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 No. Ill 
 
 Health, Education, Recreation 
 
 THE MONEY COST OF REPETITION 
 
 Versus 
 
 THE MONEY SAVING THROUGH 
 ACCELERATION 
 
 LEONARD P. AYRES, Ph.D. 
 
 :^in I ("i 
 
 Reprinted from 
 The American School Board Journal, January, 1912 
 
 BY the 
 
 Department of Child Hygiene 
 
 Russell Sage Foundation 
 
 400 Metropolitan Tower, New York City 
 
 1-12-16 
 
^ 
 
 1-0 3 '. 
 
 The Money Cost of Repetition 
 
 versus 
 
 The Money Saving Through Acceleration 
 
 After a campaign of education extending over many years 
 Congress, through its Food and Drugs Act, has compelled manu- 
 facturers of food and medicinal products to print on the labels 
 of the packages a list of the ingredients, with the quantity of 
 each. Recently, another campaign of education has been waged 
 by schoolmen to secure in the publication of school reports a 
 plain statement of the ingredients of the statistics put out 
 for popular consumption. The second campaign resembles the 
 first in that it grew out of the discovery that educational sta- 
 tistics, like food products, are frequently adulterated with 
 dangerous coloring matter that enhances their appearance but 
 detracts from their usefulness. 
 
 The present article is an attempt to identify and measure some 
 of the ingredients that are active elements in the data that tell 
 us how much American cities spend on public education, and what 
 they get for their money. It is based on the returns from a co- 
 operative investigation conducted in the spring of 191 1 by the 
 Division of Education of the Russell Sage Foundation and the 
 superintendents of schools of twenty-nine cities. 
 
 This investigation gathered the school histories of the 206,495 
 children enrolled in the eight elementary grades of these cities 
 at the close of the school year 1910-1911, and the resulting data 
 show, among other things, the number of years of schooling re- 
 quired by each of these children to reach the grade in which he 
 was at that time. These progress data throw light on some 
 phases of the relation between school expenditures and school 
 results. 
 
 Slow, Normal, and Rapid Progress 
 
 In many studies made in the past few years investigators of 
 
 school conditions have endeavored to compute the cost to the 
 
 school system of the repetition of grades by children who make 
 
 slow progress. The common method of these investigations 
 
 3 
 
has been to find the total cost of repetition by multiplying the 
 annual per capita cost by the number of children who were re- 
 peating grades. These studies were open to criticism because 
 in general they failed to take into account the fact that while 
 many children repeat grades, and thus involve increased ex- 
 penditure, there are also many children who make rapid progress 
 and thus counterbalance part of this added expense. 
 
 Now it is evident that if the number of years lost by slow chil- 
 dren in a school system were equalled by the number of years 
 gained by those making rapid progress, the money expenditure 
 would be just the same as though every child were regularly 
 promoted every year. Moreover, this gratifying condition would 
 indicate that the course of study and system of promotions were 
 so accurately adjusted to meet the needs and abilities of the 
 children that the average children progressed at the normal rate, 
 the slow ones required somewhat more time to do the work, and 
 an equal number of bright ones were able to do it in less than the 
 normal time. The data of the investigation under discussion 
 show how nearly the different school systems studied approach 
 this standard. 
 
 For example, the records show there were 2371 children in the 
 elementary grades of Amsterdam, New York, at the close of the 
 past school year. Their distribution by grades shows how many 
 years of schooling would have been taken by these children to 
 reach their school standings at that time if they had all uni- 
 formly made normal progress. The figures are as follows: — 
 
 NUMBER OF CHILDREN BY GRADES AND TOTAL NORMAL 
 YEARS OF SCHOOLING OF CHILDREN IN ELEMENTARY 
 GRADES, AMSTERDAM, NEW YORK, JUNE, 191 1 
 
 Grade 
 
 Number 
 
 
 School Years at 
 Normal Progress 
 
 
 Total Normal Years 
 OF Schooling 
 
 I 
 
 323 
 354 
 362 
 
 413 
 330 
 227 
 182 
 180 
 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 
 I 
 2 
 
 3 
 4 
 5 
 6 
 
 7 
 8 
 
 
 = 
 
 
 323 
 
 708 
 
 1086 
 
 2 
 
 ■5 
 
 4. 
 
