Class Size and School Progress
- Author:
Philip A. Boyer,
Thomas Jefferson Public School, Philadelphia.
It is generally accepted that there are limits to the efficient educative contact between pupil and teacher. The number of pupils per teacher as set by the educational theorist varies from one to thirty or forty. In practice, classes of from fifteen to thirty are the rule in private schools where expense is not an all-important determining element. In public school systems where the budget must be pruned with care, regular classes range in size from forty to fifty, with by far the largest number of classes nearing fifty and with a few classes well above that figure. Do classes of this size permit of maximum efficiency in educational work? If not, how small should classes be in order to meet efficiency requirements? And, we must add, would the increased efficiency of smaller classes warrant the additional expenditure which their establishment would necessitate?
In order to discover the relation existing between the size of classes and school progress, an investigation was made of the promotion records for June, 1913, of the public schools of Philadelphia. In each of the city’s ten districts, the classes were divided according to size into six groups as follows: under 30, 30 to 34, 35 to 39, 40 to 44, 45 to 49, 50 and over. The percentage of promotion was then determined for each group. Individual classes showed the widest possible variations in promotion percentages, there being one class in which no promotions were made, and several in which 100 per cent were advanced. In general, however, the variation was limited to a range of twenty points from 75 to 95 per cent with the highest rates occurring most frequently in the upper grammar grades. In District No. 7, of the four hundred twelve regular classes, there are ten classes in Group I (under 30), twenty classes in Group II (30-34), and eighty classes in Group III (35-39). The number of classes with less than forty belonging (one hundred ten in all) is 27 per cent of the total number of classes in the district. The largest number of classes in any one group is found in Group IV (40 4) which has one hundred thirty-nine classes. Groups V and VI show one hundred four, and fifty-nine classes respectively. Reference to table I will show these groups and the percentage of the total number of classes which each constitutes.
TABLE I.?DISTRIBUTION OF CLASSES AMONG SIZE GROUPS?DISTRICT NO. 7. Groups I. ( -30). II. (30- 4). III. (35- 9). IV. (40- 4). V. (45- 9). VI. (50+). Total. Number of Classes in Each Group 10 20 80 139 104 59 412 Per Cent of Total Number of Classes 2.4 4.8 19.4 33.7 25.2 14.3 99.8
The ten classes of Group I are distributed among five grades and the percentages of promotion are higher than those of all other groups in three of these five grades, the 6th, 4th, and 1st. The twenty classes of Group II are distributed among seven grades and show highest promotion percentages in three of these grades, the 8th, 5th, and 3rd. The eighty classes of Group III represent all grades and show highest promotion percentages in two grades, the 7th and 2nd. Combining the three small groups, which, as we have seen, comprise 27 per cent of the total number of classes in the district, we find that in every one of the eight grades, the highest rate of promotion is secured in classes having less than forty on roll. That school progress, as indicated by promotion percentages, does not vary greatly save in exceptional instances, is indicated by table II, where percentages are given for each grade in each group. TABLE II.?PROMOTION PERCENTAGES IN EACH GRADE-GROUP?DISTRICT NO. 7. Groups I. ( -30) II. (30- 4) III. (35- 9) IV. (40- 4) V.(45- 9) VI. (50-f- ) Grades 88.3 90.3 84.5 89.8 89.0 86.5 85.7
83.4 66.7 96.4 76.4 78.2 81.7 81.9 81.7 62.5 87.9 82.5 83.2 80.4 80.5 87.0 70.7 84.4 81.2 82.8 79.7 94.1 85.0 82.5 81.4 77.3 81.8 82.9 82.5 77.8 82.0 90.8 70.9 73.9 81.9 74.9 73.7 Total Gram. 85.3 88.2 83.1 83.9 81.9 80.1 Total Primary 89.4 73.7 81.1 82.0 79.1 78.8 Total 87.4 79.5 81.9 82.8 79.9 79.1
Nevertheless, that minority of pupils fortunate enough to find themselves in small classes would seem to be the favored few. The complexity of the situation, the many diverse factors which enter into promotion, do not warrant us in expecting to find a regular and gradual decrease in promotion rates as classes increase in size. But table II shows some glaring irregularities, e. g. the lowest percentages in four grades, (8th, 6th, 4th, 1st), are found in the group next larger than the one showing the highest percentage. Again, in the fifth grade an exceptionally low percentage is shown in the smallest size group. This represents only one class, however, and is an illustration of the operation of other forces than class size. It is probable that in this small class were concentrated the “slow” fifth grade pupils of the school concerned in order that special attention might be afforded. That such irregularities are exceptional is indicated by the fact that on massing together the grammar classes, the highest percentage, 88.2, falls in Group II, even though Groups I, II, and III, have shown three lowest percentages. The same is true of primary classes which show two lowest percentages in Group II, while the highest percentage for total primary is found in Group I (89.4). In the total of all grades the highest percentage, 87.4, is found in the smallest group, and the other percentages vary less, as might be expected.
