Elimination of Pupils from School
A Review of Recent Investigations. The Psychological Clinic Vol. II. No. 9. February 15, 1909. :Author: Roland P. Faxjgster, Ph.D.,
In Charge of School Inquiries for V. S. Immigration Commission. Of the many effects of retardation in our public schools, probably none is more important than the elimination of pupils from school before the completion of the elementary course. All recent studies of retardation show that a large percentage of pupils fail to finish the elementary schools. In a vague way it has long been known that many children left school early, but recent efforts to measure the extent to which this occurs have fairly startled the public and in some instances at least have opened the eyes of schoolmen to the existence of evils in our school system of which they had never dreamed. Believing as he does that “the most reprehensible thing in educational administration is baseless conceit, and the most senseless policy is the hiding of distasteful facts,”1 Hon. A. S. Draper, Commissioner of Education of the State of JSTew York, frankly confesses:
“I have assumed that practically all of the children who do not go to the high schools do finish the elementary schools. That is not the fact. * * * I confess that it startles me to find that certainly not more than two-fifths, and undoubtedly not more than a third of the children who enter our elementary schools ever finish them, and that not more than one-half of them go beyond the fifth or sixth grade.”
Even if we had cherished no illusion that practically all of the children who enter elementary schools finished the course in them, we may share Dr Draper’s surprise that the proportion who get through appears to be so painfully small. Admitting the fact, its magnitude, as here stated, is appalling. Report, 1906, p. 532.
Table Showing Successive Grades in New York Cities First Year 1899 Albany 1765 Amsterdam 402 Buffalo 6937 Cohoes 544 Corning 137 Elmira 838 Fulton 316 Geneva 162 Gloversville 536 Hornell 217 Hudson 161 Jamestown 524 Johnstown 266 Little Falls 189 Lockport 362 Middletown 550 Mount Vernon 589 Newburgh 652 New Rochelle 426 Olean 286 Poughkeepsie 462 Rensselaer 276 Rochester 3939 Rome 306 Watertown 678 % 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Second Year 1900 j % Third Year 1901 1213 68.7 317 i 78.8 6937 425 129 623 304 99 359 163 125 430 243 117 325 475 482 493 419 280 367 208 2241 278 472 100 78.1 94.2 74.3 96.2 61.1 67 75.1 77.6 82.1 91.4 61.9 89.8 86.4 81.8 75.6 98.4 97.9 79.4 75.4 56.9 90.8 69.6 1185 342 6792 461 119 608 294 96 399 198 113 416 237 129 300 408 519 465 366 281 351 197 2150 202 402 % 67 85.1 97.9 84.7 86.8 72.6 93 59.3 74.4 91.2 70.2 79.4 89.1 68.3 82.9 74.2 88.1 71.3 85.9 98.3 76 71.4 54.6 66 59.3 Fourth Year 1902 1138 316 6427 365 114 535 307 91 328 183 125 404 218 138 276 340 420 412 277 264 342 193 2129 197 379 % 64.5 78.6 92.6 Fifth Year 1903 i % 1324 241 5772 67.1 S 228 83.2 i 85 63.8 97.1 56.2 61.2 84.3 438 248 105 314 165 77.6 j 114 77.1 82 73 76.2 61.8 71.3 63.2 65 92.3 74 69.9 54.1 64.4 55.9 465 190 98 233 249 413 401 210 219 333 177 1881 159 333 75 60 83.2 41.9 62 52.3 78.5 64.8 58.6 76 70.8 88.7 71.4 51.9 64.4 45.3 70.1 61.5 49.3 76.6 72.1 64.1 47.8 52 49.1 Sixth Year 1904 989 226 4968 183 87 414 189 93 258 148 117 469 174 85 204 228 370 372 153 167 281 120 1727 146 295 % 56 56.2 71.6 33.6 63.5 49.4 59.8 57.4 48.1 68.2 72.7 89.5 65.4 45 56.4 41.5 62.8 57.1 35.9 58.4 60.8 43.5 43.8 47.7 43.5 Seventh Year 1905 573 167 4043 145 83 370 156 81 214 162 85 276 142 64 187 208 348 254 89 166 235 153 1511 170 270 % 32.5 41.5 58.3 26.7 60.6 44.2 49.4 50 39.9 74.7 52.8 52.7 53.4 33.9 51.7 37.8 59.1 39 20.9 58 50.9 55.4 38.4 56 39.8 Eighth Year 1900 528 117 3729 122 72 276 128 83 151 123 91 245 114 43 150 178 262 212 51 148 156 99 1228 94 177
But is the extent of tlie dropping out of school correctly stated? The matter is so important that no pains should be spared to arrive, if possible, at the exact truth. We therefore reproduce here the table upon which Dr Draper’s conclusion was based.2
The recent article in The Psychological Clinic on “Some Factors affecting Grade Distribution,” by Mr. Leonard P. Ayres,3 gives us some important clues for the interpretation of this table. Mr. Ayres pointed out three important factors in producing grade inequalities; two of them, retardation and the population factor, exerting their influence by increasing the lower grades as compared with the higher, while the third, elimination, shows its force in thinning out the ranks of the higher grades.
