CHAPTER XIV. THE AGE OF WITHDRAWAL FROM THE PUBLIC SCHOOLS.1 [In determining to what extent the public schools are utilized, or how many years each child attends school, it becomes important to know the average age of withdrawal, or time of leaving school. Attention was called to prevailing misconceptions on the subject in the St. Louis school report of 1878-79, and a method, devised by Prof. C. M. Woodward, was there given for computing the average age of pupils at the time of leaving school. In order to bring this method more fully to the notice of the public it has been deemed advisable to reproduce it here.] In considering the question of the usefulness of public schools, as well as in discussing the propriety of admitting pupils at an early age, it is the custom to have recourse to the statistics of the ages of those enrolled. These statistics show the number who attend school at each age. Nothing seems simpler than to determine from this the average time of leaving school. "If 9 years and 4 months is the average age of those in attendance on school, it shows that the average age of leaving school is less than 10 years." Yet this is wholly fallacious, as will appear from the following consideration: If the course of study in a school lasted for twelve years, and the classes continued throughout the entire course without change of individuals, or diminution in numbers, or loss of grade or rank, an equal number entering every year in the first year's course, would give, in the course of twelve years, an equal number of pupils in each class, from the highest to the lowest. There would be, say 50 pupils in each grade or year's work, and 600 in the whole school. Supposing the pupils to enter at 6 years and graduate at 18 years, there would be 50 pupils at 6 years, 50 pupils at 7 years, etc., and the average of the entire school would be 12 years of age; and yet from this it is clear that we could not infer that the average pupil leaves at 12 years, because each and every one continues until he is 18 years of age. It is clear that this average age is found only by comparing the number of pupils in the graduating class with the same class when it entered. If it entered with 100 and graduated with 100, the course of study of each and every one in the class averages twelve years, and the average pupil of that class will get the twelve years' schooling. If the class enters with 240, and graduates with 20, losing one-twelfth each year, it will follow that the twelve years apiece which the 20 get, will, if averaged, give the whole 240 each one year. The eleven years which the next 20 get will give the 240 eleven-twelfths of a year, etc. The average amount of schooling would be six and one-half years, and the From the St. Louis school report, 1878-'79, W. T. Harris, superintendent. average age of leaving school (if entered at 6) would be 12 years, although the table of ages of a school of 1,560 pupils, arranged according to the supposed scale, would give only one and three-tenths per centum in the senior class, and only two and six-tenths per centum in the class next to the senior class; and under such circumstances some would-be economical reformer might use this argument against the high school department (which would include the last four years of this twelve-year course), and say: "Less than 2 pupils in a hundred ever graduate from the high school; it is for the few only; it is a rich man's institution," etc., and yet of the class of 240 who entered, there were 20 left, or 1 in 12-84 in 100 instead of 1.3. Hence, we may infer on comparison of those of 14 years of age (4 per centum) with those at 8 years (12 per centum), that at least one-third of those at 8 years of age remain in school until they are 14 years of age. But the city is increasing in population rapidly, both by immigration and by the birthrate. The latter item continues to give us larger numbers of pupils in the primary grades. A reliable estimate must take into account all those items of fluctuationbirthrate, death rate among children, access and depletion from migration at different ages, etc. This topic is so important that I make a long extract from an exhaustive article treating the subject, which appeared in the American Journal of Education (published by J. B. Merwin), St. Louis, May, 1879 (omitting the algebraic table [No. II], in which Prof. Woodward has generalized his results and given a general formula for obtaining the average age at which school children leave school): AT WHAT AGE DO PUPILS WITHDRAW FROM THE ST. LOUIS PUBLIC SCHOOLS? 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 this paper in a somewhat restricted sense, and as properly excluding the effect of mortality among school children; that is to say, I exclude from among 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 in St. Louis is small, but it is not on that account to be ignored. The propriety of omitting those who die, from my calculations, can not be seriously questioned. The practical inquiry is: At what age do pupils leave school to enter upon the active duties of life? and it should not be complicated with the very different question of the age at which pupils die without completing the course of study contemplated. Though nearly one-half of all the children born in this city die without reaching the age of 5 years, we plan for each newcomer on the basis of a probable long life. Again, although the average length of human life in St. Louis appears, from the recorded ages of those who die, to be less than 22 years, our systems of education rest upon the supposition that, among other responsibilities for the discharge of which children must be educated, the boys, at least, must be prepared for the duties of electors, though such duties do not come till after the age of 21. 3. The value of my results will, of course, depend upon my assumptions, as well as upon absolute data and my methods of calculation. In 1868-'69, I find that 2,917 children were registered at 8 years old. I propose to follow these 2,917 children through their career as pupils of the public schools, noting the number dropping out cach year till all are gone; then I shall find the average age at withdrawal. The annual registers of the schools contain, of course, all needed information, but it would be an endless task to follow the pupils as they change from school to school, finally disappearing from the records altogether. I must, therefore, abstract their history from such other records as are at my command. For my data I rely almost entirely upon the annual reports of Superintendent Harris. Each of these reports gives a table of the "number of pupils of different ages registered during the year." With the exception of the last two or three reports the number of children "7 years and under" is given without subdivisions, and in all reports those of "16 years and over” are grouped together. I have, therefore, been obliged to begin my investigation with those who are 8 years of age. 4. I assume that in the sense in which I use the word, no child under 8 years of age in St. Louis ever "withdraws" from school. The enrollment of names is made when the pupils enter the school, which is generally in September; the enrollment made at other times is very small, the spring registrations being mainly those of young pupils first entering school. 