 1652 
 1650 
 1362 
 1274 
 1440 
 
 C 
 
 6 
 
 7 
 
 8 
 
 
 Total 
 
 2371 
 
 
 
 
 
 
 9495 
 
5 
 
 Now, in point of fact these 2371 children had not made uni- 
 formly normal progress. Their actual progress records showed 
 the following: — 
 
 5 years slower than normal i 
 
 4 years slower than normal 3 
 
 3 years slower than normal 31 
 
 2 years slower than normal 135 
 
 I year slower than normal 321 
 
 Normal Progress 1 167 
 
 1 year faster than normal 675 
 
 2 years faster than normal 30 
 
 3 years faster than normal 6 
 
 4 years faster than normal i 
 
 6 years faster than normal i 
 
 A computation based on these figures shows that the children 
 who had made slow progress had lost a total of 701 years, while 
 the rapid ones had gained a total of 763 school years. This 
 makes Amsterdam's accounting for all the children in her ele- 
 mentary schools the following : — 
 
 Total normal years of schooling, all pupils 9.495 
 
 Debit: Years lost by slow pupils 701 
 
 10,196 
 
 Credit: Years gained by rapid pupils 763 
 
 Years actually required by all pupils 9.433 
 
 This accounting shows that the years actually required by 
 all the pupils in the Amsterdam schools to reach their present 
 standing was slightly less than the normal number of years. 
 In terms of percentage it was 99.3 per cent of normal. To put 
 this in another way, the taxpayers of Amsterdam have a right 
 to demand that their public schools shall carry each child through 
 as many progressive steps of the educational system as is com- 
 patible with covering each step thoroughly. They expect to 
 pay extra for each child who must do one unit of work twice, 
 and they expect to pay less for the education of the bright child 
 who completes the work in less than the normal time. In point 
 of fact, the rapid children a little more than counterbalance the 
 slow ones, with the result that the taxpayers actually pay ninety- 
 nine cents for each dollar's worth of school progress made by 
 her public school children. 
 
 But the situation in Amsterdam is almost unique. There 
 are few cities where the years lost by slow pupils are so nearly 
 
counterbalanced by those gained by the rapid ones. The fol- 
 lowing table shows the relation between years lost and years 
 gained in each of the twenty-nine cities : — 
 
 II. PUPILS IN THE ELEMENTARY GRADES, TOTAL NUMBER OF 
 YEARS LOST BY SLOW PUPILS, TOTAL NUMBER OF YEARS 
 GAINED BY RAPID PUPILS, AND RATIO OF YEARS LOST TO 
 YEARS GAINED, JUNE, 191 1 
 
 City 
 
 Amsterdam, N. Y 
 
 Bayonne, N. J 
 
 Canton, Ohio 
 
 Danbury, Conn 
 
 Danville, 111 
 
 East St. Louis, 111 
 
 Elizabeth, N. J 
 
 Elmira, N. Y 
 
 Hazleton, Penn 
 
 Indianapolis, Ind 
 
 Kenosha, Wis 
 
 Milwaukee, Wis 
 
 Montclair, N. J 
 
 Muskegon, Mich 
 
 New Orleans, La. White. . 
 
