Promotion, Retardation, and Elimination.
- Author:
Edward L. Thorndike, Ph.D.,
Teachers College, Columbia University.
It is or should be well known that in every administrative educational unit such as a city school system or a private secondary school, the fractions of the total course nominally to be completed in equal times,?for example, the grades of the elementary school, or the years of the secondary school,?may actually require unequal periods. This requirement of unequal periods is disclosed by the fact that a large percentage of the pupils spend more time in one grade than in another. Nevertheless a year or half year, as the case may be, is assumed to be the normal time for all pupils and all grades alike.
The general tendency of the elementary or secondary schools in this country is not known. If there is a general tendency affecting some particular grade or grades, the fact is of importance for three reasons. If there is a general tendency such as to make the completion of the second grade in the “normal” unit of time a specially difficult task for the pupil who reaches it, it would probably be advisable to eleminate this tendency. Teachers, pupils, and parents would thereby comprehend more easily the work of the school and what is necessary to its satisfactory completion. If the inequality is not removed, its existence should at least be made known to teachers, pupils, and parents. A more precise knowledge of these inequalities will also help us to estimate the nature and amount of the retardation of pupils in school, and the elimination of pupils from school.
I propose, therefore, to measure the extent to which the different grades of the elementary and high schools are, in American cities in general, of unequal length.
The most desirable material from which to calculate this measurement would be a sufficient number of individual educational histories, giving accurately how long each pupil took to complete grade 1, how long to complete grade 2, etc. Such life histories do not exist at all in published form, only rarely in the written records of school officers, and could be secured in adequate number only at a cost for travel, time, and clerical assistance which is for the author prohibitive. The facts can be fairly well deter(232) mined, however, from the city school reports, from an examination of the not infrequent statements of the number of promotions by grades. This method is the one which I shall employ.
By examining the reports of over one hundred cities and towns, covering a period of from one to five years, I have obtained fifteen statements from which one can infer with fair accuracy, the comparative lengths of the elementary school grades for each city in question, and four in which the same is true for the high school grades also.
Although it is the relative length of the different grades which is to be measured, I shall give first the actual percentages of pupils who at the end of the year fail to be promoted, and would therefore be compelled to repeat the work of the grade if they remained in school. I give them because they are the original data bearing on the general problem of retardation, and are in some respects superior to the statistics of over-age pupils that have hitherto been collected. These percentages of pupils failing of promotion are calculated, when it is possible, directly as percentages of those enrolled in the grade at the end of the year, but in the case of three cities, Chicago, Kansas City, Mo., and Rochester, the best that could be done was to infer the enrolment at the end of the year according to the method shown in the appendix at the end of this part of the article. The sources of the data, with methods of inferring the June enrolment in the cases where it is not directly given, are presented in the appendix. The calculated proportion of pupils enrolled at the end of the year who failed of promotion, is given in table I, on the following page.