The irregularities of table II, together with the fact that a somewhat similar investigation pursued by Dr 0. P. Cornman,1 in District No. 6, in January 1909, showed very different results, led to the extension of this study to include the other nine districts of the city. Classes were distributed into six size groups, promotion percentages computed, and tables similar to table II constructed. In none of these nine districts were the highest percentages concentrated so overwhelmingly in the smallest size groups. Districts No. 1 and 5 each showed seven highest percentages in groups under forty; Districts Nos. 2, 4, and 10, each showed six grades having highest percentages in groups of classes under forty with two highest percentages in larger class groups. Districts Nos. 3 and 8 each had five highest percentages in groups under forty and three highest percentages in larger class groups. Hence, in these eight districts the great majority of highest percentages was in classes under forty, and it may be assumed that the greatest school progress was made in these smaller classes which constituted from 10 per cent (District 3) to 30 per cent (District 10) of the total number of classes in the district. Table III shows the number of classes in each district, the percentage of this number of classes which had less than forty on roll, and the number of the highest percentages found in Groups I, II, III (under forty) and in Groups IV, V, VI (over forty). i Cornman, O. P. Size of Classes and School Progress. The Psychological Clinic, Vol. III, p. 206. CLASS SIZE AND SCHOOL PROGRESS. 85 TABLE III.?PER CENT OF CLASSES UNDER 40 AND THE NUMBER OF HIGHEST PROMOTION PERCENTAGES BY DISTRICTS. District Number 1. 2. 34. 5. 678. 9. 10. Total. Total Number of Classes 258 352 453. 320 416 368* 412 346 367 310 3602 Per Cent of Classes in Groups I, II, III 20 18 10 20 29 24 27 25 22 30 22.4 No. of Highest Promotion Percentages in Groups I, II, III 7 6 5 6 7 4 8 5 3 6 57 No. of Highest Promotion Percentages in Groups IV, V, VI 23 f * Two schools omitted because of special conditions. t 6 of these are in Group VI) In District No. 6, where the highest rates are evenly divided, the four highest percentages found in the larger classes (Groups IV, V, and VI) are all in grammar grades. There are no grammar classes in Group I. The highest percentages are only very slightly in advance of the percentages shown in the smallest groups except in the sixth grade, where a specially low percentage is shown in Group II. In the four primary grades the highest rates are found in the three smallest groups. (Table IV.) TABLE IV.?PER CENT PROMOTED BY GRADE-GROUPS?DISTRICT NO. 6. Groups Grades I. -30 II. 30-4 III. 35-9 IV. 40-4 V. 45-9 VI. 50+ 91.8 84.0 88.3 89.7 93.3 90.9 88.4 91.6 82.6 79.8 64.5 86.2 79.9 86.3 85.5 86.0 85.3 83.8 86.2 83.6 75.4 88.7 85.1 87.2 84.4 89.0 73.8 80.0 76.8 85.9 75.0 62.0 90.8 83.8 85.5 85.7 80.7 89.2 87.1 67.0 65.3 77.1 68.7
District No. 9 is the only one having the greater number of highest percentages in groups of classes over forty. Examination of table V will show that of the five highest percentages in larger groups, four are found in Group IV (40-4) and only one in the very largest group (50 and over). Even this is not a bad showing when we remember that only 22 per cent of the total number of classes in the district are found in Groups I, II, III, and that these groups have three of the eight highest percentages.
