v-wf,tvt*i»*-'4V^«^>^"V'-^^'?ii> - '"'^aYHff*"^-^ : alional fepclittkp 'plii^i^^- ^ \f^ iui i Lvu n nww > ^ i w iii ii i i- i 'i i i i nr "' — — " HWi H ^. n . WH i'Nii "* *' "Wi» ili i) i WW i !ujtaWMkw«B>aa^ iis** ' « i*ll » y " W fi ifa ^^^'-J'r ALBERT R. MANN LIBRARY New York State Colleges OF Agriculture and Home Economics AT Cornell University Cornell University Library LB 3063.G77 Variations in the grades of high school 3 1924 013 088 996 The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924013088996 VARIATIONS IN THE GRADES OF HIGH SCHOOL PUPILS gattralional jpagtlfologg jMniiogtaplfH No. 8 Variations in the Grades of High School Pupils By CLARENCE TRUMAN GRAY, A. M. Instructor in the Department of Education, University of Texas. VsMimatt, H. ». A. WARWICK & YORK, Inc. 1913 Copytieht, 1913 WARWICK Ic YORK, Inc. EDITOR'S PREFACE. II Ten years ago no serious attempt had been made tc study scientifically the relative merits of various systems of grading students, despite the fact that statistical meth- ods for undertaking such studies were fully available and that grading plays so large a r61e in the school career of hundreds of thousands of school children." In the last five years, however, this inviting field has been the scene of numerous important investigations, so that we have at least arrived at a better understanding of the nature of the problem and of the general line along which progress must be made. In the present monograph, Mr. Gray reports the methods and results of his investigation of one phase of the general problem, viz : the nature, degree and causes of the varia- tions occurring in the grades of high-school pupils. His work should interest all teachers and more particularly all school administrators, because he not only shows clearly how unreliable are the gradalfcommonly given by teachers and makes evident the neerof instruction and training in grading, but also presents a relatively simple method by means of which any high-school principal can study the condition of the grading in his own school and take due steps to remedy the faults that he may find. It is hoped that this monograph may be followed in the near future by one or more other studies of the distribu- tion of grades. G. M. W. AUTHOR'S PREFACE. The general and specific purposes of the monograph are stated in the first few pages. The methods used are similar to those used by Ayres, Dearborn and Thorndike. One great value of this type of investigation is that it raises as many problems at is solves. Attention has been called to a number of these problems at various points in the text. The work was done at Chicago University under the direction of Dr. 0. H. Judd, Director of the School of Education, and Dr. W. F. Dearborn, Professor of Edu- cation. To these men I owe the greatest debt of grati- tude, for without their sympathy and assistance the inves- tigation could not have been made. I acknowledge very gratefully valuable suggestions upon method from Mr. Walter P. Morgan of Englewood High School, Chicago, and the indispensable aid given me by those principals and superintendents from whose schools the material was secured. Much credit is also due my wife, Bessie Stretcher Gray, for her help upon the clerical work which it was necessary to do in order to get the results. G. T. Gray. Austin, Texas, July, 1912. CONTENTS. FAGB Inteoductoey 7 The Peoblbm 11 Reasons foe Taking Up the Peoblem 11 The Mateeial 23 The Method 25 The Results : A. Variations in Different Subjects in the Sev- eral Schools 34 B. Variations of Pupils of Different Quintiles . 49 Explanation op the Vaeiations : A. Explanation of Some Individual Cases . . 51 B. Some Alleged General Causes of Variations. 56 C. Distribution of Grades as a Factor in Varia- tion 58 D. Different Types of Variation 90 E. Variation in the Grading of the Same Papers by Different Teachers 107 Geneeal Conclusions feom the Study 113 Bibliogeaphy 115 INTRODUCTORY. The general aim of this study is to base an edu- cational investigation upon school grades. Students of education have been very slow to enter this field for material in their studies. It is usually argued that such marks are inaccurate, that they are com- plex, that they are not scientific, and above all that it is impossible to measure mental traits by such cold statistics as grades afford. In direct contrast to these arguments stands the fact that all promotions from the kindergarten through the university are based upon these so-called inaccurate, complex, un- scientific and cold estimates of progress and achieve- ment. One of the most vital and fundamental prin- ciples of any school system is its plan of promotions, and because of the close relation between promotions and grades there is the most urgent need that school- men become interested in the problems of grading. In this connection Professor Cattell says,* "In ex- amination and grades which attempt to determine individual differences and to select individuals for special purposes, it seems strange that no scientific *See bibliography at end of tbe book for list of references on the problems of grading. 7 8 VAEIATIONS IN GRADES study of any consequence has been made to deter- mine the validity of our methods, to standardize and improve them. It is quite possible that the assign- ing of grades to school children and college students as a kind of reward or punishment is useless or worse. Its value could and should be determined. But when students are excluded from college because they do not secure a certain grade in a written exami- nation or when candidates for positions in govern- ment service are selected as a result of a written ex- amination, we assume a serious responsibility. The least that we can do is to make a scientific study of our methods and results." If we grant the arguments against such material, the need for such investigations is made the more apparent because the only way that these faults and limitations in our grading system can be remedied is by such scientific study as will reveal just w'here these defects are. Then suggestions can be made intelligently. One of Professor Dearborn's strong arguments for this type of investigation is that all grades may be considered the records of school experiments. He says, "In arguing for the school experiment the writer would not have it forgotten that in existing school records and reports and in present school practices there is already accumulated or available a body of data which, if properly evaluated, just as truly represents the results of experimental invest- gation as new experiments might do. School prac- tices always represent great educational experi- ments."