 New Rochelle, N. Y 
 
 Niagara Falls, N. Y 
 
 Passaic, N. J 
 
 Perth Amboy, N. J 
 
 Plainfield, N. J 
 
 Quincy, Mass 
 
 Racine, Wis 
 
 Reading, Penn 
 
 Rockford, 111 
 
 Schenectady, N. Y 
 
 Syracuse, N. Y 
 
 Topeka, Kansas 
 
 Trenton, N. J 
 
 Watertown, N. Y 
 
 Total 
 
 PuPrLS IN 
 
 Years 
 
 Years 
 
 Element- 
 
 Lost by 
 
 Gained 
 
 ary 
 
 Slow 
 
 BY Rapid 
 
 Grades 
 
 Pupils 
 
 Pupils 
 
 . 2,371 
 
 701 
 
 763 
 
 7.033 
 
 3,741 
 
 1,516 
 
 5.567 
 
 3,445 
 
 120 
 
 1.967 
 
 761 
 
 467 
 
 2,260 
 
 1,197 
 
 164 
 
 5.380 
 
 2,883 
 
 933 
 
 7.058 
 
 3,777 
 
 987 
 
 2,487 
 
 1,383 
 
 314 
 
 2,655 
 
 1,577 
 
 77 
 
 23.874 
 
 7,721 
 
 5.261 
 
 2,223 
 
 1,265 
 
 174 
 
 32,251 
 
 9.115 
 
 6,019 
 
 2,568 
 
 1,880 
 
 277 
 
 3.163 
 
 1.419 
 
 447 
 
 23.664 
 
 11,714 
 
 3.638 
 
 3.641 
 
 1,804 
 
 880 
 
 3.244 
 
 1,506 
 
 195 
 
 5.541 
 
 3.200 
 
 895 
 
 3.947 
 
 2,878 
 
 639 
 
 2,312 
 
 1.253 
 
 171 
 
 4.540 
 
 2,705 
 
 190 
 
 4.075 
 
 1,496 
 
 138 
 
 10,585 
 
 7,860 
 
 683 
 
 5,649 
 
 2,156 
 
 963 
 
 7.846 
 
 4,002 
 
 867 
 
 13,610 
 
 7,118 
 
 1. 177 
 
 4.894 
 
 1,913 
 
 627 
 
 8,787 
 
 5.507 
 
 789 
 
 3.303 
 
 2,023 
 
 392 
 
 206,495 
 
 98,000 
 
 29,763 
 
 Ratio or Years 
 Lost to Gained 
 
 0.9 to I 
 
 2.5 to I 
 
 28.7 to I 
 
 1.6 to I 
 
 7.3 to I 
 
 3.1 to I 
 3.8 to I 
 
 4.4 to I 
 20.5 to I 
 
 1-5 to I 
 7.3 to I 
 
 1.5 to I 
 8.3 to I 
 
 3.2 to I 
 
 3.2 to I 
 
 2.1 to I 
 
 7.7 to I 
 
 3.6 to I 
 4-5 to I 
 
 7.3 to I 
 14.2 to I 
 
 10.8 to I 
 II. 5 to I 
 
 2.2 to I 
 4.6 to I 
 6.0 to I 
 3.0 to I 
 7.0 to I 
 5-2 to I 
 
 Average, 6.5 to i 
 
 A glance at the figures in the right-hand column shows that 
 conditions vary so greatly in these school systems that the 
 proportion between years lost and years gained ranges from 
 virtual equality in such cities as Amsterdam, Milwaukee, and 
 Indianapolis to extreme inequality in cities where the number of 
 years lost is from twenty to thirty times as great as the number 
 
of years gained. In the average city the ratio is six and one-half 
 years lost by slow progress for every year gained through rapid 
 progress. No clearer demonstration could be made of the very 
 significant fact that in American school systems in general 
 the course of study and schemes of promotion are adjusted to 
 meet the needs and abilities of the brighter and stronger child 
 rather than those of the average child. 
 
 Time is Money 
 
 This condition has a direct relation to our figures for school 
 expenditure, for if these figures are to serve a truly useful end 
 they must evaluate endeavor, not merely by bulk, but in terms 
 of results. They must contain some expression of what we get 
 for our money. It is not enough to know that the annual per 
 capita cost for the child is $30 unless we know something definite, 
 of what we purchase for that sum. 
 
 This new element will be added when we change our unit of 
 inquiry in reckoning per capita cost. At present the unit of 
 inquiry is the average expenditure for each child in the school 
 system. That is to say, the figure tells us how much it costs 
 to keep a child sitting at a desk for one school year. The unit 
 of inquiry which will give us much more significant information 
 is the one which will tell how much it costs, on the average, to 
 enable the child to take one step forward on his educational 
 journey through the grades. 
 
 In systems where the time lost by slow pupils is counter- 
 balanced by the time gained by rapid ones, the average expense 
 of keeping a child in school one year and the expense entailed 
 in sending him forward one grade are just the same. In most 
 systems, however, as we have seen, the time lost by slow pupils ^ 
 is distinctly greater than that gained by rapid ones, and thus the v 
 per capita cost of one year's progress is more than the per capita 
 cost of keeping the child in school for one year. 
 
