EXCHANGE 
 
Studies of Mental Fatigue 
 
 In Relation to the Daily School Program 
 
 W. H. HECK, M. A. 
 
 PROFESSOR OF EDUCATION, UNIVERSITY OF VIRGINIA 
 
 AUTHOR OF 
 "MENTAL DISCIPLINE AND EDUCATIONAL VALUES" 
 
 SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 
 FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN COLUMBIA UNIVERSITY 
 
 LYNCHBURG, VIRGINIA 
 
 J. P. BELL COMPANY, INCORPORATED, PRINTERS 
 1914 
 
LBlc 
 
 TABLE OF CONTENTS 
 
 PAGE 
 
 INTRODUCTION 3 
 
 FIRST STUDY 5 
 
 Conditions 5 
 
 Material 6 
 
 Method 10 
 
 Grading 15 
 
 Kesults 17 
 
 SECOND STUDY 27 
 
 THIRD STUDY 33 
 
 CONCLUSIONS 37 
 
STUDIES OF MENTAL FATIGUE 
 
 INTRODUCTION 
 
 American books on school management and hygiene 1 show a 
 practical though not complete agreement as to the curves of 
 fatigue in relation to the daily school program. Conclusions 
 from German experiments on fatigue are the main bases for 
 this American opinion, which is somewhat as follows: The 
 child's efficiency, on the average, is greatest from about 9 :30 
 (after a period for settling down to work) to 11 A. M., and then 
 declines until the noon intermission; the child comes back in 
 the afternoon partially refreshed by the long recess and the mid- 
 day meal, depending of course upon the length of the recess 
 (usually one hour) and the quantity and quality of the food 
 eaten ; the second high plateau of efficiency, which is lower than 
 the corresponding plateau of the morning session, extends from 
 about 1 :30 to 2 :30 P. M., and is followed by a decline to the 
 lowest point of the day at the time of dismissal. Some writers 
 believe that the second plateau occurs later in the afternoon 
 than 1 :30 p. M. In a one-session school day the decline from 
 the high morning plateau is interrupted to only a small degree 
 by one or two short recesses, and extends to a point below that 
 at the close of the morning session of a two-session day. 
 
 Such text-book opinions are fast becoming guides for making 
 daily school programs throughout the United States. Univer- 
 sity departments of education, normal schools, summer schools, 
 and teachers' reading circles are also urging reform in programs 
 according to the following suggestions: The most difficult sub- 
 jects in the curriculum, if they can be determined for a particu- 
 lar class, should be placed, both for class recitation and for 
 individual study, at the periods of greatest efficiency, with 
 special emphasis upon the high morning plateau for arithmetic 
 
 *For example: Arnold, School and Class Management, Vol. II, p. 33; 
 Bagley, Educative Process, pp. 340-2, and Classroom Management, p. 57; 
 Bolton, Principles of Education, pp. 274-5; Chancellor, Class Teaching and 
 Management, pp. 122, 3; Colgrove, The Teacher and the School, p. 180; 
 Cornell, Health and Medical Inspection of School Children, p. 193; 
 Hellister, High School Administration, p. 254; O'Shea, Dynamic Factors 
 in Education, pp. 286-290; Perry, Management of a City School, pp. 99, 
 100; Roark, Economy in Education, pp. 65, 94; Seeley, New School 
 Management, p. 49; Shaw, School Hygiene, pp. 230, 1. 
 
4 STUDIES OF MENTAL FATIGUE 
 
 or language drill ; the less difficult subjects should be distributed 
 appropriately along the curves of fatigue ; and recesses, relaxa- 
 tion exercises, and alternations of recitation with study periods 
 should be used to defer and lessen the decrease in efficiency. 
 Thus the waste of the child's energy would be checked and more 
 school work be accomplished in a given time. 
 
 The purpose of this monograph is not to review the vast and 
 bewildering literature on fatigue, or even that which has domi- 
 nated American thought on the daily school program, but to re- 
 port experiments testing the validity of the prevailing American 
 opinion and the suggestions based thereon. 1 
 
 *I am greatly indebted to Dr. Edward L. Thorndike, Teachers' College, 
 Columbia University, for many suggestions regarding this work. The sum- 
 maries of experiments on Fatigue in his Educational Psychology, vol. iii, 
 and in Offner's Mental Fatigue (English translation by Whjpple) render 
 unnecessary any bibliographical discussion in this monograph. My second 
 and third experiments were reported in the PsycJiological Clinic and the 
 Journal of Educational Psychology. 
 
FIRST STUDY 
 
 CONDITIONS. 
 
 The tests were given during the session 1911-12 to forty 
 classes, 1,153 children, in four New York City schools, repre- 
 senting different nationalities and different grades of social and 
 hygienic opportunities. On four days (each being four or five 
 days apart) in December, 1911, four classes of fifth-grade girls, 
 mainly Russian Jews, were tested in Public School 177 ; on 
 four Fridays in January, 1912, eight classes of 5A boys, and on 
 four Mondays eight classes of 5B boys, mainly Italians and Pol- 
 ish Jews, were tested in Public School 83 ; on four Wednesdays 
 in January four fourth-grade and four fifth-grade boys and 
 girls, mainly Irish, German, and American, were tested in Pub- 
 lic School 27; on two Wednesdays in March and two in April 
 six fifth-grade and six sixth-grade boys and girls, mainly Ameri- 
 can (with several negroes), were tested in Public School 3, 
 Brooklyn. Fifteen of the forty classes tested were 5A classes 
 and fifteen were 5B classes. Together they furnished the stand- 
 ard for the work, but two 4A, two 4B, three 6A, and three 6B 
 classes were chosen to represent other stages of advancement. 
 The normal-aged and over-aged (E) sections of the half-grades 
 in P. S. 177 and the high (a), middle (b), and low (c) sections 
 of the half-grades in P. S. 3 were included, as were also the un- 
 differentiated sections in P. S. 83 and 27. Of course the differ- 
 ent ability of classes of different stages of advancement did not 
 affect my results, because in any comparison of the work at the 
 four periods of the school day the work of the same class would 
 be represented at each period, and thus would be compared with 
 itself and not with a less or more advanced class. The tests in 
 P. S. 177, 83, and 27 came before the mid-session promotion; 
 those in P. S. 3 came after, and therefore were given to some- 
 what younger and less advanced children according to grade. 
 Though more boys than girls took all four of the tests, the re- 
 sults fairly represent both sexes. The December, March, and 
 April tests were given in mild weather, the January tests in 
 cold weather; and the ventilation of the classrooms was corre- 
 spondingly varied, especially by the use of window ventilation. 
 The ventilating and lighting systems were excellent in P. S. 
 27, good in P. S. 177, and fair in P. S. 83 and 3. Twenty 
 classes were tested on Wednesdays, eight on Fridays, eight on 
 Mondays, and four on different days in the week, thus repre- 
 senting supposedly varied degrees of freshness in children in 
 relation to the week's schooling. The children, tested were 
 
6 STUDIES OF MENTAL FATIGUE 
 
 under medical supervision and their most obvious physical 
 defects, especially of a contagious kind, had been looked after ; 
 but very few children had been given a general routine exam- 
 ination by the school doctors. The daily school programs were 
 not uniform, sometimes even in the same school, but showed a 
 general tendency to give arithmetic in the early morning. In 
 P. S. 83 a group system was used throughout^ about half of a 
 class being grouped around the teacher for study while the 
 other half carried out previous directions as to work at black- 
 boards or desks. 
 
 The differences as to social and hygienic condition of children 
 and schools, and as to months and days, did not affect my com- 
 parisons of the work of the classes at four periods of the school 
 day, because the classes were tested and compared in groups 
 of four, every class in a group having almost the same conditions 
 and being tested on the same days. These variations in the 
 groups as a whole were purposely sought to see if any conse- 
 quent changes could be noticed in the work of the groups as com- 
 pared with each other, but they were so slight as to be negligible. 
 The differences in children and schools were representative 
 of New York City school conditions, though the four schools 
 selected were superior in supervision. 
 
 MATERIAL. 
 
 As my aim was to find out what decrease in efficiency re- 
 sulted from the progress of the day and especially of the school 
 work, I determined to test a large number of children at four 
 different periods of the school day and compare the quantity 
 and the quality of the work done. Xot the slightest change 
 was to be made in the ordinary school routine except the in- 
 terruptions for the short time necessary to give the tests. My 
 desire was to select test material as nearly like the actual lessons 
 of the children as possible and thus avoid the artificiality, at 
 least for my purpose, of most of the physiological and psycho- 
 logical tests so far made. I therefore chose, as most suitable 
 for my purpose, the four fundamental operations of addition, 
 subtraction, multiplication, and division with whole numbers. 
 Of course these operations could not represent all of arithmetic 
 or all of the curriculum, but neither could any other test 
 material; and as the basis of all number work they were as 
 representative as any part of the elementary curriculum 
 could be. 
 
 In order to carry out my plan of testing children at four 
 periods of the school day, and comparing the work done, I had 
 
MATERIAL 7 
 
 /to have four different tests so similar in quantity and quality 
 that a certain proportion of correct and incorrect work in the 
 first test would be as nearly equal as possible to the same pro- 
 portion in any one of the other three tests. Only in this way 
 could the work at the four periods be conveniently compared. 
 Of course it was impossible to have four different tests exactly 
 equal as to quantity and quality, but the reader can see from 
 the third and fourth tests herein printed that this result was 
 very nearly approached. 
 
 As the Standard Tests in Arithmetic, by Mr. S. A. Courtis 
 of Detroit, are widely recognized as well planned and graded, 
 I obtained Mr. Courtis' kind permission to modify and use 
 his Test No. 7, and also his imitation of it, which differed 
 almost entirely by a shifting of the figures in each example. 
 With my first and second tests thus furnished, I made out the 
 third and fourth in imitation of these by a similar shifting of 
 the figures. In the few examples where a figure was substituted 
 by Mr. Courtis in the second test for one in the first, that 
 figure reappeared in the fourth test but not in the third. Mr. 
 Courtis' tests were not entirely suitable for my purpose in three 
 particulars: (1) The required transfer by the child of the 
 examples and of the answers could not be reduced to a propor- 
 tionate measurement along with the work in the operations 
 themselves. Consequently each example in my tests was 
 printed in workable form with space underneath for the figures 
 to be made by the child. (2) The arithmetical symbols were 
 eliminated, and the operations necessary were designated by 
 the words, "Add," etc., above the examples. (3) Example 
 la, 2 a, 9, and 17 were omitted, thus making each test consist 
 of three examples each in addition, subtraction, multiplication, 
 and division. The examples were printed in three parallel 
 rows, each row with one example in each operation in the order 
 just given. (These modifications were made by me without 
 consulting Mr. Courtis, and he is in no way responsible for 
 them.) The first row contained examples with no, the second 
 with simple, and the third with advanced, borrowing and carry- 
 ing. However advantageous it might have seemed for all the 
 examples to have been of approximately equal difficulty, the 
 wisdom of Mr. Courtis' three grades of difficulty was shown 
 in the zest gained by the children in my tests from the rapid 
 start with the easy examples of the first row. (The third and 
 fourth tests are herewith given, the original size 8% x 11 
 inches and type being reduced.) 
 
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10 STUDIES OF MENTAL FATIGUE 
 
 METHOD. 
 
 I explained to the teachers beforehand the purpose and 
 method of my experiments and asked them to remain in the 
 room while the tests were being given. They were earnestly 
 requested not to take any part in explaining or directing the 
 work, not to discuss the tests with the children at other times, 
 and not to vary the prescribed arithmetic lessons in the slightest 
 so as to stress the four fundamental operations. (The children 
 were doing more advanced work.) As far as I know, these 
 requests were faithfully carried out, and the teachers were 
 always courteous in making way for my work. I eliminated 
 the teachers from any part in conducting the tests, because 
 uniformity in method was possible only with one conductor 
 throughout. 
 
