THE HIGH SCHOOL FAILURES
A STUDY OF THE SCHOOL RECORDS OF PUPILS FAILING IN ACADEMIC OR COMMERCIAL HIGH SCHOOL SUBJECTS
FRANCIS P. OBRIEN
Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the Faculty of Philosophy, Columbia University
PUBLISHED BY Teachers College, Columbia University NEW YORK CITY 1919
Copyright, 1919, by FRANCIS P. OBRIEN
Grateful acknowledgment is due the principals of each of the high schools whose records are included in this study, for the courteous and helpful attitude which they and their assistants manifested in the work of securing the data. Thanks are due Dr. John S. Tildsley for his generous permission to consult the records in each or any of the New York City high schools. But the fullest appreciation is felt and acknowledged for the ready criticism and encouragement received from Professor Thomas H. Briggs and Professor George D. Strayer at each stage from the inception to the completion of this study.
PAGE I.—THE GENERAL INTRODUCTION OF THE SUBJECT
1. The Relevance of This Study 1
2. The Meaning of Failure in This Study 3
3. Scope and Content of the Field Covered 4
4. Sources of the Data Employed 6
5. Selection and Reliability of These Sources 8
6. Summary of Chapter, and References 11
II.—HOW EXTENSIVE ARE THE FAILURES OF THE HIGH SCHOOL PUPILS?
1. A Distribution of All Entrants in Reference to Failure 12
2. The Later Distribution of the Pupils by Semesters 14
3. The Distribution of the Failures—by Ages and by Semesters 14
4. Distribution of the Failures by Subjects 19
5. The Pupils Dropping Out—Time and Age 24
6. Summary of Chapter, and References 27
III.—WHAT BASIS IS DISCOVERABLE FOR A PROGNOSIS OF THE OCCURRENCE OR THE NUMBER OF FAILURES?
1. Some Possible Factors—Attendance, Mental and Physical Defects, Size of Classes 29
2. Employment of the School Entering Age for the Purpose of Prognosis 31
3. The Percentage of Failure at Each Age on the Possibility of Failures for That Age 36
4. The Initial Record in High School 37
5. Prognosis of Failure by Subject Selection 39
6. The Time Period and the Number of Failures 40
7. Similarity of Facts for Boys and Girls 45
8. Summary of Chapter, and References 45
IV.—HOW MUCH IS GRADUATION OR THE PERSISTENCE IN SCHOOL CONDITIONED BY THE OCCURRENCE OR BY THE NUMBER OF FAILURES?
1. Comparison of the Failing and the Non-failing Groups in Reference to Graduation and Persistence 48
2. The Number of Failures and the Years Required to Graduate 49
3. The Number of Failures and the Semesters of Dropping Out, for Non-graduates 51
4. The Percentages That the Non-graduate Groups Form of the Pupils Who Have Each Successively Higher Number of Failures 55
5. Time Extension for the Failing Graduates 56
6. Summary of Chapter, and References 57
V.—ARE THE SCHOOL AGENCIES EMPLOYED IN REMEDYING THE FAILURES ADEQUATE FOR THE PURPOSE?
1. Repetition as a Remedy for Failures 60 a. Size of Schedule and Results of Repeating. b. Later Grades in the Same Kind of Subjects, Following Repetition and Without it. c. The Grades in Repeated Subjects and in New Work. d. The Number and Results of Identical Repetitions.
2. Discontinuance of the Subject or Course, and the Substitution of Others 68
3. The Employment of School Examinations 69
4. The Service Rendered by the Regents' Examinations in New York 70
5. Continuation of Subjects Without Repetition or Examination 73
6. Summary of Chapter, and References 74
VI.—DO THE FAILURES REPRESENT A LACK OF CAPABILITY OR OF FITNESS FOR HIGH SCHOOL WORK ON THE PART OF THOSE PUPILS?
1. Some Are Evidently Misfits 76
2. Most of the Failing Pupils Lack Neither Ability nor Earnestness 77
3. The School Emphasis and the School Failures Are Both Culminative in Particular School Subjects 81
4. An Indictment Against the Subject-Matter and the Teaching Ends as Factors in Producing Failures 83
5. Summary of Chapter, and References 85
VII.—WHAT TREATMENT IS SUGGESTED BY THE DIAGNOSIS OF THE FACTS OF FAILURE?
1. Organization and Adaptation in Recognition of the Individual Differences in Abilities and Interests 87
2. Faculty Student Advisers from the Time of Entrance 89
3. Greater Flexibility and Differentiation Required 90
4. Provision for the Direction of the Pupils' Study 92
5. A Greater Recognition and Exposition of the Facts as Revealed by Accurate and Complete School Records 94
6. Summary of Chapter, and References 96
A STUDY OF THE SCHOOL RECORDS OF THE PUPILS FAILING IN ACADEMIC OR COMMERCIAL HIGH SCHOOL SUBJECTS
GENERAL INTRODUCTION OF THE SUBJECT
1. THE RELEVANCE OF THIS STUDY
As the measuring of the achievements of the public schools has become a distinctive feature of the more recent activities in the educational field, the failure in expected accomplishment by the school, and its proficiency in turning out a negative product, have been forced upon our attention rather emphatically. The striking growth in the number of school surveys, measuring scales, questionnaires, and standardized tests, together with many significant school experiments and readjustments, bears testimony of our evident demand for a closer diagnosis of the practices and conditions which are no longer accepted with complacency.
The American people have expressed their faith in a scheme of universal democratic education, and have committed themselves to the support of the free public high school. They have been liberal in their financing and strong in their faith regarding this enterprise, so typically American, to a degree that a secondary education may no longer be regarded as a luxury or a heritage of the rich. No longer may the field be treated as either optional or exclusive. The statutes of several of our states now expressly or impliedly extend their compulsory attendance requirements beyond the elementary years of school. Many, too, are the lines of more desirable employment for young people which demand or give preference to graduates of a high school. At the same time there has been no decline in the importance of high school graduation for entering the learned or professional pursuits. Accordingly, it seems highly probable that, with such an extended and authoritative sphere of influence, a stricter business accounting will be exacted of the public high school, as the great after-war burdens make the public less willing to depend on faith in financing so great an experiment. They will ask, ever more insistently, for facts as to the expenditures, the finished product, the internal adjustments, and the waste product of our secondary schools. Such inquiries will indeed seem justifiable.
It is estimated that the public high schools had 84 per cent of all the pupils (above 1,500,000) enrolled in the secondary schools of the United States in 1916. The majority of these pupils are lost from school—whatever the cause—before the completion of their courses; and, again, the majority of those who do graduate have on graduation ended their school days. Consequently, it becomes more and more evident how momentous is the influence of the public high school in conditioning the life activities and opportunities of our youthful citizens who have entered its doors. Before being entitled to be considered a "big business enterprise," it seems imperative that our "American High School" must rapidly come to utilize more of business methods of accounting and of efficiency, so as to recognize the tremendous waste product of our educational machinery.
The aim of this study is to trace as carefully and completely as may be the facts relative to that major portion of our high school population, the pupils who fail in their school subjects, and to note something of the significance of these findings. If we are to proceed wisely in reference to the failing pupils in the high school, it is admittedly of importance that such procedure should be based on a definite knowledge of the facts. The value of such a study will in turn be conditioned by the scrupulous care and scientific accuracy in the securing and handling of the facts. It is believed that the causes of and the remedies for failure are necessarily closely linked with factors found in the school and with the school experiences of failing pupils, so that the problem cannot be solved by merely labeling such pupils as the unfit. There is no attempt in this study to treat all failures as in any single category. The causes of the failures are not assumed at the start nor given the place of chief emphasis, but are regarded as incidental to and dependent upon what the evidence itself discloses. The success of the failing pupils after they leave the high school is not included in this undertaking, but is itself a field worthy of extended study. Even our knowledge of what later happens to the more successful and the graduating high school pupils is limited mainly to those who go on to college or to other higher institutions. One of the more familiar attempts to evaluate the later influence of the high school illustrates the fallacy of overlooking the process of selection involved, and of treating its influence in conjunction with the training as though it were the result of school training alone.
2. THE MEANING OF 'FAILURE' IN THIS STUDY
The term 'failure' is employed in this study to signify the non-passing of a pupil in any semester-subject of his school work. The school decision is not questioned in the matter of a recorded failure. And although it is usually understood to negate "ability plus accomplishment," it may, and undoubtedly does, at times imply other meanings, such as a punitive mark, a teacher's prejudice, or a deferred judgment. The mark may at times tell more about the teacher who gave it than about the pupil who received it. These peculiarities of the individual teacher or pupil are pretty well compensated for by the large number of teachers and of pupils involved. The decisive factor in this matter is that the school refuses to grant credit for the work pursued. The failure for a semester seems to be a more adaptable unit in this connection than the subject-failure for a year. However, it necessitates the treatment of the subject-failure for a year as equivalent to a failure for each of the two semesters. Two of the schools involved in this study (comprising about 11 per cent of the pupils) recorded grades only at the end of the year. It is quite probable that the marking by semesters would actually have increased the number of failures in these schools, as there are many teachers who confess that they are less willing to make a pupil repeat a year than a semester.
By employing this unit of failure, the failures in the different subjects are regarded as comparable. Since only the academic and commercial subjects are considered, and since they are almost uniformly scheduled for four or five hours a week, the failures will seem to be of something near equal gravity and to represent a similar amount of non-performance or of unsatisfactory results. There were also a few failures included here for those subjects which had only three hours a week credit, mainly in the commercial subjects. But failures were unnoted when the subject was listed for less than three hours a week.
