A New Method for Determining Rate of Progress M A Small School System
- Author:
Nobman Cameron, Ph.D., ^
West Chester, Pa.
Almost all of the articles appearing within the past few years 011 retardation and elimination have been based upon a study o arge school systems, because, in the first place, city systems urnish uniform conditions of grading; and in the second place, arge masses of statistics preclude the erroneous conclusions which ^ ou d result from insufficient data. In this paper, on the conrary, care has been taken to study the school history of each individual pupil in a small school system, and to ascertain accurately the vital statistics necessary to define the true state of affairs.
The present investigation was undertaken with five purposes in view: !? To find out the actual conditions existing in a small school system over a number of years; -? To learn the real extent of retardation, acceleration, and elimination of pupils by following their progress from the day they entered school until the day they finally left it;
3. To draw a valid contrast between the number beginning and the number leaving school; 4. To compare actual with hypothetical results; and, 5. To make such suggestions as may help in ameliorating the conditions which are found to exist.
The facts have been obtained largely from the reports of the ^’hite schools of Elkton, Maryland, and through the cooperation of many teachers and students in the schools and of friends outside it was possible to obtain much valuable data which the reports could not furnish. Many of the teachers had taught in the schools for a period as long as that covered by the investigation, and the writer himself, a citizen of the town, was for some time connected with the schools. The facts are considered under two heads: (1) the elementary and high school history of 295 males and females during the years 1891-1892 to 1908-9, inclusive; and (2) the progress of pupils (1514 in all) in the elementary and high schools for eleven years, from 1898-9 to 1908-9, inclusive.
The town in question is a small county seat. Its population has remained about the same for the past twenty years, and the few industries and the number of employees have not changed materially in that time. The economic conditions are such that practically all the children could remain in school until graduation. The high school was for a number of years the only one in the county, and is still much the largest and best equipped. Until 1902-3 there were six grades in the elementary school, and four in the high school. In that year one grade was added to the elementary course, thus requiring the normal child to remain in school eleven years before graduation. The high school course of study was not affected in any important degree by the change. Two additional facts have an important bearing on this investigation: (1) the age of entrance is six years, and (2) there is no compulsory attendance law in Maryland. The writer believes he is justified in calling his method “new” for the following reasons: (1) the complete school history of 295 pupils and the school history of 1514 pupils during the time spent in the Elkton system are the basis for obtaining his results; (2) elimination is based on the actual number of beginners; (3) the rate of progress and retardation is based on a system of units of progress; and (4) his measure of the efficiency of a school system is new.
The conclusions arrived at in the following pages will not, of course, apply in all respects to every city school system. They will be indicative, however, of what may be found in communities where conditions are similar to those here prevailing, and a knowledge of the facts of retardation, elimination, etc., is quite as indispensable in the administration of a small as of a large school system.
Retardation. At the outset of this discussion it seems necessary to define certain terms already in use in the study of school statistics and to introduce some others.
There are three classes of pupils who drop out of school: (1) those who graduate; (2) those who transfer to other schools; ?and (3) those who leave for other causes. It is to this latter class that the word elimination usually refers.
The rate of progress for a school means the average progress of all pupils through the grades; that is to say, the record of the school system will be a summation upon the records made by the individual pupils in it. The movement of a pupil through his course may be composed of three elements or forces; (1) a normal forward movement, of a unit of work done in one term; (2) a doubly rapid movement of two units of work in one term; and (3) a retarded movement of one unit of work in two or more terms. When a pupil moves faster than the normal rate, i.e. does a unit of work in less than the required time, he is said to be accelerated in his movement through the grades. This term is properly the converse of retarded in its customary meaning.
Among those interested in the work of our public schools there is a demand to know not only that a pupil is moving at an abnormal rate of speed, but what the rate of that movement is. Host writers on the subject of retardation have used the term retarded to mean that a pupil is above age for his grade, irrespective of the reason. Thus a pupil twelve years of age and in the second grade, would be considered retarded whether he had attended school two years or six. For others the word signifies that a pupil has failed of promotion one or more times, and is in consequence behind his class for as many years. The first interpretation of the word has no doubt arisen out of the method necessary for the study of large masses of school statistics, and it has been tentatively accepted by most persons with the recognition that the results are only approximately correct and in most cases merely indicate a tendency. Its second use has been advocated by some who believe that the former method does not give exact results; that it is unfair to the school because it considers a pupil retarded who has entered school late, and because it takes no account of a large number of pupils who have advanced faster than one grade per year.