 The presence of the teacher in a classroom gave the customary 
 organization as a background for my tests. The method of 
 presenting the tests to the children was worked out with great 
 care. When I entered a classroom for the first time, the teacher 
 directed the children to put aside whatever work they were 
 doing individually or collectively. I then explained the nature 
 of my four tests, the order in which the examples were to be 
 done (with a caution not to skip the examples in division) , and 
 the directions for starting and stopping work immediately on 
 signal. These explanations were almost the same to all classes 
 and seemed so clear that most of the children began the first 
 test with nearly as much understanding as they did the other 
 three. An inevitable initial interest partly balanced whatever 
 initial disadvantage the children may have had in the first test. 
 The introductions to the later tests were very brief. The 
 children thought they were being examined for correctness in 
 speed and never realized the main purpose of the tests. More- 
 over, they did not know that their results would have no effect 
 upon their school standing. 
 
 When all pencils were ready (in P. S. 83 pens were used) 
 the teacher and I put on each desk one test sheet with the back 
 side up. The children were not allowed to touch the tests until 
 told to write on the back of the sheets the number of the school, 
 the date, and the name, age, and class of pupil. (Later on I 
 inserted the time of day when the test began.) On signal, the 
 children turned the papers over immediately and began to work 
 the examples in the numbered order. They worked steadily as 
 directed, with surprisingly little hurry or interruption, until 
 
METHOD 11 
 
 told to stop, when they turned their papers over without put- 
 ting down another figure. During the test, I quietly watched 
 the children and their papers, so as to prevent cheating, toward 
 which there was little inclination, and to see that the examples 
 were worked in proper order and without hurry, especially 
 toward the end. The children did not know how much time 
 was being allowed, the progress of time was not mentioned, and 
 I consulted my watch almost without being noticed. 
 
 The time limit for each test was ten minutes, not long enough 
 for the children to be fatigued by the test itself. Great care 
 was taken to be exact in starting and stopping. The first four 
 (those in P. S. 177) of the forty classes tested were given 
 twelve minutes, which time, of course, was maintained through- 
 out the four tests with these classes, and did not affect the total 
 results as far as my purpose was concerned the twelve-minute 
 tests being compared only with each other. But as many 
 children in these four classes finished in ten or eleven minutes, 
 the time limit was reduced to ten with the other classes. Even 
 then several children finished a little before ten minutes and 
 generally spent the extra time in looking over and correcting 
 their work. 
 
 Those children that finished early put themselves at a 
 possible disadvantage, if, in their speed, they sacrificed quality 
 to quantity and were unable to increase the quantity further 
 by working extra examples up to the full time allowed. How- 
 ever, as the total tests showed slightly more work and a slightly 
 greater per cent of error at the periods after the first period, 
 these disadvantages might have had slightly more influence 
 and been added to the fatigue effect at those periods. That 
 this difference is small is shown by the fact that the five groups 
 which included far more than half of the completed tests had, 
 as averages for the five groups and for the three periods, a 
 smaller increase in amount of 0.47 per cent, and only a greater 
 decrease in correct work of 0.04 per cent than did all the ten 
 groups combined into one total group. If any possible dis- 
 advantage affected the results of these five groups, it was 
 swallowed up in their superior ability. In a note on page 21 
 are given the comparisons of the four periods, after the results 
 of the twelve-minute tests in P. S. 177, which many children 
 finished, were subtracted from the total group with its similar 
 comparisons. The comparisons, before and after this subtrac- 
 tion, are so nearly alike and the slight differences are so con- 
 
12 STUDIES OF MENTAL FATIGUE 
 
 flicting, as signs of fatigue, that it matters little whether the 
 differences be attributed to early finishing or to chance varia- 
 tion in P. S. 177. Whatever small effect early finishing in 
 the ten groups tested may have had upon my results, this effect 
 would strengthen my conclusions as to the little fatigue shown 
 in my tests, because the subtraction of it from the fatigue 
 effect would lessen, of course, the signs of fatigue just to that 
 degree. In fact, I might emphasize the advantage to my con- 
 clusions of the possible disadvantage of early finishing. 
 
 The children seemed to enjoy the tests. I was surprised at 
 my success in keeping their interest nearly the same at all four 
 periods of the school day, so that their zeal in the work would 
 be as constant as possible and not in favor of any period. In 
 this way there was eliminated almost entirely the element of 
 boredom probably the greatest influence in decreasing the 
 quantity and quality of work in the ordinary routine of the 
 school day. Studies of mental fatigue should be well guarded 
 against the interference by boredom, which is often confused 
 with fatigue, and which has vitiated the results of several ex- 
 periments. This confusion is general in teachers' estimates 
 of fatigue and renders them of little value for scientific study. 
 
 The time schedule 1 was arranged so as to test the children at 
 approximately 9:10 A. M., 11:05 A. M., 1:10 P. M., and 2:30 
 p. M. near the opening (after a brief period for settling down 
 to work) and the close of the morning and afternoon sessions. 
 The exact time varied from these points according to the number 
 of classes to be tested in a day, the time of my arrival in a 
 classroom, and the length of preparation necessary. The classes 
 in the different schools were combined into groups of four, 
 either one, two, or three groups being tested in a day. With 
 only one group in P. S. 177 2 the above schedule could be closely 
 adhered to ; but with two groups a day in P. S. 27 and 83, and 
 three groups in P. S. 3, two classes and three classes, re- 
 spectively one from each group were tested in immediate 
 succession at each of the four periods of the school day. 
 The classes of the second group followed the corresponding 
 classes of the first group just as soon as I could get from the 
 
 x ln most classes there were two-minute formal gymnastic drills at eleven 
 and two o'clock. I was unable to detect any effect of these drills toward 
 increasing or decreasing fatigue; but the eleven o'clock drill may have 
 benefited the work at the second period to a slight degree. 
 
 2 In this school an extra class was tested at an odd period but had no 
 place in my experiment. x 
 
METHOD 
 
 13 
 
 one classroom to the other and start the test with the later class. 
 In P. S. 3 the classes of the third group followed those of the 
 second group in a similar time relationship. With two or 
 three groups to he tested , the fourth period was begun before 
 2.30 P. M. so that the work could be completed before the 
 3 :00 p. M. dismissal. The following time schedule is typical : 
 
 Time Schedule Public School 83 5B Classes. 
 
 Group 
 
 Class 
 
 First Test 
 
 Second Test 
 
 Third Test 
 
 Fourth Test 
 
 
 
 Jan. 8 
 
 Jan. 15 
 
 Jan. 22 
 
 Jan. 29 
 
 1 
 
 5B1 
 
 9:12 
 
 11:06 
 
 1:04 
 
 2:24 
 
 2 
 
 5B2 
 
 9:34y 2 
 
 ll:22i/3 
 
 1:20 
 
 2:39 
 
 1 
 
 5B3 
 
 11:04 
 
 l:04i/2 
 
 2:23 
 
 9:lli/2 
 
 2 
 
 5B4 
 
 Il:23y 2 
 
 1:20 
 
 2:38i/2 
 
 9:26i/2 
 
 1 
 
 5B5 
 
 l:08i/2 
 
 2:25 
 
 9:05i/2 
 
 ll:04i/2 
 
 2 
 
 5B6 
 
 1:29 
 
 2:41 
 
 9:22 
 
 11:22 
 
 1 
 
 5B7 
 
 2:23i/2 
 
 9:08i/2 
 
 11:05 
 
 I:08y 2 
 
 2 
 
 5B8 
 
 2:44i/2 
 
 9:26 
 
 11:21 
 
 1:25 
 
 It is evident that the time relationship of the classes 
 of the first group to each other was almost the same as 
 that of the classes of the second, or of the third, group to 
 each other. The results for my purpose were not affected by 
 thus testing the classes of one group after the corresponding 
 classes of a preceding group, because each group constituted a 
 unit by itself for my comparison of the four periods of the 
 school day. In fact, the advantage of a wider representation 
 of the morning and afternoon sessions was thereby gained. For 
 instance, the tests with the first groups about 9 :10 A. M., which 
 might possibly have come in a few classes before the children 
 had settled down, were balanced in the total results by the tests 
 with the second groups about 9 :2T A. M. However, a compari- 
 son of the fatigue shown by these groups gives no preference 
 to either time for the first period. 
 
 The most important features of the time schedule were the 
 balancing and consequent neutralization of the practice effect 
 in the second, third, and fourth tests. Thereby the fatigue 
 effect was left free for my comparison of the quantity and 
 quality of the work at the four periods. This was done by 
 having each of the four tests taken at each of the four periods 
 by one of the four classes in a group. The first test was taken 
 at the first period by the first class, at the second period by the 
 second class, at the third period by the third class, and at the 
 
14 STUDIES OF MENTAL FATIGUE 
 
 fourth period by the fourth class; the second test was taken 
 at the first period by the fourth class, at the second period by 
 the first class, at the third period by the second class, and at the 
 fourth period by the third class; the third test was taken at 
 the first period by the third class, at the second period by the 
 fourth class, at the third period by the first class, and at the 
 fourth period by the second class ; the fourth test was taken at 
 the first period by the second class, at the second period by 
 the third class, at the third period by the fourth class, and at 
 the fourth period by the first class. With two groups to be 
 tested in one day, the four classes in the second group followed 
 the above schedule about seventeen minutes after the correspond- 
 ing classes of the first group. In P. S. 3 the third group fol- 
 lowed the second group in similar order. By such a schedule the 
 work of the group at each period included all four tests (each 
 test was generally taken a week apart), and consequently the 
 practice effect of one class at the second period, of another class 
 at the third period, and of another class at the fourth period. 
 
 This arrangement was based on the belief that, if each test 
 were taken by each class at the same period, the practice effect 
 of any one class in the second, third, or fourth test would be 
 almost equal to the practice effect of any other class in its 
 group in the corresponding test; and that, as each period in- 
 cluded the practice effects in the second, third, and fourth tests, 
 the sum of the three practice effects of a group at any one 
 period would be balanced and neutralized by the sum of the 
 three almost equal practice effects of the same group at any 
 other period. This belief in the approximate equality of the 
 practice effect of the four classes in a group can not be proved 
 or disproved by my results, because the same test was taken 
 at different periods by the four classes, and the practice effect 
 of any class was thereby complicated with a different fatigue 
 effect and rendered incomparable with the practice effect of 
 any other class in its group in the same test. If there were 
 differences in the practice effect of the four classes in a group, 
 especially of those classes at different stages of advancement, 
 they were probably very slight. Even these differences were 
 partially neutralized in my total results, since the classes in 
 different groups were not tested in the same order of advance- 
 ment: in P. S. 177 in ascending order, in P. S. -83 on the 
 same level of advancement, in P. S. 27 in descending order, 
 and in P. S. 3 in ascending order. (As the four half-grades in 
 P. S. 3 were divided into a, b, arid c sections according to 
 
GRADING 15 
 
 ability, these sections were combined into a, b, and c groups; 
 and the results show some positive though not consistent corre- 
 lation between ability and resistance to fatigue.) This varia- 
 tion gave a different relationship between practice and fatigue 
 effects in the different groups according to the periods at which 
 the corresponding tests were taken by the more advanced and 
 by the less advanced classes. 
 
 The figures on page 26 show that the practice effect in the 
 forty classes tested was small, especially because (1) an initial 
 interest partly balanced whatever initial disadvantage the 
 children may have had in the first test, (2) the work was rapid 
 and short, (3) a week generally intervened between the tests, 
 and (4) no class drill on the subject-matter of the tests was 
 allowed. However, the elimination of the practice effect from 
 my results frees this experiment from the error common to 
 most of the experiments on mental fatigue in relation to the 
 daily school program. 
 
 The practice effect within a single test was not considered. 
 With tests having simple examples of the same kind, such a 
 result were possible; but with the variety of examples in my 
 tests, both in kind and in difficulty, the accumulation of a 
 practice effect during the ten minutes could hardly have taken 
 place. Even if there were such practice effect in my results, it 
 would have been balanced against itself in my comparison of 
 the four tests at the four periods. 
 