To get from these figures the relative length of the grades in such form that the facts may be most conveniently examined, I have computed the proportion which each is of the average for grades 2 to 8 of the city in question. This gives the figures of table II. If the figure is over 1.00, it means that the percentage of pupils enrolled at the end of the year who failed of promotion in that grade, is greater than the percentage for grades 2 to 8 of that city taken together (regardless of the number of pupils in each grade), i. e. the grade is “longer” than the average of grades 2 to 8 in that city. If the figure is under 1.00, it means that the grade is “shorter” than the average of grades 2 to 8 in that city. Of course, any other division could be used. The process alters no relation, but only makes the facts for each city clearer, and the measurement of the general tendency of the cities as a group more convenient. I have used grades 2 to 8 rather than 1 to 8. because
TABLE I. PROPORTION OF PUPILS ENROLLED AT THE END OF THE YEAR WHO FAIL OF PROMOTION. Grades Brooklyn, N. Y., 1908 Chester, Pa., 1903… Chicago, 111., 1899… Columbus, Ohio, 1902 Elgin, 111., 1901 Jamestown, N. Y 1898 and 1899…. Kansas City, Mo 190 7 Manhattan, N. Y 190 8 Pasadena, Cal., 1900 and 1902 Rochester, N. Y 1897 San Francisco, Cal 1892 Stockton, Cal., 1893. Trenton, N. J., 1896 and 1897 Utica, N. Y., 1900 1901,and 1902… Wheeling, W. Va 1908 C3 >.5 a ^ to 505 510 34? .28 .145 .23 .36 .38 .035 .24 .26 ,290 .150 .30 .36 .19 .32 .50 125 .130 .12 .18 .10 .05 .15 .11 .135 .130 .17 .14 .23 .08 .10c .30 135 .135 .135 .130 .16 .15 .16 .06 .14 .13 .21 .14 .21 .08 .10 .24 130 .130.140 .150 .27 .16 .27 .17 .12 .27 .24 .16 .25 .19 .13 .35 ,160 .150 .23 .18 .19 .09 .12 .24 ,165 .160 .21 .18 .25 .15 .08 .10d .34 .160 .160 .34 .17 .18 .09 .09 .28 .150 .145 .22 .15 .23 .06 .09 .13 .180 .160 .27 .16 .09 .10 .14 .25 ,185 .140 .25 .22 .17 .16 .09 .13 .21 145 .090 .40 .30 .18 .12 .30 .17 .155 .170 .32 .20 .10 .06 .18 .23 .08 .24 0 .26 10 1 H .03 .24 .20 .22 .09 2 H .15 .20 .20
a “Receiving class.” &The figure for grade 1 will be very high, as the enrolment of grade 1 is very much larger than that of 2 or 3. cFor grades 1, 2, and 3 together. <*For grades 4, 5, and 6 together.
TABLE II. PROPORTION (IN HUNDREDTHS) WHICH THE PERCENTAGE OP PUPILS ENROLLED AT THE END OF THE YEAR WHO FAIL OF PROMOTION IN EACH GRADE, IS OF THE AVERAGES OF SUCH PERCENTAGES FOR GRADE 2 TO LAST GRAMMAR GRADE (INCLUSIVE) IN THE CITY IN QUESTION. Grades Brooklyn 3.61 2.00 1.04 Chester 11 … I -93 Chicago Columbus Elgin Jamestown. Kansas City Manhattan Pasadena Rochester San Francisco Stockton Trenton Utica Wheeling 2.25 2.17 .41 1.64 1.32 1.95 1.01 1.25 1.97 1.58a .89 3.21 b 3.42 2.08 .91 .49 1.13 .59 .59 1.01 .56 .89 .70 .79 1.09 .83 .72c’ 1.25 .96 .65 .94 .93 .75 .93 .65 .87 1.12 .90 1.24 1.66 1.04 1.13 ?99? .85 .88 1.20 .99 .68 1.21 .98 1.00 .89 1.16 1.87 1.13 1.46 l.lOi .93 1.13 1.09 1.00 .82 1.42 1.09 .88 .99 1.16 1.49 .70 .69^ 1.42 1.14 1.38 1.06 1.05 1.05 .61 1.29 .99 .93 .84 1.09 .60 .78 .54’ 1.21 J 1.09 1.00 1.04 .64 1.62 .81 1.12 1.03 1.15 1.36 .97 2.00 1.09 1.04 1.14 1.03 1.35 1.19 1.10 .81 .45 1.60 .64 .78 1.57 .93 1.64 .88 .33 1.30 o” 1.89 10 .30 1 H 2 H .97 1.25 1.26 .85 .61 1.25 1.14 3 H 4 H .89 1.00 1.93 0 .13 .48
a “Receiving class.” &The total enrolment in Trenton in grade 1 shows that this relation would be much over 1. cFor grades 1, 2, and 3 together. dFor grades 4, 5, and 6 together.