In the present study the second point of view (progress method) has been accepted principally because it shows the actual condition of retardation. At the same time comparisons of results with the aggregate standard will be made to note how far the schools from which the facts have been collected agree in this respect. One would hardly be justified in applying this method to a large school svstem. The vast amount of time necessary, and the utter impossibility of securing certain facts, would make it impracticable. In the judgment of the writer, it is of great, importance in the present state of school records that a method approximating as nearly as possible the real conditions, be devised for measuring the degree of retardation in our schools. uc a one is herein described. It will show definitely the extent of retardation for which the system is responsible.
Since the word retardation, in the second sense, refers to the progress of a pupil through the grades, it is necessary that a new set of terms be adopted to designate the different degrees of retardation. Three boys may begin school the same year; at the end of the eleventh year one may be in the last year of the high school, one in the second year, and the third in the fourth grade of the elementary school. It is obvious that these pupils have passed through the grades at different rates of speed, and it is important to measure the rate. For this reason the terms units of normal progress, minus progress, and plus progress are here proposed to convey the manner and rate of movement of a pupil through the grades. A unit of normal progress means that a pupil completes a term’s work on time; a unit of minus progress, that he completes the term’s work in double the required time; and a unit of plus progress, that he completes two terms in the time required for one. For example, a pupil in the fifth grade in the eighth year of his school life may be there because he has made one unit of plus and four units of minus progress, or three units of minus progress, etc. Instead of saying that a pupil is retarded or accelerated so many years, it is possible to express his school status in terms of so many units of plus, normal, or minus progress, thus using a definite terminology for designating the manner by which he has arrived at any point in his school career. The word retardation may still be used as before to denote the condition, but without the duty of serving also as the measure of this condition.
As stated before it was not possible to secure absolutely complete records, yet 295 pupils were found who had passed their whole school life in the Elkton schools and had either dropped out or graduated. It is first attempted to show the exact amount of retardation among these pupils, and subsequently, to study it among 1514 pupils who attended school during some part or all of eleven years. Table I (B) shows the distribution of these pupils from the first year of their school life until the last one dropped out in the fourteenth year. The numbers above the black lino give the percentages of those making normal progress, while the numbers below the line indicate the percentages retarded . Instead of finding an ideal attendance of 100 per cent in the next higher grade each succeeding year, we find the real condition as displayed in the table. TTere are 205 different, pupil3 o a ?”3 c E * J? ? 2 .18 .87 1.58 2.35 3.02 3.87 4.72 5.54 6.55 7.7 8.58 9.09 4 - n, o ? o-a Z ? ! ? a ?.2 Si ? ? OH OS c_ M– 1 tC-g c! g C3 ?? a a TABLE I. RETARDATION AND UNITS OF PROGRESS DURING THE COMPLETE SCHOOL HISTORY OF 295 PUPILS a | i CJ o 3 ?o , So 3 ‘ -vjs i -2js a i h-w ca ?> h ! c3 O t. O “S S ; ? a D ; o ! ? Q) ?3 O (-< fc-i Q ^ 3 ? , g *? g S S.S s : js a! ?? ua < : ^ =j ! h B S)w O O i Pk ! Ph : P4 2.12 2.28 2.45 2.45 2.3 2.42 2.91 7 Grades Elementary School School h. S. with 6 with 7 Elem. ~ . Grades Elem- Grades .75 .07 1 1.13 ‘ .02 2.02 1.4 .03 3.01 1.G4 I .00 4.05 1.97 : .06 j 5.05 .07 | 6.00 .07 .09 .1 .04 7.07 8.08 9.1 10.04 0 ! 11 0 | 12 0 i 11 100 76 31 11 2 1 2 3 4 5 6 I 2 7 1 9 10 11 12 13 14 A Units of progress 23 48 30 13 5 1 1 1 20 45 38 ] 36 23 10 5 4 1 33 24 13 7 10 1 10 28 31 i 24 u 7_ 18 I 31 17 3 8 16 2 S 2 5 4 100 Ll 76 79 86 89 91 91 91 93 90 87 100 100 100 36 100 64 76 i 24 0 36 ; 64 a ? ? J2 ? ft 100 24 7 j 93 j 24 | 75 j 21 19 81 43 I 56 14 30 70 52 47 11 38 62 58 41 9 47 53 60 39 ; 9 51 49 64 j 35 j 9 52 48 67 32 7 51 49 | 69 | 30 j 10 53 47 72 27 ! 13 49 51 77 23 54 46 78 22 ! 0 B ? Units of progress Distribution by per cents expressed in per cents 295 294 290 287 281 270 242 208 145 91 53 24 10 1