* *8ohool Review Monographs, No, 1. INTBODUCTOBY 9 Similarly, Dr. Clement remarks: "When marks are recorded in a complete, accurate and intelligent manner, and when they cover a series of years, they furnish one important means among many of evalu- ating a school system. Let it be clear that it may not be the only means. But since marks have been used and are now used, they furnish one clue to the efficiency both of individuals and of institutions, "t Another phase of this matter which cannot be too strongly emphasized is the form and filing of school records. In one or two places where the writer went to get material it was so scattered and incomplete that it was worthless. In other places the records were kept in dingy and dusty store rooms in such form that to procure the needed data would have re- quired an excessive expenditure of time. These con- ditions exist not because school officials are negli- gent, but because they have not seen the value of con- tinuous school records. If they are convinced of their importance and practical value, conditions will immediately improve. On the other hand, it should be stated that in most places the grades were kept in bound volumes and were entirely accessible. In very few places, however, was any effort made to keep continuous, individual records. The record of a given pupil for a given year was in most cases en- tirely separate from his record for any other year. It was found, too, that records of attendance are con- ' sidered of very little importance after a school term ends. In no case was any effort made in any way to associate the grades of a pupil with his attendance records. These remarks will serve to emphasize the ^standardization of the Schools of Kansas, page 4. 10 VABIATIONS IN GBADBS fact that we need to have some practical work done upon school records. As to just what the correct form is there is great difference of opinion, but the data should certainly be rendered more imiform, more complete and more continuous. THE PROBLEM. The specific problem is concerned with the relative standing of pupils in the different years of the high- school curriculum, as indicated by their marks and grades. Suppose a pupil at the end of the first year has a mark of 80 points (per cent.), then our first problem is to determine whether this pupil's mark for the other three years remains near 80 points or goes up or down. Again, we may give the problem a somewhat dif- ferent turn by using relative position rather than points. If we divide any class into five equal parts, putting the highest grades in the first quintile, our problem will be to determine whether any given pupil does or does not remain in the same quintile throughout the four years. REASONS FOR TAKING UP THIS PROBLEM. First, it is evident that by comparing grades of high-school students we shall procure data which will make possible the comparison of different de- partments in the same high school. If pupils in one department make a much greater variation than those in another, there ought to be some way of ex- 11 12 VARIATIONS IN GEADBS plaining the greater variation, or the variation should be reduced. For instance, in one school un- der investigation there is a department which shows an average variation of 6.2 points, in mathematics, while in another department there is only a varia- tion of 3.2 points. Here, evidently, is a problem for the first department, because there is no obvious reason why pupils should make a higher variation in one subject than in another. It is of interest to compare the grading of one de- partment with that of another. The first graph be- low shows the distribution of grades of a class of twenty-five in first-year history. The second graph shows the distribution of grades of the same pupils in first-year English. NO. I. 6 s 5 o 4 ^ 1 i 00 00 10 9 3. NO. 7 6 5 4 3 2 1 1 fi5 1 The altitude of any rectangle represents the num- ber of pupils in that particular group. The grades range from 70 to 100, and are divided into six THE PBOBLEM 13 groups, as shown by the numbers in each rectangle. Thus, in history there are six pupils in the group. 70-74, two in the group 75-79, and so on. It is evi- dent that these two departments are marking ia such a manner as to get a very different distribution of grades. The history grades run either high or low, while in English the majority of the class is put in the middle group. The material is also of interest to us because it makes possible a comparison of the grades which a department gives to the same pupils from year to year. The graphs on pages 14-19 give such data for one of the high schools studied. The distri- bution of the English grades is especially interesting because of the large numbers placed in the lowest groups for the fourth year. Comparing the English with the Science, the graphs show that the policies of the two departments differ radically. The way in which the particular English department marks is probably related to the practice of a neighboring college which is very severe in its grading. There is certainly a problem here for the English depart- ment. Either their peculiar practice should be ex- plained or it should be changed, for the natural ex- pectation would be that classes would improve in the later years in a subject. In collecting this material one principal was found * who had used this same kind of data to assure him- self that his teachers were using grades which meant the same to all. He submitted all the grades of a given pupil to all the instructors of that pupil. At first the teachers regarded the plan as a criticism, but later took it as a help and were eager to examine PLATE 1. DISTRIBUTION OF ENGLISH GRADES FDR nRST YEAR. ATL 30 .2^ 10. 7S-79 80-34 S5-89 90-94 Sg-lOO 14 PLATE %. DISTRIBUTION OF ENGLISH GRADES FOR SECOND YEAR. 1 T^Q 20 90-95 10 75-73 50-34 as-a9 95-100 15 PLATE 3, CISTRIBimON OF ENGLISH GRADES FOR THIRD YEAR 30 20 10 |7r-79 60-34 85-69 90- 9» 95-100 16 __so. 40 ._ao. 20 10 PLATE 4. DISTRIBUTION OF ENGLISH GRADES FOR FOURTH YEAR . 75-79 60-84 Sg-de 90-94 9g-100 17 PLATE 5. DISTRIBUTION OF GRADES IN THIRD YEAR SCIENCE. 40 _acL 20 10 3 75-79 ao-84 85-89 90-95 95-100 18 PLATE 6. DISTRIBUTION OF'GfiA0ES IN FOURTH YEAR SQENCE. 30 1 20 10 75-79 80-84 85-89 90-94 95-lOoi 10 20 VABIATIONS IN GEADES the data, because if a pupil was making 95 in three departments and only 80 in the fourth, there was probably some reason for the low mark which the teacher could find out. A further use to which a study of grades may be put can be described by calling attention to the fact that a principal can compare his high school with any college to which a number of his pupils go. To illus- trate, suppose a principal has a graduating class of fifty. He can easily divide this class into quintiles, and so find the relative position of each pupil in any or all subjects. Then, if ten of this class, two from each quintile, enter the same college and join a class of one hundred, he can, at the end of the year, obtain the grades of the Freshman class in one or more sub- jects. He should divide this college class into quin- tiles ; he then has a right to expect to find his pupils taking their respective places in these quintiles. If they have lost in position, either the college work is pitched too high or the high-school work is pitched too low. / Furthermore, not only can a high school be com- pared with a college, but through the college various high schools may be compared with each other. To compare one high school with other high schools rep- resented in the college Freshman class it would be necessary to get the grades from all the high schools, so that the relative positions of the members of