In the foregoing table from Dr Draper’s report there is a distinct effort to take into account the population factor, since the grades compared are not those of the same year but of successive years. On the other hand, there is no consideration Avhatever of the important factor of retardation. It is manifestly assumed that the children found in the first grade all entered school in that year, since this first grade figure is taken as a basis wherewith to compare the higher grades in subsequent years. This is obviously incorrect. There is no grade in which the proportion of children left over from the preceding year is so large as the first. If there were no direct evidence of this fact, there would still be the strongest kind of presumptive evidence in the table which we are now considering. Take, for instance, the city of Rochester. For 100 pupils in the first grade there are reported 56.9 pupils in the second. According to the reading which is given to this table, this would mean that 43.1 per cent of the children left in the first year’s schooling. Now, is there anyone rash enough to affirm that there is any American city anywhere in the United States which is able to hold no more than 56.9 per cent of its pupils until they reach the second grade ?
But there is no lack of direct evidence that the first grade is unduly swelled by those who are left behind from the preceding year and is far from being a true criterion of the number of children entering school for the first time. Indeed, the evidence is so abundant that a few characteristic figures only can be cited. Before doing this, however, it might be well to remark that while upper grades receive newcomers almost exclusively by promotion ‘Report, 1908, p. 580. ?Vol. II, No. 5. from lower grades, the first grade receives its recruits from those who have never attended school before. While promotions occur at stated intervals, new admissions are occurring constantly throughout the year. Hence at the end of the year there is in the first grade a much larger proportion than in the upper grades of those who have been in school a portion of the year only and cannot rightly anticipate promotion. This would in part account for the fact that the proportion of children repeating the grade is so much greater than in the higher grades.
A few ascertained facts may, however, be cited in proof of this proposition. Some pertinent information is found in the statistics of promotions, which show that advance is less frequent in the first than in the upper grades. Thus in Philadelphia in June, 1908, the children promoted from the first grade were 78.2 per cent of all children in that grade, but those promoted from all the other grades were 83.1 per cent of all the children. Again, in Somerville, Mass., the school report shows as many as 16.6 per cent left behind in the first grade against only 9.2 per cent left behind in all other grades. In the same city there were in the first grade in 1907, 1210 children who had never been in school before, but the whole number of children in the first grade was 1532. Similar figures are reported from Reading, Pa., where the number of beginners enrolled in 1905-06 was 1434, but the number of children in the first grade was 1915.
It follows clearly from the foregoing that in the table cited from the ISTew York report the divisors are too large and the quotients are too small. The number of children entering school is less than the number registered in the first grade, and hence the proportion remaining in school until the higher grades is larger than the percentages recorded in the table.
The findings of Dr Draper have been instanced because they illustrate with such unmistakable clearness one of the important elements in the problem of elimination. These results, which were after all somewhat incidental to a forceful plea for vocational training, a plea which is one of the most convincing documents which has been issued in that now popular cause, did not evoke the storm of criticism and the murmurs of discontent which greeted the publication by the United States Bureau of Education of a bulletin on “Elimination of Pupils from School,” by Prof. E. L. Thorndike, of the Teachers’ College of New York City. If the general results of the inquiry stated with admirable terseness by Dr Thorndike in his introduction were caviar to the genELIMINATION OF PUPILS. 259 eral public, the particular results stated in the text were wormwood and gall to the school superintendents of those cities whose systems appeared in an unfavorable light. We must again distinguish between tlie fact disclosed and the measurement of it. The fact deserves all emphasis, and if public opinion can be jolted into activity only by rude shocks perhaps one should not quarrel with the method. Whatever good might be accomplished by hard hitting has probably been secured, and now that nearly a year has elapsed there can be no harm in a dispassionate effort to discover, if possible, whether Dr Thorndike’s indictment (for such it seems to be) of our public school system is in every respect just. Is the picture which is painted correct or is it overdrawn ? Is the light given full play or are the shadows too deep ?
It is, I am prone to confess, not without misgiving that I undertake such an inquiry. I am led into it not so much by an assurance of my own powers, as by the conviction that Dr Thorndike’s study touches upon one of the most vital problems of our school administration, that furthermore there are many who cannot accept his conclusion, and that this non-concurrence should find a voice. The difficulty of the undertaking is enhanced by the singularly elusive character of the argument, and by the very unusual structure of the document, which defies all laws of logical arrangement, as that is generally understood, and thus furnishes innumerable opportunities for hiding away important truths in unexpected places.
The main results of Dr Thorndike’s calculations are certain estimates of the number of pupils entering school who remain in school till they reach certain grades. They are here reproduced so far as the elementary grades are concerned in two sections? “A” and “B”. The cities named in the latter group have not, according to the author, been subjected to the same minute analysis as those in Group “A,” but the results given are believed by him to be substantially accurate.