 This may be illustrated by considering the case of Danville, 
 Illinois, where the relation between the aggregate number of 
 years that it would have required for all the pupils to reach the 
 grades in which they were last June if they had made normal 
 progress, and the number of years of school attendance actually 
 required is shown in the following table: — 
 
8 
 
 III DISTRIBUTION OF PUPILS BY GRADES. AGGREGATE YEARS' 
 
 ■ ATTENDANCE RFCOUIRED FOR THEM TO REACH THOSE 
 
 GRADES AT NORMAL PROGRESS, AND AGGREGATE NUMBER 
 
 OF YEARS ACTUALLY REQUIRED. DANVILLE, ILLINOIS, 
 
 JUNE, 1911 
 
 The figures show that if the years lost by slow children in the 
 Danville schools had been counterbalanced by the years gained 
 by rapid pupils, the aggregate number of years of schooling of the 
 children in the elementary grades would have been 9030. The 
 records show, however, that the slow children lost more time than 
 the rapid ones gained, and so the actual aggregate years of 
 attendance was 10,063, or 1033 years more than the normal 
 number. 
 
 This is peculiarly a situation where "time is money." The 
 lack of balance between the two groups of slow and rapid pupils 
 in this city has entailed an expenditure on the part of the tax- 
 payers to defray the cost of 1033 extra years of schooling for 
 the children in the elementary grades alone. According to the 
 data published in the report of the United States Commissioner 
 of Education for 1910, the running expenses in the Danville schools 
 amount each year to about $20 per capita, and this figure cannot 
 be far from accurate when applied to the children in the ele- 
 mentary schools. This means that the citizens of Danville 
 have paid about $20,660 extra for the schooling of these children. 
 
 Every city where the school years lost amount to more than 
 those gained pays a similar educational tax, the size of which is 
 determined by the preponderance of years lost over years gained 
 and the amount of the annual per capita cost of education in 
 that city. The following table shows the difference between 
 
the number of years lost and the number gained by the ele- 
 mentary school pupils of each city, the per capita cost of school- 
 ing, and the loss entailed in paying for the lack of balance be- 
 tween time lost and time gained : — 
 
 IV. SURPLUS OF YEARS LOST OVER YEARS GAINED, PER CAPITA 
 COST OF ONE YEAR'S SCHOOLING, AND AGGREGATE EX- 
 PENSE INVOLVED IN PAYING FOR THE SURPLUS TIME 
 LOST BY PUPILS, BASED ON RECORDS OF PUPILS IN ELE- 
 MENTARY GRADES, JUNE, 191 1 
 
 City 
 
 Amsterdam . . . 
 
 Bayonne 
 
 Canton 
 
 Danbury 
 
 Danville 
 
 E. St. Louis. . 
 Elizabeth .... 
 
 Elmira 
 
 Hazleton 
 
 Indianapolis . . 
 Kenosha . -. . . . 
 Milwaukee . . . 
 Montclair . . . . 
 Muskegon. . . . 
 New Orleans . 
 New Rochelle . 
 Niagara Falls . 
 
 Passaic 
 
 Perth Amboy . 
 Plainfield .... 
 
 Quincy 
 
 Racine 
 
 Reading 
 
 Rockford . . . . 
 Schenectady . . 
 Syracuse .... 
 
 Topeka 
 
 Trenton 
 
 Watertown . . 
 
 Surplus of 
 
 Years Lost Over 
 
 Years Gained 
 
 62* 
 2,225 
 
 3.325 
 294 
 
 1.033 
 1.950 
 2,790 
 1,069 
 1,500 
 2,460 
 1,091 
 3.096 
 
 1.653 
 972 
 8,076 
 924 
 I.311 
 2,305 
 2,239 
 1,082 
 2,515 
 1,358 
 7.177 
 1,193 
 3,135 
 5,941 
 1,286 
 4,718 
 1. 63 1 
 
 Total . 
 