this college class in their respective high schools could be determined. If in any other high school as many pupils had lost in position as in the high school under consideration, then the principal could conclude that the college work was pitched too high for this enter- THE PBOBLEM 21 ing class. While, on the other hand, if the majority of the pupils from this group of high schools held their positions when they reached the college, then the principal could feel sure that his own school was pitched too low, and his problem would be to raise his standard. This same method of comparison by means of the college work can be used in the comparison of teach- ers, because, if the the pupils of one teacher exhibit little variation when they go to college, it is reason- ably sure that they are working in the same way as the college, while if the pupils of another teacher exhibit wide variation in the direction of loss in posi- tion, then it is evident that the high-school work is not so conducted as to give adequate preparation. It might be argued that such variations as those mentioned above might be due to changes in subject- matter, or that the teacher does not have the ability to discriminate carefully in her grading. If this is true, the problem still exists just the same, and should be met. It is true, too, that facts of this sort would be in- valuable to university inspectors and State high- school inspectors, because the thing in which they are primarily interested is the quality and consist- ency of the work of each school under consideration. The present method of these inspectors is to get this knowledge by a day's visit and by general observa- tion of the external affairs of the school, whereas, if they had at hand a quantity of such material col- lected through several years, they would have a much more rational basis from which to draw their con- clusions. 22 VABIATIONS IN GRADES la fact, the purpose of this work is to get at what may be called an internal analysis and comparison of high schools. This is better than mere reliance upon external characteristics, such as attendance, buildings, number of teachers, laboratories, etc., which have thus far supplied the basis for estimates of school efficiency. THE MATERIAL. The grades used are from two of the public schools in Chicago and eight Indiana schools. The material from Indiana was procured at Indianapolis, Terre Haute, Elwood, Alexandria, Tipton, Oakland City, Madison and Spencer. The schools in Chicago are two of the largest and best organized in the city. One of them is a large Manual Training School. Indianapolis and Terre Haute are cities which represent large business in- terests. In both places the high schools operate un- der good conditions. The remaining cities vary in population from three to fifteen thousand. While they have some manufacturing, they are for the most part in the midst of large agricultural districts, and have a large number of students from the country. With the exception of one of the smaller cities, all have good conditions for school work. The enroll- ment of these schools varies from one hundred and twenty-five to fifteen hundred. Almost any phase of high-school work which can be found anywhere can be found in some one of these schools, so that the material is certainly representative. The grades used in most cases are the year-grades in English, History, Mathematics, Latin, Modern Languages and Science. The only exception is in the 23 24 VABIATIONS IN GBADES case of the Manual Training School, where English, Drawing, Shop Work, Mathematics and Science were procured. In a few places the marks were in such a form as to make it impossible to get just what was wanted. For instance, in one place a mark was given each month, and at the end of a half-year a term-examination was required: no average was given, and because of the great labor required in computing averages the average of the marks for the first two months in the year was used as the year- grade for the first two years, and the average for the last two months was used as the year-grade for the last two years. In two places the grades were in letters, and these were transformed to points (per cents.) according to the key furnished by the prin- cipal. The grades for one school were gotten for each quarter in the year. By getting the grades of twenty-five pupils through the first year and twenty- five through the second, third and fourth years, there is the opportunity of finding what variations are made in any one year. THE METHOD. In gathering the material cards were printed and filled out as is shown herewith : Name or number 1 Second -High School. 1st Year 2d Year 3d Year 4th Year Gain Loss Pos. Bal. Neg. Bal. Total Enslish Grade.... 89 92 84 85 4 8 4 12 Position .. History Grade.... 85 83 82 3 3 3 Position .. Mathematics... Grade.... 88 84 80 8 8 8 Position .. Grade.... 88 78 79 79 1 10 9 11 Position.. Modern Grade.... Position.. Science Grade.... 80 91 11 11 11 Position .. It will be noted that this pupil had four years of English, three years of mathematics, four years of Latin, two years of science and three years of his- tory. 25 26 VABIATIONS IN GBADBS The grades in English usually included both the literature and the composition work. History in- cluded any history work done, and in some cases a half-year of civics. Mathematics means algebra, geometry, trigonometry, and in most of the Indiana schools a half-year of arithmetic. Modern lan- guages includes both German and French. The greatest range of subjects is foimd in science. In- cluded in it are physics, chemistry, botany, zoology, physical geography and physiology. In the case here chosen as an example we will omit for the time the matter of position and study the variations in points. If the second-year mark is higher than the first-year mark, then there is a gain from the first to the second year. There will also be a gain if the third-year grade is higher than the sec- ond, or the fourth-year higher than the third. On the other hand, if the second-year grade is lower than the first or the third lower than the second or the fourth lower than the third, then there is a loss. The sum of all the gains is put in the gain column ; the sum of all the losses is put in the loss column. If the gains are larger than the losses, then there is a positive balance; if the losses are larger than the gains, then the difference is a negative balance. The sum of all the gains and losses, regardless of sign, is put in the total column. In the subject of English (on the card chosen for an example) it will be noted that from first to the second year there is a gain of 3 points, and that from the third to the fourth year another gain of 1 point is made, so that there is a total gain of 4 points, which is placed in the gain column From the second to the THE METHOD 27 third year there is a loss of 8 points, which is placed in the loss column. The loss is 4 greater than the gain, so that there is a negative balance of 4. The sum of 4 and 8 gives the total variation, 12. To. get the average variation for a class we make an actual count of the variations from the first to the second year, then from the second to the third year, and finally from the third to the fourth year. In one class of 26 the following results were gotten in the manner indicated above : Variaions in Points from First to Second Tear. ipils. Variations. Totals. 