There are certain other elements of assumption in the treatment of the failures, which seemed to be unavoidable. They are, first, that failure in any subject is the same fact for boys and for girls; second, that failures in different years of work or with different teachers are equivalent; third, that failures in elective and in required subjects are of the same gravity. It was found practically impossible to differentiate required and elective subjects, however desirable it would have been, for the subjects that are theoretically elective often are in fact virtually required, the electives of one course are required in another, and on many of the records consulted neither the courses nor the electives are clearly designated.
3. THE SCOPE AND CONTENT OF THE FIELD COVERED
As any intensive study must almost necessarily be limited in its scope, so this one comprises for its purposes the high school records for 6,141 pupils belonging to eight different high schools located in New York and New Jersey. For two of these schools the records for all the pupils that entered are included here for five successive years, and for their full period in high school. In two other schools the records of all pupils that entered for four successive years were secured. In four of the schools the records of all pupils who entered in February and September of one year constituted the number studied. There is apparently no reason to believe that a longer period of years would be more representative of the facts for at least three of these four schools, in view of the situation that they had for years enjoyed a continuity of administration and that they possess a well-established organization. The fourth one of these schools had less complete records than were desired, but even in that the one year was representative of the other years' records. The distribution of the 6,141 pupils by schools and by years of entering high school is given below.
HIGH SCHOOL PUPILS IN: ENTERING HIGH SCHOOL NUMBER IN THE YEARS STUDIED
White Plains, N.Y. 1908, '09, '10, '11, '12 659 Dunkirk, N.Y. 1909, '10, '11, '12 370 Mount Vernon, N.Y. 1912 224 Montclair, N.J. 1908, '09, '10, '11, '12 946 Hackensack, N.J. 1909, '10, '11, '12 736 Elizabeth, N.J. 1912 333 Morris H.S.—Bronx 1912 1712 Erasmus Hall H.S.—Brooklyn 1912 1161 —— TOTAL 6141
As it is essential for the purposes of this study to have the complete record of the pupils for their full time in the high school, the 6,141 pupils include none who entered later than 1912. Thus all were allowed at least five and one-half or six years in which to terminate their individual high school history, of successes or of failures, before the time of making this inquiry into their records. No pupils who were transferred from another high school or who did not start with the class as beginning high school students were included among those studied. Post-graduate records were not considered, neither was any attempt made to trace the record of drop-outs who entered other schools. Manifestly the percentage of graduation would be higher in any school if the recruits from other schools and the drop-backs from other classes in the school were included.
No attempt has been made to trace the elementary school or college records of the failing pupils, for our purpose does not reach beyond the sphere of the high school records. In reference to the differentiation by school courses, some facts were at first collected, but these were later discarded, as the courses represent no standardization in terminology or content, and they promised to give nothing of definite value. As might be expected, the schools lacked agreement or uniformity in the number of courses offered. One school had no commercial classes, as that work was assigned to a separate school; another school offered only typewriting and stenography of the commercial subjects; a third had placed rather slight emphasis on the commercial subjects until recently. Only four of the schools had pupils in Greek. The Spanish classes outnumbered the Greek both by schools and by enrollment. In the classification by subjects, English is made to include (in addition to the usual subjects of that name) grammar, literature, and business English. Mathematics includes all subjects of that class except commercial arithmetic, which is treated as a commercial subject, and shop-mathematics, which is classed as non-academic. Industrial history, and 'political and social science' are regarded along with academic subjects; likewise household chemistry is included with the science classification. Economics is treated as a commercial subject. At least a dozen other subjects, not classified as academic or commercial, including also spelling and penmanship, were taken by a portion of these pupils, but the records for these subjects do not enter this study in determining the successful and failing grades or the sizes of schedule. Yet it is true that such subjects do demand time and work from those pupils.
4. SOURCES OF THE DATA EMPLOYED
The only records employed in this whole problem of research were the official school records. No questionnaires were used, and no statements of pupils or opinions of teachers as such were sought. The facts are the most authoritative and dependable available, and are the very same upon which the administrative procedure of the school relative to the pupil is mainly dependent. The individual, cumulative records for the pupils provided the chief source of the facts secured. These school records, as might be expected, varied considerably as to the form, the size, the simplicity in stating facts, and the method of filing; but they were quite similar in the facts recorded, as well as in the completeness and care with which the records were compiled. It may be added that only schools having such records were included in the investigation.
After the meanings of symbols and devices and the methods of recording the facts had been fully explained and carefully studied for the records of any school, the selection of the pupil records was then made, on the basis of the year of the pupils' entrance to the school, including all the pupils who had actually entered and undertaken work. (Pupils who registered but failed to take up school work were entirely disregarded.) These individual records were classified into the failing and the non-failing divisions, then into graduating and non-graduating groups, with the boys and girls differentiated throughout. As fast as the records were read and interpreted into the terms required they were transcribed, with the pupils' names, by the author himself, to large sheets (16x20) from which the tabulations were later made. There was always an opportunity to ask questions and to make appeals for information either to the principal himself or to the secretary in charge of the records. This tended to reduce greatly the danger of mistakes other than those of chance error. The task of transcribing the data was both tedious and prolonged. This process alone required as much as four weeks for each of the larger schools, and without the continued and courteous cooperation of the principals and their assistants it would have been altogether impossible in that time.
Some arbitrary decisions and classifications proved necessary in reference to certain facts involved in the data employed in this study. All statements of age will be understood as applying to within the nearest half year; that is, fifteen years of age will mean within the period from fourteen years and a half to fifteen years and a half. The classification in the following pages by school years or semesters (half-years) is dependent upon the time of entrance into school. In this sense, a pupil who entered either in September or in February is regarded as a first semester pupil, however the school classes are named. As promotions are on a subject basis in each of the schools there is no attempt to classify later by promotions, but the time-in-school basis is retained. In reference to school marks or grades, letters are here employed, although four of the eight schools employ percentage grading. Whether the passing mark is 60, as in some of the schools, or 70, as in others, the letter C is used to represent one-third of the distance from the failing mark to 100 per cent; B is used to represent the next third of the distance; and A is used to express the upper third of the distance. The plus and minus signs, attached to the gradings in three of the schools, are disregarded for the purposes of this study, except that when D+ occurred as a conditional passing mark it was treated as a C. Otherwise D has been used to signify a failing grade in a subject, which means that the grade is somewhere below the passing mark. The term 'graduates' is meant to include all who graduate, either by diploma or by certificate. Any statement made in the following pages of 'time in school' or of time spent for 'securing graduation' will not include as a part of such period a semester in which the pupil is absent all or nearly all of the time, as in the case of absence due to illness.
5. THE SELECTION AND RELIABILITY OF THESE SOURCES OF DATA
By employing data secured only from official school records and in the manner stated, this study has been limited to those schools that provide the cumulative pupil records, with continuity and completeness, for a sufficient period of years. Some schools had to be eliminated from consideration for our purposes because the cumulative records covered too brief a period of years. In other schools administrative changes had broken the continuity of the records, making them difficult to interpret or undependable for this study. The shortage of clerical help was the reason given in one school for completing only the records of the graduates. In addition to the requirements pertaining to records, only publicly administered and co-educational schools have been included among those whose records are used. It was also considered important to have schools representing the large as well as the small city on the list of those studied. Since many schools do not possess these important records, or do not recognize their value, it is quite probable that the conditions prescribed here tended to a selection of schools superior in reference to systematic procedure, definite standards, and stable organization, as compared to those in general which lack adequate records.
The reliability and correctness of these records for the schools named are vouched for and verbally certified by the principals as the most dependable and in large part the only information of its kind in the possession of the schools. In each of these schools the principals have capable assistants who are charged with the keeping of the records, although they are aided at times by teachers or pupils who work under direction. In three of the larger schools a special secretary has full charge of the records, and is even expected to make suggestions for revisions and improvements of the forms and methods. In view of such facts it seems doubtful that one could anywhere find more dependable school records of this sort. It was true of one of the schools that the records previous to 1909 proved to be unreliable. There is no inclination here to deny the existence of defects and limitations to these records, but the intimate acquaintance resulting from close inquiry, involving nearly every factor which the records contain, is convincing that for these schools at least the records are highly dependable.
However, there is some tendency for even the best school records to understate the full situation regarding failure, while there is no corresponding tendency to overstate or to record failures not made. Not infrequently the pupils who drop out after previously failing may receive no mark or an incomplete one for the last semester in school. Although a portion or all of such work may obviously merit failure, yet it is not usually so recorded. In a similar manner pupils who remain in school one or two semesters or less, but take no examinations and receive no semester grades, might reasonably be considered to have failed if they shunned examinations merely to escape the recording of failures, as sometimes appears to be the case when judged from the incomplete grades recorded for only a part of the semester. A few pupils will elect to 'skip' the regular term examination, and then repeat the work of that semester, but no failures are recorded in such instances. Some teachers, when recording for their own subjects, prefer to indicate a failure by a dash mark or by a blank space until after the subject is satisfied later, and the passing mark is then filled in. One school indicates failure entirely by a short dash in the space provided, and then at times there occurs the 'cond' (conditioned) in pencil, apparently to avoid the classification as a failure by the usual sign. One finds some instances of a '?' or an 'inc' (incomplete) as a substitute for a mark of failure. Again, where there is no indication of failure recorded, the dates accompanying the grades for the subjects may tell the tale that two semesters were required to complete one semester's work in a subject. Some of these situations were easily discernible, and the indisputable failures treated as such in the succeeding tabulations; but in many instances this was not possible, and partial statement of these cases is all that is attempted.
