246 



SCIENCE 



[N. S. Vol. XXVIII. No. 712 



not the exclusive condition on whicli the pos- 

 sibility of reexamination depends. 



To eliminate as much as possible the per- 

 sonal element from, the publication of the 

 results of this investigation, I have not given 

 the names of the teachers, but only the sub- 

 jects taught, and in the case of several teach- 

 ers of the same subject I have added Eoman 

 numerals for distinction. For the student of 

 similar phenomena I have added the total 

 number of records of each teacher, the number 

 of classes, in order to indicate the average size 

 of the classes, and the coefficients of variabil- 

 ity. In the first case of the table the average 

 total per cent, of A's is given as 55 and the 

 coefficient as .2. This means that in a class 

 of 100 students of this teacher it is just as 

 probable that the number of A's will be be- 

 tween 44 and 66 as it is that the number of 

 A's will be outside of these limits; and that 

 it is three times as probable that the number 

 of A's will be less than 66 per cent, as it is 

 that it will be more. In the last case of the 

 table the total percentage of A's is 1 and the 

 coefficient 1. This means that it is three 

 times as probable that in a class of one hun- 

 dred there will be one or two A's as it is that 

 there will be none. 



Let any one look over the four columns of 

 the 50 per cent, medium students and ask 

 himself if he can see uniformity of grading. 

 Above we see that none of the students of 

 medium ability receive the grades of C or F, 

 but all receive either A or B. Below we see 

 that none of the students of medium ability 

 receive the grades of A or B, but all receive 

 either C or F. And yet, on the basis of these 

 grades the faculty gives " honors," returns to 

 their parents students who have " accumulated 

 failures," compels students to take twice the 

 same work if this happens to be required for 

 graduation, and prevents students from taking 

 up work in departments to which they are 

 drawn by their natural inclinations and from 

 which they might derive the greatest benefit 

 for their later life. But let no one think that 

 this proves that the University of Missouri is 

 in a pretty bad shape. It is not likely that 

 other institutions are better off. Only, no one 



has investigated the matter. Education is 

 just beginning to realize that it is not merely 

 an art, but an applied science. 



Can anything be done to make such in- 

 equalities of grading impossible? There is 

 no reason why one should believe that this 

 could not be accomplished. I shall outline a 

 method by which one might proceed. 



It seems plausible to start from the assump- 

 tion that the combined mental and moral abil- 

 ity which we want to measure is distributed 

 among different people in accordance with the 

 probability curve which describes, e. g., the 

 distribution of accidental errors in scientific 

 observation. Fig. 2 shows such a curve. The 



+3110 



total area enclosed represents one hundred 

 students making up the membership of a par- 

 ticular class. The first problem which con- 

 fronts us is the division of this area. It 

 seems best not to proceed entirely arbitrarily 

 in this division, but to follow the custom 

 already established. Whenever this curve is 

 used for scientific purposes, its area is divided 

 by verticals in such a manner that a middle 

 area is cut out which is equal to the sum of 

 the two areas left at the sides. The signifi- 

 cance of this division is this: If we pick out 

 a student at random from a crowd of one 

 hundred, the chances are the same that we 

 shall have a student of medium ability as that 

 we shall have one who is not of medium abil- 

 ity. If the latter happens to be the case, he 

 may be either a superior or an inferior stu- 

 dent. Before we discuss the problem of fur- 

 ther division, let us give an answer to the 