Retention op Pupils in Elementary Grades According to Dr Thorndike’s Calculations PERCENTAGE OF PUPILS ENTERING WHO REACH THE FOURTH AND SUBSEQUENT GRADES Cities Group A. (p. 15) Baltimore Boston Cambridge Chicago Cleveland Denver Jersey City Kansas City, Mo Los Angeles Maiden Minneapolis Newport Newark New Haven New York Paterson St. Louis (white) Springfield, Mass Trenton Washington (white).. Water bury Wilmington Worcester Group B. (p. 47) Fourth Grade 71.0 85.0 90.3 86.3 97.2 98 75.9 96.5 95.4 86.7 85.7 91.7 78 85 90 86.4 94 99 86.6 93.4 84 90.6 99 100 99 85 96 100 86 Buffalo Chelsea Cincinnati Dayton Medford Milwaukee New Orleans Philadelphia Portland, Me Salt Lake City Springfield, O [ 100 Syracuse, N. Y 93 Fifth Grade 53.0 80.5 82.0 85.2 79.6 86 65.5 75.3 95 85.4 69.7 85.6 58.3 76 77 71.8 63 82.4 73.2 86.9 81 81.1 94 93 87 69 84 93 76 90 i 66 71 I 56 96 90 82 82 92 80 Sixth Grade 32.0 76.3 62.9 62.3 61.9 78 50.6 62.4 80 79.8 57.1 71.4 45.8 68 58 52.4 35 78 57.3 70.6 64 73.8 94 78 84 55 66 89 62 45 38 71 68 76 66 Seventh Grade 22.0 65.8 57.8 49.2 45.3 57 35.6 49.4 61.5 65.9 45.7 58.1 33.3 57 43 32 27 66.2 48 57.5 54 Eighth Grade 14.4 52.2 55.7 35 33.1 44 26.4 45.1 62.4 32 53 25 35 37.7 19.4 21 53.4 30.6 52.1 43 51.6 I 39 72 ! 72 65 68 38 53 83 48 31 26 60 53 52 50 25 38 69 34 20 18 47 44 60 1 46 53 I 43 Ninth Grade 47.0 41.9 54 44.9 38.5 58 40 60
The most striking impression which we gain from this table is that so few children reach the upper grades of the elementary schools. Fixing our attention on the eighth grade, we find that by the best record?Worcester, Mass.?only 72 per cent reach the eighth grade, and that by the worst?Baltimore?the proportion dwindles to an insignificant 14.4 per cent. But this is not all. If we examine the table closely we are disconcerted to find that in some cities a relatively large proportion leave school before reaching even the fourth grade, that is, in the first three grades. In Philadelphia and Baltimore we are told that this is as much as 29 per cent of the pupils, in Boston 15 per cent, while in other towns no children whatever are alleged to leave school at this early age.
It may be well to systematize these first impressions. Let us examine first the number who are said to leave school before reaching the third grade. For convenience of study the cities may be arranged in groups according to the percentage supposed to be eliminated at this very early stage of school work. Loss of Pupils in Grades 1, 2 and 3 According to Dr Thorndike’s Calculations
PERCENTAGE OF PUPILS ENTERING ANNUALLY Group 1 0.0?4.99 per cent Group 2 5.00?9.99 per cent Group 3 10.?14.99 per cent Group 4 15?19.99 per cent Buffalo 0.0 Medford 0.0 Springfield, O., 0.0 Chelsea 1.0 Springfield, Mass 1.0 Worcester 1.0 Denver 2.0 Cleveland 2.8 Kansas City,Mo3.5 Dayton 4.0 Portland, Me.. .4.0 Los Angeles… .4.6 St. Louis* 6.0 Washington*. ..6.6 Syracuse 7.0 Newport 8.3 Wilmington… .9.4 Cambridge 9.7 New Orleans…10.0 New York… .10.0 Salt LakeCity .10.0 Maiden 13.3 Trenton 13.4 Paterson 13.6 Chicago 13.7 Milwaukee…. 14.0 Minneapolis. ..14.6 Boston 15.0 Cincinnati.… 15.0 New Haven …15.0 Waterbury 16.0 Group 5 20.0?24.99 per cent Newark 22.0 Jersey City.. .24.9 Group 6 25 per cent and over Baltimore…. 29.0 Philadelphia.. 29.0 * White.