 GRADING. 
 
 The papers were filed and graded, and the results tabulated, 
 according to school, test, class, and name. Only full sets of 
 four tests per child were used, all partial sets being thrown out. 
 Unless called back to their former class for my work, the 
 children who were removed to another class, after one or more 
 tests, took the remaining tests at wrong periods, thus causing 
 all their papers to be thrown out. In spite of many absences 
 and removals, 1,153 children in the forty classes worked the 
 four tests in proper order. 
 
 The grading of the 4,612 papers necessitated such tedious 
 and conscientious attention to details, that it was not "farmed 
 out" to others, who might have been careless, but was done 
 entirely by my wife and me. The care taken to be exact and 
 to go over the papers again in search for possible errors in 
 grading extended the time for this work to four months. In 
 
16 STUDIES OF MENTAL FATIGUE 
 
 the detailed method used, every figure the child put down in 
 working the examples was graded right or wrong, a complete 
 paper in each test including 190 figures. ~No child was given 
 a total credit of right or wrong figures for an example or part 
 of an example greater than that necessary for the correct work- 
 ing of that example or that part, though the mistake of a child 
 would often involve a greater number of figures. On the other 
 hand, the completion of work on an example or part of an 
 example gave the child the total credit of right or wrong 
 figures for that example or that part, whether the child had 
 put down that number of figures or not. Misplaced figures 
 were counted wrong, as were also the omitted figures in those 
 examples that had been worked by the child. In addition to 
 these main rules for grading the papers, there were many sub- 
 sidiary and consistent rules for special cases, which helped 
 greatly in threading the jungle of right and wrong figures 
 which a child would sometimes create. 
 
 Every method of grading arithmetic papers is open to objec- 
 tions, but, for my exact comparison of the work at four periods 
 of the school day, the detailed method used seemed far prefer- 
 able. Most of the objections which might be urged against 
 this method would not apply to the present case, as the aim 
 was not to give an absolute grading of ability in the four 
 fundamental operations, but simply to be consistent in judging 
 the quantity and quality of the work at the four periods. It 
 might be urged that the value of the figures in some examples 
 or parts of examples was not equal to that of those in other 
 examples or parts of examples. But where a child worked the 
 similar examples in all four tests the method of marking was 
 the same for all tests, and therefore for all periods. It is only 
 where a child worked one or more examples in one or more 
 tests, but not the similar examples in the other tests, and where 
 the figures in these particular examples could be shown to be 
 r : : rvalued in comparison with the figures in those examples 
 t 1 '{ had been worked in all four tests, that the above-mentioned 
 objection has any validity. The valuation of the figures in the 
 ninth example in comparison with that of those in the fifth, 
 in the few cases where the ninth example was worked by a 
 child in some tests but not in others, is the only illustration 
 that might possibly affect my results to more than a negligible 
 degree. Whatever small effect a possible disparity in the value 
 of figures in these and other examples might have had upon 
 my results would strengthen my conclusions as to the little 
 
RESULTS 17 
 
 fatigue shown in my tests, because the subtraction of this effect 
 from the fatigue effect would lessen, of course, the signs of 
 fatigue just to that degree. In fact, I might emphasize the 
 advantage to my conclusions of this possible disparity. 
 
 Another objection may be made that an initial wrong figure 
 may involve a series of figures which, though wrong, are really 
 the correct consequence of the first mistake and that, therefore, 
 only the initial figure should be counted wrong. To trace out 
 from every initial wrong figure in every example in 4,612 
 papers all the consequent figures, and to determine whether 
 the latter figures were correct consequences of the former, would 
 be an interminable task. Even then there would never be cer- 
 tainty that the consequent figures, in individual papers, did not 
 include more initial wrong figures than the first one. As the 
 necessary thing in my experiment was to grade consistently the 
 work at all four periods, and, as every figure was graded accord- 
 ing to the same rules for these periods, the change suggested, 
 even if possible, would not have affected my results. 
 
 In order to strengthen my comparison of the work at the 
 four periods by using two different methods of grading, rather 
 than one alone, all the papers were graded again by a gross 
 method in which only the answers were considered. The gross 
 method chosen was very similar to that used by Mr. Courtis. 
 The first and second examples were together credited with one 
 point, this point being counted wrong on account of one or 
 more mistakes in either example ; the third, fourth, fifth, sixth, 
 and tenth examples were each credited with one point, the 
 point for a given example being counted wrong on account of 
 one or more mistakes in that example; the seventh, eighth, 
 ninth, eleventh, and twelfth examples were each credited with 
 two points, one point for a given example being counted wrong 
 on account of one mistake, and two points being counted wrong 
 on account of two or more mistakes in that example. 
 
 RESULTS. 
 
 After the results for each child were graded by the detailed 
 method and tabulated, the number of right and wrong figures 
 for each class in each test was averaged, and then the number 
 of right and wrong figures for each group of four classes at 
 each of the four periods of the school day. The individual 
 variations in the children were first merged in the class aver- 
 
18 
 
 STUDIES OF MENTAL FATIGUE 
 
 ages and again in the group averages. From 
 were made tables for each of the ten groups, 
 table is typical: 
 
 these 
 
 The following 
 
 Table of Results Group 2 Public School 27. 
 
 00 
 
 5 
 
 
 
 FIRST PERIOD 
 
 SECOND PERIOD 
 
 THIRD PERIOD 
 
 FOURTH PERIOD 
 
 Test 
 
 Eight 
 
 Wrong 
 
 Test 
 
 Right 
 
 Wrong 
 
 Test 
 
 Right 
 
 Wrong 
 
 Test 
 
 Right 
 
 Wrong 
 
 5B1 
 5A1 
 4B2 
 
 4A2 
 4 
 
 26 
 43 
 32 
 26 
 127 
 
 1 
 
 4 
 3 
 2 
 
 129.69 
 149.07 
 131.53 
 112.08 
 130.59 
 
 14.92 
 15.98 
 17.53 
 20.65 
 17.27 
 
 2 
 1 
 
 4 
 3 
 
 132.35 
 126.98 
 122.72 
 126.69 
 127.18 
 
 25.31 
 12.12 
 
 24.84 
 24.69 
 21.74 
 
 3 
 2 
 1 
 4 
 
 142.77 
 142.16 
 109.56 
 122.96 
 129.36 
 
 23.42 
 21.44 
 22.25 
 
 28.35 
 23.86 
 
 4 
 3 
 2 
 
 1 
 
 140.31 
 145.28 
 124.50 
 101.88 
 127.99 
 
 25.27 
 20.21 
 20.47 
 23.58 
 22.38 
 
 Sum o 
 wrong 
 Relative 
 Per cen 
 Eelati 
 right 
 
 f right and 
 
 147 
 
 .86 
 .00 
 .32 
 
 00 
 
 148.92 
 100.72 
 85.40 
 
 96.69 
 
 153.22 
 103.63 
 84.43 
 
 95.64 
 
 150.37 
 101.70 
 85.12 
 
 96.38 
 
 amouD 
 : right 
 ve pe 
 
 t done 100 
 88 
 
 r cent 
 . 100 
 
 
 These tables gave answers to two questions, which formed 
 the core of the investigation. The answer to first question, 
 What was the difference in the quantity of work done at the 
 four periods?, was reached by getting the sum of right and 
 wrong figures at each period, by giving the value of 100.00 to 
 the sum at the first period (of course any other period could 
 have been taken as the standard of comparison), and then by 
 calculating the per cents of this sum represented by the sum at 
 each of the other three periods. These per cents for the ten 
 groups were as follows, the per cent for the first period being 
 100.00 in every group: 
 
 Group 
 
 School 
 
 Second Period 
 
 Third Period 
 
 Fourth Period 
 
 1 
 
 177 
 
 103.16 
 
 101.36 
 
 103.19 
 
 2 
 
 27 
 
 100.72 
 
 103.63 
 
 101.70 
 
 3 
 
 27 
 
 100.14 
 
 98.28 
 
 96.62 
 
 4 
 
 83 
 
 100.49 
 
 100.37 
 
 105.81 
 
 5 
 
 83 
 
 98.85 
 
 98.60 
 
 104.05 
 
 6 
 
 83 
 
 102.42 
 
 101.65 
 
 103.52 
 
 7 
 
 83 
 
 102.15 
 
 102.17 
 
 101.87 
 
 8 
 
 3 
 
 101.41 
 
 101.20 
 
 103.74 
 
 9 
 
 3 
 
 101.05 
 
 104.40 
 
 99.99 
 
 10 
 
 3 
 
 104.34 
 
 104.26 
 
 104.54 
 
RESULTS 
 
 19 
 
 The answer to the second question, What was the difference 
 in the quality of work done at the four periods?, was reached 
 by calculating the per cent right of the sum of right and wrong 
 figures at each period, by giving the value of 100.00 to the 
 per cent right at the first period, and then by calculating the 
 per cent of this per cent right represented by the per cent at 
 each of the other three periods. These per cents for the ten 
 groups were as follows, the per cent for the first period being 
 100.00 in every case : 
 
 Group 
 
 School 
 
 Second Period 
 
 Third Period 
 
 Fourth Period 
 
 1 
 
 177 
 
 97.53 
 
 97.58 
 
 97.37 
 
 2 
 
 27 
 
 96.69 
 
 95.64 
 
 96.38 
 
 3 
 
 27 
 
 98.86 
 
 97.34 
 
 97.54 
 
 4 
 
 83 
 
 100.39 
 
 98.65 
 
 97.94 
 
 5 
 
 83 
 
 98.92 
 
 96.90 
 
 95.89 
 
 6 
 
 83 
 
 97.64 
 
 100.94 
 
 98.65 
 
 7 
 
 83 
 
 97.81 
 
 99.12 
 
 98.91 
 
 8 
 
 3 
 
 101.74 
 
 101.39 
 
 100.52 
 
 9 
 
 3 
 
 98.75 
 
 99.15 
 
 97.45 
 
 10 
 
 3 
 
 96.75 
 
 99.06 
 
 97.08 
 
 In quantity of work done (sum of right and wrong figures) 
 as compared with the first period, seven of the ten groups tested 
 showed an increase at three periods, one an increase at two 
 periods and a decrease at one period, and two an increase at 
 one period and a decrease at two periods. In all, there were 
 twenty-five cases of increase, averaging 2.53 per cent; and 
 five cases of decrease, averaging 1.53 per cent. The same facts 
 by periods were as follows: at the second period an average 
 increase of 1.76 per cent in nine groups and a decrease of 1.15 
 per cent in one; at the third period an average increase of 2.38 
 per cent in eight groups and an average decrease of 1.56 per 
 cent in two; at the fourth period an average increase of 3.55 
 per cent in eight groups and an average decrease of 1.69 per 
 cent in two. 
 
