A New Method for Determining Rate of Progress in a Small School System
- Author:
Nokman Cameron, Ph.D.,
West Chester, Pa. (Concluded.) Acceleration.
In all the discussion on the subject of retardation scarcely any consideration has been given to the neutralizing force of acceleration or double promotions. There may be much of it in larger school units as stated by Thorndike (4), Greenwood (5) and Wagner (6), but in the smaller ones its effect in offsetting failures is insignificant.
In the Elkton schools, of the total number of units (2221) made by 295 pupils, 19 were units of plus progress; and of 3938 units of all kinds made by 1051 pupils, 26 were units of plus progress. In either case they represent less than 1 per cent of the whole number of units. Special inquiry, moreover, reveals the fact that more than one-half of these double promotions were the result of work done in the summer under private tutors. Double promotions made under such conditions are merely evidence of ambition and ability on the part of the pupils making them, as testified by the fact that approximately 80 per cent of such pupils reached the high school. That there is not in many schools more promotion during the year on account of special fitness, is largely due to the fact that there is no person who will assume the authority to put pupils up on trial. There is too little of this sort of necessary supervision in our schools, especially in the grades where it is most needed.
Rate of Progress through the Grades. By the rate of progress is meant the rate at which the average pupil passes through the grades. It is evident that for the individual this rate varies, being dependent upon the ratio of failures to promotions.
If a pupil completed five grades of work in five years, or eight grades in eight years, i.e. a grade for each year in school, we would classify him as normalif he did the same amount of work in less than that time, as supernormal; and if in more than tliat time, as subnormal. Of the 295 pupils under consideration, according to this classification, 2 would be supernormal, 23 normal, and 270 subnormal. It will be seen that a very small per cent of pupils pass through the grades at a normal rate of speed. Perhaps it would be well to classify all who reach the high school with only one failure as normal, for it is doubtless true that the majority of such pupils have failed once. From this point of view, the requirements of the course of study might even be considered supernormal.
Table 1A* gives the average of each kind of units and the average total for each year. For example, the pupils in the eighth year of school have completed 4.79 grades, whereas they should have completed seven grades. In the eleventh year those still in school have completed 7.74 grades instead of ten. At the same rate it would require the pupils in the eighth year approximately 14.6 years to complete ten grades, and those in the eleventh year 13 years to complete the same number of grades. It is clear that the greatly retarded ones in the eighth year have dropped out before the eleventh year, as is evidenced by the differences in time necessary to complete the ten grades. Taken altogether the 295 pupils made 1513 units of normal and plus progress in 2202 units of time, or an average of 1.45 years for a grade. At this rate it would require the average pupil 14.5 years to finish ten grades. Pupils moving at this rate through the grades do not graduate. Those in school in 1908-09 have completed 1254 units of normal and plus progress in 1627 units (years) of time, which is equivalent to an average of 10 grades in 13 years. This is probably too low a rate of progress for the system over a period of time, 14.5 years being more nearly correct. Due weight is given to the fact that the pupils in school in 1908-09 have not been in this system from the time they first began school. Consequently, many of the units of minus progress made in the early grades are not included in calculating the rate of progress for those pupils.
Ayres shows (8) that “the average child in the average city school system progresses through the grades at tho rate of eight grades in ten years.” On the same average such a child would complete ten grades in approximately 12.5 years, or two years less than the average child in the Elkton system. There can be no question that the rate of progress will vary with the system. According to the Ayres method it would require 11.2 years for Aurora, 111., and for Erie, Pa., 16.6 years, for the completion of ten grades.
Leaving School.
Pupils leaving school come under three heads,?graduates, those leaving to enter another school, and those dropping out finally before graduation from the schools.
The graduates of a system represent its finished product; and the larger the number of these, other things being equal, the more efficient is the system. That this finished product is very small in proportion to the raw material is generally known. Out of our 295 beginners, only 8.5 per cent graduated, that is, approximately 17 out of every 200 finished the course. In order to estimate roughly the per cent of graduates for eleven years, a number equal to one-eleventh of the whole number of beginners has been taken as a basis. The reason for this is that the number of beginners is about equal to one-half the number of enrolments in the first grade for the eleven years. The number of beginners is 555, one-eleventh of which is 50.5. The number of graduates during this time is 172, an average of 15.6 per year, or 31 per cent completing the course. If the rate of progress is as we have shown it to be, it is evident that this per cent is too high. The explanation is to be found in the fact that 44 per cent of the students in the high school have entered it directly from other schools, and that a fair percentage of these remain to graduate. It is probably more nearly correct to say that the percentage of graduates from the high school under normal conditions is about eight.