This table gives some startling surprises.. In at least eight towns we are told that fifteen per cent or more of the children entering school leave before they reach the fourth grade, and we are naturally surprised to find among them Boston and Is ew Haven. It is not so much the record of any individual city which excites surprise and wonderment as the comparison between them. Does it seem probable, on the face of it, that Boston loses fifteen children out of every hundred and that Worcester, Springfield, and the neighboring city of Chelsea lose only one, while Medford loses none at all ? Is it at all likely that ISTew York loses ten children Loss of Pupils in Grades 1 to 7, According to Dr Thorndike’s Calculations PERCENTAGE OF PUPILS ENTERING ANNUALLY Less than 40 per cent 40?44.99 45?49.99 50?54.99 55?59.99 Worcester 28.0 Medford 31.0 Maiden 37.6 Cambridge 44.3 Springfield, Mass 46.6 Newport 47.0 Boston 47.8 Washington 47.9 Buffalo 48.0 Chelsea 50.0 Portland, Me 53.0 Springfield, 0 54.0 Los Angeles 54.9 Denver 56.0 Salt Lake City 56.0 Syracuse 57.0 Water bury 57.0 60?64.99 65?69.99 70?74.99 75?79.S 80 and over Wilmington 61.0 Dayton 62.0 Chicago 65 0 New Haven 65.0 Milwaukee 66.0 New York 66.3 Cleveland 66.9 Minneapolis 68.0 Trenton 69.4 Jersey City 73.6 Cincinnati 75.0 Newark 75.0 St. Louis 79.0 New Orleans 80.0 Paterson 80.6 Philadelphia 82.0 Baltimore 85.6
in every hundred who enter and that Jersey City loses practically twenty-five and Buffalo loses none whatsoever ? Is it reasonable to suppose that fifteen out of every hundred drop out in Cincinnati, while in other Ohio cities four disappear in Dayton, three in Cleveland and none at all in Springfield? Would anyone anticipate, again, that in Minneapolis fourteen children would drop out in the first three grades in every hundred, while only three drop out in Kansas City ? Or, turning again to Massachusetts, would anyone have expected to find the school conditions in Maiden so inferior to those in Medford or Chelsea ? Just as we arranged the cities in the order of early elimination to clarify our impressions, we shall find a like procedure useful with respect to those who drop out before the eighth grade. This is shown in the table on the preceding page.
If these results are accurate, Worcester stands at the head of the list, having lost only 28 pupils out of a hundred. Other Massachusetts cities follow. Boston is well up towards the head of the list, but observe again the comparison with Chelsea: lost in grades 1-3, Boston 15, Chelsea 1; lost in grades 4-7, Boston 32, Chelsea 49. Few of the large cities make a very good showing, and it is certainly strange that while Boston and Buffalo lose less than half their children, Chicago, Cleveland, New York and other cities lose two-thirds, St. Louis and Cincinnati three-quarters and Philadelphia and Baltimore as much as four-fifths.
Turning b?ck for a moment to the main table, I would call attention to the very peculiar process of elimination imputed to Worcester, Mass. Here five pupils leave in the fourth grade, none in the fifth. Twenty-two are said to leave in the sixth grade, but none whatever in the seventh. If this be true, it is positively unique in school experience. Our questioning of these figures almost instinctively turns to distrust, and this is heightened by observing Cambridge in the list of cities. As is well known, Cambidge has in its gram|mar grades (above the third) a double system of classification?an A, B, C and D series of classes for those who finish in four years, and a 4, 5, 6, 7, 8 and 9 series for those who finish in six years. To transmute this double series into a single one is a task which might well give the statistician pause, but our author is not daunted by such an obstacle. How was the feat accomplished ? I cite from page 38 of Dr Thorndike’s Bulletin the figures given by him for 1901 for the grades in Cambridge and compare them with those given in the school report of that city for the year 1901-02. The figures relate to December, 1901:
GRADES IN CAMBRIDGE, MASS. Tliorndike Report. Grades Grades Grades 4 1,691 4 1,382 A 309 5 1,467 5 1,213 B 254 6 1,082 6 1,082 C 139 7 1,027 7 1,027 D 90 8 910 8 771 9 677 9 587
Now, it will be observed that the students in the lettered grades have been so accredited to the numbered grades that grades 4 and 5, and 8 and 9 have been increased, but not grades 6 and 7. Is it not a wonderful assumption that none of the pupils in the A and D groups should be at the same stage of advancement as those in the 6th and 7th grades of the numbered series ? In other words, the handling of this problem is wholly arbitrary and indubitably wrong. Is it then any wonder that we should be distrustful of results obtained from processes which permit such a palpable mishandling of the figures ?
Those who have had the patience to read thus far may be prone to ask why all this pother about results ? If not satisfied with them, why not test their accuracy ? Why not examine whether the original data are correct, whether the method of treatment is correct and whether it has been properly applied $ This is indeed just what we would be glad to do if it were possible. But the author has not disclosed his method, unless the following quotation be deemed an adequate explanation: “My own estimates for twenty-three cities have been given in Table 1 (page 15). These estimates involve the use of the facts of the school grade populations given in Table 9 corrected, (1) by data concerning the death rate during the school age; (2) by data concerning the growth of the cities; (3) by data concerning the school grade populations of successive years (that is by comparison of, say, the second grade population of 1898 with the third grade population of 1899, the fourth grade population of 1900, etc.); (4) by data concerning the relation between the first, second and third grade populations and the number entering school in a year; and (5) by data concerning the intermigration of city and country children of school age. It would be unprofitable to anyone except the critical student of statistical problems for me to rehearse the details of this tedious process of corrections. ‘x’ * * “The hardest correction to make intelligently is that for the inequality of the different grades in length. Some systems apparently
keep pupils nearly twice as long in the first grade as in the third. (It would of course be absurd to suppose that the great drop in grade populations from grade 1 to grade 2 is due to actual elimination from school.) The number of pupils entering school is in many cases less than the number in the first grade, and even less than one-third of the number in grades 1, 2, and 3.