5. I assume that those who leave the public schools at the age of 9 years or more stop going to school altogether, though it is well known that many do attend other schools. 6. I exclude from my calculations those children who enter the public schools for the first time when 9 or more years of age. It is quite possible that the entire school period of such is greater than the average, but there are no available data on which to base a determination. 7. I assume that one-half of those reported as "16 years and over" are 16, and that the other half average 17 years of age at the time of enrollment. Actual figures would perhaps show an average somewhat greater. 8. I now call attention to Table I, which needs but a few words of explanation. The figures are taken from the reports of the superintendent without change, except in the case of the report of 1872-'73, from which the suburban schools of the (old) Thirteenth ward have been omitted, and the report of 1877-'78, from which I have eliminated the 16 suburban schools, as they do not appear in former reports. The arrangement of the table is such that the pupils who were enrolled year after year, and appear in different reports under different ages, are here placed in the same column, the age of each class being given in heavy type. Three of these columns are nearly complete, headed A, B, C. I use these columns for three independent calculations. The last two lines contain some estimates which the rest of the table will justify. 9. Let us examine column A. The report of 1868-69 shows the enrollment of 2,917 children during that scholastic year who were in their ninth year. The next year these children were all in their tenth year and they numbered 3,161. This increase can be accounted for only by immigration of 9-year-old children, and by the enrollment 'Some of the later reports may seem to prove this assumption to be not well founded, inasmuch as the number recorded as 8 years old may be considerably less than the number enrolled as 7 years old the previous year. In such an event, it is well to consider the spring enrollment of those who are "7 years old," and who do not become 8 till after September, and consequently are a second time enrolled as "7 years old." The result is the "7 years" list is abnormally large. of city children who, during the previous year, had either not attended school at all or had attended private schools. But it is not probable that all of the 2,917 returned to school in 1869-'70. Some had died; some had moved from the city; some had gone to private schools; some, perhaps, had stopped going to school. Now, before we can approximate the number of those who had left, we must arrive at a fair estimate of the number of new scholars in the class. For the latter purpose we must compare classes of the same age in the two years, i. e., those of 8 years, 9 years, etc., in 1868-69, with those of 8 years, 9 years, etc., in 1869-'70. We find an average increase of 123 per cent pretty evenly distributed through all the school ages. It is therefore probable that the addition to our class under discussion was in the same ratio, or 12 per cent of 2,917, which is 373. Had no pupils left the class it would have numbered, with this increase, 2,917+373=3,290. As the enrollment was only 3,161, it is evident that 129 must have left during or at the end of the year 1868–69. A comparison of the classes of 1869-'70 with those of the same age in 1870-'71 shows a growth of 12 per cent. Twelve per cent of 3,161 is 379, which is the growth of the schools in the 10-year-old class. The enrollment of the year shows 3,368; hence the loss during, or at the end of, 1869-'70 was 3,161+379-3,368=172. In the same way the total loss has been worked out for each of the years in column A. Unquestionably, my figures vary considerably from the facts in individual cases, but it may safely be assumed that the errors balance. The "annual increase" is given in Table I in per cents. The growth of classes, the "possible number" (had the class suffered no loss), and the total loss are given for each year of column A, in Table II. The annual increase from 1877-78 to 1878-'79 and from 1879 to 1879-'80 has been assumed as 6 per cent. more. 10. Let us now consider these columns of "total loss." The 129 lost the first year, column A, were all out of the original 2,917. The 3,161 of the next year contained only 2,788 old scholars and 373 new ones. Now, in the course of a year they lost 172 I assume that this loss was distributed among the old and new scholars in proportion to their number. This results in a loss to the original class during this second year of 152, reducing it to 2,636. In the same way I find that of the 573 lost the next year, 448 were from the original class. The seventh column in Table II gives these proportionate losses from the original class, and the eighth column gives the number of the 2,917 with whom we started, remaining in school year after year. The last division left school in June, 1878. Few of that class may be left in the high and the normal schools, but they would only serve to show that my result is too small. Tables III and IV contain similar columns, though the intermediate columns are omitted. 11. I now come to the last correction to be applied to the annual losses, and that is the deduction of the number of those who died while they were virtually pupils of the schools. Reports show that the death rate for school children is about four per 1,000 annually. I have, therefore, assumed that each year a part of the losses are from death, and I have deducted from the loss four-thousandths of the number remaining from the original class during the previous year. The remainders are clearly the numbers "withdrawn" and are entered in the next column. 12. The last column contains merely the products of the number of pupils withdrawing, multiplied by their age. The withdrawals do not always occur at the end of the year. I assume that, on the average, pupils withdraw six months from the beginning of the year. The average age, for example, of those registered as 10 years is 10 years and 6 months at the time of registration; those leaving before another enrollment are, therefore, 11 years old. Thus the 117 who withdrew in 1868-69 were 9 years old, the 141 were 10 years old, etc. 13. The average age obtained from A is 13.7 years; from B, 13.5 years; from C 13.6 years. WASHINGTON UNIVERSITY, St. Louis. C. M. WOODWARD. |