who have started the race of school life together, scattered along the course, further and further apart with the passing of each year. In the eighth year eighteen are beginning another lap together, having kept up the required speed, two have gained a lap, and 178 are falling behind, some one lap, some three, and a few as many as six laps. Again, in the eleventh year, when most of them should have crossed the finishing line together, only six do so without having lost ground. One has lost one lap and regained it, and still another has lost a lap and not regained it, but finishes with the other seven on account of the shorter course. What has become of the other 287 in these eleven years ? Two hundred and forty-two have dropped out and the remaining fortyfive are found in all the grades from the fourth up to and including the third year of the high school.
Taking as a basis the number of children in school, about one out of ten in the eleventh year of school life has passed through the grades without failure, and considering the number of beginners as a basis the ratio is almost one to fifty. Ayres (1) says: “In our city schools on an average, three out of every four have failed at least once by the time the eighth year of school life is reached, and the whole number of failures is so large as not to fall far short of averaging two for each pupil who has failed.” By reference to table I (A), it will be observed that the whole number of pupils in school this year average 2.28 units of minus progress. Of the pupils in school during the eighth year, 45 have failed once; 68, twice; 39, three times; 27, four times; 10, five times, and 3, six times, an average of 2.5 failures for 192 pupils. Hence, the average number of failures is somewhat larger than that found by Ayres. ” 5
In the same table are given the percentages of the retarded and non-retarded for each year according to the progress (exact) method and the age-grade method so extensively applied by many investigators, the latter considering as retarded all pupils of the first grade who are nine years or over, all in the second grade, ten years or over, and so on. We are struck with the great disparity in the results obtained from the two methods. In the first few years the age-grade standard shows a low percentage of retardation, with a gradual increase in the later years; for example, only 19 per cent were retarded the third year, 30 per cent the fourth year, 38 per cent in the fifth year, and 47 per cent the sixth year, whereas the actual retardation for these same years based on the number of pupils in school was 79, 86, 89 and 91 per cent, respectively. The increase in percentages of retardation, according to the age-grade standard, indicates that the degree of retardation is becoming greater with each added year. Only two of the beginners were retarded by this method, and accordingly it is only as they lagged behind that they passed over into the retarded class. To illustrate the failure of this method to catch the retarded, it may be said that while it gives 39 per cent of the pupils of the first grade in the third year as retarded, as a matter of fact every child in that grade has twice failed of promotion.
Seventy-six per cent of the pupils failed in the first grade the first year, which throws light upon the large percentage of retarded pupils in the later years. Of the number of pupils who failed in the first year and who were in school at least eight years, twenty-three progressed normally for the remaining time, eleven of them being present seventy-five per cent of the year or more. If the failures in the first year be excluded from the calculations, 147, or 71 per cent, of the 208 pupils in the eighth year fall into the retarded class. From the point of view of the child there seems to be no good reason for not counting the first year of school life, since the added year becomes a prolific cause of elimination when the child finds himself behind grade in his fourteenth year. From the point of view of the school system there may be reasons for omitting it.
Passing to the study of retardation among 1514 pupils as found in the various grades in eleven years of this same school system, one is confronted with the problem of devising a method to show the per cent of retardation for each grade during any year and the extent to which each pupil is retarded, i. c. the number of failures, or units of minus progress made for the time by each pupil.