“Moreover, we have no assurance that the later grades are equal in respect to the proportion of pupils who take more than a year to complete them, though the differences are here probably small, and may be neglected fo r the purposes of this study. The main difficulty is in inferring from the number in grades 1, 2, and 3 the number beginning school in the course of a year.
“My correction for this is arbitrary. I have simply made the estimate of the number of pupils beginning school for any city which seemed most likely in view of the comparative sizes of the populations of grades 1, 2, 3, 4, and 5, and of whatever other relevant information I possessed concerning the city.
“Tor instance, in Baltimore, where the grade populations are as follows : Population. Population.
First grade 54,097 Fourth grade 25,373 Second grade 35,328 Fifth grade 18,921 Third grade 29,284 and the j?f ~ P_us ?gUres 39,570, I have, in view of the other O known facts about the city, taken the population of grade 2 as a measure of the number of pupils beginning school. In Denver, New Haven, St. Louis, Waterbury, and Worcester, I have judged that +1^ ^ ? ^US _ 3 figure was a correct representative of the number of pupils beginning school annually. In Trenton, where the first grade population is over twice the second in size, but the third practically equal to the second (the populations being respectively 7361, 3348, 3320, and 2985) I have taken a figure about 3 per cent larger than the second grade population as the correct representative of the number of pupils beginning school.”
I11 another place he says (p. 13) : “Also the number of children entering school is not given, but has to be inferred from the number in the first, second and third grades.” There is thus cumulative evidence that the author gives great weight, though not exclusive weight, to the average of the first three grades as an approximation of the number of children entering school each year. If lie has done so, and if it can be proven that the average of the first three grades is generally larger than the number of children entering school, then obviously the basis of his calculations is wrong. As he uses this as a divisor to get his first raw material (p. 42), it is clear that as his divisor is too large, his quotients, which show the percentage of retention, must be too small. There may be an elaborate system of “corrections” too recondite for the ordinary mind to grasp, but we cannot accept the validity of the results of an undisclosed system of “corrections” when there is a strong presumption of an underlying logical mistake in the material worked upon.
Let us consider the concrete instance cited. In the case of Baltimore he gives us the “grade populations.” It may be incidentally remarked that the figures cited are not for any particular year, but the sum of the three years?1898, 1899 and 1902. The average can be obtained by dividing by three, as follows: First grade 18,032 Second grade 11,776 Third grade 9,761 Fourth grade :… . 8,458 Fifth grade 6,307 This is a more appropriate series from which to deduce the number of children who annually enter school. Dr Thorndike takes the population of the second grade, 11,776, as a measure of those who enter. Is this measure correct % In answering this question I should like first to establish an important principle; namely, that the number of children entering school is approximately equal to the generation entering upon the school age. A generation is here used in the statistical sense of the persons born in a given year. The children who at any time are ten years old form a generation, those nine years old another and those eight years old a third. Now, should all children enter school at exactly the age of eight, as the compulsory laws in most of our states require, it is plain that the number who enter must in each year equal the number who become eight years old in that year. But if all do not enter at eight years, some coming at seven and others waiting till nine years of age, it is equally true that the number entering on a series of years cannot on the average exceed the number who on the average become eight years of age. ISTor need we assume that all the children enter school, or, perhaps better, that all the children enter public school. It still remains true that the number of children who are respecELIMINATION OF PUPILS. 267 tively eight, nine and ten years old (minus a few who have died) are the best indication which we possess of the number of children who enter school annually. Suppose you have a city in which the ages of children in the public school run as follows (Chicago, 1900) :
7 years 32,423 8 years 29,805 9 years 28,25G 10 years 27,091 11 years 25,042 12 years 24,062
As it is generally conceded that there is practically no elimination before thirteen years of age, these figures represent successive generations of school children. Whether these children first went to school at six or seven, the number entering in any given year must have been approximately the equivalent of the appropriate generation.
Let us now turn back to the case of Baltimore, where Dr. Thorndike opines that the number entering school annually can be estimated as 11,776. His pamphlet on page 52 records the ages of children in Baltimore schools for the years 1897, 1898 and 1901. Averaging these series, I calculate the age groups as follows: 6 years 6,217 7 years 7,137 8 years 7,551 9 years 7,730 10 years 7,793 11 years 7,193 12 years 6,554
Now, it would seem clear that the number of children entering school could hardly be 11,776. It might be about 8,000, and, then, if as previously stated, there were about 8,000 in the fourth grade (exact figures cannot be cited because the years do not coincide) it is somewhat difficult to imagine that 29 children out of 100 dropped out of school before they reached the fourth grade. In Denver, again, Dr Thorndike conceives the average of the first three grades to be a correct measure of the number of children entering school. Again, we have figures in his pamphlet for-both the grades and the ages, but they are not for the same years. However, the year 1901 is common to both. In this year the average of the first three grades is 190G, but the largest generation represented in the school is, at the age of nine, only 1403. In the other cases in which Dr Thorndike admits that he has taken the average of the first three grades as his starting point,?New Haven, St. Louis, Waterbury and Worcester,?no ages are given by which we can make this useful comparison.