3 make equals a 1 3 2 2 4 4 3 12 1 4 4 3 5 15 2 6 12 1 7 7 2 8 16 2 9 18 2 10 20 1 15 15 26 126 To determine the average variation it is only nec- essary to divide the total number of variations by the number of pupils; that is, 126 divided by 26 equals 4.8, which is the average variation* of the •The term "Average Variation" Is not used here with the mean- ing usually given it in statistical work, but refers to the averages of the variations which a group of pupils make in their grades or rank as they pass from year to year. 28 VAEIATIONS IN GRADES class from the first to the second year. It will be noted, too, from the table that the variations are relatively small. Only ten pupils vary more than five points, and only three vary ten or more points. Variations in Points from the Second to the Third Year, ipils. Variations. Totals, 4 5 1 5 3 2 6 3 4 12 4 5 20 1 6 6 1 7 7 1 8 8 3 11 33 1 13 13 26 110 110 divided by 26 equals 4.2, Av. Var. Here, again, the great majority of these pupils have less than five points of variation. Variation im, Pomts from the Third to the Fourth Year. Pupils. Variations. Totals, 5 6 1 6 6 2 12 3 3 9 2 4 8 1 5 6 2 7 14 1 8 8 1 10 10 26 71 71 divided by 26 gives 2.7, Av. Var. THE METHOD 29 To determine the average variation for the four years, we may take the average of the three varia- tions already found. This is 3,9, Now, the same material may be worked over to find the positional variations. In order to give each pupil a relative position in a class of 25, the class was divided into quintiles. In making these divisions the five highest grades Were put in the first division, the next highest five in the second division, and so on until the twenty-five are canvassed. In one class of 25 the divisions* for the first year English work were as follows (Roman figures indi- cate the quintiles) : I. II. III. IV. V. 95 86 85 80 76 92 86 84 80 74 91 86 82 79 73 90 85 81 78 72 89 85 81 76 71 The position, i e., the quintile, of each pupil is marked on his card for this year in English, and the same process is gone through for the second and sub- sequent years, so that finally each pupil has a 'posi- tion' in each subject for each year. When the pupil has been given a position in each subject, his card will resemble the following: *It might be noted that the lowest grade in the second quintile is 85, and that the highest grade in the third quintile is also 85. The like fact also appears in the fourth and fifth quintiles. This is simply a shortcoming of the machinery of the investigation, and while tt may raise the average variation in position, yet the results will not be materially changed. In any case the variations are not likely to be lowered by these accidents in the methods of calcu- lation. 30 VAEIATIONS IN GRADES Name- or number 14 k]DU -High School. 1st Year 2d Year 8d Year 4th Year Gain Loss Pos. Bal. Nee. Bal. Total Enelieh Grade.... 70 70 70 72 Position .. 5 5 5 5 HistorT Grade.... 70 71 75 Position .. 5 5 4 Mathematics. . . Grade.... 72 77 73 75 Position .. 5 3 4 5 Grade.... Position.. Modern Grade.... 74 77 70 Lansuases... Position.. 4 5 5 Science Grade.... 75 72 71 Position.. 5 5 5 In mathematics from the first to the second year this pupil passes from the fifth to the third quintile, so that a gain of two positions is placed in the gain colmnn. From the second to the third year there is a loss of one position and from the third to the fourth year there is a loss of another position, making a total loss of two positions, which is placed in the loss column. Since the loss is equal the gains, there is neither a negative or positive balance. The total variation is 4. When each school subject has been treated in this manner, the card will appear as follows : THE METHOD 31 Name- or number 14 Second -High School. 1st Year 2d Year 3d Year 4th Year Gain Loss Pos. Bal. ^1f: Total English Grade.... 70 70 70 72 Position .. 5 5 5 5 Grade.... 70 71 75 Position.. 5 5 4 1 _ _ 1 1 Mathematics .. Grade .. . . 72 77 73 75 Position.. 5 3 4 5 2 2 4 Grade.... Position.. Modern Grade.... 74 77 70 Languages... Position.. 4 5 5 1 1 1 Grade.... 75 72 71 Position.. 5 5 5 The next step is to make out tables similar to those made out for the variations in points. The following table was secured for a class of 25 in English from the first to the second year : upils. Variations. Totals 9 13 1 13 2 2 4 1 3 3 25 20 20 -f- 25 ^ .80 as the average variation in position. In like manner other tables could be arranged for the variations from the second to the third or from the third to the fourth year. 32 VAEIATIONS IN GRADES The three tables for either the variations in points or in position can be reduced to one table by taking into consideration the results given in the total col- uTTiTi and the number of opportunities which each pupil has for variation. The opportunities depend upon the number of years that a pupil pursues a sub- ject. That is, if algebra is studied two years, there is only one opportunity to vary, since there can be no variation until after the pupil has received one grade. In the same way if a study is pursued for three years, there are two opportunities for varia- tion ; if for four years, three opportunities. The following table will illustrate the above points : Opportunities Total Pupils. for each. opportunities. Variations. Totals. 2 3 6 2 4 1 3 3 4 4 2 3 6 5 10 3 3 9 6 18 3 3 9 7 21 2 3 6 9 18 3 3 10 10 3 3 11 11 3 3 12 12 3 3 14 14 3 3 15 15 3 3 16 16 3 3 19 19 3 3 20 20 3 3 21 21 3 3 23 23 3 3 3 3 29 43 29 43 25 75 308 308 (the total number of variations) divided by 75 (the number of opportunities) gives 4.0 average variation. THE METHOD 33 In most cases the number of opportunities is not so easily calculated, because not all the pupils pursue the same subject for the same length of time. Thus, many take history for two years, while others con- tinue it for three or four years. This makes it nec- essary to count the opportunities for each pupil. For this reason the number of opportunities has been in- dicated at the end of each table. RESULTS. A. Variations in Different Subjects in the Several Schools. The following tables show the results for the dif- ferent schools in the different subjects: TABLE 1. )r Total Variations in Pointa for EngUsh. — ScJ 'uplls. Variations. Totals, 1 1 1 6 3 18 3 4 12 10 5 60 6 6 30 10 7 70 13 8 104 8 9 72 8 10 80 12 11 132 9 12 108 6 13 78 5 14 70 4 15 60 7 16 112 5 17 85 2 18 36 3 19 57 2 20 40 5 22 110 2 23 46 2 24 48 128 1419 Total Opportunities, 374. 1419 H- 374 = 3.7, Av. Var. 34 THE BESULTS TABLE 2. ^ Table for Gains in Points in English.- -School 1. Pupils. Variations. Totala, 29 16 1 16 21 2 42 15 3 45 10 4 40 10 5 50 7 6 42 6 7 42 7 8 56 1 9 9 3 10 30 2 11 22 1 13 13 35 128 407 Total Opportunities, 374. 407 ^ 374 = 1.06, Av. Gain. TABLE 3. able for Losses in Points in English- -School 1. 'upil 's. Variations. Totals, 3 3 1 3 10 3 30 10 4 40 10 5 50 10 6 60 14 7 98 12 8 96 16 9 144 8 10 80 10 11 110 5 12 60 4 13 52 8 14 112 3 15 45 2 16 32 128 1012 Total Opportunities, 374. 