of the very great variability among cities in the proportion of failures in the first grade, and because of certain eccentricities in the reports of first grade enrolments, which will be discussed later. Before applying these facts to the discussion of the course of study, retardation, and elimination, we must consider how far these percentages of failures on enrolments at the end of the year, are valid measures of the inequality of the grades in length. The first inadequacy of these data as measures of the relative length of the different grades, is that no account is taken by them of children who did the work of a grade in less than the normal time. Indeed, a child who is promoted during the year from grade 3 to grade 4, and then fails to be promoted at the end of the year to grade 5, may be recorded not at all for grade 3, and as a failure for grade 4, though he really completes grades 3 and 4 in two years, and though his “failure” with grade 4 is not a proper measure of its relative difficulty compared with grade 5, which he later completes in one year. But, as a matter of fact, for the relative lengths of the different grades, our reports of conditions at the end of the year are not seriously affected by this inadequacy; first, because the pupil who is promoted during the year and is permitted to stay in the advanced grade until the end of the year, rarely if ever fails to be promoted from it at the close; and secondly, because there is a strong inverse correlation between the percentages of failures in a given city and the percentages of achievements in less than the “normal” time. For the first of these statements I have no evidence other than general observation, but I believe that no competent student of school administration will dispute it. The second I am able to demonstrate from the cases of Galesburg, 111., and Utica, N”. Y., in whose reports the percentages of more rapid advance than usual are given. The relevant facts are given in table III.
The second inadequacy is due to the fact that the second or third annual failure of a pupil after two or more years in a grade is not given any more weight than a first failure. Here, again, the probability is that for our purpose the injury done is slight or none at all. There is probably a very close direct correlation between the percentages of failures as here measured, and the percentages with due weight attached to second and third failures. Of course, as I have already stated, the school histories of individual pupils are the proper data for our measurement. But the general relations in the whole group of cities, between the relative lengths of the grades as calculated from the percentages of failures alone, are probably much the same as they would be if calculated from the time spent in each grade by the individuals completing it.
The third inadequacy is due to the fact that each percentage of failures is based on the number of pupils in that grade at the end of the year, not of those who reached the grade and attempted its work, much less of children of equal original capacity. This
TABLE III. DATA SHOWING INVERSE CORRELATION BETWEEN FAILURES AND RAPID PROMOTIONS. Galesburg, III., 1898, p. 40. Grades Per cent of those promoted who complete the grade in Less than 1 yr. More than 1 yr. Utica, N. Y., 1900, 1901, and 1902. Per cent of June enrolment completing grade i year or more ahead of class. Per cent of June enrolment fail ingof promotion 35 26 14 11 17 21 17 7 34 13 24 18 17 32 26 45 12 10 12 10 8 13 23 26 inadequacy does no harm if only it is kept in mind. We must remember, for instance, that if all the pupils who began the work of the sixth grade had stayed in school until the end of the year, the percentage of failures would probably have risen, because the older, less scholarly, and duller pupils in the sixth grade probably tend more often to be eliminated. If all the pupils who completed the second grade stayed in school long enough to spend one year in the fourth high school, the percentage of failures there would almost certainly be very much higher, supposing present standards for promotion to be maintained.
“Equally long” for our purpose has to mean of any grade “equally long for such pupils as go to the end of it”. The second and eighth grades are, for example, equally “long”, if the time spent in the second grade by those who complete it equals the time spent in the eighth grade by those who complete it. There are a number of other important ways in which the second and eighth grades might be equally “long”.
A fourth source of inadequacy is the complex nature of the figures for enrolment of grade 1, particularly the fact that the enrolment at the end of the year may include many children who have not spent the “normal” time in the grade, having entered school in the course of the year. For a full study of first grade retardation, this factor is of very great importance and should be measured. The figures for the first grade in tables I and II are undoubtedly higher than similar figures would be if calculated on the number of children enrolled at the end of the year who have been in the grades at least nine-tenths of the “normal” time. This is evidenced both by direct observation of school practice, and by the exceptionally low ratios of attendance to enrolment for the first grades.
It is also a fact that children may be freely admitted to the first grade, wTho are not yet ready to do its work even very slowly. This cannot occur in later grades except by unusual grading of the schools. It is sure to happen as a result of the normal variability of human intellect and character if the first grade work is such as the average child of normal age is ready for, so long as admission to the first grade is determined, without an examination, on age as the main requirement. It therefore happens that the first grade is in part a mere abiding place for children until they are able to do its work.