 Per Capita Cost 
 
 FOR One Year's 
 
 Schooling 
 
 68,287 
 
 $29.47 
 32.66 
 26.06 
 
 25-03 
 20.39 
 27,42 
 21,76 
 25.88 
 19-63 
 32.13 
 22.12 
 
 31-32 
 58.30 
 
 25-49 
 24.58 
 44-05 
 28.68 
 27.40 
 23-40 
 36.42 
 22.15 
 24-93 
 24-34 
 56.55 
 28.45 
 28.23 
 28.88 
 29.91 
 23.25 
 
 Aggregate Expense 
 
 of Surplus Time 
 
 Lost 
 
 $1,827* 
 7,267 
 8,665 
 
 735 
 2,106 
 
 5,346 
 6,071 
 2,766 
 2,944 
 7.903 
 2,413 
 9,696 
 
 9,637 
 2,477 
 
 19,850 
 4,070 
 5,193 
 6,315 
 5,239 
 3.940 
 5,570 
 3,385 
 
 17,468 
 6,746 
 8,919 
 
 16,771 
 3.713 
 
 14,111 
 3,792 
 
 $191,281 
 
 * 62 years gained at a saving of $1,827. 
 
 The grand total of $191,281 is the extra amount that it has 
 cost for the maladjustment of courses of study and systems of 
 promotion to the abilities of the children in these schools. This 
 
10 
 
 is not annual cost, but the total involved in the schooling of all 
 the children whose records were studied. As the average number 
 of years of school attendance among these children is almost 
 exactly 4.2 years, the annual expenditure for the surplus of lost 
 time is about $45,543. 
 
 Annual Per Capita Cost 
 
 The foregoing figures furnish measures of the extent and money 
 cost of the maladjustment between the capabilities of the chil- 
 dren, the difficulty of their school work, and the flexibility of the 
 promotion systems, but they do not give us any expression of the 
 comparative degree of importance of this maladjustment in the 
 different cities, or its effect on the per capita cost of school sup- 
 port. How these data may be secured is illustrated by referring 
 back to the case of Danville. As Table III shows, the aggregate 
 number of years of schooling for all the children at normal 
 progress would be 9,030, while the actual aggregate years of 
 attendance are 10,063. 
 
 This is III per cent of the normal number. In Danville the 
 annual per capita cost of keeping a child in school is $20.39. As 
 the actual time required by the children to reach their present 
 grades is iii per cent of the normal time, the cost of completing 
 the work of each grade is 1 11 per cent of the cost of keeping the 
 child in school one year, or $22.63. In a similar way we may 
 compute for each city the relation in percentages between the 
 normal time and the actual time required to complete any unit 
 of work, and how this affects the cost of carrying a child forward 
 one grade as contrasted with merely keeping him in school one 
 year. These computations follow on p. 11. 
 
 Summary: — 
 
 1 . A study of the school histories of 206,495 children in the 
 
 elementary grades of twenty-nine cities indicates that 
 in most cities the years lost by slow pupils amount to 
 much more than the years gained by rapid pupils, the 
 proportion in the average city being 6.5 years lost for 
 every year gained. 
 
 2. In most cities the course of study and system of promo- 
 
 tions are adapted to the capabilities of the bright rather 
 than to those of the average child. 
 
II 
 
 PER CENT THAT ACTUAL AGGREGATE YEARS OF SCHOOLING 
 ARE OF NORMAL YEARS OF SCHOOLING, AND ANNUAL PER 
 CAPITA COST OF PROMOTING ONE CHILD ONE GRADE IN 
 EACH OF TWENTY-NINE CITY SCHOOL SYSTEMS RANKED 
 ACCORDING TO THE PERCENTAGES 
 
 C. 
 
 No. 
 
 I 
 
 2 
 
 3 
 4 
 5 
 6 
 
 7 
 8 
 
 9 
 lo 
 II 
 
 12 
 
 13 
 H 
 15 
 i6 
 
 17 
 i8 
 
 19 
 
 20 
 21 
 22 
 
 23 
 
 24 
 25 
 26 
 
 27 
 28 
 
 29 
 
 City 
 
 Amsterdam . . 
 Milwaukee. . . 
 Indianapolis . . 
 Rockford .... 
 New Rochelle . 
 