 In quality of work done (per cent of sum right) as compared 
 with the first period, seven of the ten groups tested showed a 
 decrease at three periods, two a decrease at two periods and 
 an increase at one period, and one an increase at all periods. 
 In all, there were twenty-five cases of decrease, averaging 2.26 
 per cent, and five cases of increase averaging 1.00 per cent. 
 (The five cases of increase in quality occurred in different 
 groups from those having the five cases of decrease in quantity ; 
 consequently there was no connection between them.) The 
 
20 STUDIES or MENTAL FATIGUE 
 
 same facts by periods were as follows: At the second period 
 an average decrease of 2.13 per cent in eight groups and an 
 average increase of 1.06 per cent in two groups; at the third 
 period an average decrease of 2.07 per cent in eight groups and 
 an average increase of 1.16 per cent in two groups; at the 
 fourth period an average decrease of 2.53 per cent in nine 
 groups and an increase of 0.52 per cent in one group. 1 
 
 The most important summary of results is shown in the total 
 table combining the forty classes of the ten groups tested, in 
 which individual, class, and group variations were all merged. 
 The average of the forty class averages for each period was 
 used as the material for calculating the comparative per cents 
 of quantity and quality exactly in the same way that the aver- 
 age of four class averages for each period was used in a table 
 for each single group. 2 The balanced relation to each other 
 of the four classes in each group was not disturbed by this com- 
 bination, which tended, however, to neutralize whatever chance 
 variations may have occurred in the single groups.? In quantity 
 of work done (sum of right and wrong figures} as compared 
 with the first period of the school day, the ten groups together 
 showed a respective increase of 1.51, 1.6J+, and 2.36 per cent 
 at the second, third, and fourth periods; and in quality of work 
 done (per cent of sum right) a respective decrease of 1.51, 1.^1, 
 and 2.22 per cent at the second, third, and fourth periods. For 
 comparison with these results, obtained by the detailed method 
 of grading, a similar total table was made with the class aver- 
 ages by the gross method of grading, and the following per 
 cents were calculated: In quantity of work done (sum of right 
 and wrong points) as compared with the first period, the ten 
 groups together showed a respective increase of 1.92, 1.31, and 
 2.21 at the second, third, and fourth periods; and in quality 
 of work done (per cent of sum right) a respective decrease of 
 
 ^n order to give also the results by schools, the first and second groups 
 of P. S. 27, of P. S. 83-5A, and of P. S. 83-5B, and the first, second, and 
 third groups of P. S. 3, were combined into four tables by getting the 
 group averages for each period of the eight or twelve class averages in the 
 groups combined, and calculating therewith the comparative per cent of 
 quantity and quality exactly in the same way as in the single groups. 
 
 2 The average of the forty class averages was used instead of the average 
 of the ten group averages, as being more representative of the total con- 
 ditions; but the difference between the two total averages would be very 
 small. 
 
RESULTS 21 
 
 5.74* 4-56, and 6.66 at the second, third, and fourth periods. 1 
 The per cents of increase in quantity in the two tables are sur- 
 prisingly similar; the per cents of decrease in quality in the 
 second table are a little over three times as large as those in 
 the first table, but are still very small. This difference is 
 probably due to the greater weight given errors by the gross 
 method of grading, one error in the answer to any example 
 making wrong one point out of a total of sixteen points for 
 the entire test. This seems to me a defect natural to any gross 
 method of grading for purposes of scientific study. (Notice 
 the difference in the per cents of decrease in quality in the 
 practice results on page 26.) However, it would be inevitable 
 that any two, or any three, methods of grading would show 
 some differences in results. The two total tables are given 
 herewith. The one for the gross method of grading contains, 
 of course, all the class averages necessary to make out the single 
 table for each group ; but this extra work was not needed and 
 therefore was not undertaken. 
 
 Subtracting the four classes of P. S. 177, as suggested on page 12, we 
 have for thirty-six classes, by the detailed method of grading, an increase 
 of 1.35, 1.68, and 2.24 per cent, respectively, in quantity, and a decrease 
 of 1.39, 1.26, and 2.17 per cent, respectively, in quality; by the gross 
 method of grading an increase of 1.70, 1.52, and 1.97 per cent, respectively, 
 in quantity, and a decrease of 6.31, 4.41, and 6.59 per cent, respectively, 
 in quality. 
 
9,9, 
 
 STUDIES OF MENTAL FATIGUE 
 
 Forty Classes (Ten Groups) Combined Into One Group. 
 Detailed Method of Grading. 
 
 D. 
 
 3 
 
 "o 
 
 Q 
 
 
 GO 
 
 S3 
 
 FIRST PERIOD 
 
 SECOND PERIOD 
 
 THIRD PERIOD 
 
 FOURTH PERIOD 
 
 1 
 
 1 
 
 02 
 
 
 
 1 
 
 
 
 
 