1012 -H 374 = 2.66, Av. Loss. 36 VAKIATIONS IN GBADES A comparison of Tables 2 and 3 shows that there is a strong tendency in this school to mark more severely in English during the later years than dur- ing the earlier ones, since losses predominate over gains. TABLE 4. 3 for Total Variations in Points in History. — Schi Pupils. Variations. Totals, 17 2 1 2 7 2 14 12 4 48 21 5 105 2 6 12 14 8 112 3 9 27 4 10 40 4 12 48 3 13 39 3 14 42 2 15 30 2 16 32 3 17 51 4 18 72 1 19 19 1 20 20 1 21 21 2 22 44 1 27 27 1 28 28 1 35 35 111 868 Opportunities to vary ,259, 868 H H 259 = 3.3, Av. Var. THE EESTJLTS TABLE 5. Ota] ! Foriafions in Points in Mathematics. — i ipils i. Variations. Totals. 2 4 8 1 5 5 1 6 6 1 8 8 1 9 9 1 10 10 2 11 22 1 12 12 2 13 26 2 15 30 2 17 34 1 18 18 1 19 19 3 21 63 1 22 22 1 24 24 1 28 28 1 37 37 37 25 381 Opportunities to vary, 75. 381 -^ 75 = 5.0, At. Var. TABLE 6. e for Total Variations in Points in Latin. — Sohoi Pupils. Variations. Totals. 1 1 1 2 7 14 2 8 16 2 9 18 1 13 13 3 15 45 2 16 32 2 18 36 1 19 19 2 20 40 1 21 21 3 22 66 1 24 24 23 345 Opportunities to vary, 68. 345 -H 68 = 5.0, Av. Var. 38 VAEIATIONS IN GEADES TABLE 7. Table for Total Variations in Modern Languages in Points,- School 7. Pupils. Variations. Totals. 2 6 1 5 2 2 4 2 3 6 3 4 12 2 5 10 1 6 6 3 8 24 9 9 10 10 11 11 12 48 14 14 16 16 19 19 30 194 Opportunities to vary, 55. 194 -H 55 = 3.5, Av. Var. THE BESUIiTS 39 TABLE 8. ! for Total Va/riations in Points in Science. — Schc Pupils. Variations. Totals. 2 6 1 6 2 2 4 4 3 12 6 4 24 12 5 60 5 6 30 8 7 56 T 8 56 7 9 63 16 10 160 8 11 88 9 12 108 7 13 91 2 14 28 2 15 30 2 16 32 4 17 68 2 18 36 4 19 76 2 20 40 1 21 21 1 22 22 4 23 92 1 30 30 1 33 33 125 1269 Opportunities to vary, 251. 1269 -H 251 = 5.0, Av. Var. 40 VAEIATIONS IN GRADES TABLE 9. tor Total Va/riations in Position in English. — 8c) Pupils. Variations. Totals, 19 25 1 25 23 2 46 21 3 63 16 4 64 9 5 45 3 6 18 2 7 14 128 275 Total Opportunities, 374. 275 -T- 374 = 0.74, Av. Var. TABLE 10. lie for Gains in Position in English.- — School . apils. Variations. Totals. 46 42 1 42 24 2 48 11 3 33 2 4 8 3 5 15 128 146 Total Opportunities, 374. 146 -^ 374 = 0.39, Av. Gain. THE BESULTS 41 TABLE H. Table for Losses m Position in English. — School 1. Variations. Totals. 1 45 2 54 3 36 4 24 128 159 Total Opportunities, 374. 159 -H 374 = 0.43, Av. Loss. TABLE 12. for Variations in Position in Mathematics. — Soh Pupils. Variations. Totals. 33 26 1 26 42 2 84 ^ 8 75 10 4 40 7 5 35 2 6 12 145 272 Total Opportunities, 278. 272 -r- 278 = 0.97, Av. Var. TABLE 13. Taile for Variations in Position in History. — School S, Second Year. Pupils. Variations. Totals. 5 8 18 5 2 10 3 3 9 3 4 12 15 5 25 44 Total Opportunities, 75. 44 ^ 75 = 0.58, Av. Var. 42 VARIATIONS IN GEADES TABLE 14. Table for Total Variations in Position in Latin. — School 1. Pupils. Variations. Totals, 26 26 1 26 25 2 50 10 3 30 4 4 16 1 5 5 92 127 Total Opportunities, 107. 127 -H 107 = 1.2, Av. Var. TABLE 15. Table for Total Variations in Position in Modern Lomguages.- School 3. Pupils. Variations. Totals. 15 19 1 19 13 2 26 10 3 30 2 4 8 1 6 6 60 Total Opportunities, 109. 89 -H 109 = 0.81, At. Var. 89 TABLE 16. Table for Variations in Position in Science. — School S. Pupils. Variations. Totals. 23 38 1 38 28 2 66 22 3 66 10 4 40 2 5 10 3 6 18 126 Total Opportunities, 809. 228-5-309 = 0.80, Av. Var. 228 PLATE 7. CURVE BASED CM THE TOTkL \ARIATI0NS IN PERCENT IN MATHEMATICS FOR SCHOOL 9. AB5C1SSA=V?\RIAT10NS. ORDINATE= PUPILS. 43 PL^E 8. CURVE BASED ON THE TOTAL WilATIOHS IN POSITION HISTORY SCHOOL 1 . ABSCISSA=\?yiI AT lONS . ORDTNArE= PUPILS. 44 THE RESULTS 45 TABLE 17. Table Comparing Averages for Variations in Points. Subject, English. Totals. Gains. School 1 , 3.7 1.0 School 2 — 1 yr 4.1 1.9 2 yr 3.3 1.6 3 yr 3.0 2.0 4 yr 4.4 3.1 Average 3.7 2.1 School 3 4.1 2.6 School 4 3.6 1.8 School 5 5:6 2.4 School 6 3.5 1.4 School 7 4.0 2.8 School 8 3.8 1.4 School 9 4.2 2.8 School 10 3.9 Average 4.0 2.0 Losses. 2.6 2.2 1.8 1.0 1.7 1.7 1.5 1.8 3.2 2.1 1.2 2.4 1.4 1.9 TABLE 18. Comparing Variations in Points in History. Totals. School 1 4.4 School 2—1 yr 3.8 2 yr. 3.0 3 yr 2.7 4 yr 3.5 Average 3.3 School 3 3.3 School 4 3.8 School 5 4.1 School 6 3.5 School 7 5.3 School 8 3.6 School 9 2.8 Average 3.8 Gains. 2.2 2.0 1.5 1.0 1.4 1.5 2.1 1.9 1.8 1.7 2.9 0.7 1.5 1.8 Losses. 2.2 1.8 1.5 1.7 2.1 1.8 1.2 1.9 2.3 1.8 2.4 2.8 1.3 1.9 46 VABIATIONS IN GEADES TABLE 19. Comparing Variations im Points in Mathematics. Totals. School 1 4.7 School 2—1 yr 6.2 2 yr. 4.6 3 yr 5.2 4 yr 3.0 Average 4.7 School 3 4.6 School 4 5.0 School 5 5.9 School 6 4.1 School 7 3.7 School 8 4.4 School 9 1.5 School 10 4.5 Average 4.3 Gains. 1.6 2.8 2.3 2.5 2.0 2.4 1.6 2.8 2.8 1.7 20 1.2 0.6 1.8 Losses. 3.1 3.5 2.5 3.0 1.0 2.3 3.0 2.2 3.1 2.4 1.7 8,2 0.9 2.4 TABLE 20. Comparing Variations in Points in Latin. Totals. Gains. School 1 3.5 1.0 School 2—1 yr. 3.2 1.4 2 yr 3.9 2.3 3 yr. 2.2 1.6 4 yr 2.1 1.1 Average 2.8 1.6 School 3 3.6 1.7 School 4 4.4 1.9 School 5 5.0 1.6 School 6 2.5 1.5 School 7 3.2 1.1 School 8 3.2 1.1 School 9 3.6 1.2 Average 3.5 1.4 Losses. 25 1.8 1.6 0.6 1.0 1.2 1.9 2.5 3.4 1.0 2.1 2.1 2.4 2.1 THE BBSULTS 47 TABLE 21. Comparing Variations in Points in Modern Languages, Totals. School 1 4.0 School 2 * School 3 3.4 School 4 3.1 School 5 * School 6 2.3 School 7 * School 8 3.5 School 9 3.2 Average 3.2 *Data insufficient. Gains. Losses. 0.9 3.1 • * 2.0 1.4 2.2 0.9 * * 1.6 0.7 * * 1.2 2.3 1.9 1.3 1.6 1.6 TABLE 22. Comparing Variations in Points in Science. Totals. Gains. Losses. School 1 5.0 1.6 3.4 School 2 • * * School 3 3.6 1.5 2.1 School 4 8.0 1.0 2.0 School 5 5.4 2.1 3.3 School 6 6.3 2.4 3.9 School 7 • • * School 8 5.0 2.3 2.7 School 9 4.6 2.6 2.0 School 10 4.9 Average 3.7 1.5 2.1 *Data insufficient. The variations of School 10 in drawing is 3.9, and in shop work 46. 48 VABIATIONS IN GEADES TABLE 23. Comparing Variations in Position. Mathe- Mod. English. History, matics. Latin. Lang. Science. School 1 1.00 0.76 1.00 1.20 0.84 1.10 School 2 0.66 0.93 0.88 0.50 School 3 0.86 0.56 0.97 0.74 0.81 0.80 School 4 0.69 0.88 0.76 0.82 0.67 0.54 School 5 1.80 1.10 1.20 1.00 ... 1.30 School 6 0.76 0.76 0.80 0.44 0.46 0.88 School 7 0.78 0.83 0.40 0.69 School 8 1.00 0.64 1.00 0.80 0.85 1.10 School 9 0.80 0.78 0.43 0.77 0.04 1.30 Average... 