For later grades, then, our percentages are of those pupils who have been put there at the beginning of the year by school officers after the experience of the lower grades, while for grade 1 our percentages are of those who have got into the grade somehow, chiefly because they were of a certain age, and have stayed there from some date or other until the end of the year or half year.
It is very significant that in the cities where my records are for half grades, the second half of the first grade is hardly “longer” than the later half grades (see the data for Brooklyn and Manhattan), and that in San Francisco, when the first grade was preceded by a “receiving class”, the first grade was a “short” grade. Consequently, I estimate that if a kindergarten or other preparatory course were required of all, and admission to the first grade made only at the beginning of the year or half year and only upon promotion from the preparatory course, the proportion for grade 1 in table II would drop to approximately 1.00. There are other interesting considerations with respect to what these statistics of failure do not mean and do not imply. But
TABLE IV. PROPORTION (in HUNDREDTHS) “WHICH THE PERCENTAGE OF PUPILS ENROLLED AT THE END OF THE YEAR WHO FAIL OF PROMOTION, IS OF THE AVERAGE OF SUCH PERCENTAGES FOR GRADE 2 TO LAST GRAMMAR GRADE, INCLUSIVE, IN THE CITY IN QUESTION. Grades Cincinnati, Ohio, 1906 Fort Wayne, Ind.. 1907 Haverhill, Mass., 1907 Louisville, Ky., 1905 Maiden, Mass., 1907 Medford, Mass., 1907 Philadelphia, Pa., 1908 Providence, R. I., 1908 Salt Lake City, Utah, 1907, Somerville, Mass., 1907 Springfield, Ohio, 1907 Wilkesbarre, Pa., 1905 Williamsport, Pa., 1908.… 1.82 2.13 1.82 1.30 2.71 2.47 1.24 .99 1.51 1.74 1.40 .45 1.63 1.20 .87 1.09 .99 1.23 1.23 1.18 .61 1.21 1.20 .94 1.09 1.07 1.06 .94 1.65 S .59 1.07 1.02 50 i .85 1.03 .92 1.32 .50 1.45 1.20 1.05 .97 .84 1.06 .94 .96 .78 1.23 1.03 1.18 .40 1.33 .94 1.22 1.09 1.22 .94 1.30 1.19 1.21 1.10 .82 1.03 .71 1.21 .84 1.45 1.30 .94 1.06 .96 1.35 .89 1.33 1.25 1.11 .96 88 1.08 .97 .99 1.41 .94 .90 1.49 .96 1.33 .81 1.41 .84 .70 .98 .85 .61 1.30 .59 .90 .85 .48 .72 .22 2.22 .60 42 1 H 2 H 3 H 4 H 1.32 1.32 30 54 .75 66
it will be better to devote the remaining space to showing what they do mean, first, with respect to the course of study, secondly with respect to retardation, and thirdly with respect to elimination. Fortunately, in considering these topics we can use measurements of the relative length of the grades from more cities than I have reported. Ayres,1 working with recent reports, has found records in sixteen cities, thirteen of which are not included in my list. USTo substantial difference appears between the results from combining all the cities in both studies, and the results from either set separately, but the reliability is, of course, about one and four-tenths times as great. I have therefore recalculated all my results, after adding the thirteen cities. In combining Ayres’ records I shall count one city only once when there are two records, and use the records in the form of per cent failing, instead of per cent promoted.
We have then as the percentages of the June enrolment which fail of promotion these central tendencies for the grades in order.2 Grades 2 3 4 5 6 7 Last grammar 1H 2H 3H 4H Medians…12.25 14. 14.75 16. 14.25 15. 12.5 21 20 16 5 As an addition to our table II, we have from Ayres’ cities the facts of table IV, and as a central tendency for all the cities with respect to relative lengths of the grades we have, Grades 1 2 3 4 5 6 7 Last grammar 1H 2H 3H 4H Medians…160 953 94 99.5 109 102 99.5 89 125 125 100 30.5 ^yres, Leonard P. Laggards in our Schools. New York: Charities Publication Committee, 1909, p. 143. 2Using the average of the A and B halves of the grades for Manhattan and Brooklyn.