How far these selected schools, their pupils, and the facts relating to them are representative or typical of the schools, the pupils, and the same facts for the states of New Jersey and New York, cannot be definitely known from the information that is now available. It seems indisputable, however, that the schools concerned in this study are at least among the better schools of these two states. If we may feel assured that the 6,141 pupils here included are fairly and generally representative of the facts for the eight schools to which they belong and which had an enrollment of 14,620 pupils in 1916; and if we are justified in classing these schools as averaging above the median rank of the schools for these states, then the statistical facts presented in the following pages may seem to be a rather moderate statement regarding the failures of high school pupils for the states referred to. It must be noted in this connection, however, that it is not unlikely that such schools, with their adequate records, will have the facts concerning failure more certainly recorded than will those whose records are incomplete, neglected, or poorly systematized.
A partial comparison of the teachers is possible between the schools represented here and those of New York and New Jersey. More than four hundred teachers comprised the teaching staff for the 6,141 pupils of the eight schools reported here. Of these about 40 per cent were men, while the percentage of men of all high school teachers in New Jersey and New York was about 38 for the year 1916. The men in these schools comprised 50 per cent of the teachers in the subjects which prove most difficult by producing the most failures, and they were more frequently found teaching in the advanced years of these subjects. It is not assumed here that men are superior as high school teachers, but the endeavor is rather to show that the teaching force was by its constitution not unrepresentative. It may be added here that few high schools anywhere have a more highly selected and better paid staff of teachers than are found in this group of schools. It is indeed not easy to believe that the situation in these eight selected schools regarding failure and its contributing factors could not be readily duplicated elsewhere within the same states.
A SUMMARY OF CHAPTER I
The American people have a large faith in the public high school. It enrolls approximately 84 per cent of the secondary school pupils of the United States. High school attendance is becoming legally and vocationally compulsory. The size of the waste product demands a diagnosis of the facts. This study aims to discover the significant facts relative to the failing pupils.
Failure is used in the unit sense of non-passing in a semester subject. Failures are then counted in terms of these units.
This study includes 6,141 pupils belonging to eight different high schools and distributed throughout two states. The cumulative, official, school records for these pupils formed the basis of the data used.
The schools were selected primarily for their possession of adequate records. More dependable school records than those employed are not likely to be found, yet they tend to understate the facts of failure. It is quite possible that a superior school, and one with a high grade teaching staff, is actually selected by the requirements of the study.
1. Annual Report of United States Commissioner of Education for 1917.
2. Josslyn, H.W. Chapter IV, in Johnson's Modern High School.
3. The Money Value of Education. Bulletin No. 22, 1917, United States Bureau of Education.
4. New York and New Jersey State School Reports for 1917.
HOW EXTENSIVE ARE THE FAILURES OF THE HIGH SCHOOL PUPILS?
1. A DISTRIBUTION OF ALL ENTRANTS IN REFERENCE TO FAILURE
With no purpose of making this a comparative study of schools, the separate units or schools indicated in Chapter I will from this point be combined into a composite and treated as a single group. It becomes possible, with the complete and tabulated facts pertaining to a group of pupils, after their high school period has ended, to get a comprehensive survey of their school records and to answer such questions as: (1) What part of the total number of boys or of girls have school failures? (2) To what extent are the non-failing pupils the ones who succeed in graduating? (3) To what extent do the failing pupils withdraw early? The following tabulation will show how two of these questions are answered for the 6,141 pupils here reported on.
ALL ALL ENTRANTS FAILING GRADUATES FAILING
Totals 6,141 3,573 (58.2%) 1,936 1,125 (58.1%) Boys 2,646 1,645 (62.1%) 796 489 (61.4%) Girls 3,495 1,928 (55.1%) 1,140 639 (55.8%)
From this distribution we readily compute that the percentage of pupils who fail is 58.2 per cent (boys—62.1, girls—55.1). But this statement is itself inadequate. It does not take into account the 808 pupils who received no grades and had no chance to be classed as failing, but who were in most cases in school long enough to receive marks, and a portion of whom were either eliminated earlier or deterred from examinations by the expectation of failing. It seems entirely safe to estimate that no less than 60 per cent of this non-credited number should be treated as of the failing group of pupils. Then the percentage of pupils to be classed as failing in school subjects becomes 66 per cent (boys—69.6, girls—63.4).
In considering the second inquiry above, we find from the preceding distribution of pupils that 58.1 per cent (boys—61.4, girls—55.8) of all pupils that graduate have failed in one or more subjects one or more times. This percentage varies from 34 per cent to 73 per cent by schools, but in only two instances does the percentage fall below 50 per cent, and in one of these two it is almost 50 per cent.
We may now ask, when do the failing and the non-failing non-graduates drop out of school? Of the total number of non-graduates (4,205), there are 2,448 who drop out after failing one or more times, and 1,757 who drop out without failing. The cumulative percentages of the non-graduates in reference to dropping out are here given.
CUMULATIVE PERCENTAGES OF THE FAILING NON-GRADUATES AS THEY ARE LOST BY SEMESTERS
LOST BY END OF SEMESTER 1 2 3 4 5 6 7 8 9
Per Cent 14.1 33.9 46.4 64.9 72.9 85.2 91.9 97.6 99.1
CUMULATIVE PERCENTAGES OF NON-FAILING NON-GRADUATES AS THEY ARE LOST BY SEMESTERS
LOST BY END OF SEMESTER 1 2 3 4 5 6 7 8 9
Per Cent 61.1 78.0 85.9 92.1 94.5 98.4 99.5 .. ..
Briefly stated, the above percentages assert that more than three fourths of those who neither fail nor graduate have left school by the end of the first year, while only 33.9 per cent of those non-graduates who fail have left so early. More than 50 per cent of the failing non-graduates continue in school to near the end of the second year. By that time about 90 per cent of the non-failing non-graduates have been lost from school. By a combination of the above groups we get the percentages of all non-graduates lost by successive semesters.
CUMULATIVE PERCENTAGES OF ALL NON-GRADUATES LOST BY SUCCESSIVE SEMESTERS
LOST BY END OF SEMESTER 1 2 3 4 5 6 7 8
Per Cent 33.7 53.4 62.6 76.2 81.9 90.7 94.0 98.6
These percentages of non-graduates indicate that more than 50 per cent of those who do not graduate are gone by the end of the first year, but that there are a few who continue beyond four years without graduating.
2. THE LATER DISTRIBUTION OF PUPILS BY SEMESTERS
Consideration is here given to the number of the total entrants remaining in school for each successive semester, and then to the accompanying percentages of failure for each group. The following figures show the rapid decline in numbers.
THE PERSISTENCE OF PUPILS IN SCHOOL, BY SEMESTERS
END OF SEMESTER 1 2 3 4 5 6 Graduate
6,141 (Total) 4,723 3,893 3,508 2,935 2,697 2,234 1,936
Percentages 76.9 63.4 57.1 47.8 43.9 36.4 31.5
As was pointed out in Section 3 of Chapter I, the above group does not include any increment to its own numbers by means of transfer from other classes or schools. We find, accompanying this reduction in the number of pupils, which shows more than 50 per cent gone by the end of the second year in school, that there is no corresponding reduction in the percentage of pupils failing each semester on the basis of the number of those in school for that semester.
PERCENTAGE OF PUPILS FAILING OF THE PUPILS IN SCHOOL FOR THAT PERIOD
Semesters 1 2 3 4 5 6 7 8
Per Cent 34.2 37.3 38.5 40.2 38.2 37.1 30.0 24.0
There is no difficulty in grasping the simple and definite significance of these figures, for they tell us that the percentage of pupils failing increases for the first four semesters, slightly declines for two semesters, with a greater decline for two more semesters. These percentages of failures are based on the number of pupils enrolled at the beginning of the semester, and are accordingly lower than the facts would really warrant since that number is in each case considerably reduced by the end of the same semester.
3. THE DISTRIBUTION OF FAILURES
That the failures are widely distributed by semesters, by ages, and for both boys and girls, is shown in Table I.
THE DISTRIBUTION OF FAILURES ACCORDING TO THE AGE AND THE SEMESTER OF THEIR OCCURRENCE[A]
SEMES- AGES UNDISTRIB- TERS 12 13 14 15 16 17 18 19 20 21 22 UTED TOTALS
1 B. 0 20 321 650 575 167 34 16 2 .. .. 10 1795 G. 1 19 356 813 611 236 67 3 0 .. .. 13 2119 3914 2 B. .. 2 95 423 534 256 57 27 4 .. .. 5 1403 G. .. 6 99 483 589 280 91 5 0 .. .. 7 1560 2963 3 B. .. 0 17 267 443 363 96 22 5 0 .. 2 1215 G. .. 1 28 318 548 317 99 15 0 2 .. 1 1329 2544 4 B. .. .. 5 101 437 403 169 32 7 2 .. 5 1161 G. .. .. 4 102 475 425 160 39 6 2 .. 6 1219 2380 5 B. .. .. 1 19 195 377 214 61 13 3 .. 6 889 G. .. .. 0 15 277 438 212 60 15 0 .. 3 1020 1909 6 B. .. .. .. 4 70 322 326 99 33 3 .. 6 863 G. .. .. .. 9 117 407 349 78 33 4 .. 3 1000 1863 7 B. .. .. 1 0 17 155 227 106 16 4 1 4 531 G. .. .. 0 2 14 200 299 127 38 0 0 3 683 1214 8 B. .. .. .. .. 0 42 173 109 49 2 .. 5 380 G. .. .. .. .. 2 58 244 140 49 10 .. 3 506 886 9 B. .. .. .. .. .. 0 31 32 18 1 .. .. 82 G. .. .. .. .. .. 4 39 67 31 5 .. .. 146 228 10 B. .. .. .. .. .. .. 1 16 9 3 0 .. 29 G. .. .. .. .. .. .. 3 13 10 3 1 .. 30 59 Summary B. 0 22 440 1464 2271 2085 1328 520 156 18 1 43 8348 G. 1 26 487 1742 2633 2365 1563 547 182 26 1 39 9612 17,960
[Footnote A: The expression of the above facts in terms of percentages for each age group was found to be difficult, since failures and not pupils are designated. But the total failures for each age group are expressed (on p. 36) as percentages of the entire number of subjects taken by these pupils for the semesters in which they failed. Such percentages increase as the ages rise. A similar statement of the percentages of failure by semesters will be found on p. 41.]
