the fourth column I have the rates of external increase already obtained. The next column gives the theoretical "external" increase in numbers, and in the sixth column the "possible" or ideal number for each age, obtained by adding the increase to the enrollment of the previous year. Now subtract the actual attendance from the "possible" attendance and we have, of course, the number who during the year withdrew.

11. It is evident that the average age of those withdrawing during any one year is one year greater than their age when they were last enrolled. For example: At enrollment the pupils in their fifteenth year are enrolled as 14, and it is evident that their average age is 14. Then those who withdraw before the next enrollment are on the average half a year older, so that those 14-year-old pupils who do not reappear withdraw on the average when just 15 years old. Hence it makes no

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