Of the 1514 pupils in school during eleven years, 360 left TABLE IV.?NUMBER AND PER CENT ELIMINATED BY THE END OF EACH GRADE. (Graduates not included.) Grades
a f | S J u N ( Pupils Per cents. a ~ f Pupils (1-11 of number for 11 yrs.). Per cents… Elementary School 1.55 33 12 4 .55 4 42 14 5.2 14 86 29 6.6 27 122 41 6.4 40 6 167 56 6.7 53 196 66 4.5 62 High School 1 I 241 815 12.3 86 261 6.7 100 269 91 4.5 109 270 o92 1.36 112
(a) 8.5 % graduated. 282 THE PSYCHOLOGICAL CLINIC. TABLE V.?PER CENT ELIMINATED BY THE END OF EACH TEAR OP AGE. (Graduates not included.) Ages 295 Group… 1514 Group b 10 11 10 10 12 16 19 13 37 35 14 61 55 15 77 80 16 87 97 17 90 108 18 91 110 19 a92 112 20 112
8.5 % graduated.
Calculated as in Table IV.
to enter other schools. Thirteen per cent of the 360 transferred from the high school and 87 per cent from the elementary school. On the other hand, 44 per cent of the students coming from other schools enroll in the high school. The great disparity in percentages of pupils leaving and entering the high school, is to be accounted for by the fact that most of the pupils leaving the high school are compelled to give up their public school education altogether. The discussion of the vast number of pupils who actually quit the grades and leave unfinished the education which the state provides, will centre around two questions: (1) In what grades and at what ages do the pupils leave school? (2) What are the causes for this dropping out?
The percentages in table IV answer the first of these questions. It will be seen that with both groups of pupils, 295 and 1514, the eliminating process begins early in the grades, being heaviest in the fourth, fifth and sixth grades, and in the first year of the high school. In the last grade mentioned there is an elimination of 24 per cent in the large group. The same peculiarity is manifested in table V, which gives the elimination by ages, where 25 per cent drop out at fifteen, and 17 per cent at sixteen. This large amount of elimination in the first year of the high school and at the ages of fifteen and sixteen is due to the large number (44 per cent) of pupils entering the high school from the outside. Up to the last grammar grade the percentages of elimination for the two groups are approximately the same for the different ages and grades.
Ayres (9) and Thorndike (10) express contradictory opinions on a fundamental fact concerning elimination in the early grades. The former contends that “there is abundant evidence that the general tendency of our schools is to hold practically all of the pupils to the sixth grade,” while the latter believes that “pupils leave in considerable numbers from almost the beginning of the elementary school course.” No doubt there are sysRATE OF PROGRESS. 283 tems which will furnish evidence for each opinion. In the Elkton schools the figures corroborate the fact that many pupils leave in the early grades, and it is probably true that this is the general tendency throughout the schools of Maryland, outside of Baltimore. In the former there is no compulsory attendance law to hold them to a specified age. Consequently, many leave who would continue longer in the grades of systems where such a law is enforced. If the failures are very heavy in the first six grades, elimination may be concealed by the seeming equality of these grades; but the natural inference that there is little or no dropping out there would be unjustified. Thorndike shows an elimination of GO per cent by the last grammar grade, Ayres 49 per cent, while in Elkton approximately 66 per cent have dropped out before the high school is reached. The larger percentages of elimination in the earlier grades in these schools, as compared with other studies, may be partly chargeable to the absence of a compulsory attendance law and partly to the large number of failures in these grades.