Table I reads: the boys had 20 failures and the girls had 19 failures in the first semester and at the age of thirteen; in the second semester, at the age of thirteen, the boys had 2 failures and the girls 6. For each semester, the first line represents boys, the second line girls. There is a total of 17,960 failures listed in this table. In addition to this number there are 1,947 uncompleted grades for the failing non-graduates. The semesters were frequently completed by such pupils but the records were left incomplete. Their previous records and their prospects of further partial or complete failure seem to justify an estimate of 55 per cent (1,070) of these uncompleted grades as either tentative or actual but unrecorded failures. Therefore we virtually have 1,070 other failures belonging to these pupils which are not included in Table I. Accordingly, since the number can only be estimated, the fact that they are not incorporated in that table suggests that the information which it discloses is something less than a full statement of the school failures for these pupils. In the distribution of the totals for ages, the mode appears plainly at 16, but with an evident skewness toward the upper ages. The failures for the years 16, 17, and 18, when added together, form 68.1 per cent of the total failures. If those for 15 years are also included, the result is 86 per cent of the total. Of the total failures, 65.7 per cent are found in the first two years (11,801 out of the total of 17,960). But the really striking fact is that 34.3 per cent of the failures occur after the end of the first two years, after 52.2 per cent of the pupils are gone, and with other hundreds leaving in each succeeding semester before even the end of the eighth. In Table II we have similar facts for the pupils who graduate.
THE DISTRIBUTION OF FAILURES ACCORDING TO THE AGES AND THE SEMESTERS OF THEIR OCCURRENCE FOR THE GRADUATING PUPILS
AGES SEMESTERS 13 14 15 16 17 18 19 20 21 22 TOTALS
1 B. 0 66 84 60 5 2 3 .. .. .. 220 G. 4 68 123 68 23 4 0 .. .. .. 290 510 2 B. 0 30 95 96 41 3 2 .. .. .. 267 G. 1 25 119 121 30 11 2 .. .. .. 309 576 3 B. 0 6 108 98 71 22 1 3 .. .. 309 G. 1 15 101 158 78 20 5 0 .. .. 378 687 4 B. .. 4 54 157 107 36 6 0 .. .. 364 G. .. 1 45 186 143 51 7 2 .. .. 435 799 5 B. .. 1 10 82 142 82 17 4 3 .. 341 G. .. 0 9 145 187 88 22 9 0 .. 460 801 6 B. .. .. 4 34 158 139 32 9 2 .. 378 G. .. .. 2 70 235 178 40 13 1 .. 539 917 7 B. .. 1 0 10 115 140 65 4 4 1 340 G. .. 0 2 7 130 187 69 19 0 0 414 754 8 B. .. .. .. 0 31 122 65 25 2 .. 245 G. .. .. .. 2 45 150 95 37 2 .. 331 576 9 B. .. .. .. .. 0 24 23 13 1 .. 61 G. .. .. .. .. 4 32 40 24 0 .. 100 161 10 B. .. .. .. .. .. 1 11 5 3 .. 20 G. .. .. .. .. .. 3 12 6 1 .. 22 42 Summary B. .. 108 355 537 670 571 225 63 15 1 2545 G. 6 109 401 757 875 724 292 110 4 0 3278 5823
[Footnote: In the facts which are involved and in the manner of reading them, this table is similar to Table I. The mode of the distribution of totals for the ages is at 17 in this table. Further reference will be made to both Tables I and II in later chapters of this study. (See pages 36, 37, 41, 42).]
A further analysis of the failures is here made in reference to the number of pupils and the number of failures each.
A DISTRIBUTION OF FAILING PUPILS ACCORDING TO THE NUMBER OF FAILURES PER PUPIL, IN EACH SEMESTER
NO. OF SEMESTERS TOTALS FAILURES 1 2 3 4 5 6 7 8 9 10
1 B. 459 430 375 352 271 221 157 113 22 11 2411 G. 561 535 428 421 328 261 167 123 35 9 2868 —————————————- 32.5% 5279
2 B. 271 242 211 206 149 144 79 68 19 4 1393 G. 271 253 238 204 177 142 127 84 17 6 1519 —————————————- 34.9% 2912
3 B. 144 106 81 73 59 60 45 27 6 2 603 G. 207 103 81 75 75 83 52 38 20 3 737 —————————————- 35% 1340
4 B. 83 39 33 30 27 32 10 10 1 1 266 G. 95 50 38 35 27 39 19 19 3 0 325 —————————————- 31.8% 591
5 B. 6 3 5 8 7 8 7 2 0 .. 46 G. 3 2 6 5 1 10 6 5 1 .. 39 —————————————- 55.3% 85
6 B. .. .. 3 3 0 1 1 .. .. .. 8 G. .. .. .. .. .. .. .. .. .. .. .. —————————————- 25% 8
Tot. B. 963 820 708 672 513 466 299 220 48 18 4727 G. 1137 943 791 740 608 535 371 269 76 18 5488 10,215
Table III tells us that 459 boys and 561 girls have one failure each in the first semester of their high school work; 271 boys and the same number of girls have two failures in the first semester, and so on, for the ten semesters and for as many as six failures per pupil. The failures represented by these pupils give a total of 17,960. A distribution of the total failures per pupil, and the facts relative thereto, will be considered in Chapter IV of this study.
The above distribution of Table III is repeated here in Table IV, so far as it relates to the failing graduates only.
A DISTRIBUTION OF THE FAILING PUPILS WHO GRADUATE, ACCORDING TO THE NUMBER OF FAILURES PER PUPIL IN EACH SEMESTER
NO. OF SEMESTERS TOTALS FAILURES 1 2 3 4 5 6 7 8 9 10
1 B. 110 131 137 150 162 139 120 118 19 11 1097 G. 136 142 181 200 197 180 121 89 20 3 1269 —————————————— 50% 2366
2 B. 34 49 61 69 61 75 47 28 15 3 442 G. 49 64 63 86 81 73 81 62 10 5 574 —————————————— 53.2% 1016
3 B. 10 10 14 18 12 17 27 17 4 1 130 G. 16 9 14 13 27 43 30 20 16 3 191 —————————————— 67.6% 321
4 B. 3 2 2 3 4 8 6 5 0 .. 33 G. 2 3 6 6 5 16 9 12 3 .. 62 —————————————— 71.6% 95
5 B. .. .. 0 2 1 0 3 0 .. .. 6 G. .. .. 1 0 0 4 1 2 .. .. 8 —————————————— 78.6% 14
6 B. .. .. .. .. .. 1 1 .. .. .. 2 G. .. .. .. .. 0 0 .. .. .. 0 —————————————— 100% 2
Tot. B. 157 192 214 237 240 240 204 163 48 15 1710 G. 203 218 265 305 310 316 242 185 49 11 2104 3814
This table reads similarly to Table III. There is not the element of continuous dropping out to be considered, as in Table III, until after the sixth semester is passed, for no pupils graduate in less than three years. The failures represented in this table number 5,823. This same distribution will be the subject of further comment later on. It discloses some facts that Table III tends to conceal, for instance, that the greater number of graduating pupils who have 2, 3, 4, 5, and 6 failures in a semester are found after the end of the second year.
4. DISTRIBUTION OF THE FAILURES IN REFERENCE TO THE SUBJECTS IN WHICH THEY OCCUR
The following tabulation of failures will show how they were shared by both boys and girls in each of the school subjects which provided the failures here listed.