 Test 
 
 Eight 
 
 Wrong 
 
 Test 
 
 Eight 
 
 Wrong 
 
 Test 
 
 Eight 
 
 Wrong 
 
 Test 
 
 Eight 
 
 Wrong 
 
 1 
 
 177 
 
 5A1 
 
 29 
 
 1 
 
 150.34 
 
 10.59 
 
 2 
 
 155.28 
 
 23.17 
 
 3 
 
 162.07 
 
 16.31 
 
 4 
 
 167.79 
 
 19.14 
 
 2 
 
 27 
 
 5B1 
 
 26 
 
 
 129.27 
 
 15.35 
 
 2 
 
 131.96 
 
 25.31 
 
 3 
 
 142.77 
 
 23.42 
 
 4 
 
 140.31 
 
 25.27 
 
 3 
 
 27 
 
 5B2 
 
 25 
 
 
 135.80 
 
 15.52 
 
 2 
 
 142.76 
 
 26.56 
 
 3 
 
 144.36 
 
 27.48 
 
 4 
 
 137.36 
 
 28.56 
 
 4 
 
 83 
 
 5A1 
 
 35 
 
 
 99.09 
 
 19.00 
 
 2 
 
 108.09 
 
 16.94 
 
 3 
 
 113.26 
 
 19.60 
 
 4 
 
 116.97 
 
 28.86 
 
 5 
 
 83 
 
 5A2 
 
 37 
 
 
 92.22 
 
 19.51 
 
 2 
 
 103.57 
 
 19.19 
 
 3 
 
 109.16 
 
 21.49 
 
 4 
 
 109.57 
 
 27.24 
 
 6 
 
 83 
 
 5B1 
 
 36 
 
 
 100.47 
 
 12.69 
 
 2 
 
 110.33 
 
 16.72 
 
 3 
 
 123.42 
 
 11.28 
 
 4 
 
 119.78 
 
 17.19 
 
 7 
 
 83 
 
 5B2 
 
 32 
 
 
 114.12 
 
 9.91 
 
 2 
 
 117.41 
 
 19.91 
 
 3 
 
 126.06 
 
 14.16 
 
 4 
 
 123.78 
 
 15.06 
 
 8 
 
 3 
 
 5Aa 
 
 28 
 
 1 
 
 110.11 
 
 15.46 
 
 2 
 
 115.86 
 
 17.54 
 
 3 
 
 125.14 
 
 15.68 
 
 4 
 
 127.54 
 
 18.18 
 
 9 
 
 3 
 
 5Ab 
 
 19 
 
 1 
 
 109.89 
 
 23.74 
 
 2 
 
 115.47 
 
 23.32 
 
 3 
 
 130.37 
 
 29.16 
 
 4 
 
 112.79 
 
 30.76 
 
 10 
 
 3 
 
 5Ac 
 
 19 
 
 1 
 
 92.95 
 
 14.05 
 
 2 
 
 96.42 
 
 24.11 
 
 3 
 
 113.79 
 
 21.89 
 
 4 
 
 101.47 
 
 25.16 
 
 1 
 
 177 
 
 5B1 
 
 38 
 
 4 
 
 159.67 
 
 11.34 
 
 
 155.68 
 
 12.42 
 
 2 
 
 158.53 
 
 11.11 
 
 3 
 
 164.32 
 
 10.53 
 
 2 
 
 27 
 
 5A1 
 
 43 
 
 4 
 
 148.81 
 
 16.58 
 
 
 126.93 
 
 12.16 
 
 2 
 
 142.88 
 
 21.70 
 
 3 
 
 144.88 
 
 20.21 
 
 3 
 
 27 
 
 5A2 
 
 31 
 
 4 
 
 153.16 
 
 17.71 
 
 
 138.13 
 
 12.06 
 
 2 
 
 144.00 
 
 21.00 
 
 3 
 
 151.84 
 
 22.06 
 
 4 
 
 83 
 
 5A3 
 
 38 
 
 4 
 
 102.92 
 
 20.89 
 
 
 92.63 
 
 16.08 
 
 2 
 
 99.05 
 
 18.79 
 
 3 
 
 112.92 
 
 17.71 
 
 5 
 
 83 
 
 5A4 
 
 26 
 
 4 
 
 110.46 
 
 25.81 
 
 
 87.62 
 
 18.12 
 
 2 
 
 98.35 
 
 25.81 
 
 3 
 
 111.19 
 
 25.92 
 
 6 
 
 83 
 
 5B3 
 
 28 
 
 4 
 
 111.86 
 
 18.43 
 
 
 100.32 
 
 15.61 
 
 2 
 
 110.68 
 
 15.50 
 
 3 
 
 112.43 
 
 18.89 
 
 7 
 
 83 
 
 5B4 
 
 27 
 
 4 
 
 114.78 
 
 20.15 
 
 
 98.63 
 
 18.30 
 
 2 
 
 113.07 
 
 18.26 
 
 3 
 
 118.96 
 
 21.00 
 
 8 
 
 3 
 
 5Ba 
 
 29 
 
 4 
 
 132.14 
 
 16.93 
 
 
 126.17 
 
 15.14 
 
 2 
 
 127.59 
 
 20.66 
 
 3 
 
 133.07 
 
 17.79 
 
 9 
 
 3 
 
 5Bb 
 
 23 
 
 4 
 
 126.43 
 
 24.43 
 
 
 116.04 
 
 25.96 
 
 2 
 
 122.30 
 
 29.00 
 
 3 
 
 123.74 
 
 23.26 
 
 10 
 
 3 
 
 5Bc 
 
 15 
 
 4 
 
 106.67 
 
 28.00 
 
 
 106.13 
 
 26.60 
 
 2 
 
 113.40 
 
 28.87 
 
 3 
 
 111.20 
 
 32.60 
 
 1 
 
 177 
 
 5Ea 
 
 40 
 
 3 
 
 164.60 
 
 8.92 
 
 4 
 
 158.17 
 
 13.35 
 
 1 
 
 136.35 
 
 16.15 
 
 2 
 
 143.62 
 
 16.07 
 
 2 
 
 27 
 
 4B2 
 
 32 
 
 3 
 
 131.66 
 
 17.56 
 
 4 
 
 122.53 
 
 24.84 
 
 1 
 
 109.22 
 
 22.56 
 
 2 
 
 123.87 
 
 21.03 
 
 3 
 
 27 
 
 4B3 
 
 27 
 
 3 
 
 137.37 
 
 22.85 
 
 4 
 
 130.33 
 
 31.59 
 
 1 
 
 113.37 
 
 22.89 
 
 2 
 
 123.48 
 
 25.15 
 
 4 
 
 83 
 
 5A5 
 
 40 
 
 3 
 
 107.42 
 
 20.07 
 
 4 
 
 106.60 
 
 24.40 
 
 1 
 
 93.12 
 
 18.00 
 
 2 
 
 105.47 
 
 23.05 
 
 5 
 
 83 
 
 5A6 
 
 29 
 
 3 
 
 116.59 
 
 13.14 
 
 4 
 
 117.41 
 
 17.90 
 
 1 
 
 90.14 
 
 17.62 
 
 2 
 
 105.79 
 
 19.01 
 
 6 
 
 83 
 
 5B5 
 
 25 
 
 3 
 
 110.60 
 
 11.80 
 
 4 
 
 106.04 
 
 20.60 
 
 1 
 
 89.24 
 
 11.04 
 
 2 
 
 107.00 
 
 18.04 
 
 7 
 
 83 
 
 5B6 
 
 27 
 
 3 
 
 108.15 
 
 20.26 
 
 4 
 
 108.63 
 
 22.56 
 
 1 
 
 95.04 
 
 19.59 
 
 2 
 
 104.07 
 
 21.44 
 
 8 
 
 3 
 
 6Aa 
 
 30 
 
 3 
 
 155.97 
 
 14.47 
 
 4 
 
 156.93 
 
 12.83 
 
 1 
 
 151.90 
 
 9.97 
 
 2 
 
 152.77 
 
 18.20 
 
 9 
 
 3 
 
 6Ab 
 
 34 
 
 3 
 
 149.76 
 
 15.68 
 
 4 
 
 143.68 
 
 20.91 
 
 1 
 
 136.03 
 
 19.50 
 
 2 
 
 138.85 
 
 21.91 
 
 10 
 
 3 
 
 6Ac 
 
 24 
 
 3 
 
 126.04 
 
 21.50 
 
 4 
 
 120.29 
 
 31.00 
 
 1 
 
 112.21 
 
 24.29 
 
 2 
 
 122.12 
 
 25.54 
 
 1 
 
 177 
 
 5Eb 
 
 31 
 
 2 
 
 152.26 
 
 13.71 
 
 3 
 
 161.61 
 
 13.00 
 
 4 
 
 163.10 
 
 16.94 
 
 1 
 
 154.16 
 
 17.23 
 
 2 
 
 27 
 
 4A2 
 
 26 
 
 2 
 
 112.08 
 
 20.65 
 
 3 
 
 126.65 
 
 24.73 
 
 4 
 
 122.96 
 
 28.35 
 
 1 
 
 101.88 
 
 23.58 
 
 3 
 
 27 
 
 4A3 
 
 25 
 
 2 
 
 101.88 
 
 31.96 
 
 3 
 
 114.12 
 
 22.12 
 
 4 
 
 105.92 
 
 27.60 
 
 1 
 
 86.56 
 
 20.48 
 
 4 
 
 83 
 
 5A7 
 
 29 
 
 2 
 
 99.31 
 
 14.17 
 
 3 
 
 105.00 
 
 19.45 
 
 4 
 
 99.28 
 
 23.55 
 
 1 
 
 88.21 
 
 17.72 
 
 5 
 
 83 
 
 5A8 
 
 29 
 
 2 
 
 94.79 
 
 11.86 
 
 3 
 
 96.28 
 
 18.72 
 
 4 
 
 97.93 
 
 17.07 
 
 1 
 
 86.52 
 
 18.72 
 
 6 
 
 83 
 
 5B7 
 
 26 
 
 2 
 
 122.50 
 
 16.73 
 
 3 
 
 128.77 
 
 18.92 
 
 4 
 
 133.73 
 
 18.50 
 
 1 
 
 113.46 
 
 16.46 
 
 7 
 
 83 
 
 5B8 
 
 21 
 
 2 
 
 115.95 
 
 16.86 
 
 3 
 
 127.95 
 
 18.00 
 
 4 
 
 124.57 
 
 20.71 
 
 1 
 
 109.62 
 
 15.95 
 
 8 
 
 3 
 
 6Ba 
 
 28 
 
 2 
 
 140.07 
 
 20.07 
 
 3 
 
 156.43 
 
 12.86 
 
 4 
 
 147.64 
 
 13.86 
 
 1 
 
 147.89 
 
 12.39 
 
 9 
 
 3 
 
 6Bb 
 
 25 
 
 2 
 
 128.80 
 
 17.36 
 
 3 
 
 138.64 
 
 18.32 
 
 4 
 
 144.32 
 
 11.68 
 
 1 
 
 126.36 
 
 18.40 
 
 10 
 
 3 
 
 6Bc 
 
 21 
 
 2 
 
 130.19 
 
 21.71 
 
 3 
 
 137.38 
 
 22.67 
 
 4 
 
 131.43 
 
 18.24 
 
 1 
 
 127.86 
 
 19.71 
 
 
 
 40 
 
 1,153 
 
 
 122.68 
 
 17.69 
 
 
 122.72 
 
 19.85 
 
 
 122.94 
 
 19.73 
 
 
 122.79 
 
 20.89 
 
 Sum of right and 
 
 
 
 
 wrong . . . 140 37 
 
 142.57 
 
 142.67 
 
 143.68 
 
 Relative amount done 100.00 
 
 101.57 
 
 101.64 
 
 102.36 
 
 Per cent right 87.40 
 
 86.08 
 
 86.17 
 
 85.46 
 
 Relative per cent right 100.00 
 
 98.49 
 
 98.59 
 
 97.78 
 
RESULTS 
 
 23 
 
 Forty Classes (Ten Groups) Combined Into One Group. 
 Gross Method of Grading. 
 
 e. 
 
 73 
 
 
 
 
 FIRST PERIOD 
 
 SECOND PERIOD 
 
 THIRD PERIOD 
 
 FOURTH PERIOD 
 
 D 
 
 o 
 
 i 
 
 1 
 
 
 
 
 