In calculating the number of pupils retained to the several grades both Ayres and Thorndike have used as a basis a number of beginners variously estimated. Applied to the Elkton statistics the Ayres’ method gives a number of beginners too small by 10 per cent, while the number obtained by the first of Thorndike’s methods is too large by 42 per cent, and by his second, by about 8 per cent. The latter investigator does not state which method would be applicable to small systems. If the first of the two were used the inferences based on the results would have little or no value. Ayres’ method of calculating the beginners gives a number not far from the true one in systems where the migratory movement of the population is not large. If, however, unusual conditions of change prevail in a school population, it will be difficult to determine the true retention and elimination in the grades except by having exact data as the basis for such calculation.
Summary on Leaving School. Approximately eight out of every hundred beginners remain to graduate.
Eighty-seven out of every hundred transfers are from the elementary schools.
About three and one-half times as many pupils enter the Elkton high school from the outside as leave it to go elsewhere. Elimination forces are operative in all the elementary grades, being strongest in the fourth, fifth and sixth grades. Approximately 66 per cent of the pupils have left school before the first high school year is reached. Causes of Elimination.
This brings us to the second question, What are the causes for this dropping out process?
Retardation is both an effect and a cause. Irregular attendance, incapacity, late entrance, etc., produce it, and in turn it is the most potent cause of elimination. Whenever the work of the grade must be repeated, indifference is often engendered, a dislike for work follows, and the pupil leaves. It is, indeed, rare that a pupil will remain to complete the high school course who has failed more than twice. If we assume that he enters at the age of six and fails twice, he will be almost twenty years of age when he graduates. Boys, in particular, have no inclination to remain in the secondary school until twenty-one. By applying the age-grade method to the 622 pupils leaving finally in eleven years, it is found that 60 per cent are retarded as compared with 31 per cent for the whole number in school for the same time. Again, of these same pupils the average number of units of minus progress for those leaving is 1.14 and for the whole number in school .89. Here is evidence, then, that retardation brought about through failure to make promotion, is an important cause of leaving school.
A second important cause of elimination is age. Of the 270 pupils leaving school the largest proportion, 21 per cent, drop out in the eighth year. This brings the child to the age of fourteen or fifteen, the age at which the largest per cent of pupils leave school. Pupils will remain in school during their early years, despite failures to accomplish the work, but when they reach their thirteenth, fourteenth or fifteenth year and find themselves in the lower grade, they see the hopelessness of their attempt to finish the course, and if most of their companions have left school, or are in the higher grades, they leave to take up some occupation in which they can do something. In schools where an effective compulsory attendance law precludes leaving school until fourteen, large numbers drop out of the elementary school at this age. Retention to this age, however, has an effect of tiding over the critical period for many boy and girls, with the result that they remain to complete the course. This fine influence is lost to the schools where the statute books contain no such act. There are many other conditions which indirectly are the cause of pupils leaving school. Many of these, such as ill health, needed at home, sickness of others, etc., are merely the last straw. Forces have long been at work impelling to this final day in school. So long as the centripetal forces towards the school are stronger in the aggregate than the centrifugal forces away from it, the child remains. But once the balance begins to swing tne other way, it moves rapidly and is hard to check in its course. That this ultimate elimination in nine out of ten cases is not the result of any one impelling cause, admits of no doubt. An accumulation of gathering forces, as the pupil wends his way along the school course, is the real cause of leaving. The home and school and society in general are all more or less responsible for the final outcome, leaving school.
Measuring the Efficiency of a School System. Many methods have been adopted for comparing the relative merits of different school systems; oftentimes a method is advocated merely because of the favorable showing it makes for the system interested. As soon as it fails to do this it falls into disuse. Frequently a system boasts of the large number of members in its graduating class, or the number of the first year of the high school who reach the last year, or the per cent the number in the last year of the high school is of the whole number in the school. All these provide means of comparing some feature of one system with the same feature of another, but they do not accurately determine what the real efficiency of the system is. Ayres (11) has proposed a method for estimating the efficiency of a system which seems at first glance to offer a fair basis for comparison. Two factors are considered: first, the per cent of output on the basis of one thousand beginners, which gives efficiency from the point of view of product; and secondly, the per cent the ideal number of pupils is of the actual number necessary to produce the output, which gives the efficiency from the point of view of plant economy. The first of these multiplied by the second expresses the index of efficiency of the system. That is, if a school has in its eighth grade, or last year of the elementary school, for every one thousand beginners, four hundred pupils, the first factor of efficiency would be represented by 40 per cent. If instead of eight thousand pupils in the eight grades, there are nine thousand, then the efficiency from the second point of view would be 88.8 per cent. The product of these two gives 35.5 per cent as the index of efficiency for the school.