NUMBER OF FAILURES DISTRIBUTED BY SCHOOL SUBJECTS
Total Math. Eng. Latin Ger. Fr. Hist. Sci. Bus. Span. or Subj's. Greek
B. 8348 2015 1555 1523 917 473 571 850 424 20 G. 9612 2300 1424 1833 812 588 1036 1013 593 13 Per Cent of Total 24.1 16.5 18.7 9.6 5.9 8.9 10.3 5.6 .2
The abbreviated headings above will be self-explanatory by reference to section 3 of Chapter I. The first line of numbers gives the failures for the boys, the second line for the girls. Mathematics has 24.1 per cent of all the failures for all the pupils. Latin claims 18.7 per cent and English 16.5 per cent of all the failures. These three subjects make a total of nearly 60 per cent of the failures for the nine subject groups appearing here. But still this is only a partial statement of the facts as they are, since the total enrollment by subjects is an independent matter and far from being equally divided among all the subjects concerned. The subject enrollment may sometimes be relatively high and the percentage of failure for that subject correspondingly lower than for a subject with the same number of failures but a smaller enrollment. This fact becomes quite apparent from the following percentages taken in comparison with the ones just preceding:
PERCENTAGES ENROLLED IN EACH SUBJECT OF THE SUM TOTAL OF THE SUBJECT ENROLLMENTS FOR ALL PUPILS AND ALL SEMESTERS
Math. Eng. Latin Ger. Fr. Hist. Sci. Bus. Span. or Subj's. Greek
17.3 24.0 11.9 8.5 6.8 10.2 12.5 8.3 .5
We note that the percentages for mathematics and English, which represent their portions of the grand total of subject enrollments, are virtually the reverse of the percentages which designate the amount of total failures produced by the same two subjects. That means that the percentage of the total failures produced by mathematics is really greater than was at first apparent, while the percentages of failures for English is not so great relatively as the statement of the total failures above would alone indicate. In a similar manner, we note that Latin has 18.7 per cent of all the failures, but its portion of the total enrollment for all subjects is only 11.9 per cent. If the failures in this subject were in proportion to the enrollment, its percentage of the failures would be reduced by 6.8 per cent. On the other hand, if the failures for English were in the same proportion to the total as is its subject enrollment, it would claim 7.5 per cent more of all the failures. In the same sense, French, history, science, and the business subjects have a smaller proportion of all the failures than of all the subject enrollments.
The comparison of failures by subjects may be continued still further by computing the percentage of failures in each subject as based on the number enrolled in that subject. Such percentages are here presented for each subject.
PERCENTAGE OF THE NUMBER TAKING THE SUBJECT WHO FAIL IN THAT SUBJECT
Latin Math. Ger. Fr. Hist. Sci. Eng. Bus. Span. or Subj's. Greek
18.7 16.0 13.5 11.6 10.4 9.8 8.2 8.0 4.1
It becomes evident at once that the largest percentage of failures, based on the pupils taking the subject, is in Latin, although we have already found that mathematics has the greatest percentage of all the failures recorded (p. 19). But here mathematics follows Latin, with German coming next in order as ranked by its high percentage of failure for those enrolled in the subject. History has the median percentage for the failures as listed for the nine subjects above.
The failures as reported by subjects for other schools and other pupils will provide a comparison which may indicate something of the relative standing of this group of schools in reference to failures. The failures are presented below for thirteen high schools in New Jersey, involving 24,895 grades, as reported by D.C. Bliss in 1917. As the schools were reported singly, the median percentage of failure for each subject is used here for our purpose. But Mr. Bliss' figures are computed from the promotion sheets for June, 1915, and include none of those who had dropped out. In this sense they are not comparable to the percentages of failure as presented in this study. Yet with the one exception of Latin these median percentages are higher. The percentages as presented below for St. Paul are in each case based on the total number taking the subject for a single semester, and include about 4,000 pupils, in all the classes, in the four high schools of the city.[B]
[Footnote B: It is a significant fact, and one worthy of note here, that the report for St. Paul is apparently the only one of the surveys which also states the number taking each subject, as well as the percentages of failure. Percentages alone do not tell the whole story, and they do not promote the further utilization of the facts to discover other relationships.]
The facts presented for St. Louis are for one school only, with 2,089 pupils, as recorded for the first half of the year 1915-16. All foreign languages as reported for this school are grouped together. History is the only subject that has a percentage of failure lower than that of the corresponding subjects for our eight schools. The figures for both St. Paul and St. Louis are based on the grades for all classes in school, but for only a single semester. One cannot avoid feeling that a statement of facts for so limited a period may or may not be dependable and representative for all periods. The percentages for Paterson are reported for about 4,000 pupils, in all classes, for two successive semesters, and are based on the number examined. For Denver, the records are reported for 4,120 pupils, and cover a two-year period. The percentages for Butte are based on the records for 3,110 pupils, for one school semester. The figures reported by Rounds and Kingsbury are for only two subjects, but for forty-six widely separated high schools, whose enrollment for these two subjects was 57,680.
PERCENTAGES OF FAILURE BY SUBJECTS—QUOTED FOR OTHER SCHOOLS
Math. Latin Ger. Fren. Eng. Hist. Sci. Bus. Subj's.
13 N.J. H.S.'s. 20.0 18.0 16.0 .. 14.0 11.0 .. 11.5 St. Paul 21.8 13.6 14.3 17.0 10.0 10.9 7.3 11.7 St. Louis 18.0 [———-16———] 13.0 7.0 19.0 .. Paterson 23.1 21.6 23.4 .. 12.2 13.9 18.3 8.5 Denver 24.0 21.0 12.0 .. 11.7 11.0 17.0 11.0 Butte 18.6 25.0 24.0 32.6 5.4 7.0 13.0 8.4 R and K 24.7 .. .. .. 18.5 .. .. .. Our 8 H.S.'s 16.0 18.7 13.5 11.6 8.2 10.4 9.8 8.0
In some schools the reports were not available for all subjects. It is not at all probable, so far as information could be obtained, that the failures of the drop-out pupils for any of the schools were included in the percentages as reported above, or that the percentages are based on the total number in the given subjects, with the exception of one school. Moreover, it is certain for at least some of the schools that neither the failures of the drop-outs nor the pupils who were in the class for less than a whole semester were considered in the percentages above. So far, however, as these comparisons may be justified, the suggestion made in Chapter I that the schools included in this study are doubtless a superior group with respect to failures appears to be strengthened by the comparisons made above.
It becomes more apparent, as we attempt to offer a statement of failures as taken from the various reports, that they are not truly comparable. The bases of such percentages are not at all uniform. The basis used most frequently is the number enrolled at the end of the period rather than the total number enrolled for any class, for which the school has had to provide, and which should most reasonably form the basis of the percentage of failure. Furthermore, the failures for pupils who drop out are not usually counted. Yet, in most of the reports, the situation is not clearly indicated for either of the facts referred to. Still more difficult is the task of securing a general statement of failures by subjects, since the percentages are most frequently reported separately for each class, in each subject, and for different buildings, but with the number of pupils stated for neither the failures nor the enrollment. The St. Paul report is an exception in this regard.
To present the full situation it is indeed necessary to know the failures for particular teachers, subjects, and buildings, but it is also frequently necessary to be able to make a comparison of results for different systems. Consequently, in order to use the varied reports for the attempted comparison above, the plan was pursued of averaging the percentages as stated for the different classes, semesters, and years of a subject, in each school separately, and then selecting the median school thus determined as the one best representing the city or the system. This method was employed to modify the reports, and to secure the percentages as stated above for Denver, Paterson, and Butte. Any plan of averaging the percentages for the four years of English, or similarly for any other subject, may actually tend to misstate the facts, when the percentages or the numbers represented are not very nearly equal. But, in an incidental way, the difficulty serves to emphasize the inadequacy and the incomparability in the reporting of failures as found in the various studies, as well as to warn us of the hopelessness of reaching any conclusions apart from a knowledge of the procedure employed in securing the data.
The basis is also provided for some interesting comparisons by isolating from the general distribution of failures by school subjects (p. 19) the same facts for the failing graduates. That gives the following distribution.
THE FAILURES BY SCHOOL SUBJECTS FOR GRADUATES ONLY
Total Math. Eng. Latin Ger. Fr. Hist. Sci. Bus. Span. or Subj's. Greek
5803 B. 660 403 521 241 191 180 251 91 7 6334 G. 782 347 673 257 240 410 394 162 12 Per Cent of Totals 24.8 12.9 20.5 8.5 7.4 10.1 11. 4.3 .3
SIMILAR PERCENTAGES FOR THE NON-GRADUATES
As above 23.6 18.3 17.7 10.1 5.3 8.4 10. 6.3 .1
It is a noteworthy fact that the percentages of failure (based on the total failures for the graduates) run higher in mathematics, Latin, history, French, and science for the graduates than for the whole composite number (page 19). The non-graduates have a correspondingly lower percentage of failure in these subjects, as is indicated above. The school influences in respect to the failures of the non-graduates differ from those of the graduates chiefly in the fact that the failures of the former tend to occur to a greater extent in the earlier years of these subjects, since so many of the non-graduates are in the school for only those earlier years; while the failures of the graduates range more widely and have a tendency to predominate in the upper years of the subject, as will be further emphasized in the later pages of this report (see also Table IV).
5. DISTRIBUTION OF PUPILS DROPPING OUT—SEMESTERS—AGES
Table V presents the facts concerning the time and the age at which the failing pupils drop out of school. Table VI furnishes the corresponding facts for the non-failing drop-outs.