 O 
 
 1 
 
 3 
 
 i 
 
 Test 
 
 Bight 
 
 Wrong 
 
 Test 
 
 Right 
 
 Wrong 
 
 Test 
 
 Eight 
 
 Wrong 
 
 Test 
 
 Right 
 
 Wrong 
 
 1 
 
 177 
 
 5A1 
 
 29 
 
 1 
 
 11.38 
 
 2.21 
 
 2 
 
 10.69 
 
 3.90 
 
 3 
 
 11.28 
 
 3.62 
 
 4 
 
 11.66 
 
 3.79 
 
 2 
 
 27 
 
 5B1 
 
 26 
 
 1 
 
 9.23 
 
 2.96 
 
 2 
 
 8.58 
 
 4.35 
 
 3 
 
 9.27 
 
 4.54 
 
 4 
 
 9.00 
 
 4.65 
 
 3 
 
 27 
 
 5B2 
 
 25 
 
 1 
 
 9.40 
 
 3.28 
 
 2 
 
 9.20 
 
 5.00 
 
 3 
 
 8.92 
 
 5.36 
 
 4 
 
 8.48 
 
 5.20 
 
 4 
 
 83 
 
 5A1 
 
 35 
 
 1 
 
 6.14 
 
 2.89 
 
 2 
 
 6.51 
 
 3.80 
 
 3 
 
 6.91 
 
 3.71 
 
 4 
 
 7.11 
 
 4.66 
 
 5 
 
 83 
 
 5A2 
 
 37 
 
 1 
 
 6.03 
 
 3.24 
 
 2 
 
 6.38 
 
 3.43 
 
 3 
 
 6.46 
 
 4.62 
 
 4 
 
 6.49 
 
 4.84 
 
 6 
 
 83 
 
 5B1 
 
 36 
 
 1 
 
 6.56 
 
 2.22 
 
 2 
 
 7.33 
 
 2.75 
 
 3 
 
 8.44 
 
 2.47 
 
 4 
 
 7.92 
 
 3.33 
 
 7 
 
 83 
 
 5B2 
 
 32 
 
 1 
 
 7.28 
 
 2.62 
 
 2 
 
 7.28 
 
 4.16 
 
 3 
 
 8.62 
 
 3.16 
 
 4 
 
 7.84 
 
 3.87 
 
 8 
 
 3 
 
 5Aa 
 
 28 
 
 1 
 
 7.57 
 
 2.50 
 
 2 
 
 7.21 
 
 3.75 
 
 3 
 
 8.46 
 
 3.25 
 
 4 
 
 7.89 
 
 3.64 
 
 9 
 
 3 
 
 5Ab 
 
 19 
 
 1 
 
 7.11 
 
 4.32 
 
 2 
 
 7.42 
 
 4.37 
 
 3 
 
 7.89 
 
 5.32 
 
 4 
 
 5.84 
 
 5.79 
 
 10 
 
 3 
 
 5Ac 
 
 19 
 
 1 
 
 5.79 
 
 2.26 
 
 2 
 
 5.47 
 
 4.63 
 
 3 
 
 6.89 
 
 4.53 
 
 4 
 
 6.16 
 
 4.32 
 
 1 
 
 177 
 
 5B1 
 
 38 
 
 4 
 
 11.42 
 
 2.76 
 
 1 
 
 10.92 
 
 3.18 
 
 2 
 
 11.76 
 
 1.87 
 
 3 
 
 11.66 
 
 2.84 
 
 2 
 
 27 
 
 5A1 
 
 43 
 
 4 
 
 10.30 
 
 3.33 
 
 1 
 
 8.35 
 
 3.12 
 
 2 
 
 9.47 
 
 4.07 
 
 3 
 
 8.84 
 
 4.79 
 
 3 
 
 27 
 
 5A2 
 
 31 
 
 4 
 
 10.10 
 
 3.90 
 
 1 
 
 9.61 
 
 3.00 
 
 2 
 
 9.74 
 
 3.90 
 
 3 
 
 9.52 
 
 4.90 
 
 4 
 
 83 
 
 5A3 
 
 38 
 
 4 
 
 6.76 
 
 2.87 
 
 1 
 
 5.82 
 
 2.39 
 
 2 
 
 6.13 
 
 3.32 
 
 3 
 
 7.18 
 
 3.68 
 
 5 
 
 835A4 
 
 26 
 
 4 
 
 6.92 
 
 3.88 
 
 1 
 
 5.15 
 
 3.08 
 
 2 
 
 5.77 
 
 3.92 
 
 3 
 
 6.42 
 
 4.96 
 
 6 
 
 83 
 
 5B3 
 
 28 
 
 4 
 
 7.46 
 
 3.04 
 
 1 
 
 6.14 
 
 3.07 
 
 2 
 
 7.11 
 
 3.04 
 
 3 
 
 7.07 
 
 3.54 
 
 7 
 
 83 
 
 5B4 
 
 27 
 
 4 
 
 7.04 
 
 3.96 
 
 1 
 
 5.85 
 
 3.78 
 
 2 
 
 7.26 
 
 3.33 
 
 3 
 
 6.93 
 
 4.15 
 
 8 
 
 3 
 
 5Ba 
 
 29 
 
 4 
 
 8.59 
 
 3.48 
 
 1 
 
 7.48 
 
 3.72 
 
 2 
 
 8.28 
 
 3.83 
 
 3 
 
 8.07 
 
 4.07 
 
 9 
 
 3 
 
 5Bb 
 
 23 
 
 4 
 
 7.61 
 
 4.65 
 
 1 
 
 6.57 
 
 4.78 
 
 2 
 
 7.30 
 
 4.83 
 
 3 
 
 7.57 
 
 4.48 
 
 10 
 
 3 
 
 5Bc 
 
 15 
 
 4 
 
 6.80 
 
 4.33 
 
 1 
 
 6.73 
 
 4.27 
 
 2 
 
 6.13 
 
 5.53 
 
 3 
 
 6.53 
 
 5.27 
 
 1 
 
 111 
 
 5Ea 
 
 40 
 
 3 
 
 11.92 
 
 2.42 
 
 4 
 
 11.52 
 
 2.92 
 
 1 
 
 9.20 
 
 3.20 
 
 2 
 
 10.37 
 
 3.02 
 
 2 
 
 27 
 
 4B2 
 
 32 
 
 3 
 
 8.59 
 
 3.72 
 
 4 
 
 7.16 
 
 4.91 
 
 1 
 
 6.12 
 
 4.34 
 
 2 
 
 7.84 
 
 4.06 
 
 3 
 
 27 
 
 4B3 
 
 27 
 
 3 
 
 8.74 
 
 4.30 
 
 4 
 
 8.07 
 
 5.37 
 
 1 
 
 6.67 
 
 4.44 
 
 2 
 
 7.70 
 
 4.37 
 
 4 
 
 83 
 
 5A5 
 
 40 
 
 3 
 
 5.90 
 
 4.20 
 
 4 
 
 6.67 
 
 3.80 
 
 1 
 
 5.67 
 
 2.50 
 
 2 
 
 6.65 
 
 3.07 
 
 5 
 
 83 
 
 5A6 
 
 29 
 
 3 
 
 7.79 
 
 2.62 
 
 4 
 
 7.59 
 
 3.31 
 
 1 
 
 5.59 
 
 2.45 
 
 2 
 
 7.00 
 
 3.00 
 
 6 
 
 83 
 
 5B5 
 
 25 
 
 3 
 
 7.20 
 
 2.80 
 
 4 
 
 6.80 
 
 3.64 
 
 1 
 
 5.16 
 
 2.40 
 
 2 
 
 6.12 
 
 3.60 
 
 7 
 
 83 
 
 5B6 
 
 27 
 
 3 
 
 7.48 
 
 2.85 
 
 4 
 
 7.07 
 
 3.44 
 
 1 
 
 5.96 
 
 3.19 
 
 2 
 
 6.67 
 
 3.19 
 
 8 
 
 3 
 
 6Aa 
 
 30 
 
 3 
 
 10.77 
 
 3.43 
 
 4 
 
 10.57 
 
 3.47 
 
 1 
 
 10.97 
 
 2.40 
 
 2 
 
 10.63 
 
 3.60 
 
 9 
 
 3 
 
 6Ab 
 
 34 
 
 3 
 
 9.71 
 
 4.21 
 
 4 
 
 9.41 
 
 4.00 
 
 1 
 
 8.76 
 
 4.24 
 
 2 
 
 9.29 
 
 4.00 
 
 10 
 
 3 
 
 6Ac 
 
 24 
 
 3 
 
 8.21 
 
 4.17 
 
 4 
 
 6.96 
 
 5.29 
 
 1 
 
 7.25 
 
 3.92 
 
 2 
 
 7.00 
 
 5.00 
 
 1 
 
 177 
 
 5Eb 
 
 31 
 
 2 
 
 11.45 
 
 2.39 
 
 3 
 
 11.13 
 
 3.23 
 
 4 
 
 11.32 
 
 3.35 
 
 1 
 
 10.74 
 
 3.71 
 
 2 
 
 27 
 
 4A2 
 
 26 
 
 2 
 
 7.23 
 
 3.27 
 
 3 
 
 7.62 
 
 4.69 
 
 4 
 
 7.50 
 
 4.58 
 
 1 
 
 6.31 
 
 3.42 
 
 3 
 
 27 
 
 4A3 
 
 25 
 
 2 
 
 6.12 
 
 4.72 
 
 3 
 
 7.20 
 
 3.96 
 
 4 
 
 6.04 
 
 4.48 
 
 1 
 
 5.32 
 
 3.08 
 
 4 
 
 83 
 
 5A7 
 
 29 
 
 2 
 
 6.14 
 
 2.93 
 
 3 
 
 6.86 
 
 3.72 
 
 4 
 
 6.17 
 
 4.03 
 
 1 
 
 5.34 
 
 2.79 
 
 5 
 
 83 
 
 5A8 
 
 29 
 
 2 
 
 6.17 
 
 2.52 
 
 3 
 
 5.66 
 
 3.41 
 
 4 
 
 5.66 
 
 3.24 
 
 1 
 
 5.34 
 
 3.03 
 
 6 
 
 83 
 
 5B7 
 
 26 
 
 2 
 
 8.65 
 
 2.65 
 
 3 
 
 8.12 
 
 4.04 
 
 4 
 
 9.35 
 
 3.27 
 
 1 
 
 7.35 
 
 3.15 
 
 7 
 
 83 
 
 5B8 
 
 21 
 
 2 
 
 8.33 
 
 2.52 
 
 3 
 
 8.90 
 
 3.05 
 
 4 
 
 8.24 
 
 3.38 
 
 1 
 
 7.05 
 
 3.14 
 
 8 
 
 3 
 
 6Ba 
 
 28 
 
 2 
 
 9.39 
 
 3.79 
 
 3 
 
 10.46 
 
 3.50 
 
 4 
 
 9.64 
 
 3.36 
 
 1 
 
 10.25 
 
 2.96 
 
 9 
 
 3 
 
 6Bb 
 
 25 
 
 2 
 
 8.24 
 
 3.72 
 
 3 
 
 8.48 
 
 4.52 
 
 4 
 
 9.72 
 
 3.32 
 
 1 
 
 8.04 
 
 3.76 
 
 10 
 
 3 
 
 6Bc 
 
 21 
 
 2 
 
 8.95 
 
 3.76 
 
 3 
 
 8.62 
 
 4.48 
 
 4 
 
 8.48 
 
 3.90 
 
 1 
 
 8.43 
 
 3.95 
 
 
 
 40 
 
 1,153 
 
 
 8.16 
 
 3.29 
 
 
 7.84 
 
 3.83 
 
 
 7.89 
 
 3.71 
 
 
 7.79 
 
 3.92 
 
 Sum of right and 
 
 
 
 
 wrong 11 . 45 
 
 11 67 
 
 11.60 
 
 11.71 
 
 Relative amount done 100.00 
 
 101.92 
 
 101.31 
 
 102.27 
 
 Per cent right 71 27 
 
 67.18 
 
 68.02 
 
 66.52 
 
 Relative per cent right 100.00 
 
 94.26 
 
 95.44 
 
 93.34 
 
24 STUDIES OF MENTAL FATIGUE 
 
 The following diagram illustrates these comparative per 
 cents of increase in quantity (above the heavy horizontal line) 
 and of decrease in quality (below the heavy horizontal line). 
 The continuous lines represent the results by the detailed 
 method of grading, and the dotted lines the results by the gross 
 method of grading. 
 
 l i 
 
 B 
 
 /oo.oo 
 
 Increase 
 
 in 
 Quantity 
 
 /oo.oo 
 
 Decrease 
 
 in 
 Quality 
 
 In these two series of per cents are apparently opposing 
 results a fairly continuous increase in quantity of work done 
 at the four successive periods, with a very small increase in the 
 second table at the third period; and a fairly continuous 
 decrease in quality, with a very small increase in the first 
 table and a small increase in the second table at the third 
 period. (These variations at the third period were due to the 
 influence of the intermission from twelve to one o'clock. ) How- 
 ever, this opposition may be more apparent than real. Fatigue 
 often shows itself in a weakening of that inhibition which as- 
 sures slower but more careful and consequently more correct 
 work, the speed of the fatigued worker generally being a sign 
 of decreased efficiency. (This result is evident in many 
 
RESULTS 25 
 
 different experiments.) But a claim that all the above- 
 mentioned increase in quantity is due to fatigue would be a 
 biased interpretation, though the influence of the noon inter- 
 mission in arresting the increase at the third period and the 
 presence of the greatest increase at the fourth period strengthen 
 this claim. It is possible that some of the increase may be due 
 to increased efficiency as the day advances, the children becom- 
 ing more habituated to school work having a greater "swing," 
 as Offner says. The decrease in quality of work done at the 
 four successive periods may more justly be considered as due 
 almost entirely to fatigue, which is arrested by the noon inter- 
 mission but is greatest at the fourth period. A slight boredom 
 and consequent carelessness as the day advances may have 
 affected the results in spite of my efforts to keep the interest 
 nearly the same at all four periods. Altogether, we may con- 
 sider that most, though not all, of this increase in quantity 
 and decrease in quality is a sign of fatigue. 
 
 It is impossible to combine accurately into one series for 
 each table the per cents of quantity and of quality at each of 
 the four periods in order to make a single comparison of the 
 work done. Any such combination, though arbitrary, ought 
 to be based upon a just proportion of value between the two 
 series. For instance, one per cent of increase in quantity 
 should not cancel one per cent of decrease in quality because 
 the latter per cent has more value than the former, more 
 weight in grading ability. A suggestive proportion is that 
 based upon the per cents right of the sum of right and wrong 
 figures (or points) at the second, third, and fourth periods, 
 these being in the first table 86.06, 86.17, and 85.46 per 
 cent, respectively. These per cents give a ratio of value of 
 1.00:. 8608 between the sum and the per cent right at the 
 second period, a ratio of 1.00: .8617 at the third period, and 
 a ratio of 1.00:. 8546 at the fourth period. For the second 
 period we multiply the 1.57 per cent in quantity by .8608 
 and the 1.51 per cent in quality by 1.00, in order to reduce 
 the per cents to equal value, and get 1.35 and 1.51 per cent, 
 respectively. By subtracting the per cent of increase in 
 quantity from the per cent of decrease in quality, we get a 
 remaining decrease of .16 per cent. This gives 99.84 as the 
 combined per cent of quantity and quality at the second period. 
 In the same way we get 100.00 as the combined per cent at the 
 third period and 99.80 at the fourth. The combined per cents 
 in the second table are 95.55, 96.33, and 94.85 for the second, 
 
26 STUDIES OF MENTAL 
 
 third, and fourth periods, respectively. It might be objected 
 that, as both the increase in quantity and the decrease in quality 
 are mainly due to fatigue, they should not be balanced against 
 each other and only the remainder be subtracted from the 
 100.00 per cent standard of the first period. One might even 
 go so far as to suggest subtracting from this 100.00 per cent 
 standard the sum of the per cents of increase and decrease. 
 The reply is that the per cents of comparison must be based 
 upon the actual work done, not upon an interpretation of the 
 causes thereof, and that in grading such work an increase in 
 quantity would naturally tend to offset a decrease in quality 
 and vice versa, whether or not both the increase and the de- 
 crease could be attributed to one cause. However, my sug- 
 gested combination may show too little fatigue and is offered 
 simply as an illustration of a possible method of reaching one 
 series of per cents for purposes of comparison. 
 
 The practice effect was calculated by rearranging the figures 
 in the 'two total tables in columns according to tests rather than 
 periods. As each test was given forty times ten times at each 
 of the four periods the total result for each test combined the 
 work at each of the four periods and thus neutralized the fatigue 
 effect, which has often influenced the results in practice experi- 
 ments. These total results were compared to find the practice 
 effect. By the detailed method of grading, in quantity of work 
 (sum of right and wrong figures) as compared with the first test, 
 the ten groups together showed a respective increase of 8.91, 
 14.09, and 13.67 per cent in the second, third, and fourth tests; 
 in quality of work done (per cent of sum right) a respective de- 
 crease of 1.35 and 1.31 per cent in the second and fourth tests, 
 and an increase of 0.46 per cent in the third test. By the gross 
 method of grading, in quantity of work done (sum of right 
 and wrong points) as compared with the first test, the ten 
 groups together showed a respective increase of 8.97, 15.39, 
 and 13.97 per cent in the second, third, and fourth tests; and 
 in quality of work done (per cent of sum right) a respective 
 decrease of 2.00, 2.28, and 3.20 per cent in the second, third, 
 and fourth tests. 
 
SECOND STUDY 
 
 The tests were given in February and March, 1913, to sixteen 
 classes, 573 pupils, in three Lynchburg, Va., schools. The im- 
 portant difference between this experiment and that in New 
 York City is the amount of continuous work required by the 
 tests. The New York classes were given four ten-minute tests 
 at four periods of the school day, the Lynchburg classes two 
 twenty-five minute tests at two periods. 1 The subject matter 
 used was the same in both experiments, but the Lynchburg 
 classes took two tests as one. The reason for this extension of 
 time was the supposition that a ten-minute spurt might not reveal 
 the amount of fatigue present, the pupils working the short test 
 with fairly unform efficiency at four periods of the school day. 
 A continuous application for twenty-five minutes could hardly 
 fail to reveal most of the fatigue present at the time of starting 
 the test and the further possible fatigue from the longer test 
 itself. If the fatigue from the test itself were equally present in 
 the morning and in the afternoon work, it would be neutralized 
 in the results; but if it were greater in the afternoon on ac- 
 count of greater fatigue at the time of starting, the difference 
 would be evident in the results. The longer test, therefore, has 
 two possibilities of revealing fatigue and is also a better illus- 
 tration of the time required, though with less continuous pres- 
 sure, for study and recitation in actual school practice. 
 
 The Lynchburg tests were given on February 25 and 27, 
 1913, to the 5A, 5B, 6A, and 6B classes in Biggers School; on 
 February 26 and 28 to the 5A, 5B, 6A, and 6B classes in Mon- 
 roe School; on March 11 and 13 to the 7B, 7A, 6B, and 6A1 
 classes in Federal School; on March 12 and 14 to the 6A2, 
 5Bl, 5B2, and 5 A classes in Federal School. The weather was 
 mild, and window ventilation was used in addition to the fur- 
 nace system. The schools had a one-session day, with a fifteen- 
 minute recess soon after the morning tests and a twenty (some- 
 times fifteen) minute recess before the afternoon tests. During 
 the second recess many pupils ate lunch at home or school. 
 This recess probably increased the efficiency in the afternoon 
 tests ; but as every school has or should have a recess near this 
 period of the school day, the conditions of the Lynchburg tests 
 were typical, certainly for a one-session school day. The de- 
 
 *As the Lynchburg classes were slower in this kind of work, twenty-five 
 rather than twenty minutes were allowed. 
 