 Topeka 
 
 Danbury .... 
 Muskegon . . . 
 
 Bayonne 
 
 Racine 
 
 New Orleans . 
 E. St. Louis. . 
 Niagara Falls . 
 
 Danville 
 
 Elizabeth .... 
 Schenectady . . 
 
 Syracuse 
 
 Passaic 
 
 Plainfield 
 
 Quincy 
 
 Watertown . . . 
 Hazleton .... 
 
 Kenosha 
 
 Canton 
 
 Elmira 
 
 Montclair . . . . 
 Perth Amboy . 
 
 Reading 
 
 Trenton 
 
 Per Cent 
 Actual Years 
 OF Schooling 
 ARE OF Nor- 
 mal Years 
 OF Schooling 
 
 Average . 
 
 99 
 
 lOI 
 102 
 105 
 106 
 106 
 107 
 107 
 108 
 108 
 109 
 
 no 
 no 
 III 
 III 
 III 
 III 
 
 112 
 112 
 112 
 112 
 114 
 114 
 115 
 115 
 116 
 116 
 119 
 132 
 
 Actual Annual 
 
 Per Capita 
 
 Cost 
 
 $29.47 
 31-32 
 32.13 
 56.55 
 44.05 
 28.88 
 
 25.03 
 25.49 
 32.66 
 
 24.93 
 24.58 
 27.42 
 28.68 
 20.39 
 21.76 
 
 28.45 
 28.23 
 27.40 
 36.42 
 22.15 
 2325 
 19.63 
 22.12 
 26.06 
 25.88 
 58.30 
 23.40 
 
 24.34 
 29.91 
 
 $29.27 
 
 Cost of Promot 
 
 ING One Child 
 
 One Grade 
 
 $29.18 
 31.63 
 32.77 
 59.38 
 46.69 
 30.61 
 26.78 
 27.27 
 
 35-27 
 26.92 
 26.79 
 30.16 
 
 31-55 
 22.63 
 24.15 
 31-58 
 
 31-34 
 30.69 
 40.79 
 24.81 
 26.04 
 22.38 
 25.22 
 29.97 
 29.76 
 67.63 
 27.14 
 28.96 
 39-48 
 
 $32.33 
 
 In these twenty-nine cities the annual money cost to the 
 taxpayers of the maladjustment of the course of study 
 and systems of promotion to the capabilities of the 
 children amounts to about $45,543. 
 
 In the average city this maladjustment involves an in- 
 crease in school expense amounting to about 11 per 
 cent. 
 
Some Pamphlets on Measurements in Education 
 
 Issued by the Department of Child Hygiene, 
 
 Russell Sage Foundation 
 
 No. 6i. The Relation of Physical Defects to School 
 Progress. Leonard P. Ayres, Ph.D. 
 A statistical study based on 7608 cases. 9 pp. 
 
 No. 77. Why 250,000 Children Quit School. 
 Luther H. Gulick, M.D. 
 An account of an investigation of the reasons why 
 so large a proportion of children fail to complete the 
 school course. 30 pp. 
 
 No. 94. Measurements as Applied to School Hygiene. 
 Luther H. Gulick, M.D. 
 A presentation of the need for measuring the 
 results of our present school processes. 7 pp. 
 
 No. 107. The Binet-Simon Measuring Scale for Intelli- 
 gence: Some Criticisms and' Suggestions. 
 Leonard P. Ayres, Ph.D. 
 A critical study of these tests as used in American 
 schools, and suggestions as to their adaptation to 
 our conditions. 12 pp. 
 
 No. 108. The Identification of the Misfit Child. 
 Leonard P. Ayres, Ph.D. 
 Data from a study of the age and progress records 
 of school children in twenty-nine cities. 13 pp. 
 
 No. no. The Relative Responsibility of School and Soci- 
 ety FOR THE Over-age Child. 
 Leonard P. Ayres, Ph.D. 
 Data from a study of the age and progress records 
 of school children in twenty-nine cities, showing the 
 number of children over-age because of late entrance, 
 slow progress, and both causes combined. 
 
 12 
 
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