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 1889-90 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 1881, 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 1889 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 tho 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 difference at what date during the year the ages are registered, provided the date is always the same. 12. The average age of withdrawal is of course found by adding all the products found by multiplying the number of pupils withdrawing each year by their age, and dividing the sum by the total number of withdrawals. 13. It will be noticed in certain tables that not only is the rate of external gain minus, showing loss of school population, but in some cases they show a negative withdrawal, or an abnormal entrance of new pupils. This involves, of course, an unusual withdrawal during the same year from other groups or columns, as the rate of increase is calculated from all ages. I have carried out all such negative results, subtracting such amounts as have prefixed a minus sign. 14. Results.-Table XIII gives the results of the nine calculations. I submit them without comment. 15. The average age of withdrawal v. The average age of children in school.--I was originally led to this discussion by what I regard as erroneous statements in regard to the average length of time that the children attend school; and I am convinced that a great deal of confusion exists on this point in the minds of both teachers and school superintendents. For the purpose of clearing up this matter, I desire to state, first, the average age at which pupils withdraw from the public schools is a very different thing from the average age of pupils in the public schools. For example: I have shown by the results in Table XIII that the average age at which pupils withdraw from the St. Louis schools is approximately 13.3 years. Now the average age of the pupils in the St. Louis schools at the time of their enrollment in the year 1894-95 was 10.2 years, which is evidently a very different thing. In the same way the average ago at which pupils withdraw from the Chicago schools I have found to be approximately 15.5 years. The average age of pupils in the Chicago schools at the time of their enrollment in the year 1894-95 was 10.1 years. So in the Boston schools the average age of withdrawal is approximately 15.9 years; while the average of those in the Boston schools at the time of their registration in 1894-95 was 10.52 years. However, this result must not be compared with the averages in St. Louis and Chicago for the reason that in the Boston schools pupils are admitted under 4 years of age, while in St. Louis no pupils are admitted until they are 6 years old. In Chicago all those under 7 years old are grouped together without specifying how old they are, whether 4, 5, or 6; consequently no comparison can be made except for those who are 7 years old and over. Using the figures given in Tables I, II, and III for the year 1894–95, for the three cities, I find the average age of all those children who were above 7 years of age at the date of registration in the public schools in 1894-95 to be as follows: St. Louis, 10.83; Chicago, 10.87; Boston, 11.56. I wish now to show how entirely reasonable it is that the average age of those in school should be very different from the average age at the time of withdrawal. Let us suppose that in an ideal city 1,000 pupils enter the schools every year at exactly the age of 6 years. Let us also suppose that this number of pupils remains without change—that is, there are no deaths, no removals, no additions, no withdrawals, but every pupil remains in school until the age of 20, and then withdraws. Under such an ideal condition of things it is evident that the average age at the time of withdrawal would be exactly 20 years; and yet the average age at the time of registration at the beginning of any one year would be exactly 12 years, which is clearly seen to be a very different thing. This, of course, is an ideal and an extreme or limiting case toward which results may approximate more and more as the attendance is extended more and more generally throughout the course of the public schools. 7 9 10 11 12 8 7 9 10 11 12 13 4.8 3.2 7 9 8 7 7,959 7,075 6, 207 1.9 0.3 2.2 0.6 9 10 11 9 10 11 13 15 4, 158 2,946 1,741 1,069 616 267 103 3.1 1.5 16 17 18 19 13 14 15 16 12 17 18 19 726 314 121 5.9 4.3 16 17 18 19 7 19, 855 17, 207,16, 116 15, 782 14, 404 14, 025 11, 231 12 8 9 10 11 13 14 15 16 * 17 7 14 21, 758 19, 639 17, 514 16, 571 15, 228 14, 473 11, 783 8,042 4, 564 2,563 1,491 8 12 9 10 11 7 13 22, 584 21, 623 19, 743 18, 196 16, 159, 14, 819 12, 076 * 17 662 5.7 3.7 4.5 2.5 5.8. 3.8 2.5 0.5 14 6, 431 15 15 16 * 17 4, 540 2,391 2,162 16 17 18 19 1891-92 639 237 8.3 6.3 7 10 12 14 17 24, 996 22, 629 21, 841,20, 363 17, 567 16, 261 13, 220 8, 628 5, 009 2, 661 1, C03 7 8 9 10 11 12 13 14 17 25, 748 23, 793 22, 263 21, 840 19, 581 17, 963,14, 408, 9, 783 5,809 3,081 1,903 13 15 16 18 19 687 254 9.0 7.0 t 15 16 18 19 815 302 7.4 5.4 7 9 10 11 1886-87. 8 5,571 6, 103 6, 146 6, 234 6,074 6,087 5, 335 3, 984 2,550 1,431 12 13 14 15 16 1889-90. 5, 558, 5, 885 5, 957 6, 020 5,844 6,028 5, 638, 4, 546 3, 000 1,647 816 326 163 -1.5-2.2 7 9 8 |