Granting then that Mr. Ayres’ methods of obtaining the number of beginners and the number reaching the last grade of the elementary school would give approximately the correct results for a school system where no pupils entered from the outside and none left to enter other schools, a just comparison of the efficiency of different systems could be made.
But do all the children who begin in a school system remain in it until they leave finally? Is the number that enters the schools of any community, borough, or township, from other schools of any considerable magnitude ? The answer to the first question must be in the negative; not only do they not remain in the system, but a very large percentage of them leave to enter other schools. Of the 1514 different pupils who were in the Elkton schools during eleven years, 3G0, or 24 per cent, left to enter other schools; 46, or 3 per cent of these were high school pupils, and 314, or 21 per cent, were from the elementary grades. It must be borne in mind here that of these 1514 pupils 3GO of them were still in school in September of 1900, so that the basis on which these percentages are estimated is too large. If they were calculated on a basis of 1514 minus 3G0, or 1154, the results would be 4 and 27 per cent respectively. Here, then, it is evident that many pupils leave one system to enter another, and that most of the transferring is among the elementary grades. Now for the second question: Is the number that enters from other schools of any considerable magnitude? Out of the 1514 pupils just referred to, 501 or 30 per cent, came from outside schools. Of this last number 330, or 22 per cent, entered the elementary grades, and 2G1, or 17 per cent, entered the high school.
This estimate does not allow for the fact that 367 of the 522 pupils in the school in 1808-00 were there beforo that year. If this number bo deducted from the 1514, and the difference, 1147 be taken as a basis, the pupils entering from other schools will be 20 and 23 per cent respectively.
If the conditions shown to bo true in the Elkton schools prevail in other systems, and there is every reason to believo they do, for this is a community in which the population makes no more than the average change from year to year, then the question arises: What system does Ayres* index of efficiency measure?
If 30 per cent of the pupils in the school aro from other systems, his method gives a value which is made up of the elements good and bad of numerous systems. From what systems these pupils came, and how many from each, are questions that a lack of data prevents our answering. It is probable that many of the pupils who enter a highly organized system, suffer more in the system from which they come than they would during the same period in the one they enter. This being the case, does the index of efficiency determined by the method described justly estimate a system’s worth ? It seems evident that such a procedure would place responsibility on the wrong shoulders.
Some plan is necessary that will show what the system has done and is doing for the pupils for the length of time they have been under its influence. What would be better than all else from the point of view of the public school system in general, would be to have a complete record of each individual pupil in order that the effect of the whole educational process on the child might be known. This, in our present condition of school records, is beyond our power to measure, but something can be done in the way of determining the effect of the different factors of a system on the pupils within it.
It has been shown in previous sections on retardation and leaving school, that failure of promotion produces retardation, and that elimination is due to a high degree of retardation, or frequent failures, or in other words, that the larger the number of units of minus progress as compared with that of normal and plus progress combined, the older the pupils become in the lower grades, and the greater will be the per cent of elimination in these grades.
Moreover, the more pupils drop out in the lower grades the fewer there will be in the first and subsequent years of the high school. Since there is this definite relation between the numbers of these different kinds of units of progress, the efficiency of a system may well be measured by a per cent obtained by dividing the combined number of units of normal and plus progress by the sum of the units of normal and minus progress. For example, the 1514 different pupils who were in the Elkton schools during the eleven years made 3001 units of normal and plus progress and 3912 units of normal and minus progress. The former divided by the latter gives 11 as the index of efficiency for the system during eleven years. While this illustrates well enough the method of obtaining the per cent, it would be impracticable to apply it to so long a period of time. What every superintendent of schools should be able to do in any given year, is to report upon what his system has done for the pupils who have been under its influence.
A study of the records of those pupils who are in school at the beginning of 1908-9 and who have been in the present system during previous years reveals the fact that the total number of units of normal and plus progress is 1254 as compared with 1627 units of normal and minus progress. This gives as the index of efficiency 77, or practically the same as that for the eleven years.