DISTRIBUTION OF THE FAILING NON-GRADUATES, SHOWING THE SEMESTER AND THE AGE AT THE TIME OF DROPPING OUT
AGES UNDIS- SEMESTERS 13 14 15 16 17 18 19 20 21 22 TRIB. TOTALS
1 B. 1 40 49 50 18 0 1 1 .. .. 1 160 G. 3 40 65 47 23 4 0 0 .. .. 3 185 345 2 B. .. 9 56 88 56 22 6 2 .. .. 3 242 G. .. 6 72 119 61 24 3 0 .. .. 6 291 533 3 B. .. 4 30 40 23 10 7 .. .. .. 0 114 G. .. 3 35 51 32 13 7 .. .. .. 1 142 256 4 B. .. 1 16 66 86 34 16 2 .. .. 3 224 G. .. 1 19 60 70 59 18 3 .. .. 0 230 454 5 B. .. .. 2 12 36 21 8 4 .. .. 3 86 G. .. .. 4 17 48 28 9 3 .. .. 1 110 196 6 B. .. .. 1 6 48 52 38 10 .. .. 1 156 G. .. .. 1 11 52 49 26 5 .. .. 2 146 302 7 B. .. .. .. 2 12 35 21 7 0 .. 1 78 G. .. .. .. 2 15 21 15 4 1 .. 0 59 137 8 B. .. .. .. 0 10 23 19 19 2 0 2 75 G. .. .. .. 2 10 31 29 10 4 2 3 91 166 9 B. .. .. .. .. 1 4 4 2 .. 1 1 13 G. .. .. .. .. 1 6 12 4 .. 0 0 23 36 10 B. .. .. .. .. .. .. 1 3 3 1 .. 8 G. .. .. .. .. .. .. 4 3 3 1 .. 11 19 11 B. .. .. .. .. .. .. .. 0 0 0 .. 0 G. .. .. .. .. .. .. .. 2 1 1 .. 4 4 Tot. B. 1 54 154 264 290 201 120 50 6 2 14 1156 G. 3 50 196 309 312 235 123 34 9 4 16 1292 2448
Table V reads: In the first semester 1 boy and 3 girls drop out at age 13; 40 boys and 40 girls drop out at the age of 14; 49 boys and 65 girls, at the age of 15. In this table, as elsewhere, age 15 means from 141/2 to 151/2, and so on. Any drop-out, as for the second semester, means either during or at the end of that semester.
DISTRIBUTION OF THE NON-FAILING NON-GRADUATES, SHOWING THE SEMESTER AND THE AGE AT THE TIME OF DROPPING OUT
AGES SEMESTER 13 14 15 16 17 18 19 20 21 TOTALS
1 B. 17 118 141 106 39 3 4 1 1 430 G. 11 159 235 160 51 19 4 4 0 643 1073 2 B. 0 7 49 50 18 7 3 0 .. 134 G. 1 1 59 42 31 10 7 2 .. 163 297 3 B. .. .. 7 16 11 5 1 0 .. 40 G. .. .. 14 22 33 15 3 2 .. 89 129 4 B. .. .. 5 13 11 10 1 0 1 41 G. .. .. 7 20 31 16 2 1 1 78 119 5 B. .. .. 1 2 9 1 2 0 .. 15 G. .. .. 0 3 10 9 4 1 .. 27 42 6 B. .. .. 1 4 14 3 2 0 .. 24 G. .. .. 0 5 17 13 7 3 .. 45 69 7 B. .. .. .. 0 2 2 2 1 .. 7 G. .. .. .. 1 2 7 1 1 .. 12 19 8 B. .. .. .. .. .. 1 1 1 .. 3 G. .. .. .. .. .. 3 1 1 .. 5 8 9 B. .. .. .. .. .. .. .. 0 .. 0 G. .. .. .. .. .. .. .. 1 .. 1 1 Tot. B. 17 125 204 191 104 32 16 3 2 694 G. 12 170 315 253 175 92 29 16 1 1063 1757
Table VI reads similarly to Table V. The distribution of the age totals for the pupils dropping out gives us medians which, for both boys and girls, fall within the 17-year group for the failing pupils, but within the 16-year group for the non-failing pupils. For Table V the mode of the distribution is at 17, but for Table VI it is at 15. The percentages of dropping out for each age group are given below. First, all the pupils of Tables V and VI are grouped together for this purpose, then the boys and the girls for Tables V and VI are considered separately to facilitate the comparison of facts.
PERCENTAGES IN EACH AGE GROUP OF THE TOTAL NUMBER DROPPING OUT
Ages 13 14 15 16 17 18 19 20 21
Per Cent 0.8 9.5 20.7 24.2 21.0 13.3 6.8 2.4 1.2
It is readily seen from the above percentages that, as would be expected, the drop-outs are most frequent for the very ages which are most common in the high school. There is no special accumulation of drop-outs for either the earlier or the later ages. But, if in any semester we consider the drop-outs for each age as a percentage of the total pupils represented for that age, the facts are more fully revealed, as is indicated below for certain semesters.
PERCENTAGES OF DROP-OUTS FOR EACH AGE, ON THE TOTALS FOR SUCH AGE IN THE FIRST, SECOND AND FOURTH SEMESTERS
AGES 13 14 15 16 17 18 19 20 21
Semester 1 6.8 18.2 23.1 32.6 38.3 35.0 40.0 40.0 .. Semester 2 4.0 8.1 14.8 18.3 22.2 30.0 40.0 33.0 .. Semester 4 0 9.0 11.8 12.5 16.5 24.6 35.2 50.0 ..
If these semesters may be taken as indicative of all, an almost steady increase will be expected in the percentages of drop-outs as the ages of the pupils rise. It follows, then, that the older ages have the higher percentages of drop-outs when this basis of the computation is employed. We may, however, make some helpful comparisons of the ages of drop-outs for boys and for girls by merely using the percentages of total drop-outs for the purpose.
PERCENTAGES OF FAILING DROP-OUTS IN EACH AGE GROUP, FOR BOYS AND GIRLS SEPARATELY
AGES 13 14 15 16 17 18 19 20 21
Boys 0 4.6 12.5 22.8 25.1 17.4 10.3 4.3 1.9 Girls .2 3.8 15.1 23.9 24.1 19.0 9.5 2.6 2.2
Here it appears that, of all the boys and girls who fail before dropping out, the school loses at the age of 14, for example, 4.6 per cent for the boys and 3.8 per cent for the girls. As a matter of mere convenience, the percentages for age 21 are made to include also the undistributed pupils in Table V.
PERCENTAGES OF THE NON-FAILING DROP-OUTS IN EACH AGE GROUP, FOR BOYS AND GIRLS SEPARATELY
AGES 13 14 15 16 17 18 19 20
Boys 2.4 18.0 29.4 27.1 15.0 4.4 2.3 0.7 Girls 1.1 16.0 29.6 23.8 16.4 8.6 2.7 1.6
These percentages are computed from the age totals in Table VI, just as the ones preceding are computed from Table V. It seems worthy of note here that close to 50 per cent of the non-failing drop-outs occur under 16 years of age, for both the boys and the girls; but that the number of the failing pupils who drop out does not reach 20 per cent for the boys or the girls in these same years. It is likewise remarkable in these distributions that the percentages for boys and for girls show such slight differences in either of the two groupings.
SUMMARY OF CHAPTER II
If to the recorded failures the virtual but unrecorded ones are added, the percentage of failing pupils is 66 per cent. This percentage is higher for the boys than for the girls by a difference of 6 per cent.
Of the graduating pupils, 58.1 per cent fail one or more times.
Of the non-failing non-graduates 78 per cent are lost from school by the end of their first year. But the failing non-graduates have not lost such a percentage before the end of the third year.
The percentage of pupils failing increases for the first four semesters, and lowers but little for two more semesters. One third to one half of the pupils fail in each semester to seventh.
In the distribution of failures by ages and semesters, 86 per cent are found from ages 15 to 18 inclusive. Thirty-four per cent of the failures occur after the end of the second year, when 52.2 per cent of the pupils have been lost and others are leaving continuously.
Mathematics, Latin, and English head the list in the percentages of total failures, and together provide nearly 60 per cent of the failures; but English has a large subject-enrollment to balance its count in failures.
Mathematics, Latin, and German fail the highest percentages on the number of pupils taking the subjects.
In several subjects the percentages of failure based on the total failures are higher for the graduates than for the non-graduates.
For the pupils dropping out without failure the median age is at 16, with the mode at 15. For the failing drop-outs both the median and the mode are at the age of 17. Nearly 50 per cent of the non-failing drop-outs occur under age 16, but not 20 per cent of the failing non-graduates are gone by that age. The percentage of drop-outs is higher for older pupils.
5. Kelley, T.L. "A Study of High School and University Grades, with Reference to Their Intercorrelation and the Causes of Elimination," Journal of Educational Psychology, 6:365.
6. Johnson, G.R. "Qualitative Elimination in High School," School Review, 18:680.
7. Bliss, D.C. "High School Failures," Educational Administration and Supervision, Vol. 3.
8. Strayer, G.D., Coffman, L.D., Prosser, C.A. Report of a Survey of the School System of St. Paul, Minnesota.
9. Meredith, A.B. Survey of the St. Louis Public Schools, 1917, Vol. III, p. 51.
10. Annual Report of the Board of Education, Paterson, New Jersey, 1915.
11. Bobbitt, J.F. Report of the School Survey of Denver, 1916.
12. Strayer, G.D. A Survey of the Public Schools of Butte, 1914.
13. Rounds, C.R., Kingsbury, H.B. "Do Too Many Students Fail?" School Review, 21:585.
WHAT BASIS IS DISCOVERABLE FOR PROGNOSTICATING THE OCCURRENCE OF OR THE NUMBER OF FAILURES?
1. ATTENDANCE, MENTAL OR PHYSICAL DEFECTS, AND SIZE OF CLASSES ARE POSSIBLE FACTORS
Any definite factors available for the school that have a prognostic value in reference to school failures will help to perform a function quite comparable to the science of preventive medicine in its field, and in contrast with the older art of doctoring the malady after it has been permitted to develop. Such prognostication of failure, however, need not imply a complete knowledge of the causes of the failures. It may simply signify that in certain situations the causes are less active or are partly overcome by other factors.