The important thing to know about the child is not how many years he is behind the theoretical grade for his age, but (1) whether or not he has been retarded in the system in question, and (2) if retarded, how many units of minus progress he has made. With this in mind the present method of determining the first of the factors named above has been adopted,^ and all Pupils that were not present during two years were eliminated from the calculations on the ground that a child must be m the system for this period of time to show retardation at all. Table II gives the per cents retarded for each grade and each year. In the first line for each year are the per cents retarded by the progress method. The second line contains the per cents according to the age-grade method. Owing to the fact that in the application of the progress method all pupils who have not been present during two years are omitted from the discussion, there are no per cents for the year 1898-9 for this method. The per cent of retardation increases rapidly from 1899-1900 when the pupils had been in school only two years to 64 per
TABLE II. PERCENTAGES RETARDED BY PROGRESS AND AGE-GRADE METHODS. (1514 PUPILS.) (The upper line for each year gives the per cent for the progress method, the lower line for the age-grade method.) Elementary School High School Years I 1 |2|3|4|5|6|7|1|2|3|4 1898-1899 21 1899-1900 I 100 21 1900-1901 100 23 1901-1902 100 15 1902-1903 1903-1904 1904-1905 1905-1906 1906-1907 1907-1908 100 15 100 9 100 7 100 13 100 17 47 31 60 20 63 23 23 63 > 66 20 38 61 i 71 10 32 100 i 70 14 25 1908-1909 tOO 62 11 ! 16 44 0 44 17 40 50 29 46 ! 32 46 ! 50 34 I 29 74 | 51 33 | 38 60 j 70 27 i 25 65 ! 55 27 I 27 64 26 73 28 61 38 35 41 57 7 33 : 26 SO 36 50 42 41 38 18 21 20 14 22 22 6 41 27 24 27 21 48 25 45 29 33 36 18 11 9 5 21 10 27 34 35 49 32 65 32 66 28 39 ! 39 14 33 25 34 22 17 56 37 64 i 37 25 1 30 66 24 66 23 68 25 71 26 25 21 29 14 26 22 11 69 43 23 I 20 34 47 33 55 31 64 30 58 36 59 25 56 23 56 23 62 20 63 23 cent in 1902-03. From that point there is a decline for two or three years, with a rise to G3 per cent in 1908-09. The greatest amount of retardation, as one would expect, is in the earlier grades. Here most of the failures occur, and here is found the greatest congestion, which is relieved only by the dropping out process that takes place at the ages of twelve, thirteen and fourteen. The first grade shows one hundred per cent retarded in each year, due to the fact that the only pupils considered in our calculations must have been in school more than one year. The next largest percentages of retardation are in the second, third, fourth, and fifth grades. A glance at the columns headed “E” (elementary school), “II” (high school), will give sufficient evidence that a larger per cent of the pupils in the elementary school is retarded than in the high school. This proves that the pupils making the most failures drop out in the lower grades. After the year 1899-1900 there is an almost continuously increasing difference between the percentages calculated by this method and those by the age-grade method. This difference reaches its maximum in the last two years, where the per cent of retarded according to the progress method is approximately three times that of the other method. It is probably more nearly correct to say that if the same pupils were involved in the two methods, the former would show more than twice as many retarded as the latter. The reason for this conclusion is that all beginners are excluded in the first and included in the last method. Moreover, out of the 1051 pupils in the schools more than one year, 587, or 56 per cent failed at least once, i. e. the system’s retardation is 56 per cent. According to the age-grade standard it is 28 per cent for the 1514 pupils. Superintendent Lurton shows (2) that the percentages of retardation based on the Minnesota standard (pupils under seven in the first grade, under eight in the second grade, and so on for the other grades, being classed as non-retarded) are approximately double those based on the age-grade standard. That the latter method gives results greatly in favor of the system, there seems to be no reasonable doubt, its chief value consisting in the fact that it discloses a tendency toward retardation and offers a facile method of comparing the percentages of retardation from year to year, and its chief defect being that it fails to show the correct extent of that retardation.
According to Ayres’ (3) ‘list of 33 cities, Elkton by is standard of measurement would range from twenty-fourth place in 1898-99 to eighth place in 1908-09. There is little doubt that the retarding forces were stronger eleven years ago in this town than they are to-day, but they are still too potent in the early grades for the welfare of the child.