0.87 0.80 0.82 0.77 0.74 1.00 In the averages, the greatest variation is in Science, with English next. The large variation in Science can possibly be explained by the fact that the mate- rial used in the different years is unrelated ; that is, the work in Physiography of the first year would be of little help to the work in Physics in the third year. The large variation in English seems to be due in a large degree to the eratic grading of this depart- ment in many of the schools. School 5 exhibits the greatest variability. The probable explanation is to be found in a severe strug- gle which this school has had with fraternities. It is not at all strange that such a struggle should affect the grades of the school. School 10 is a well-established Manual Training School in Chicago. This school was put in the list because it was suggested that the interest of the pupils in their work in such a school would reduce the variations to a marked degree. This proves not to be true, for the variations made are approximately those made by other schools. If the interest of the THE RESULTS 49 pupils is greater (wMcli may, with good reasons, be doubted), these data only indicate that the varia- tion of a pupil's work is due to a large extent to in- fluences over which the pupil has no control. B. Variations of Pupils of Different Quintiles. The question may now be raised: Which of the five groups of pupils shows the greatest variation? To answer this question those who are in the first quintile the first year are taken as the first quintile ; those who are in the second quintile for the first year are considered as the second quintile, and so on to the fifth quintile. The total number of variations in position for each quintile is then determined. Some typical results follow : TABLE 24. Variations of Pupils of Different Quintiles. -School 4. ( , School 6- Quintile. Variation. Quintile. Variation. English 15 18 2 11 2 16 3 17 3 13 4 10 4 14 5 8 5 13 History 16 18 2 6 2 12 3 14 3 9 4 9 4 8 5 9 5 6 Mathematics 1 7 1 11 2 15 2 20 3 11 3 17 4 12 4 13 5 13 5 6 Science 1 5 1 7 2 6 2 14 3 9 3 9 4 15 4 8 5 5 5 9 50 VABIATIOKS IIT OBADES It will be noted that in not a few cases the first and fifth quintiles make the fewest variations, while the third makes the most. The fact that the first and fifth make the fewest variations may be due to the fact that these quintiles have only half as many chances to vary as the other quintiles; that is, the first quintile cannot go into a higher quintile and those in the fifth cannot go lower if they are to re- main in the class. On the other hand, it may be argued that the first quintile stands for greater abil- ity, energy, etc., and so is a more constant quantity. It might also be said of the fifth quintile that it is composed of pupils of less ability, and, since the only change which this group can make is an advance, the chances are that those in it will not change posi- tion. The reason the third quintile is the one to exhibit the largest variation seems to be that this group comes at a place in the grading scale where it is easier to change position than at any other place. By this is meant that it is much easier to shift from 85 to 88 than from 95 to 98, and that it is not so serious to shift from 85 to 80 as from 75 to 70, so that the tendency will be for teachers to vary the marks of this group more than those of the other groups. EXPLANATION OF THE VARIATIONS. A. Explanation of Some Individual Variations. The pupils in School 2 were all well known to the author, so that explanations can be offered for some individual cases. In the following tables those pupils that show an average variability greater than 5 are indicated by figures at the left. In a few cases it is possible to give an explanation for pupils whose average variation is less than 5. These pupils are indicated by letters at the left. TABLE 25. Variations in English. — First Tear, in, Points, hy Quarters. Pupils. VariationB. Totals. 2 2 4 14 4 2 5 10 3 6 18 3 7 21 2 9 18 1 10 10 1 11 11 1 12 12 (a) 1 14 14 (b) 1 15 15 (1) 1 16 16 (2) 1 19 19 (3) 1 20 20 (4) 1 21 21 (5) 1 23 23 (6) 1 29 29 (7) 1 43 43 51 52 VABIATIONS IN GBADES No. 7 was a coixntry student who had had little or no training in English. He could do some of the work well, but some of it scarcely at all, so that as the work changed from quarter to quarter his grades went up and down. His health was also a hindrance. No. 6 was a boy who did poor work at the begin- ning of the year, but who, by the end of the first half- year, was doing work of 90 per cent, grade. By the close of the year he had lost all interest, and did not return the next year. No. 5 was a boy who had the idea that the high school was a place for fun. After a severe punish- ment for some misconduct he settled down and did good work for a while, but was soon back at his old tricks. No. 4 was a very bright girl, but her teachers al- ways complained that she would not do consistent work. No. 3 was a girl who attempted to copy her way through school. She copied her written work from day to day, and used every means to copy on tests and examinations. When the teachers applied means to stop this, her grades naturally fell off decidedly. She never graduated. No. 2 was a boy who was very much interested in the outside affairs of the school. Later in his course he made several failures. No. 1 was a student from the country. While a consistent student, it seemed to take her the first quarter to get settled in her new surroundings. Most of her variation was made from the first to the second quarter. Very little explanation can be given for (a) and EXPLANATION OP THE VAEIATIONS 53 (&). Lack of interest near the end of tlie year may account for a part of it. For the other students in Table 25 no explanation can be given. TABLE 26. e for Variations in History. — First Year ', ScTwc Pupils. Variations. Totals. 1 2 2 3 3 9 4 4 5 5 6 6 7 7 8 16 9 9 10 10 12 12 (1) 1 16 16 (2) 2 17 34 (3) 1 20 20 (4) 1 21 21 (5) 1 28 28 (6) 1 33 33 No. 6 is the same pupil as No. 2 in English (Table 25). No. 5 was a country student who did poor work for the first two quarters, and then did 90 per cent, work for the remainder of the time. No. 4 is No. 7 in English. No. 3 is No. 6 in English. One of the two numbered 2 was a student who started in this subject at 78 per cent., but by the end of the year was doing work worth 95 per cent. The second one numbered 2 is Pupil 1 in English. No. 1 was a boy who had to do much outside work in order to be able to stay in school. For the remaining pupils no explanation can be offered. It is to be noted that several pupils who 54 VABIATIONS IN QBADES show large variations here are those who show large variations in English. In this manner each subject for each year was canvassed. The following table (No. 27) will indi- cate that pupils who exhibit marked variation in one subject will, in many cases, exhibit marked variation in one or more other subjects. The X indicates the subject where the pupil's vari- ation first appears. The R indicates that the varia- tion is also shown in the subject opposite. TABLE3 27. First Year Pupils. — School 2. Pupils. 1 2 3 4 5 6 7 8 9 10 H 13 13 English XXXXXXX — — — — — — History RR R RX X X — — — Mathematics. RR RR — R R — — — X X X Latin — R R — R R — — _ TABLE 28. Per Cent, of Pupils Whose Average Variation la Greater or Less than Five Points. Eng- His- Mod. School. Variation. lish. tory. Math. Latin. Lang. Science, No. 3.— Five or less than 5... 61 74 67 68 75 73 Greater than 5 39 26 33 32 25 27 No. 4.— Five or less than 5... 72 72 56 76 81 80 Greater than 5 28 28 44 24 19 20 No. 5. — Five or less than 5. . . 48 74 52 48 . . 65 Greater than 5 52 26 48 52 . . 35 No. 6.— Five or less than 5... 75 63 68 84 90 64 Greater than 5 ..25 37 32 16 10 36 No. 7.— Five or less than 5.. . 70 46 76 70 Greater than 5 30 54 24 30 No. 8.— Five or less than 5... 76 72 63 74 70 50 Greater than 5 24 28 37 26 30 50 No. 9.