In the other cities where the methods are not disclosed and where the comparison can be made, I give from his pamphlet the average of the first three grades and the largest generation in the same years.
CityBoston Chicago Cleveland Jersey City Kansas City, Mo. Los Angeles Minneapolis Newark Springfield, Mass. Year 1897 1900 1901 1899 1900 1900 1898 1903 1900 Average of First Three Grades 9229 38174 9804 4768 4675 2991 6237 6023’ 1359 Largest Generation 6807 39716 * 8753 3971 2938 2125 4639 4873 924
Of course, it will be understood that the foregoing table signifies only that if in the case of these cities Dr Thorndike relied largely upon the average of the first three grades (and we have merely presumptive evidence that he did so), then again his divisors were too high and his resulting retention was too low.
While I was thoroughly convinced that these general considerations demonstrated the probable error involved in Dr Tliomdike’s estimate of the number of the pupils entering school annually, an effort was made to test the argument by an appeal to the records. In the case of Reading, Pa., not included in Dr Thorn*1 cite the figures given in the pamphlet for the age six years. They agree with those given in the Chicago report, but I have some misgivings as to their accuracy. In 1897-8 ages are given as under seven, and there are 39,942 in the group. In 1899-1900, we find under six 9472, six 39,345, or under siven 49,817. In 1900-01 we find under six 9828, six 39,716, the figure quoted above, or under seven 49,544. On the other hand, in 1905-06 we find under six 20,308, six 32,312, or a total under seven of 52,620. It will be noted that there are now fewer children of six years than in 1900-01, which is highly improbable, and suggests that in the latter year the numbers are incorrectly counted.
dike’s calculations, the number of beginners in 1905-06 was reported as 1434, while 1, 2, 3 were respectively 1915, 1694, and 1719. In Somerville, Mass., again, the report for 1907 gives the number of children who were never in school before as 1210, while the number in grades 1, 2, and 3 were 1532, 1384, and 1375 respectively. In both cases it will be noted that the number of beginners is smaller than any of the first three grades. It seemed possible, that although not printed, the number of pupils entering school might be a matter of record in other places, and letters were accordingly written to the superintendents of schools in the twenty-three cities of group A, to ascertain whether such was the case. In a number of instances the superintendents failed to grasp the distinction between the numbers in the first grade and the number entering, and sent me the grade statistics. Quite a number wrote, recognizing the importance of the “number of beginners” and regretting that their reports did not contain the information. Superintendents Elson in Cleveland and Van Sickle in Baltimore stated their intention of making this distinction in the future. In [Newport, E. I., a record is kept of the entering pupils. In the year 1907-08 there were admitted 193 new pupils to the kindergarten and 166 to the first grade. The new pupils admitted were, therefore, 349 in number. In the same year the enrolment in the first grade was 541 pupils. Of these, 155 were new pupils, and the remainder were either promoted from the kindergarten, or left over from the previous year. As there were 196 pupils in the kindergarten at the end of 1906-07, we cannot estimate at more than 200 those promoted to the first grade. We have then as the probable number in the first grade about 350 pupils. For the year the enrolment in this grade was, as we have seen, 541, and in the second and third grades 430 and 391 respectively. Or if it be more appropriate to compare this estimate of 355 new pupils in the first grade with the grades as they existed at the end of the year, the corresponding figures for grades 1, 2 and 3 were 440, 388, and 358 respectively. In either case the estimated new entries are less in number than the population of any of the first three grades.
It may also be noted that the material on which Dr Thorndike’s study is based is not always strictly comparable. Thus in Baltimore the figures include both white and colored pupils, but in Washington and St. Louis only white pupils. It is not unlikely that this has an unfavorable effect on the calculated grade reten270 THE PSYCHOLOGICAL CLINIC. tions in Baltimore, but we are not told of any allowance being made.
Again, in a number of cities the grade statistics are based on total registrations, as in Cleveland, Kansas City, and Los Angeles, while in others, as in Springfield and Waterbury, the September enrolment is used. Different methods give different results. In Newport, R. I., in 1907, I find the following figures: Grades Total Average belonging Registration at end of year
1 541 440 2 340 388 3 391 358 4 405 372 5 365 338 6 356 323 7 310 280 8 236 219 9 177 167
Now, if we make a comparison, and adopt the method sometimes used by Dr Thorndike of dividing the fourth and later grades by the average of the first three, we get the following: Grades in Newport, R. I. Percentages which the several 1 -f- 2 -f- 3 GRADES ARE OF ? ‘ Grades Total Average belonging Enrolment at end of year 4 89.2 94.4 5 80.4 85.6 6 78.4 81.8 7 68.3 70.9 8 52.0 55.4 9 39.0 42.3
Without entering into the reasons, this one illustration shows that figures based on a single day in the year would always give more favorable results in estimating retentions than those which are based upon a total registration. So far as appears in the text, Dr Thorndike has not given this phase of the matter any consideration.