28 STUDIES OF MENTAL FATIGUE 
 
 partmental system of instruction allowed no uniform program 
 of recitations and study periods in the classes tested. The chil- 
 dren represented for the most part hygienic opportunities at 
 home and had been examined by their teachers for eyesight and 
 hearing. All the classes included both boys and girls, the total 
 being 292 boys and 281 girls. The average age was 12.55 years. 
 
 The following description is condensed and adapted from 
 the First Study, to which the reader is referred for further 
 discussion. The departmental teacher put aside her work for 
 my test, but remained in the room at my request. I gave 
 detailed directions to the class and then with the help of the 
 teacher put on each desk a test paper with the blank side up. 
 After the name, etc., had been written, the children turned the 
 papers over immediately on signal and worked steadily for 
 twenty-five minutes. Great care was taken to be exact in start- 
 ing and stopping. The children thought they were being exam- 
 ined for correctness and speed, but did not know how much time 
 was being allowed and did not rush toward the end. The very 
 few children who finished before the time was out looked over 
 part of their papers. The spirit of the work was pleasant and 
 earnest, and reduced to a minimum the element of boredom, 
 probably the greatest influence in decreasing the quantity and 
 quality of work in the ordinary routine of the school day. 
 
 The time schedule was so arranged as to test each class in the 
 morning and in the afternoon. The classes were combined into 
 groups of two, one being a half-grade below (A) or above (B) 
 the other. The first class in a group took the first test in the 
 morning of the first day and the second test in the afternoon of 
 the second day following; the second class took the first test in 
 the afternoon of the first day and the second test in the morning 
 of the second day after. In this way the practice effect of the 
 first class in the second test in the afternoon was balanced 
 against that of the second class in the morning and consequently 
 neutralized, leaving the fatigue effect free for comparison at the 
 two periods. This arrangement was based upon a belief in the 
 approximate equality of the practice effect in the two classes in 
 a group. Even the slight differences that might have occurred 
 were neutralized by giving the second test in the morning to the 
 B classes and in the afternoon to the A classes of the first four 
 groups, and then by giving the second test in the morning to the 
 A classes and in the afternoon to the B classes of the second four 
 groups. 1 
 
 1 One group was composed of 6A2 and 5B1, with the half-year relation- 
 ship between classes as in the other groups but with different grades. 
 
SECOND STUDY 29 
 
 Two groups were tested in a day, the two classes of the first 
 group at about 9 :20 A. M. and 1 :30 p. M., respectively, and the 
 two classes of the second group at about 9 :50 A. M. and 2 :00 
 p. M., respectively. On the second day following, the classes 
 tested before in the morning were tested in the afternoon, and 
 vice versa; but the classes of the second group followed as be- 
 fore immediately after the corresponding classes of the first 
 group, each group constituting a complete unit by itself with 
 the same time relationship between the classes as in all the other 
 groups. Testing two groups a day gave a wider representation 
 of the school day, fifty minutes of morning work and fifty min- 
 utes of afternoon work. 
 
 The papers were graded by me by a gross method of counting- 
 answers only, very similar to that used by Mr. Courtis. Each 
 test contained thirty-two points divided as follows : Two groups 
 of two examples were each credited with one point, this point 
 being counted wrong on account of one or more mistakes in 
 either example ; ten examples were each credited with one point, 
 the point being counted wrong on account of one or more mis- 
 takes in the example ; ten examples were each credited with two 
 points, one point being counted wrong on account of one mis- 
 take, and two points being counted wrong on account of two or 
 more mistakes, in the example. A gross method of counting 
 answers over-emphasizes mistakes in proportion to the total 
 amount of work done, not only at one period but even in a com- 
 parison between the percentage of error at two or more periods. 
 The results of my New York tests showed that in the same 
 papers the average increase in percentage of error at the three 
 periods after the first period was by the gross method 3.2659 
 times that by the detailed method of counting every figure put 
 down by a child in working the examples. The increase in per- 
 centage of error in the present results at the second period is, 
 therefore, greater than the actual decrease in efficiency of the 
 children tested. However, the gross method takes far less time 
 for grading papers and is sufficiently accurate for comparison 
 of the work at periods to which it has been uniformly applied. 
 
30 
 
 STUDIES OF MENTAL FATIGUE 
 Total Results. 
 
 
 
 
 FIRST PERIOD 
 
 SECOND PERIOD 
 
 School 
 
 Class 
 
 Pupils 
 
 Test 
 
 Right 
 
 Wrong 
 
 Test 
 
 Right 
 
 Wronsr 
 
 Biggers 5A 
 
 43 
 
 1 
 
 12.67 
 
 5.02 
 
 2 
 
 16.53 
 
 6.14 
 
 " 
 
 5B 
 
 43 
 
 2 
 
 15.53 
 
 7.42 
 
 1 
 
 12.79 
 
 6.51 
 
 " 
 
 6A 
 
 44 
 
 1 
 
 15.61 
 
 7.34 
 
 2 
 
 16.64 
 
 9.23 
 
 K 
 
 6B 
 
 39 
 
 2 
 
 19.21 
 
 7.10 
 
 1 
 
 18.18 
 
 6.23 
 
 Monroe 
 
 5A 
 
 34 
 
 1 
 
 14.09 
 
 6.44 
 
 2 
 
 15.15 
 
 8.56 
 
 " 
 
 5B 
 
 46 
 
 2 
 
 15.04 
 
 7.26 
 
 1 
 
 10.96 
 
 6.39 
 
 " 
 
 6A 
 
 35 
 
 1 
 
 17.17 
 
 4.54 
 
 2 
 
 20.14 
 
 6.54 
 
 tf 
 
 6B 
 
 32 
 
 2 
 
 21.00 
 
 6.62 
 
 I 
 
 16.59 
 
 5.94 
 
 Federal 
 
 7B 
 
 33 
 
 1 
 
 19.64 
 
 5.00 
 
 2 
 
 21.33 
 
 7.12 
 
 H 
 
 7A 
 
 41 
 
 2 
 
 19.27 
 
 7.12 
 
 1 
 
 16.98 
 
 6.66 
 
 " 
 
 6B 
 
 30 
 
 1 
 
 15.60 
 
 5.27 
 
 2 
 
 17.83 
 
 6.80 
 
 tt 
 
 6A1 
 
 28 
 
 2 
 
 21.86 
 
 7.04 
 
 1 
 
 18.43 
 
 7.54 
 
 (I 
 
 6A2 
 
 33 
 
 1 
 
 14.61 
 
 5.33 
 
 2 
 
 17.09 
 
 6.58 
 
 H 
 
 5B1 
 
 34 
 
 2 
 
 17.24 
 
 7.09 
 
 1 
 
 14.38 
 
 6.41 
 
 " 
 
 5B2 
 
 28 
 
 1 
 
 12.64 
 
 5.96 
 
 2 
 
 15.96 
 
 7.18 
 
 H 
 
 5A 
 
 30 
 
 2 
 
 14.40 
 
 6.37 
 
 1 
 
 11.47 
 
 6.60 
 
 
 16 
 
 573 
 
 
 16.60 
 
 6.31 
 
 
 16.28 
 
 6.90 
 
 Sum of right and wrong 
 
 
 
 points 
 
 22.91 
 
 23.18 
 
 Relative amount done. . 
 
 100.00 
 
 101.18 
 
 Per cent right 
 
 72.46 
 
 70.23 
 
 Relative percent right. . 
 
 100.00 
 
 96.92 
 
 The average of right and wrong points for the sixteen classes 
 at each period were added and the general average taken, in 
 which all individual, class, and group variations were merged. 
 The sum of the general average of right and wrong points at the 
 first period was compared with that at the second period, giving 
 an increase of 1.18 per cent at the second period. The per cent 
 right of the sum of right and wrong points at the first period 
 was then compared with the per cent right at the second period, 
 giving a decrease of 3.08 per cent at the second period. The in- 
 crease in quantity was probably due in part to the same influ- 
 ences as was the decrease in quality, greater speed and greater 
 carelessness often going together. 
 
 Even the slight decrease in efficiency shown by these results 
 is larger than the actual decrease in the classes tested, because 
 
SECOND STUDY 31 
 
 in Federal School the 5A class was somewhat disturbed in its 
 afternoon work by the marching out of the other classes, and 
 because the 7B and 6B classes had only a short indoor recess, 
 on account of rain, before the afternoon tests. This is partly 
 shown, though other influences may have entered, by the in- 
 crease in quantity of 2.08 per cent and the decrease in quality 
 of 3.37 per cent in the eight classes in Federal School, as com- 
 pared with the increase in quantity of 0.22 per cent and the 
 decrease in quality of 2.79 per cent in the eight classes in 
 Biggers and Monroe Schools. 
 
 As the average per cent of increase in quantity in the New 
 York tests, for the three periods after the first period, was by 
 the detailed method of grading 1.0164 times that by the gross 
 method, we can surmise that the 1.18 per cent increase in quan- 
 tity in the Lynchburg tests by the gross method would be about 
 1.20 per cent by the detailed method. And as the average de- 
 crease in quality in the New York tests was by the detailed 
 method only 0.3062 times that by the gross method, we can sur- 
 mise that the 3.08 per cent decrease in quality in the Lynch- 
 burg tests would be about 0.94 per cent by the detailed method. 
 
 By a comparison of the results by the gross method in the 
 twenty-five minute test in the afternoon in Lynchburg with the 
 average of the two ten-minute tests in the afternoon in New 
 York, we have 1.18 per cent increase in quantity in Lynchburg 
 as compared with 1.79 per cent, and 3.08 per cent decrease in 
 quality as compared with 5.61 per cent. In spite of the longer 
 requirement for continuous work, the Lynchburg children show 
 a smaller decrease in efficiency, probably on account of their 
 better hygienic opportunities at home. 
 
 In order to determine whether the decrease in efficiency at 
 the second period in Lynchburg was less in the more advanced 
 grades, the following percentages were calculated: six fifth 
 grades (three groups) showed an increase in quantity of 0.11 
 per cent and a decrease in quality of 2.82 per cent; six sixth 
 grades (three groups) showed an increase in quantity of 0.36 
 per cent and a decrease in quality of 2.74 per cent; two seventh 
 grades (one group) showed an increase in quantity of 2.08 per 
 cent and a decrease in quality of 3.54 per cent. These slight 
 differences seem to have no significance, the greater decrease 
 in quality in the seventh grades being due mainly to the fact 
 before mentioned that 7B had only a short indoor recess before 
 the afternoon test. 
 
32 STUDIES OF MENTAL FATIGUE 
 
 An important consideration is the greater decrease in effi- 
 ciency shown by the boys than by the girls, this difference even 
 being noticeable in the greater restlessness of the boys during 
 the tests. Complete tables of the sixteen class averages were 
 made of the results by the boys and the girls, and the general 
 averages, percentages, etc., were calculated. The boys showed 
 an increase in quantity of 0.74 per cent and a decrease in qual- 
 ity of 4.25 per cent; the girls showed an increase in quantity 
 of 1.62 per cent and a decrease in quality of 1.96 per cent. The 
 boys showed an increase in quantity 0.4568 times that by the 
 girls and a decrease in quality 2.1684 times that by the girls. 
 
 The practice effect was calculated by rearranging the class 
 averages in columns according to tests rather than periods, thus 
 neutralizing for the most part the decrease in efficiency at the 
 second period. The sixteen classes showed an increase in quan- 
 tity of 13.22 per cent in the second test and a decrease in qual- 
 ity of 0.50 per cent. 
 