— Five or less than 5... 66 90 97 71 95 74 Greater than 5 34 10 3 29 5 26 EXPLANATION OF THE VARIATIONS 55 In the same manner, 1 was taken as a basis for total variations in position, and the per cent, of those who showed a greater or less variation was calcu- lated in the same way. Table 29 embodies results for some of the schools. TABLE 29. Per Cent, of Pupils Whose Average Variation Is Greater or Less than One Position. Eng- His- Mod. School. Variation. Ush. tory. Math. lAtln. Lang. Science. No. 3. — One or none. 72 87 66 80 73 75 Greater than 1 28 13 34 20 27 25 No. 4. — One or none 84 80 88 100 87 96 Greater than 1 16 20 12 .^ 13 4 No. 5. — One or none 74 61 56 74 . . 61 Greater than 1 26 39 44 26 .. 39 No. 6.— One or none 79 85 72 89 90 93 Greater than 1 21 15 28 11 10 7 No. 7.— One or none. 81 72 100 92 Greater than 1 19 28 .. 8 From this examination of individual cases and tables 28 and 29 we may conclude : X (1) There is a class of students in our high schools whose work is characterized by great variability. (2) Many of those students who show high variations in one subject also show high variations in other subjects. (3) It is possible in some cases to explain a greater variation than five by means of certain ele- ments in the pupil's school life over which the pupil has more or less control, but a less variation than five evidently has some other explanation. (4) Certain causes of variation, such as lack of interest and diffi- culty of adjustment to new conditions, offer serious problems in high-school adjninistration. 56 VARIATIONS IN GRADES B. Some Alleged General Causes of Variations. While the author was collecting this material many persons suggested to him that home conditions, application, deportment and social tendencies were factors which entered into the problem to a very great degree. In order to see what effect these had upon the variations made by pupils, he took his own school, which was in a town of about 3000 inhabitants. Since he had been there a number of years and was perfectly familiar with all the .conditions, he was able to assign to each pupil a grade in each of the points mentioned above. If the home was one where the parents were inter- ested in the school and who asked about the progress of the pupil occasionally, or if they were persons to whom the teacher might go for a consultation with perfect assurance that he would be well received, that home was graded A. Other homes were graded B, C or D. In case of the social tendencies, the pupil's per- sonality, social standing and the social standing of the family were taken into consideration. The same grades. A, B, C and D, were given here and for other points mentioned. In order to check this part of the work, another teacher who was familiar with these conditions was asked to grade some of the pupils. These grades were found in nearly every case to agree with those given by the author. After the grading was done the total variations, gains and losses were counted for each grade in all the points under consideration. The only subject used was English. EXPLANATION OF THE VABIATIONS 57 The results for home conditions, deportment, ap- plication and social tendencies are shown in Tables 30-33. TABLE 30. Relation oj Home Conditions to Total Variations (1126), Gains (654) and Losses (473) in English,. r-Hom es.— X Total Variations. r— Gains.--, ,— Losses.^ Per Abso- Per Abso- Per Abso- Per Graded. cent. lute. cent. lute. cent. lute. cent. A 51 547 48 294 44 254 53 B 32 425 37 268 40 155 33 G 9 96 8 43 6 47 10 D 8 60 5 49 7 17 4 TABLE 31. Relation of Deportment to Total Variations, Gains and Losses w English. Deportment. Total Variations. r-Gains.-^ r-Losses.- Per Abso- Per Abso- Per Abso- Per Graded. cent. lute. cent. lute. cent. lute. cent. A 70 731 65 444 67 279 59 B 18 259 23 144 22 115 24 C 10 106 9.3 62 10 53 11 D 2 30 2.5 4 TABLE 32. .006 26 5 Relation of Application to Total Variations, Gains and Losses in English. Application. Total Variations. r-Gains.- -Losses.- Per Abso- Per Abso- Per Abso- Per Graded. cent. lute. cent. lute. cent. lute. cent. A 31 303 27 168 26 125 26 B 37 396 35 257 39 154 32 27 350 31 199 30 151 32 D 5 77 7 30 5 43 10 58 VAEIATIONS IS- GBADBS TABLE 33. Relation of Social Tendencies to Total Variations, Gains and Losses in English. Social Tend. Total Variations. r-Gains.— > r-liosses.- Per Abso- Per Abso- Per Abso- Per Graded. cent lute. cent lute cent lute. cent A 27 263 23 141 22 116 25 B 15 203 18 120 18 83 18 C 23 192 17 131 20 59 13 D 35 468 41 262 40 211 44 A study of these tables cannot fail to impress one with the fact that there is little or no correlation be- tween the variations and the home conditions, de- portment, application or social tendencies. The con- clusion to be reached here is that the very things which are usually supposed most to affect the vari- ability of a pupil's marks have really very little to do with them. C. Distribution of Grades As a Factor in Variation. We next enter upon a discussion of the ways in which it is possible to distribute a set of grades. This general discussion will lead to a consideration of the types of variation found in the schools above reported, and we shall then be able to see just what happened when the different variations mentioned on the preceding pages were made. A teacher gives grades to the individuals of a class in order to communicate to them her estimates of their ability. Of course, the term ability means something very different in English from what it does in mathematics, but in either case the grade is a symbol of the teacher's estimate of the pupil. In most of the schools which are included in this re- EXPLANATION OF THE . VAEIATIONS 59 port 100 points was used as the symbol of perfection, and each pupil was graded with respect to this ideal. It will be noticed, too, that as soon as a pupil is lo- cated in this way he is also located in relation to his classmates; that is, he receives a position in his class. A grade of 85 points for a pupil means that his work could have been 15 points better, and also, if others make more than 85, that some one is better than he, and that he is better than those who make less than 85. One phase of grading is usually deter- mined by the administration, namely, the range and meaning of the marks used. For instance, a super- intendent directs his teachers to use 60 or 70 for a minimal passing mark — ^to range successful pupils between this and 100. In other cases the symbols A, ' B, C, D and E are used. Either system leaves the teacher to determine what particular grades she will use for individual cases, and, above all, it leaves her to decide how many of each denomination she will give. For the moment w,e may confine ourselves to the matter of distribution within a system and ask how a teacher, or a department, or a school should dis- tribute grades between the two limits 70 and 100. If grades measure ability, what do we know about ability? What grades of ability have we a right to expect to find in a school between the limits men- tioned above? Psychologists have recently added much to our knowledge of the distribution of mental traits. They have shown that the probable distribu- tion of ability is that of a chance event. The curve 60 VABIATIONS IN GEADBS for such an event would approach the following, which is kaown in mathematics as the curve of error : BilL M£D/UM PERFECT The question now comes : Should the distribution of grades which are estimates of ability follow this distribution? Theoretically, it should. This theory is partially supported by the distribution of 8969 grades taken from Harvard College. These grades were divided into quintiles, and the per cent, falling in each division is, respectively, 7, 20, 42, 21 and 7. 