The second fact to be ascertained concerning these pupils during eleven years is the degree of retardation, i. e. the relative number of units of minus progress made by them. Collectively they made 3938 units in all, of which 26 were units of plus progress, 937 units of minus progress, and 2975 units of normal progress, an average for each pupil of 3.74, .02, .89, and 2.83, respectively, or 1, 24 and 75 per cent, respectively, for each of the three kinds of units. Three hundred and fifty pupils in school in 1908-9 averaged 1, 23, and 76 per cent, and the 295 pupils 1, 32, and 67 per cent, respectively, for the three kinds of units. The percentages of normal progress made by the first two groups is about the same, but that made by the third group is somewhat smaller. The difference is to be accounted for largely by the fact that the complete school history of the first two groups is not known, and especially that part of school life when the retarding force is strongest,?in the early grades. If we keep in mind the fact that 326 of the 1051 pupils entered the system from outside schools and that 195 of this last number entered the high school directly, we can understand the cause for the disparity in percentages of the first and third groups, and between the second and third groups. Table I (A) furnishes the same data for the 295 pupils of each year.
A casual comparison of progress with retardation might lead one to believe that the percentages contradict one another. The fact is they do not; the former corroborate the latter. What an average of 27 per cent of units of minus progress means is, that according to the progress method of determining retardation, about 90 per cent of the pupils who have been in school for eight or ten years will be retarded. This same per cent of units of minus (progress in the fifth year of school life would imply a much smaller per cent of retardation.
Causes of Retardation.
The one cause of retardation from the point of view of this investigation is failure of promotion, and the causes that produce these failures are directly responsible for the condition of retardation in schools. It has already been pointed out that a retarded pupil is one who for any reason has failed one or more times to make the next higher grade. The pupil himself may bo responsible for it, the parents may be blamed for it, or the school system itself may be at fault. It is clearly evident each year that the school is having thrust upon it greater responsibility for the social, moral, and mental welfare of the child. This does not mean that the responsibility of the home is being in any degree lessened, but that the state is assuming certain functions that neither of these agencies has exercised in the past, or if they exercised them, did so only in a spasmodic way.
By referring to table III it will he seen that the major portion of the failures is in the early grades, 78 per cent of one group and 90 per cent of the other being in the first four grades. Comparatively few failures are made in the high school. The largest per cents of failures are in the first and third grades. Consequently, we may expect to find the greatest congestion in these two grades, and such is the case in every one of the eleven years of school except two. Not only is it true for the town, but it is also true for the county, for seven out of eleven years, and in the state TABLE III.?FAILURES MADE BY 1051 AND 295 PUPILS. Grade Failures by 1051 pupils Per cent per grade failures by 295 pupils -f er cent per grade… 401 43 359 51 134 14 119 17 120 13 78 11 73 ? m t*. O ?f. to a $ 5 CO m s> 848 91 680 97 7H 6H 80 937 100 701 100
outside of Baltimore City for eight out of ten years. (7) Hence it is in these lower grades that the retarding forces are most potent.
Contributory to the principal cause of retardation are the following: irregular attendance, late entrance, leaving before final examinations, lack of capacity for work, indifference on the part of the pupil, poor teaching, physical defects, too much work and many minor causes closely related with those named.
No doubt the most important of these secondary causes is irregular attendance. Under this may be included late entrance and leaving before examinations. There is naturally supposed to be a definite relation between the content of the course of study and the time a pupil should spend in school. We provide in some districts ten months, in others nine, and in still others eight months, more or less, of school. Yet there is great uniformity in the quantity of the subjects the pupils are expected to assimilate in these different periods of time.