Still another way of showing the efficiency of a system is to find the relation between the same factors named above for all the pupils in the school for the year. This might be termed the yearly efficiency of the school system, as distinguished from the period efficiency which represents the relation of the total number of units of normal and pins progress to the number of units of normal and minus progress for the period of years chosen. As an example of the application of this method to determine yearly efficiency, the total number of units of normal and plus progress combined and of normal and minus progress are for the year 1908-9, 333 and 436, respectively. By dividing the former number by the latter the index of efficiency is found to be 76.4.
Of the three ways of applying this method, the last is the most practicable, for it is the most economical from the point of view of time and labor. Moreover, it offers a facile means, not only of comparing one system with another, but also of comparing the efficiency of the same system from year to year. Summary.
In the present state of school records the efficiency of a school system cannot be measured by a ratio between the number of beginners and the number of pupils reaching tho last grade of the elementary or high school, because of the largo percentage of pupils entering tho system from tho outside, and leaving to enter schools elsewhere.
The ratio of tho number of units of normal and plus progress to the number of units of normal and minus progress will give an adequate method for measuring efficiency. Either yearly or period efficiency of tho system may bo measured.
The efficiency of the Elkton school system is approximately .77. Suggestions to Superintendents.
In the gathering and study of the statistics in this investigation a few facts have stood out so impressively that it seems worth while to present them for the benefit of those engaged in the organization of schools.
First, the necessity of some other method of promotion than that used in many of our large school systems to-day seems imperative. It is still the custom in practically all the smaller towns and in a large number of cities to make promotions only at the end of the year. That this is a serious factor in producing retardation there can be no doubt.
If late entrance or early leaving is not due to actual absence from school, but merely to a transfer from one school to another, it is not so likely to result in failure of promotion. But if children are out of school on account of sickness or because of being needed at home in the fall or spring, they will fail to make the next higher grade at the end of the year. Of the 701 failures made by 295 pupils, 134 were made by pupils who entered late or left early. Of these 134 failures, 37 were related to late entrance, and 97 to leaving early. Investigation reveals the fact that 111 of the 134 enrolments entering late or leaving early were present either for the first half or for the last half of the year. Previously, it has been shown that 85 per cent of those making 90 per cent of attendance are promoted. Therefore, if we take 85 per cent of 111 we have 94 pupils who would have been promoted if the year’s work had been divided into two separate units, one to be completed during the first half and the other during the last half of the school year. In all there were made by these 295 pupils 701 units of minus progress. Promotions made as described above would have decreased this number 94, or 13 per cent. The system that has double promotions does more than make a saving of 13 per cent of the number of units of minus progress among those pupils that make 90 per cent of attendance for a half a year. There are some pupils who make as low as 80, 70, and 60 per cent of attendance and yet are promoted. A part of these too would be rescued from the school failures by the system of double promotions.
In this connection it may be suggested that a special class should be formed in every school to give additional instruction to pupils behind their grades. Many failures would never be made if each school system provided such a means of assisting the pupils at the time when they most need it. Many a child has received the first start toward elimination when upon returning to school after an unavoidable detention at home he has been held responsible for previous work without any assistance from the teachers or others. The special class or special teacher would have removed this cause for future failures and consequent early leaving of school.
A second matter which needs attention is examinations. In some few schools examinations have been done away with because of the feeling that they are unnecessary. To the writer they seem to have one significant implication; that the average teacher is incapable for one reason or other of judging whether or not a child is fitted to pass to the next higher grade.
In order to throw some light upon this question a special study has been made of 1514 pupils. It appears that 509 including the first and second grades (239 without them), did not attend up until the time of final examinations and yet were found in school the next year, either in the grade of the previous year or in a higher one; 171 of these including the first and second grades (80 without them), were promoted. That is, omitting pupils of the first and second grades, 17 per cent of those not attending up until the time of examinations were promoted to the next higher grades. It may bo assumed that a few of these did take the examinations at the beginning of the following year, but this was not a usual custom. Since no system of exemptions is in vogue in the Elkton schools, hero is evidence that many pupils are promoted either on trial, or in some manner make their way into the next higher grade without having to take the examinations that are considered all important.