'It is not argued that a school should follow this ideal curve exactly, but that the curve serves as a guide to keep in mind. On the following pages Plates 9 to 19 represent the total distribution of all grades in the different schools. PLATE 9. DISTRIBUTION OF ALL GRADES FOR SCHOOL 1, 30 20 /] 10 f] P in n o/ k 75 80 85* 90 9S 100 61 PLATE 10. DISTRIBUTION OF ALL GRH)ES FOR RRST YEAR. M. 4D 30 go 10 SCHOOL 2. £ nJ N^ 70 75 80 6$ 90 9? 100 62 PLATE 11. DISTRIBUTION OF GRADES FOR SECOND YEAR. SCHOOL ^. .^Q. 30 fl 20 1 10 n-iy fM I 70 75" 80 &S 90 95 100 63 PLATE 12. aSTMBUTlON OF ALL GRADES FOR THIRD YEAR. SCHOOL a. A^ 30 IQ. IQl [i£py 70 75 80 85 90 9F 100 64 PLATE 13. DISTRIBUTION OF ALL GRADES FOR FOUfiTHYEAR. SCHOOL 2. 40 30 20 10 0_. M Lq u\ 70 75 80 85 90 9S 100 PLATE 14. DISTRIBUTION OF AIL GRADES FOR SCHOOL 4-. ZO 20 JO. 4J \ 70 IS ao 85 90 9? lOO 66 PLATE IF. DISTRIBUTION OF ALL GRADES FOR SCHOOL S. 30 JQ. J M. a! O IHi-'lr' nJ ui v ^ 70 7S 80 85 90 9? KX) 67 PLATE 16. DISTRIBUTION OF ALL GRADES FOR SCHOOL 6. GRADES TRANSFERRED FROM LETTERS TO PERCENT^. SEE PAGE 7. 5CALE EXPRESSED IN PERCENT. 15; ^ M m- n u , 7a 64- 67 90 93 959697 98 PLATE 17. DISTRIBUTION OF ALL GRADES FOR SCHOOL 7. 40 30 20 1Q_ or 1 70 75" 80 85 90 «5 100 PLATE 18. DISTRIBUTION OF ALL GRADES FX)R SCHOOL 8. 40 , 30 20 r^J 10 kil in u 1 r-^ 70 75 eo 8S 90 « ICO 70 PLATE 19 DJSTRIBUriON OF ALL GRADES FOR SCHOOL 9. GRADES TRANSFERRED FROM LETTERS TO PERCENT5 SEE PAGE 7 SCALE EXPRESSED IN PERCENT. IS^ iOl M. nn i 75 77 80 83 84 87 9093 96 71 72 VABIATIONS IN GEADES An examination of these charts shows decided dif- ferences in distribution. These differences might be indicated in this manner : Scbool 1 Fairly normal. School 2 — 1 yr Very erratic. 2 yr Very erratic. 3 yr Very erratic. 4 yr Very erratic. School 4 Skewed to the right School 5 Skewed to left. School 6 Trinodal. Three grades used principally. School 7 Skewed to left. School 8 Fairly normal. School 9 Skewed to the left. Schools 1 and 8 have a distribution which is about as near the normal curve as is usually found in actual practice. It will be noted that certain grades are car- ried above the main body of the curve, while on the other hand all the grades between the limits have been used, showing that an';attempt has been made carefully to distinguish the different grades of ability. It is next to impossible to justify such a distribu- tion as that shown in the different years for School 2. An administrative feature in connection with this school is interesting. The grade 90 is an exemption- grade from the bi-monthly examinations. A casual glance shows that this grade is by far the most popu- lar one with the teachers. They intended to be rig- orous in their grading, but it seems that this feature of the marking system has caused them to be too lib- eral in their grading and to skew the curves decid- edly to the right. It is noticeable that the multiples of five are the favored grades, while certain other EXPLANATION OP THE VARIATIONS 73 grades are not used at all. The 70-column is also worthy of note. In this school it is necessary for a pupil to do a year's work entirely over if he fails in one subject ; on account of this it has become in the community generally customary for a pupil to leave school when he fails. To counteract this custom, the teachers very often condition pupils by giving them 70 instead of a mark below 70. Schools 3 and 6 represent typical distributions for a grading system where letters are used. It will be noticed that many of the columns are fairly equal in height, which is the result to be expected since there are so few groups. The principal objection to this kind of grading is that it allows no fine discrimina- tion, but rather groups the pupils into four or five general classes. School 4 has a curve which is decidedly skewed to the right, i. e., the school is liberal in its grading. The grades from 70 to 80 are rarely used. Only a few unfortxmate ones are placed here. It would be interesting to know how pupils from a school like this would fare later at a college. In Schools 5 and 9 we have a curve which is skewed to the left. It is to be supposed that this is an at- tempt to be rigorous in grading, though this may or may not be the case. The following curves (Plates 20-25) show the dis- tribution of the grades in English in different schools. PLATE 20. DISTRIBUTION OF ENGLISH GRADES FDR SCHOOL 1. 30 nJ ^0 10 Ln 1/1 ^n 75 60 6S 90 95 74 PLATE 21. DISTRIBUTION OF ENGLISH GRADES. SCHOOL £. FIRST YEAR. - 10 n ui 70 7S ao J^ 85 90 XL 95 97 75 PLATE 9.9i. DISTRIBUTION OF ENGLISH GRADES. SCHOOL 2. SECOND YEAR . iO. n n nfl Hln 70 75 SQ 65 nJ 90 Ln 95 a. 100 76 PLATE 23. DISTRIBUTION CF GRADES IN ENGLISH. SCHOOL 2. THED YEAR. 10 \ npn ilM 7S 80 65 In 90 95 _!. 100 77 PLATE 24. DISTRIBOTION or GRADES IN ENGLISH. SCHOOL S. FOURTH YEAR. 10 d Unr^j m 70 73 80 8S 90 95 100 78 PLATE 2S. DISTRIBUTION OF GRADES IN ENGLISH. SCHOOL 3. SO AO. SO 90 10 £L 75 80 85 aa 79 9S 80 VABIATIONS IN GRADES Tie salient features of these different curves are as follows: School 1 Stewed to left decidedly. School 2 — 1 yr Skewed to the right. 2 yr. Skewed to right 3 yr. Skewed to right decidedly. 4 yr Skewed to xight. School 3 Skewed to ri^it School 4 Skewed to right. School 5 Skewed to left. School 6 Skewed to right. School 7 Trinodal. School 8 Skewed to right. School 9 Binodal. None of the curves, then, approaches the normal. There seems to he a decided tendency to grade Ub- erally in this subject, as is indicated by the fact that many of the curves are skewed to the right. In sev- eral of the schools certain grades are used over- f requently, while others are not used at all. We have noted that in School 1 the curve is skewed to the left in a decided way. This school happens to be in the shadow of a great university which treats its stu- dents in English in this same manner, so that this distribution is, according to the testimony of teach- ers in the high school, a reflection of the attitude of this university. In three of these schools we have grades enough to get a good idea of the distribution for different years. These curves are shown in Plates 26-33. PLATE a6. DISTRIBUTION OF GRADES IN ENGLISH SCHOOL I FIRST YEAR. Lr 75 60 5? lu 90 9ff too 81 PLATE 27. DISTRIBUTIOM OF GBADE5 IN EN&LBH SCHOOL 1 SECOND YEAR. 82 PLATE 28. DISTRIBUTION OF GRADES IN ENGLISH. SCHOOL 1. THIRD YEAR. 10 J ^\/u 75 60 § 65 96 o 83 PLATE 29. DISTRIBUTION OF GRADES IN ENGLISH SCHOOL 1. FOURTH YEAR. iO m [Rn o_xL 7S \ 65- 06 84 PLATE 30. DISTRIBUTION OF GRADES IN EMGLISH. SCHOOL 3. FIRST YEAR. 30 20 10 n a IS 60 65 90