Groups Grades I. -30. II. 30- 4. III. 35- 9. IV. 40- 4. V. 45- 9. VI. 50+ . 87.0 86.2 78.4 92.4 84.4 93.1 91.5 82.2 83.5 87.1 90.1 100.0 86.1 82.3 81.2 87.0 81.4 81.6 85.5 83.3 77.9 75.9 ‘81.3 85.2 84.8 77.2 87.4 89.3 82.4 86.7 81.9 81.8 78.2 76.9 83.8 87.0 84.5 81.6 80.0 72.7 71.4 83.1 76.9 77.4
Re-examination of table III will show that of the total number of classes considered (3602), only 22.4 per cent have less than forty pupils belonging. In these 808 favored classes there are fifty-seven instances of highest district promotion percentages, while the classes larger than forty, numbering 2794, had only twenty-three highest district percentages. That 22 per cent of the city’s regular classes secured 71 per cent of the total number of highest district promotion percentages is significant. That each one of the 22 per cent of the classes had less than forty pupils belonging, seems to indicate that the size of class is an important element in those factors which go to make for school progress. It will be remembered, however, that these same small classes (Groups I, II, III) also showed some of the lowest district promotion percentages. Even though these were shown to be exceptional cases, by the fact that their effect was almost imperceptible on percentages for total grammar, total primary, or grand total (table II); nevertheless, they succeed in weakening conviction to a certain extent.
The effects of extraordinary conditions are sometimes shown plainly in district percentage tables such as the three given above. For example, in one district the rate of promotion in first grade classes of Group I (under thirty) is .0 per cent. This is the record of one abnormally small class (twenty-three) where manifestly abnormal conditions prevailed. On the other hand it is conceivable that a large class, working under peculiarly good conditions, might show an exceptionally high percentage. Indeed, it has sometimes been the practice in large schools to segregate the brighter pupils of a given grade into a large class in order to permit of increased personal attention to the particular shortcomings of duller pupils in smaller classes. These irregularities sometimes loom large in district percentage tables, though their occurrence has not been general. However, by massing together the number belonging and the number promoted for each district grade group, percentages for the entire city have been computed. Here the influence on promotion of other factors will diminish to smaller proportions, and the relation of class size to promotions will be more definitely indicated. Examining first the distribution of classes into the various grade groups, we find that Group I (under thirty) contains the smallest number of classes in all grades except the eighth, and that Group II contains the next smaller number of classes in all grades except the eighth and seventh. Group I comprises seventy-three classes, and Group II, two hundred two classes. Group III (35-9) contains nearly twice as many classes as Groups I and II combined (i.e. 533). These three smaller groups total 808 classes, or 22.4 per cent of the entire number. Groups IV and V include slightly over one thousand each, and it is here (between forty and forty-nine belonging) that more than one-half (58.5 per cent) of the classes are congregated. Classes in Group VI (fifty and over) number 686, or 19 per cent of the total number. This is nearly as many as the number of classes with less than forty pupils, so that the following rough generalization may be made:?one-fifth of the classes have less than forty belonging, three-fifths have between forty and forty-nine, and one-fifth have fifty or more. (Table VI.) TABLE VI.?TOTAL NUMBER OF CLASSES IN EACH GRADE-GROUP. Groups Grades Totals Per cent of Total I. 30.. II. 30- 4.. III. 35- 9.. IV. 40- 4.. V. 45- 9.. VI. 50+ .. Totals. 25 50 48 47 26 6 202 7 30 55 91 62 21 266 4 15 63 127 102 53 364 5 21 43 109 169 101 448 26 95 171 155 541 6 15 70 168 199 109 567 6 14 75 150 ;i87 *146 i? 578 14 31 84 166 179 162 636 73 202 533 1029 1079 686 2.0 5.6 14.8 28.5 29.9 19.0 3602 99.
Turning now to the promotion rates of these various groups of classes (table VII), it will be seen that highest promotion percentages in the seventh, fifth, third, and first grades are found in those classes of the city which have less than thirty pupils belonging. There are but seventy-three such classes, forming only 2 per cent of the total number, yet highest promotion rates are shown in four of the eight grades. Group II shows one highest percentage, in the eighth grade, while in Group III are found the remaining three highest rates, i.e. in the sixth, fourth, and second grades. Combining the three smaller groups we find that the 808 classes under forty, which constitute but 22.4 per cent of the total number, show highest promotion percentages in all eight grades. It will be remembered that it was this same group of smaller classes that had fifty-seven of the eighty highest district percentages (table III).1
TABLE VII.?PER CENT OF PROMOTION IN TOTAL NUMBER OP CLASSES IN EACH GRADE GROUP. Groups Grades 1 Total Grammar Total Primary City Total I. -30 ? II. 30-34 . III. 35-39 . IV. 40-44 . V. 45-49 . VI. 50 + 89.2 91.0 88.2 88.7 90.2’ 88.1 95.8 89.5 88.1 87.3 87.3 84.8 83.2 82.4 85.1 83. G 82.8 83.7 86.3 86.0 84.4 83.8 83.6 81.2 83.0 79.4 93.1 83.9 83.6 82.8 85.8 81.6 84.8 81.6 81.9 80.4 72.6 83.9 84.1 84.0 83.9 82.4 80.8 77.7 76.4 78.3 78.3 74.1 89.8 88.5 86.6 85.1 84.4 82.5 80.7 79.9 84.6 85.5 81.9 79.3 85.6 84.9 85.4 85.4 82.7 80.1