The third and perhaps most important fact that has been brought out in this study is the utter lack of data necessary f?r a proper study of school problems. A need for a uniform record card has long been recognized by those connected with educational matters, and many such cards have been proposed. In this investigation the writer has personally gathered and collated the statistics which are hero set forth in tabular form, and ho has had abundant opportunity to learn what a record card should contain. During this whole study note has been made of what facts ehoul be recorded on such a card, and it is believed that the cards here proposed give all the practical information necessary to determine at any time exactly what a system is doing for tho pupils in it, and what it has done for them in tho past, so that tho index of efficiency may be accurately determined, and valid com parisons made with tho results of other systems.
The transfer card suggested here seems to indicate all the information that one system should send to and immediately receive from another. The numbers on this card should provide a means of obtaining any additional facts that might be necessary to a complete history of the child’s school life. (Front) Record card of. School (Address) Pupil’s name Pupil’s number (in this system) (Last name) (First name) Preceding schools with pupil’s numbers (in order from first) Dates: Beginning school Leaving school (yr. mo. da.) (yr. mo.) (yr. mo.) 0 ‘“d ‘“d ?> !> M M l”dhd O O Causes of absence Causes of non-prom. ||||||t|5-l||fll|ip ffgs? UHt Will 2 5. S ra oo p b in a P ? a cu_. ^ g P p S DM o <Q q a t* CO _ _ S- CT5 ^ ? i:? eL? Zz. 2 5 2, 2. S- m p ? cr o p 2 S” D mO m cL o P 2. 2. n n tJ” O < K O 2 | If U - ?1” tl B gs tgrf ? !l Is B I ? ? i 8*5- ‘8 g. (Back) Mental record Physical record L_jjq >_I wjO>k_|C^C ^ (0 S3 ? Efp>o,SSS-to2.Bo?.p3- tds-tr1 foptr1^ s- o 3 2 a O a^o n faofBS 2. g 3. era ^ 2. sr 2- ? ^ m c ^ m 3 a P co o a P ^ 2-B?.J5.Qr, or5,2.1”(MUH ^ H g ” o 2 o re ?? -? ? ?T B B ate S ? g. 3” ? ^ g P I a ^ C g re g a g g 2
The cards proposed here are the result of educational experience covering many years of school work.* If they prove to be of use in bettering the manner of keeping our school records, the writer will feel repaid for the amount of time and thought he has given to the task. Transfer card of School (Address) Pupil’s number in system just left….. Name (Last name) (First name) Preceding schools with pupil’s numbers (in order from first) Dates: Birth Beginning school Leaving school (yr. mo. da.) (yr. mo.) (yr. mo.) Grade Present standing Physical history of abnormalities S? &*? EH V re C 3. re ~-g re ^ ^^re^trc^rePO g-S’x-S *2 ^ ^ 3 ?? S-rSrS 2-5s.’ tdpt-|^S-c3h|rec3 g ? ~ g- i 2.<g ^ |.|i i g o- ?? g pi?T. re.cr BP ^ g ” | a. ? ?” ? & B Fill out, detach, and send to School. Pupil’s number (in system just left) Name (Address) (Last name) (First name) Pupil’s new number in system just entering Grade entered When (yr. mo. da.) Principal. REFERENCES. 1 Ayres, L. P. Laggards in Our Schools. N. Y. Charities Pub. Com., 1909, p. 146. 2 Lurton, Freeman E. The Psychological Clinic, Vol. V, p. 17. 3 Ayres, L. P. Laggardsa p. 45. 4 Thorndike, E. L. The Psychological Clinic, Vol. Ill, p. 238. 5 Greenwood, J. M. Education, Vol. XXIX, p. 280. G Wagner, A. E. The Psychological Clinic, Vol. Ill, p. 1G9. 7 Reports of the State Board of Education for Maryland, 1889 to 1910. 8 Ayres, L. P. Laggards, p. 87. 9 Ayres, L. P. Laggards, p. 70. 10 Thorndike, E. L. Elimination of Pupils from School. Bulletin of U. S. Bureau of Education, 1907, p. 14. 11 Ayres, L. P. Laggards, p. 175. ? The writer is indebted to Charles A. Wagner, West Chester State Normal School, for many valuable suggestions and criticisms in the preparation of these cards.
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