Of the 295 pupils, 38 per cent of the non-promoted and 77 262 THE PSYCHOLOG1CAL CLINIC. of the promoted attended three-fourths time or over. Of the 1051 pupils the percentages for the same period are 42 and 84. That is, about 80 out of every hundred of the promoted and 40 out of the same number of non-promoted attend three-fourths time. Again, out of every hundred pupils of those whose complete school history is known, making three-fourths time or better, 82 are promoted and 18 are not. And for every hundred of the 1051 making three-fourtlis time or more, these numbers are 8G and 14. If the first and second grades are omitted in making the calculations, the number of failures made by every hundred pupils will range from 11 to 14, and the number of promotions from 86 to 80. Of the number making between one-half and three-fourths time the number of promoted and the number of non-promoted out of every hundred are 57 and 43, respectively. For those present less than one-half time, from 70 to 79 fail while from 21 to 30 succeed in getting into the next higher grade. Thus it will be seen a high per cent of attendance is a necessary qualification for promotion. In this study, “entering late” means that the pupil did not enroll the first month of the term; “leaving early,” that the pupil left before examination time at the end of the scholastic year. Of the total promoted, 10 per cent, and of the total non-promoted, 46 per cent, entered late, left early, or both entered late and left early. That is, about 10 out of every hundred promoted make the next grade in spite of the conditions, and 46 out of every hundred of the non-promoted may lay the blame in part to these conditions. Out of every hundred enrolments, 7 of those entering late or leaving early were promoted and 15 not promoted. Of these 15, 3 failed on account of late entrance, 7 on account of leaving early, and 5 on account of both of these conditions. Thus, for these two causes, twice as many failed as passed. In producing nonpromotions, leaving early seems to be more than one and one-half times as potent as entering late. This is in accord with what we might expect to find. Many pupils enter school a month late, and in the earlier grades readily make up the work and are passed into the next class. But the pupils who leave before the final examinations at the end of the year have no chance of promotion unless they are given special examinations at the beginning of the next term, or are promoted on trial.
That too much or too difficult work is an important factor in producing retardation admits of no doubt. Two pieces of evidence are offered in support of this fact. First, the per cent of failures in the third grade is almost twice as large as for the second grade. In the third grade the addition to the content of the course of study is much greater in comparison with that made to the second or fourth grades. Secondly, the per cent of failures made^ by pupils of the 1514 group in the early high school is about eight times as many as that for the later high school. The course o study was then less flexible than in later years, and in consequence students had a much greater content to master. It is also a fact that a larger per cent of pupils of the high school with six preliminary grades than of the one with seven preliminary grades made three-fourths time and failed. Since a larger pei cent^ o pupils in the first than in the second high school failed of promotion it must be attributed to either too much work, or more stringent methods of promotion.
Lack of capacity and lack of application as factors m pro dncing retardation are well illustrated among those pupi s w o make 90 per cent of attendance and yet fail of promotion. us how these failures should be distributed between the two factors is difficult to say. Seventeen per cent of the total num er o ai ures made by the 295 pupils and 19 per cent of those made by t e 1051 pupils occurred in spite of the fact that these pupi s a enl e between 90 and 100 per cent of the school year. is means probably 20 out of every hundred failures are to be charge either lack of capacity or to indifference. In order to ascertain whether or not transfernng from one school system to another occasions retardation, t e averag 422 pupils entering the first year of the high school fromjtode schools was compared with that of the pupi s en was class from the town system. The average age o e , t 14 and of the latter 14.1 years. There is no e-dence here that there is a loss in the transfer. However, there seem anv doubt that there is a loss of considerable proportion . , systems. The equality of these average ages may for by the greater retardation in the system in ‘ that from which the pupils come, but there is no evi POrttpoSo; teaching as a cause of failures in school wo^one that is difficult to estimate in its effect. rregu >n which in many cases chargeable to the linintm’^n^Sw^atever produces teachers conduct their class-room wo , . school absence from school is sufficient cause for failure in prom^tion^es ^ ^ ^ a9 ca?ses of retardation, physical defects in school children, over-crowding, lack of a compulsory attendance law, or the non-enforcement of the same, and many others are contributory to slow movement through the grades. However, there is no statistical evidence bearing upon the gravity of each of these.
Summary on Causes of Retardation. Failure of promotion is the prime cause of retardation. Failure of promotion is produced by irregular attendance, late entrance, early leaving, poor teaching, too much school work, lack of capacity, indifference, physical defects, etc.
Most of the failures take place in the early grades, between TO and 90 per cent before the sixth grade. Out of every hundred making three-fourths time from 14 to 18 fail and from 82 to 8G are promoted. A relatively larger number of non-promoted pupils in the high school than in the elementary school make threefourths time or more. Leaving early is one and one-half times as potent as late entrance in producing non-promotions.
While poor teaching and lack of capacity and too much school work are very important factors in bringing about the condition of retardation, their relative effects are hard to estimate. (To be concluded.)
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