Chicago, 32 per cent drop out before reaching the second grade, 51 per cent before reaching the third grade, 66 per cent before reaching the fourth grade, 78 per cent before reaching the grammar grades, 97 per cent before reaching the high school, and only three in a thousand graduate from the high school. While the study of one city does not prove anything outside of that city, it was the opinion of Professor Folkmar that the conditions which he found in Chicago were not peculiar to Chicago, but rather were typical of the great cities of this country, if not of the whole country, including urban and rural districts. Likewise, that these conditions are typical not only of the United States, but of every highly civilized nation. As one step toward the verification or disproval of the above proposition, I undertook in 1896 a similar study of the public schools of Milwaukee.

In the study of the duration of school attendance from data furnished by Chicago and Milwaukee, two methods* of demonstration were employed for each city, the one serving as a check upon the other. They may be designated as the deductive, or enrollment method, and the inductive, or class method. By the first the enrollment by grades for one year or the totals for a group of years are made the basis of deduction or inference as to the per cents that must have dropped out from the lower grades. By the second the enrollment of a single class entering the first grade is followed from grade to grade through the reports of successive years, the per cent that dropped out in each grade is noted, and from a comparison of these facts with corresponding facts in the history of other classes a generalization is reached inductively as to the normal per cents that drop out at each grade. Secondary considerations, such as deaths, increase of population, and promotion figures, were introduced into these studies, "on the one hand to eliminate errors so far as possible, on the other hand to determine the limits of probable error, so that, if per cents could not be determined with absolute accuracy, statements could at least be made as to the maximum and minimum limits within which the truth lay."

The following diagram is a graphic illustration of the results of the deductive method. The solid lines mark off the number that drop out before the next grade in Chicago, and the dotted lines. indicate the conditions in Milwaukee. The slight difference.

For details of method and data see "The Duration of School Attendance in Chicago and Milwaukee," by Daniel Folkmar, "Proceedings of the Wisconsin Academy of Sciences, Arts, and Letters for 1897," p. 257.

[From Vol. XII. "Transactions of the Wisconsin Academy of Sciences, Arts, and Letters."]

between the two cities is undoubtedly due to the fact that, while the figures of actual enrollment were made the basis of deduction in Chicago, in Milwaukee the figures of average enrollment were employed.*

The deductive inference suggested by an examination of these figures is: If only .26 of 1 per cent of the pupils are to be found in the twelfth grade, the remaining 99.74 per cent dropped out before reaching the twelfth grade. By the same reasoning it will be found that 97 per cent dropped out before reaching the high school, 78 per cent before reaching the grammar grades, and 32 per cent before reaching the second grade. To put these facts in fractional terms of the pupils who enter the public schools of Chicago, nearly one-third drop out before reaching the second grade, one-half before reaching the third grade, three-fourths before reaching the grammar grades, nine-tenths before reaching the seventh grade, only three in a hundred get into the high school, and only three in a thousand graduate from the high school.

Simple as this method seems, there are errors in it, some of which would make the per cents too large, while others would make them too small. Such are the double enrollment of pupils (where pupils remain two years in the same grade), the factors of death, increase of population by births, immigration, and annexation, and the employment of a base many times too large.

THE INDUCTIVE METHOD.

The second general method made use of in this study is a correction of several of these objections, since it traces a given class through a period of twelve years as well as can be done from tables of enrollment, after having made the necessary corrections for increase in population and deaths. Yet the results of the method (see Column V. of table on page 72) are still more appalling than those of the deductive method.

Admitting that the truth lies between the maximum and the minimum limits of probable error, an examination of the above table of results, obtained by various methods of computation, will prove of interest. As Column III., or the figures obtained by the deductive method without corrections, is found to be about a mean proportional between the maximum and minimum limits of error,

*The figures of actual enrollment are not published in the Annual Reports of the School Board of Milwaukee, nor are they filed in the office of the superintendent.

GRADE.

the deductive method is recommended as an easy and satisfactory one for ascertaining the duration of school attendance in any city. The results of this method were adopted by Professor Folkmar as the conclusion of his study.

CONCLUSIONS AS TO PER CENTS THAT DROP OUT.

That the conditions found in Chicago and Milwaukee hold true of all schools seems apparent from the fact that no irregularities of enrollment are observable in the entire period covered by these studies (fifteen years in the study of Chicago and eighteen years in that of Milwaukee), such as might be caused by the opening and

Not actual en

Milwaukee.

rollment.

closing of private schools, the transfer of pupils from public to parochial schools before confirmation and from parochial to public schools at other ages, by the fluctuations of immigration and emigration, etc. In the case of Chicago, where large annexations. have been made, the years 1890 (when the population was increased 40 per cent by annexation) and 1891 (when there was an increase of 10 per cent) exhibit the same regularity. Nowhere except in the first grade do we find as much as a difference of 2 per cent between successive years. The inference is that pupils transferred, annexed, or brought in by immigration from foreign countries, were divided in about the same proportions among the grades in other schools, and thus make no variation in the tables. Dr. Harris, in his report of the public schools of St. Louis in 1871 (page 25), shows that the same law of proportion of enrollment holds true for St. Louis. Similar testimony for the city of London is given by Charles Reed in a paper read at a meeting of the London School Board.

There is a slight increase in the upper grades and a corresponding decrease in the lower grades, as might be expected, as the result of the betterment of economic conditions and the increased intelligence of the people.

SOME PERTINENT QUESTIONS.

If it be true, as shown by Professor Folkmar's statistical study, that, of the pupils who enter the public schools, one-third never go beyond the first grade, one-half drop out before reaching the third grade, three-fourths never reach the grammar grades, only three in a hundred get into the high school, only three in a thousand graduate from the high school, and that the average schooling received by each pupil is less than three years, is not the question how to retain pupils in school for a longer period of time the most vital of all questions? If conditions of attendance are to remain as they are, is it not of much greater importance to consider what to teach rather than how to teach? If the average pupil can cover only three grades of work, do we not err in enriching our courses of study with non-essentials (nature study, drawing, sloyd, etc.), and thereby infringing upon the time that should be given to instruction in the essentials (the elements of

"Ten Years' Results of the London School Board," Journal of the Royal Statistical Society, vol. xliii. p. 676, December, 1880.