Perhaps one of the simplest factors with a prognostic value on failure may be found in the facts of attendance. Persistent or repeated absence from school may reach a point where it tends to affect the number of failures. It happened, unfortunately, that the reports for attendance were incomplete or lacking in a considerable portion of the records employed in this study. Consequently the influence of attendance is given no especial consideration in these pages, except as explained in Chapter I, that the pupil must have been present enough of any semester to secure his subject grades, else no failure is counted and no time is charged to his period in school. In this connection, Dr. C.H. Keyes found in a study of elementary school pupils that of 1,649 pupils losing four weeks or more in a single year 459 belonged to the accelerate pupils, 647 to those arrested, and 543 to pupils normal in their school work. He accredits such large loss of time as almost invariably the result of illness and of contagious disease. He also says, "Prolonged absence from school is appreciable in producing arrest especially when it amounts to more than 25 days in one school year." But the diseases of childhood, with the resultant absence, are less prevalent in the high school years than earlier. Furthermore, the losses due to change of residence will not be met with here, for, as explained in Chapter I, no transferred pupils are included subsequent to the time of the transference either to or from the school.
The influence of physical or mental defects also deserves recognition here as a possible factor relative to school failures, although this study has no data to offer of any statistical value in that regard. A few pupils in high school may actually reach the limits prescribed by their 'intelligence quotient' or general mental ability, or perhaps, as Bronner so interestingly points out, be handicapped by some special mental disability. If such be true, they will doubtless be found in the number of school drop-outs later referred to as failing in 50 per cent or more of their work; but we have no measurement of intelligence recorded for them to serve our purposes of prognostication. In the matter of physical defects alone, the report of Dr. L.P. Ayres on a study of 3,304 pupils, ten to fourteen years old, in New York City, states that "In every case except in that of vision the children rated as 'dull' are found to be suffering from physical defects to a greater degree than 'normal' or 'bright' children." The defects of vision, which is the exception noted, may be even partly the result of the studious habits of the pupils. Bronner remarks on the "relationships between mental and physical conditions," and also on how "the findings on tests were altogether different after the child had been built up physically." But Gulick and Ayres conclude that it is evident from the facts at hand that if vision were omitted the percentage of defects would dwindle and become comparatively small among the upper grades. This would probably be still more true for the high school; but this whole field has not yet been completely and thoroughly investigated.
It would be very desirable to have ascertained the size of the classes in which the failures were most frequent, as well as the relative success of the pupils repeating subjects in larger or in smaller classes. But, as such facts were unobtainable, it is permitted here simply to recognize the possible influence of this factor. It seems deserving in itself of careful and special study. From the standpoint of the pupil, the kind of subject, the kind of teacher, and the sort of discipline employed will tend to influence the size of class to be called normal, and to make it a sort of variable. Thirty pupils is regarded by the North Central Association as the maximum size of class in high school. Surely the size of class will react on the pupil by affecting the teacher's spirit and energy. Reference is made by Hall-Quest to an experiment, whose author is not named, in which 829 pupils stated that their "most helpful teachers were pleasant, cheerful, optimistic, enthusiastic, and young." If such be true then the very large size of classes will tend to reduce the teacher's helpfulness.
2. THE EMPLOYMENT OF THE SCHOOL ENTERING AGE FOR PROGNOSIS
A promising but less emphasized basis of prognosticating the school success or failure of the pupils is found in the employment of the school entering ages for this purpose. The distribution of all the pupils (except 30 undistributed ones, for whom the records were incomplete), according to entering age, is here presented, independently for the boys and for the girls.
DISTRIBUTION OF PUPILS BY THEIR ENTRANCE AGES TO HIGH SCHOOL
AGES Undis- Total 12 13 14 15 16 17 18 19 20 tributed
2646 B. 16 211 820 900 497 148 23 10 7 14 3495 G. 8 259 1124 1217 614 194 51 10 8 16
The entering ages of these 6,141 pupils are distributed from 12 to 20, with 30 of them for whom the age records were not given. The median age for all the entrants is 15.3. But in order to compare this with the median entering age (14.9) of the 1,033 pupils reported by King for the Iowa City high school, or with the median entering age (14.5) of 1000 high school pupils in New York City, as reported by Van Denburg, it is necessary to reduce these medians to the same basis of age classification. Since age 15 for this study starts at 141/2, then 15.3 would be only 14.8 (15.3-.5) as by their classification. The percentages of the total number of pupils for each age are given below.
PERCENTAGES OF PUPILS FOR EACH ENTERING AGE
AGES 12 13 14 15 16 17 18 19 20 Undistributed Total 0.4 7.6 31.6 34.4 18.1 5.5 1.2 1.0 Boys 0.6 8.0 31.0 37.8 18.8 5.6 0.8 1.1 Girls 0.2 7.4 32.4 34.8 17.5 5.5 1.4 1.0
We see that 84 per cent of the pupils enter at age 14, 15, and 16, or, what is perhaps more important, that nearly 40 per cent enter under 15 years of age. The similarity of percentages for boys and for girls is pronounced. The slight advantage of the boys for ages 12 and 13 may be due to home influence in restricting the early entrance of the girls, thus causing a corresponding superiority for the girls at age 14. The mode of this percentage distribution is at 15 for both boys and girls.
What portion of each entering-age-group has no failures? This question and the answer presented below direct our attention to the superiority of the pupils of the earlier entering ages. That these groups of earlier ages of entrance are comprised of pupils selected for their capabilities is shown by the successive decrease in the percentages of the non-failing as the ages of their entrance increases, up to age 18.
DISTRIBUTION OF THE PUPILS WHO DO NOT FAIL, FOR EACH ENTERING-AGE-GROUP
AGES Totals 12 13 14 15 16 17 18 19 20
1061 B. 11 102 320 309 186 56 9 4 4 1575 G. 3 133 522 545 256 73 29 7 6 % of ————————- Entrants 58.0 50.0 43.4 40.0 39.8 37.7 55.0
Here is definite evidence that the pupils of the earlier entering ages are less likely to fail in any of their school subjects than are the older ones. Those entering at ages 12 or 13 escape school failures altogether for 50 per cent or more of their numbers. Those entering at age 14 are somewhat less successful but still seem superior to those of later entrance ages. It is encouraging, then, that these three ages of entrance include nearly 40 per cent of the 6,141 pupils. There is, of course, nothing in this situation to justify any deduction of the sort that pupils entering at the age of 17 would have been more successful had they been sent to high school earlier, except that had they been able to enter high school earlier they would have represented a different selection of ability by that fact alone. There is also a sort of selection operative for the pupils entering at ages 18, 19, or 20, which tends to account at least partly for the rise in the percentage of the non-failing for these years. It is safe to believe that for the most part only the more able, ambitious, and purposeful individuals are likely to display the energy required or to discern the need of their entering high school when they have reached the age of 18 or later. The appeal of school athletics will in this case seem very inadequate to explain their entrance so late, since the girls predominate so strongly for these years. Then it may be contended further that the added maturity and experience of those later entrants may partly compensate for a lack of native ability, if such be the case, and thereby result in a relatively high percentage of non-failing pupils for this group.
It is readily conceded that the avoidance of failure in school work serves as only one criterion for gauging the pupils' accomplishment. It is accordingly important to inquire how the different age-groups of school entrants compare with reference to the persistence and ability which is represented by school graduation. A truly striking array of percentages follows in reference to the question of how many of the entering pupils in each age-group do graduate.
DISTRIBUTION OF THE PUPILS GRADUATING FOR EACH ENTERING-AGE GROUP
AGES Totals 12 13 14 15 16 17 18 19 20
796 B. 14 115 290 253 99 20 2 1 2 1140 G. 5 151 465 363 121 26 5 1 0
% of Entrants 79.1 56.6 38.8 29.9 20.0 13.4 9.1 10.0 13.3
These percentages bear convincing testimony in support of the previous evidence that the pupils of the earlier entering years are highly selected in ability. Of all the high school entrants they are the 'most fit,' the least likely to fail, and the most certain to graduate. The percentage of pupils graduating who entered at the age of 12 is approximately four times that of pupils who entered at the age of 16. Thirteen is more than four times as fruitful of graduates as age 17; fourteen bears a similar relationship to age 18; and the percentage for fifteen is three times that for age 19, as is apparent from the above figures. The fact that the decline of these percentages ceases at age 19 is probably due to the greater maturity of such later entrants.
When we make inquiry as to what portion of the graduates in each of the above groups 'goes through' in four years or less, we get the series of percentages indicated below.
PERCENTAGE OF THE GRADUATES WHO FINISH IN FOUR YEARS OR LESS, FOR EACH OF THE ENTERING-AGE GROUPS
Ages 12 13 14 15 16 17 18
% of Each Group 84.3 85.7 75.8 79.5 84.3 80.4 100
It appears that the ones in the older age-groups who do graduate are not so handicapped in reference to the time requirement for graduation as we might have expected them to be from the facts of the preceding pages. Perhaps that fact is partly accounted for by the not unusual tendency to restrain the more rapid progress of the younger pupils or to promote the older ones partly by age, so that by our school procedure the younger and the brighter pupils may at times actually be more retarded, according to mental age, than are the older and slower ones.