THIRD STUDY 
 
 The tests were given in December, 1914, to sixteen classes, 
 476 pupils, in the Intermediate School in Roanoke, Va. In 
 this experiment reasoning problems in arithmetic were used in 
 place of the four fundamental operations in the New York and 
 Lynchburg experiments. Although the continued alertness re- 
 quired of grammar-grade pupils in rapid computation may well 
 be considered indicative of hygienic efficiency for other school 
 work, it must be admitted that the four fundamental operations 
 may become partially automatic in well-drilled children, and, 
 therefore, be less affected by fatigue. Furthermore, reasoning 
 problems were used in the third experiment as involving pro- 
 cesses and effort more generally needed in meeting school re- 
 quirements. 
 
 In order to carry out in the third experiment the methods of 
 the other two, it was necessary to use two reasoning tests that 
 could be graded accurately and would be approximately equal 
 in difficulty. The tests selected were Forms 1 and 3 of the 
 Courtis Standard Test No. 8, since Mr. Courtis had proved by 
 his very wide experience that these tests were as nearly equal as 
 any so far made. They were given and scored according to the 
 Courtis method, the number of examples done and the number 
 right being calculated from the figures in the " Answer" column. 
 The non-measureable elements in this gross method were mainly 
 neutralized in the comparison of morning and afternoon work. 
 
 On Monday, December 8, Form 2 of Test No. 8 was given 
 as a preliminary test to all sixteen classes in order to acquaint 
 them with the matter and method of the succeeding tests ; but 
 the papers were not scored. By trying ten, fifteen, and twelve 
 minutes as the time limit for this preliminary test, the twelve- 
 minute limit was found to be most suitable for the classes con- 
 cerned. For the succeeding tests the classes were divided into 
 groups of four, each group containing a 7A, a 7B, a 6A, and a 
 6B class of equal rank with other classes of the same half -grade. 
 As the classes in a group were tested in rapid succession, about 
 sixty-five minutes were required for a group from 9 :25 to 
 10:30 in the morning or from 12:50 to 1:55 in the afternoon. 
 The first test was given to Group 1 on Tuesday morning, to 
 Group 2 on Tuesday afternoon, to Group 3 011 Wednesday 
 morning, and to Group 4 on Wednesday afternoon. The second 
 test was given to Group 2 on Thursday morning, to Group 1 011 
 Thursday afternoon, to Group 4 on Friday morning, and to 
 
34 STUDIES OF MENTAL FATIGUE 
 
 Group 3 on Friday afternoon. Thus each class was tested in 
 the morning and in the afternoon; and each test was given in 
 the morning and in the afternoon to the same number of classes 
 of relatively equal rank. By this method the practice effect in 
 the second test was neutralized by approximately equal repre- 
 sentation in the morning and in the afternoon results. To com- 
 plete this neutralization the classes in Groups 1 and 2 were 
 tested in descending order (7 A, 7B, 6 A, 6B), and the classes in 
 Groups 3 and 4 were tested in ascending order (6B, 6 A, 7B, 
 7A). 
 
 A teacher generally remained in the room during a test, but 
 assisted me only in distributing and collecting the papers. The 
 children enjoyed the tests, which they thought were only for 
 correctness and speed. They did not know the time limit for 
 the work ; and the few that finished early spent the extra time 
 in looking over their papers. Where children were absent from 
 one test or where they did not follow important directions, their 
 papers were thrown out. 
 
 The hygienic conditions in the new school building were un- 
 usually good, but there had been no medical inspection of the 
 children. Opening exercises were held in each room from 9 :00 
 to 9 :20, recess was given from 12 :15 to 12 :35, and the first bell 
 for dismissal was rung at 2:15. The only recess did not give 
 much invigoration, because the boys' playground was small and 
 most girls remained indoors in spite of beautiful weather. 
 Some pupils ate a light lunch at recess, but nearly all had din- 
 ner at home after school. The departmental system of instruc- 
 tion prevailed throughout with half-hour recitation periods. 
 All classes included both boys and girls, the total represented in 
 my results being 212 boys and 255 girls. The average age was 
 14.18 years. 
 
 After the papers were scored, the averages of the number of 
 examples done and the number right in the morning and in the 
 afternoon tests were made for each class. Then general aver- 
 ages were made for the sixteen classes combined, and the morn- 
 ing and the afternoon results were compared. The number of 
 examples done in the afternoon was 0.68 per cent greater than 
 in the morning; the per cent of examples right in the afternoon 
 was 3.22 per cent less than in the morning. These per cents are 
 strikingly similar to those from the Lynchburg and New York 
 (average of two afternoon tests) experiments, where the in- 
 crease in quantity in the afternoon was 1.18 and 1.79 per cent, 
 respectively, and the decrease in quality 3.08 and 5.61 per cent, 
 
TILTED STUDY 
 
 35 
 
 respectively. As was shown by the New York results, the de- 
 crease in quality would be less by a detailed method of grading. 
 
 Total Results. 
 
 Class Pupils 
 
 Test 
 
 MORNING 
 
 Examples 
 
 Right 
 
 Test 
 
 AFTEENOO 
 
 Examples 
 
 V 
 
 Right 
 
 7A1 26 
 7B1 30 
 
 1 
 
 1 
 
 5.96 
 5 60 
 
 4.50 
 4 20 
 
 2 
 2 
 
 6.73 
 5.97 
 
 5.27 
 4 77 
 
 6A1 31 
 
 1 
 
 4 87 
 
 3 81 
 
 2 
 
 5 45 
 
 4 23 
 
 6B1 29 
 
 1 
 
 4.83 
 
 3.76 
 
 2 
 
 5.07 
 
 3 97 
 
 7A2 32 
 
 2 
 
 6 84 
 
 5 44 
 
 1 
 
 5 78 
 
 4 00 
 
 7B2 35 
 
 2 
 
 6 23 
 
 5 09 
 
 1 
 
 5 97 
 
 4 31 
 
 6A2 27 
 
 2 
 
 6 37 
 
 4 81 
 
 1 
 
 5 93 
 
 4 19 
 
 6B2 25 
 
 2 
 
 5 88 
 
 4 56 
 
 1 
 
 4 96 
 
 3 00 
 
 6B3 24 
 
 1 
 
 4 96 
 
 2 71 
 
 2 
 
 5 33 
 
 3 58 
 
 6A3 26 
 
 1 
 
 5 04 
 
 3 27 
 
 2 
 
 6 42 
 
 4 19 
 
 7B3 35 
 7A3 33 
 
 1 
 1 
 
 4.74 
 6 64 
 
 3.34 
 4 70 
 
 2 
 2 
 
 6.06 
 
 7 48 
 
 4.51 
 
 5 27 
 
 6B4 28 
 
 2 
 
 6 00 
 
 4 43 
 
 1 
 
 5 39 
 
 3 54 
 
 6A4 29 
 7B4 28 
 
 2 
 2 
 
 5.79 
 6 82 
 
 3.83 
 4 93 
 
 1 
 1 
 
 5.10 
 ^ Q6 
 
 3.31 
 
 4 00 
 
 7A4 29 
 
 2 
 
 7 00 
 
 5 55 
 
 1 
 
 6 72 
 
 5 14 
 
 
 
 
 
 
 
 
 16 467 
 
 
 5.85 
 
 4.31 
 
 
 5.89 
 
 4.20 
 
 Relative number 
 done 
 
 100.00 
 
 100 68 
 
 Per cent right 
 Relative per cent 
 right 
 
 73.68 
 100 00 
 
 71.31 
 
 Qft 78 
 
 
 
 
 The practice effect was calculated by rearranging the class 
 averages according to first or second test rather than according 
 to morning and afternoon, thus neutralizing for the most part 
 the decrease in efficiency in the afternoon. The sixteen classes 
 showed in the second test an average increase of 12.43 per cent 
 in quantity and an average increase of 7.16 per cent in quality. 
 This large practice effect was mainly due to the difficulty the 
 children had at first in disregarding unnecessary figures in some 
 of the examples. 
 
 The seventh grade showed more relative efficiency in the aft- 
 ernoon than did the sixth grade, probably on account of better 
 discipline in the former. The seventh grade had an increase of 
 1.61 per cent in quantity in the afternoon and a decrease of 2.82 
 per cent in quality ; the sixth grade had a decrease of 0.04 per 
 cent in quantity and a decrease of 3.67 per cent in quality. 
 
36 STUDIES OF MENTAL FATIGUE 
 
 Complete tables of class and general averages were made for 
 the girls and for the boys, showing the greater relative efficiency 
 of the former in the afternoon. The girls had an increase of 
 1.78 per cent in quantity in the afternoon and a decrease of 2.48 
 per cent in quality; the boys a decrease of 1.30 per cent in 
 quantity and a decrease of 3.76 per cent in quality. These 
 significant results are similar to those from the Lynchburg tests. 
 
CONCLUSIONS 
 
 The most important features of these experiments were the 
 giving (a) of actual school tests (b) under actual school condi- 
 tions (c) by the same examiner with the same methods (d) to a 
 large number of classes and pupils. Every possible effort was 
 made to get the work and attitude of the routine school day and 
 to eliminate individual and group variations. The comparison 
 of morning and afternoon results probably neutralized the effect 
 of two differences from routine conditions : the tests were given 
 by an outsider and offered a break in the regular school re- 
 quirements. 
 
 The per cent of increase in quantity and of decrease in qual- 
 ity in the afternoon results, as compared with the morning re- 
 sults, by the gross method of grading, may be summarized as 
 follows : 
 
 City 
 
 Classes 
 
 Pupils 
 
 Increase in 
 Quantity 
 
 Decrease in 
 Quality 
 
 New York 1 
 
 40 
 
 1,153 
 
 1.79 
 
 5.61 
 
 L/ynchburg 
 
 16 
 
 573 
 
 1.18 
 
 3.08 
 
 Roanoke 
 
 16 
 
 476 
 
 0.68 
 
 3.22 
 
 
 
 
 
 
 2,202 
 
 1.22 
 
 3.97 
 
 Seventy-two classes, 2,202 children, in three cities, showed in 
 the afternoon results an average increase in quantity of 1.22 per 
 cent and an average decrease in quality of 3.97 per cent. 
 
 The following tentative conclusions seem justified for gram- 
 mar-grade pupils : 2 
 
 1. Mental fatigue in relation to the daily school program is 
 far less than is generally believed, even if the tendency to do a 
 greater amount of work with a greater per cent of error can be 
 partly attributed to fatigue. 
 
 ir rhe averages of the two afternoon tests in New York are compared with 
 the first morning test, as the second morning test did not represent the 
 time or freshness of the morning test in Lynchburg and Roanoke, and the 
 results were even below the afternoon average. 
 
 2 These conclusions will probably not apply to primary grades (to most 
 children under eleven years of age), without modification as to length of 
 daily school program, etc. 
 
38 STUDIES OF MENTAL FATIGUE 
 
 2. The opinion regarding the graduated advantages of suc- 
 cessive periods of the school day, and the sentiment in favor of 
 putting arithmetic and other supposedly difficult subjects near 
 the opening of the morning and afternoon sessions, with an em- 
 phasis upon the morning session, have not a sufficiently proved 
 basis. 
 
 3. The decrease in quality of work by pupils as the day ad- 
 vances, considered to be more or less general in schools, is 
 mainly due (a) to improper ventilation, lighting, heating, seat- 
 ing, etc., (b) to physical defects in the children, and (c) to loss 
 of interest by pupil and teacher in the monotonous school 
 routine. 
 
 4. With sound bodies, a hygienic school, proper classifica- 
 tion, a vital and varied curriculum, and live teachers, most 
 grammar-grade pupils will present no problem of fatigue in re- 
 lation to the daily school program. 
 
VITA. 
 
 WILLIAM HARRY HECK: Born Raleigh, N. C., 1879; B. A., 
 Wake Forest College, N. C., 1897; Assistant Principal, Raleigh 
 Male Academy, 1897-98 ; M. A., Wake Forest College, 1899 ; 
 Graduate Student, Columbia University, 1899-1902; Univer- 
 sity Fellow, 1900-01; Honorary Fellow, 1901-02; Assistant 
 Secretary, General Education Board, 1902-05 ; Professor of 
 Education, University of Virginia, 1905 ; Graduate Student, 
 Columbia University, 1911-12. 
 
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