If, by the foregoing analysis, we have demonstrated that in certain cases the starting point of Dr Thorndike’s calculation was erroneous, and have established a strong probability that in all other cases it was also erroneous, though not perhaps in a like degree, it would seem quite unnecessary to examine the application of the method. It might, however, be urged that, assuming an initial error, such error was in large part compensated by the system of “corrections” mentioned in the paragraph which has been cited from Dr Thorndike’s monograph. We are not, it is true, told how these corrections have been made, but we can form some estimate of their extent by comparing Dr Thorndike’s final results with the preliminary results obtained from ithe grade populations in the few cases in which he definitely tells us how Percentage of Retention of the Children who Enter School COMPARISON OF FINAL AND PRELIMINARY RESULTS OF DR. THORNDIKE’S CALCULATIONS
Cities Fourth Grade Fifth Grade Sixth Grade Seventh Grade 1 Eighth Grade Ninth Grade Baltimore. Final Preliminary. Difference… Denver. Final Preliminary. Difference… New Haven. Final Preliminary. Difference.. St. Louis (white). Final Preliminary Difference Trenton. Final Preliminary. Difference.. Waterbury. Final Preliminary. Difference.. Worcester. Final Preliminary. Difference.. 71.0 71.8 ?0.8 98.0 93.0 + 5.0 85.0 85.5 ?0.5 94.0 95.5 ?1.5 86.6 86.6 0j 84.0 83.0 + 1.0 99.0 96.4 + 2.6 53.0 53.6 ?0.6 86.0 78.9 + 7.1 76.0 74.4 + 1.5 63.0 60.4 + 2.6 73.2 70.1 + 3.1 81.0 78.0 + 3.0 94.0 90.4 + 3.6 32.0 35.5 ?2.5 78.0 69.3 + 8.7 68.0 63.8 + 4.2 35.0 36.7 ?1.7 57.3 55.0 + 2.3 64.0 63.0 + 1.0 94.0 89.1 + 4.9 22.0 22.2 ?0.2 57.0 49.4 + 7.6 57.0 53.0 + 4.0 27.0 24.8 + 2.2 48.0 42.3 + 6.3 54.0 48.0 + 6.0 72.0 67.4 + 4.6 14.4 14.7 ?0.3 44.0 37.5 + 6.5 35.0 32.0 + 3.0 21.0 17.2 + 3.8 30.6 27.4 + 3.2 43.0 36.0 + 7.0 72.0 66.8 + 5.2 58.0 53.0 + 5.0
lie estimated the number of children entering school each year. The final results are taken from page 15 of his pamphlet, the preliminary results from page 42, except in the case of Baltimore and Trenton which have been calculated according to the indications given on page 46. An examination of the foregoing statement does not disclose any general tendency in these corrections. While the final results are generally higher than the preliminary results, it is not always so. In Baltimore the final results are uniformly lower than the preliminary, but the difference is so slight, occurring mainly in the decimals, that one involuntarily thinks of somewhat summary rounding-off processes. With trifling exceptions, the result of corrections in the other cases is to increase the preliminary figures. In the fourth grade the corrections are very small. In seven cities there is a net increase of 5.8 points, or an average increase of less than one point. In the eighth grade, on the other hand, the corrections show 27. G points increase, or an average of nearly four points. As the bases in the eighth grade are much lower than in the fourth the percentage increase would be relatively much more. * It will be noted that the maximum plus correction is 8.7 points and the maximum minus correction, 2.5 points, and that these maxima apply to the sixth grade. The maximum plus correction in points is generally found in the sixth grade or above. If we were to calculate it in per cent it would probably always be found in the eighth grade, while, on the other hand, it would be smallest in the fourth grade.
If we examine the nature of these corrections we find them reducible to what may be termed the population factor. They relate to the changes in the school population brought about (a) by death, (b) by natural increase of population, (c) by migration. For the purposes of the study of elimination in schools the third element is a negligible quantity. The persons who flock to our cities and disturb the natural age distribution of the population are not persons of the school age. Some few, perhaps, come from country villages and towns and slightly increase the numbers in the high schools, but in the elementary schools this consideration has very little weight. The main fact, as stated with admirable clearness in Mr. Ayres’s paper on the “Factors affecting Grade Distribution,” is, in general terms, that at any given time the pupils of the eighth grade are survivors of classes entering schools at least eight years ago, while pupils of the fourth grade are survivors of those who entered at least four years ago, and that in a growing population each generation is larger than that which preceded it. While we have exact knowledge of the effects of applying the corrections in a few cases only, the general result is about what was to be anticipated: namely, to enhance the relative numbers of the eighth grade in a comparison with former entering classes, over what they would be in comparison with present entering classes.