Since the same teachers, the same schools, and the same administrative policy were involved for the different entrance-age groups, the prognostic value of the factor of age at entrance will seem to be unimpaired, whether it operates independently as a gauge of rank in mental ability, or conjointly with and indicative of the varying influence on these pupils of other concomitant factors, such as the difference of economic demands, the difference of social interests, the difference in permanence of conflicting habits of the individual, or the difference in effectiveness of the school's appeal as adapted for the several ages. One may contend, and with some success, that the high school regime is better adjusted to the younger pupils, with the consequent result that they are more successful in its requirements. The distractions of more numerous social interests may actually accompany the later years of school age. In reference to the social distractions of girls, Margaret Slattery says, "This mania for 'going' seizes many of our girls just when they need rest and natural pleasures, the great out-of-doors, and early hours of retiring." But surely such distractions are not peculiar to the girls alone. The economic needs that arise at the age of sixteen and later are often considered to constitute a pressing factor regarding the continuance in school. But VanDenburg was convinced by the investigation, in New York City, of 420 rentals for the families of pupils that "on the whole the economic status of these pupils seems to be only a slight factor in their continuance in school." A similar conclusion was reached by Wooley, in Cincinnati, after investigating 600 families, in which it was estimated that 73 per cent of the families did not need the earnings of the children who left school to go to work. The corresponding report by a commission in Massachusetts shows 76 per cent. The same facts for New York City indicate that 80 per cent of such families are independent of the child's wages. But Holley concludes, from a study of certain towns in Illinois, that "there is a high correlation between the economic, educational, and social advantages of a home and the number of years of school which its children receive." It will hardly be denied that even aside from the relation of the family means to the school persistence, the economic needs may have a direct influence on the failing of the children in their school work, either because home conditions may be decidedly unfavorable for required home study, or because of the larger portion of time that must be given to outside employment, with its consequent reduction of the normal vitality of the individual or of his readiness to study. But, in spite of the possible interrelationship of these factors, it still appears that the school entrance age of pupils will serve as a valuable sort of educational compass to foretell in part the probable direction of their later accomplishment.
3. THE AMOUNT OF FAILURE AT EACH AGE AND ITS RELATION TO THE POSSIBILITY OF FAILING FOR THAT AGE
We have considered at some length the prognostic value of the age at entrance. Here we shall briefly consider the prognostic value of age in reference to the time when failures occur and the amount of failure for such age. If we were to total all the failures for a given age, as shown in Table I, what part will that form of the total subjects taken by these pupils at the time the failures occur? In other words, what are the percentages formed by the total failures on the possibility of failing, for the same pupils and the same semesters, considered by age groups? The summary line of Table I gives the total failures according to the ages at which they occurred. The number of pupils sharing in each group of these failures is also known by a separate tabulation. Then the full number of subjects per pupil is taken as 41/2, since approximately 50 per cent of the pupils take five or more subjects each semester and the other 50 per cent take four or less (see p. 61). With the number of pupils given, and with a schedule of 41/2 subjects per pupil, we are able to compute the percentages which the failures form of the total subjects for these failing pupils at the time. These percentages are given below.
THE PERCENTAGES FORMED BY FAILURES AT EACH AGE ON THE POSSIBILITIES OF FAILING AT THAT AGE AND TIME, FOR THE SAME PUPILS
Ages 13 14 15 16 17 18 19 20 21
% 36.6 38.0 37.9 40.9 40.8 41.2 41.3 42.0 42.7
[Footnote: These percentages are computed from the data secured in Table I, as noted above.]
There is an almost unbroken rise in these percentages from 36.6 for age 13 to 42.7 for age 21. Not only do a greater number of the older pupils fail, as was previously indicated, but they also have a greater percentage of failure for the subjects which they are taking. It seems appropriate here to offer a caution that, in reading the above percentages, one must not conclude that all of age 14 fail in 38 per cent of their work, but rather that those who do fail at age 14 fail in 38 per cent of their work for that semester. The evidence does not seem to indicate that the maturity of later years operates to secure any general reduction of these percentages. The prognostic value of such facts seems to consist in leading us to expect a greater percentage of failures (on the total subjects) from the older pupils who fail than from the younger ones who fail. If it were possible to translate the above percentages to a basis of the possibility of failure for all pupils, instead of the possibility for failing pupils only, the disparity for the different ages would become more pronounced, as the earlier ages have more non-failing pupils. But this we are not able to do, as our data are not adequate for that purpose.
4. THE INITIAL RECORD IN HIGH SCHOOL FOR PROGNOSIS OF FAILURE
For this purpose the pupil record for the first year, in reference to failures, is deemed more adequate and dependable than the record for the first semester only. Accordingly, the pupils have been classified on their first year's record into those who had 0, 1, 2, 3, and up to 7 or more failures. Then these groups were further distributed into those who failed 0, 1, 2, 3, and up to 7 or more times after the first year. From such a double distribution we may get some indication of what assurance the first year's record offers on the expectation of later failures. Table VII presents these facts.
Table VII is read in this manner: Of all the pupils who have failures the first year (805 boys, and 1,129 girls) 397 boys and 672 girls have failures later, 105 boys and 130 girls have 1 failure later, 77 boys and 98 girls have 2 failures later, while 68 boys and 63 girls have seven or more failures later. The column of totals to the right gives the pupils for each number of failures for the first year. The line of totals at the bottom gives the pupils for each number of failures subsequent to the first year.
The table includes 3,508 pupils, since those who did not remain in school more than three semesters are not included (1,120 boys, 1,513 girls). Obviously, those who do not stay more than one year would have no subsequent school record, and those remaining only a brief time beyond one year would not have a record of comparable length. It seems quite significant, too, for the purposes of our prognosis, that of the 2,633 pupils dropping out in three semesters or less only about 43 per cent have ever failed (boys—46 per cent, girls—41 per cent). In contrast to this, nearly 70 per cent (69.6) of those continuing in school more than three semesters fail one or more times. Those who drop out without failure, in the three semesters or less, constitute nearly 60 per cent of the total non-failing pupils (2,568), but the failing pupils who drop out in that same period constitute less than 32 per cent of the total who fail (3,573). This situation received some emphasis in Chapter II and will be further treated in Chapter IV, under the comparison of the failing and non-failing groups.
SUBSEQUENT RECORD OF FAILURES FOR PUPILS FAILING 1, 2, 3, ETC., TIMES THE FIRST YEAR
FAILURES OF 1ST FAILURES SUBSEQUENT TO FIRST YEAR YEAR 0 1 2 3 4 5 6 7+ TOTALS
0 B. 397 105 77 50 47 37 24 68 805 G. 672 130 98 60 53 27 26 63 1129 1069 235 175 110 100 64 50 131 1934
1 B. 46 43 34 33 35 21 15 46 273 G. 65 43 53 33 33 19 17 67 330 111 86 87 66 68 40 32 113 603
2 B. 22 24 23 23 30 21 13 57 213 G. 42 32 27 21 22 13 15 83 255 64 56 50 44 52 34 28 140 468
3 B. 7 5 16 10 10 13 10 30 101 G. 8 9 7 10 17 6 7 41 105 15 14 23 20 27 19 17 71 206
4 B. 6 8 5 7 7 11 7 23 74 G. 8 7 5 6 10 8 4 27 75 14 15 10 13 17 19 11 50 149
5 B. 3 1 0 2 1 5 3 11 26 G. 5 9 5 6 5 4 2 14 50 8 10 5 8 6 9 5 25 76
6 B. 0 1 4 2 1 1 1 10 20 G. 2 1 2 2 6 2 0 6 21 2 2 6 4 7 3 1 16 41
7+ B. 3 2 1 0 1 0 2 5 14 G. 1 2 1 1 5 2 0 5 17 4 4 2 1 6 2 2 10 31
Tot. B. 484 189 160 127 132 109 75 250 1526 G. 803 233 198 139 151 81 71 306 1982 1287 422 358 266 283 190 146 556 3508
Referring directly now to Table VII, we find that 44.7 per cent of those not failing the first year do fail later. Of all those who fail the first year, 13.8 per cent escape any later failures. Of all the pupils included in this table 15.8 per cent have 7 or more failures, while of those failing in the first year 27 per cent later have 7 or more failures. For the number included in this table 30.4 per cent have no failures assigned to them.
PERCENTAGE OF FIRST YEAR FAILING GROUPS, WHO LATER HAVE NO FAILURES
No. of F's. in First Year 1 2 3 4 5 6 7+
Per Cent of Groups Having No Failures Later 18.4 13.7 7.2 9.4 10.5 5.0 12.9
About the same percentage of the boys and of the girls (near 60 per cent) is represented in Table VII. The girls have an advantage over the boys of about 8 per cent for those belonging to the group with no failures, and of about 1 per cent for the group with seven or more failures.
No unconditional conclusion seems justified by this table. In the first year's record of failures there are good grounds for the promise of later performance. We may safely say that those who do not fail the first year are much less likely to fail later, and that if they do fail later, they have less accumulation of failures. Yet some of this group have many failures after the first year, and others who have several failures the first year have none subsequently. Generally, however, the later accumulations are in almost direct ratio to the earlier record, and the later non-failures are in inverse ratio to the debits of the first year.
5. THE PROGNOSIS OF FAILURES BY THE SUBJECT SELECTION
From the distribution of failures by school subjects as presented in Chapter II, this will seem to be the easiest and almost the surest of all the factors thus far considered to employ for a prognosis of failure. For of all pupils taking Latin we may confidently expect an average of a little less than one pupil in every five to fail each semester. For the entire number taking mathematics, the expectation of failure is an average of about one in six for each semester. German comes next, and for each semester it claims for failure on the average nearly one pupil in every seven taking it. Similarly French claims for failure one in every nine; history, one in every ten; English and business subjects, less than one in every twelve. It will be noted that the average on a semester basis is employed in this part of the computation. Consequently, it is not the same as saying that such a percentage of pupils fail at some time, in the subject. The pupil who fails four times in first year mathematics is intentionally regarded here as representing four failures. Likewise, the pupil who completes four years of Latin without failure represents eight successes for the subject in calculating these percentages. Every recorded failure for each pupil is thus accounted for.