‘This (95) is the median if Trenton’s ratio for grade 2 (not directly reported) is lower than 91. It almost certainly is, for the enrolment is lower than that of grade 3. If Trenton’s ratio is 101 or over, the median is 100. If it is 99, the median is 99. If it is 97, the median is 98. If it is 95, the median is 97. If it is 93, the median is 96. APPENDIX.
Sources of the data, with the methods of inferring the June enrolments in the cases where they were not directly given. 1. Brooklyn, N. Y. Tenth Annual Report of the City Superintendent of Schools to the Board of Education of the City of New York for the year ending July 31, 1908, pp. 68-72. Number of pupils on register at end of semester; number of pupils promoted (during the semester as well as at its close) ; per cent of pupils promoted. 2. Chester, Pa. Manual of the Public Schools, 1903, p. 64. Per cent number promoted bears to number enrolled ill June. There are records for “Com’l 1st year,” and “Com’l 2d year,” in addition to those for the regular high school. I have combined them with 1 and 2 of the regular high school.
3. Chicago, III. Report of the Board of Education for the year ending June 23, 1899, pp. 123 and 242. The number promoted from grade 1 to grade 2, from grade 2 to grade 3, etc.; average daily membership. The proportions of “number promoted” to “average daily membership” are for grades 1 to 12 in order, .683, .815, .848, .862, .794, .804, .789, .862, .731, .729, .814, and 1.02. To estimate the enrolment at the end of the year from the average daily membership, we must decrease the latter for grades where pupils are dropping out during the year (e. g., first year of high school), and increase it for grades where more pupils are entering late than are dropping out early (e. g., first primary grade). Data are lacking to do this with any closeness of approximation. Roughly I estimate the proportions of number promoted to enrolment at end of year for grades 1 to 12 in order as .64, .82, .85, .86, .82, .83, .84, .87, .80, .80, .84, .98. 4. Columbus, Ohio. Report of the Public Schools for the year ending August, 1902, p. 200. The number in each grade failing of promotion and the number enrolled at the end of the year. 5. Elgin, III. Report of the Board of Education for the year ending June 30, 1901, p. 12. Report is made by semesters, but for grades 1, 2, 3, etc., not 1A, IB, 2A, 2B, etc. Number promoted to next grade; number retained; number in school at the close of the semester in each grade. There is one troublesome feature in the figures for Elgin, namely that it is hard to see how from so large a first grade, with so few held back, so small a second grade results. The figures were given definitely as a measure of the number of failures, and there is presumably some explanation of the difficulty, for instance by a custom of promotion during the year from grade 1A (higher first) to 2B and 2A, 3B and 3A. The comparative enrolment by grades (at the end of the semester) lends some support to this explanation, since the second grade is much smaller than the third, fourth, fifth, and sixth. The figures are, for the second semester,?grade 1, 614; 2, 365; 3, 416; 4, 435; 5, 458; 6, 447; 7, 300; and 8, 257. The average age of the classes promoted lends further support to this explanation.