It is clear then that the system of corrections does not relieve the situation, which, briefly, seems to be this: Present grades are compared with assumed present entering classes. These results are so corrected that higher grades are compared with corresponding former entering classes. But present entering classes are, in demonstrated cases, estimated at too high a figure. Hence, the resulting relative figures are too low throughout before the correction is applied. The correction affects the relative position of one member of the series to another, but does not materially affect the position of the series as a whole to unity, that is, its general level. The fundamental error in Dr Thorndike’s calculations seems to lie in an undue emphasis on the numbers found in the first, second, and third grades. The statement that the number of children entering school “has to be inferred from the number in the first, second, and third grades” points to this undue emphasis. He is, however, aware of the existence of the retardation factor. Tie says, “It would of course be absurd to suppose that the great drop in grade populations from grade 1 to grade 2 is due to actual elimination from school. The number of pupils entering school is in many cases less than the number in the first grade, and even less than one-third of the number in grades 1, 2 and 3.” He knows, in short, the existence of the retardation factor, but it is extremely dubious whether he realizes its full import. In view of the fact that the critical literature is almost entirely a product of the last year and a half, it is perhaps not to be wondered at that the full significance of the retardation factor should have escaped Dr Thorndike’s attention. In view of recent discussion, I think we can say Avith perfect truth that the number of children entering school each year will never be as great as the number of children in the first grade, that in all cases will it be “less than one-third of the number in grades 1, 2 and 3,” and that in almost every case it will be less than the number of children in either the second or the third grade.
The purpose of this article Avill have been accomplished if it has shown that, admirable as Dr Thorndike’s work is in many ways, there is still much to be done in the study of the problem of elimination. Striving to make this point clear it may have been necessary at times to adopt a tone of apparently hostile criticism in explaining points of difference. It would, however, be ungrateful not to acknowledge the value of Dr Thorndike’s work, for he has placed the educational world under great obligations in calling attention to this most important problem. Of the significance of the issue involved there can be no doubt. From a theoretical point of view it is of importance to test the links in his chain of reasoning and discover whether his analysis is correct both in principle and in its resulting measurements, but from a practical point of view it is perhaps more important that educators should go to work to strengthen the weak points in our educational system which he has brought clearly into light. The purpose of our article has been critical rather than constructive. It is the outgrowth of several months’ work which has been done under the auspices of the Russell Sage Foundation under the joint direction of Mr. Leonard P. Ay res and myself. Impressed as we were with the grave importance of the subjects of retardation and elimination, we undertook to collect from the school reports of one hundred of the principal cities of the United States during the past ten years all the data contained in such reports which in any way demonstrated the existence of retardation 01* helped to elucidate the problem. The material is well in hand and will soon go to the press.
The information obtained is more extensive and more valuable than we had anticipated. It is, however, most diverse as to form and manner of treatment and at a very early stage in the collection of material it became evident that the mere publication of statistical tables without an effort to interpret them would only be valuable to a relatively small number of persons thoroughly familiar with the subject and able to read the story which the figures tell.
The study of the figures has, we believe, thrown considerable light on the problem of retardation and its cognate problem of elimination. Speaking generally, while it must be admitted that the problem is one of infinite complexity, it would seem that in relation to elimination, grades and ages must be studied in closest possible relations. If children remain in school, almost without exception, until they are twelve years of age and with a loss of only about 10 per cent at thirteen years of age, it may indeed seem strange that so many leave school in the early grades. Dr. Thorndike is conscious of this anomaly and seeks to explain it.3 The explanation is excellent as far as it goes, but in the opinion of the writer it does not go far enough, and age elimination should be studied with far greater care than it has heretofore received.* The surface indications from our study of the reports mentioned and the data gathered from them are that a study of age elimination in connection with the grades will yield results which differ not a little from those obtained by Dr Thorndike. The relative position of different cities will probably be slightly modified, but the main result to be foreseen is that actual elimination, while still considerable, will undoubtedly prove less than Dr Thorndike has stated.
In conclusion I should like to emphasize the fact that the importance of the discussion lies in the subject itself rather than in the details of its treatment. If elimination is to be measured, it should be measured accurately. If, as we have sought to demonstrate, the measurements stated by Dr Thorndike are not wholly correct, it is our hope that someone will give us a measurement more” generally acceptable, which will be as convincing as the work of Dr Thorndike has been brilliant. That there should be differences of opinion, both as to measurement and as to causes in the first statement and discussion of the problem, is but natural. But these differences and their discussion should not arouse a mere delight in scientific controversy, but rather lead to a more intense interest in the subject itself and a keener realization of what every serious attempt to elucidate this important problem means as a contribution to the rational and conservative criticism of our educational system.
*In illustration of this point I would cite the case of Maiden, Mass. In Dr Thorndike’s monograph it is stated that 13.3 per cent of the children who enter school in that city never reach the fourth grade. The superintendent of schools, Mr. Henry E. Henly, claims that no children leave his schools before reaching the fourteenth birthday. He has furnished me the age and grade distribution of December 3, 1908, and his figures confirm this claim, since thirteen-year-old pupils are as numerous as twelve-year olds. In a total school population of 59S8 there are just nineteen pupils of thirteen years of age and upward in the first three grades. The maximum age class is 061 pupils. If each entering class were as large and lost as many as nineteen before reaching the fourth grade it would imply a loss of less than 3 per cent. It may be noted incidentally that repetition of the first grade is so frequent in Maiden, that this grade numbered on December 3, 1908, 1003 against 697 in the second grade.
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