Further examination of table VII will show that only in the seventh and fifth grades is there a gradual shrinkage of percentages as the classes grow larger in size, but this is not surprising in view of the unequal distribution of classes among the various size groups. Moreover, the lowest rates in the sixth, fourth, and second grades are located in groups smaller than those indicating highest percentages. But these apparently unwarranted stragglers are more than counterbalanced by the fact that in the remaining five grades, 1 Comparison of tables III and VI develops the following table of broad generalizations:
Class size-groups Under 40… 40 to 49…., 50 and over. Proportion of total number of classes 1/5 3/5 1/5 Proportion of total 80 highest district percentages 3/4 1/5 1/13 CLASS SIZE AND SCHOOL PROGRESS. 89 (eighth, seventh, fifth, third, and first) the lowest rates are shown in the largest size-group, i.e. fifty and over. On combining totals for the four grammar grades, a regular descent in promotion rate is shown, i.e. from 89.8 per cent in Group I to 82.5 per cent in Group VI (see column 9, table VII). Could we stop here, a fairly clear case for smaller classes might be established; but total primary rates seem to indicate that medium sized classes have the advantage. Groups III and IV show an average of 85 per cent while both smaller and larger groups hover around the same rate, 80 per cent. In the percentages of the grand total of elementary pupils, these advantages neutralize each other and approximately the same progress is indicated for all classes having less than fortyfive belonging. In each of these four groups the rate is very close to 85 per cent and the falling off in rates shown by larger classes is correspondingly more noticeable. These lower rates (82.7 per cent in Group V and 80.1 per cent in Group VI) are seen to be of no mean significance when it is recalled (table VI) that they are the promotion percentages of 48.9 per cent of the total number of classes in the city, and that these classes contain 55 per cent of the total number of elementary pupils.
The statistics would seem to indicate 85 per cent as a normal rate of progress. That this rate was not attained by more than half of the pupils in the system, is worthy of notice. The promotion rate of this majority of pupils in classes averaging fifty was 81 per cent. From the figures here presented, it seems reasonable to suppose that if these pupils had had the advantage of instruction in classes of forty-five or less, they, too, would have shown an average rate of progress of 85 per cent. In other words, four in every hundred of these 87,000 pupils repeated a term of school work (or did some drop out?) because of too great dissipation of the teacher’s energy. The cost to the city of this retardation at $13.00 per pupil per term, is over $45,000; the added expense to the home is great; but more important than both of these is the loss to the individual child in confidence in his own ability to achieve.
” Superintendent Elson of Cleveland has estimated that oneeighth of the money spent on education goes to pay for repetition, maladjustment, and failure to see the needs of school children.”1 The New York Committee on School Inquiry finds that, “Conditions favorable to a maximum rate of promotion have not been studied and provided for.” However, on a basis of confessedly inadequate statistical returns, the following observation is made:
1 Denison, Elsa. “Helping School Children,” N. Y., Harper, 1912, p. 300. “As promotions were made in the February-June term of 1911, oversize classes, i.e. classes having more than 50 pupils, contributed but slightly, if at all, to non-promotion, i.e. to congestion. This statement does not mean, however, that educational opportunity and achievement were as good in classes over fifty as in classes under fifty. We recommend that special investigations be made into the educational efficiency of classes of varying sizes, i.e. how much less efficient oversize classes are than smaller classes.”1 Scientific management has entered the educational field. The Courtis Tests in Arithmetic and the Hillegas Scale in Composition, when applied to the educational efficiency of classes of varying sizes, will probably show the effects of overcrowding with a far greater degree of accuracy than a study based solely on promotion rates, for these rates, it must be recognized, are often influenced by factors foreign to the individual pupil’s capacity. However, until such complex studies can be made, it would seem advisable to heed the following recommendation of the New York Committee to which this study lends its sanction: “In view of the slightly lower rate of promotion for oversize classes, but more particularly because of the acknowledged educational disadvantages of such classes, … and the prevailing practice in other cities, we recommend that all classes having more than fifty pupils should be reduced to classes of fortyfive pupils.”2 “?”School Efficiency; A Constructive Study,” by Paul H. Hanus, p. 31. 2 Ibid., p. 33.
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