6. Jamestown, N. Y. Annual Reports for the school years 1897-98 and 1898-99, pp. 21, 22, 28, and 29. Number registered, discharged, promoted at end of year, and not promoted at end of year. 7. Kansas City, Mo. Annual Report of the Board of Education for the year ending June 30, 1907, pp. 88-99. Number promoted to each grade; total enrolment in each grade; number spending more than two hundred days in the grades. I infer the June enrolment for each grade with the aid of data given concerning those leaving school permanently in grades 5, 6, and 7, and concerning the number of pupils in attendance less than 20 days, 20-39, 40-59, 60-79, etc. Thus for 1907 I take as the June enrolment for grades 5, 6, and 7, the total enrolment minus the number who left the school permanently, getting 2563, 2095, and 1813 as results; and take also the sum of pupils promoted from the grade and those spending more than two hundred days in it, getting 2903, 2294, and 1839. The averages of the results by these two methods (2733, 2195, and 1826) are sufficiently accurate for our purpose. For grades 1 to 4, I take that percentage of the total enrolment in each grade which the number of pupils attending 140 days or over in grades 1 to 7 and the kindergarten, minus the sum of 2733, 2195, and 1826, and also minus two-thirds of the total enrolment in the kindergarten, is of the total enrolment of grades 1, 2, 3, and 4 respectively. This process gives 4030, 2740, 2720, and 2610, the first three figures being significant in each case. I also take the sum of those promoted from a grade and those recorded as spending more than two hundred days in it, allowing to the first grade 1132 repeaters. This gives 4170, 3259, 3595, and 3351. The averages of the results by these two methods (4100, 3000, 3157, and 2980) are reasonably accurate, except that the actual June enrolment in the first grade may be higher than my estimate. The June enrolment in this grade of pupils who have attended 140 days or more, will bear approximately the same relation to the similar enrolment figures for other grades, as shown by my estimate. 8. Manhattan, N. Y. Tenth Annual Report of the City Superintendent of Schools to the Board of Education of the City of New York for the year ending 31, 1908, pp. f>8-72. Number of pupils on register at end of semester; number of pupils promoted (during the semester as well as at its close); per cent of pupils promoted.
9. Pasadena, Cal. Annual Report for the year ending June, 1899, pp. 68 ff; 1900, p. 37; 1901, pp. 82 ff; 1902, p. 32. Number examined; number promoted; number left over. There is sufficient evidence that the number examined equals the number in the grades at the end of the year.
10. Rochester, N. Y. Annual Report of the Public Schools, July, 1897, pp. 7 and 30. Number registered but once; promotions from grade to grade, June, 1897; average daily attendance. The proportions which the numbers promoted are of the numbers registered but once, are for grades 1 to 9 in order,?.589, .834, .814, .814, .779, .783, .737, .735, and .755. The proportions of the average daily attendance are .807, .994, .951, .951, .924, .930, .850, .861, and .789. I estimate that the proportions of those enrolled at the end of the year would be roughly .641, .856, .836, .838, .820, .847, .784, .800, and .765.
11. San Francisco, Cal. Annual Report of the Public Schools for the year ending June 30, 1892, p. 7. Number promoted and number who failed. Besides the usual eight grades, San Francisco had in 1892 a “receiving class”. If we treat this as a true first grade, making nine in all, the numbers in tables I and II for San Francisco should all be pushed on one year.
12. Stockton, Cal. School Report for 1892-93, pp. 61-64. Number promoted; number not promoted; total enrolment by grades. 13. Trenton, N. J. Annual Report of the Commissioners of Public Instruction for the year ending August 31, 1896, p. 162; 1897, p. 204. Number in grade at end of year; per cent promoted, given for grades 3 to 8 only.
14. Utica, N. Y. Annual Report of the Public Schools, 1900, p. 33; 1901, p. 27; 1902, p. 25. Number in class at close of year; number promoted (divided into “fully qualified” and others promoted); number held back. Reported for primary, intermediate, and advanced grades of a nine grade system. Reported separately for the three advanced grades in the case of a school containing about three-fourths of them. I have distributed the percentages for the advanced grades according to the distribution for this impartially selected majority of them. 15. Wheeling, W. Va. Annual Report of the Public Schools for the year ending July 31, 1907, p. 19. Number remaining in each grade; number promoted to each grade. The number enrolled at the end of the year has to be inferred in the case of grade 8 from the total enrolment. I have taken that proportion which the end-of-the-year enrolment is of the total enrolment in grades 6 and 7.
The reasons why my data are so often for the years around 1900 instead of later are, first, that I wished to use them as mentioned on p. 8 of “The Elimination of Pupils from School”, to estimate elimination from data of grade populations for the years around 1900; and secondly, that I had already some considerable familiarity with and convenient access to school reports of that date. (To be concluded.)
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