August 21, 1908] 



SCIENCE 



249 



tomarily about 25 per cent, receive tlie highest 

 grade. And to comply with this custom would 

 mean more conservatism than one can be ex- 

 pected to possess. On the other hand, equal 

 range of abilities for all grades is impossible, 

 since the probability curve extends infinitely 

 in both directions of the central point, so that 

 the range of the lowest and of the highest 

 grade must always — theoretically at least — be 

 infinite. It further seems to me of more im- 

 portance that the distances between the av- 

 erage abilities of the groups (represented by 

 the position of the geometrical center of the 

 group) be approximately the same than that 

 the ranges be the same. I shall make use of 

 this principle later on. Taking all these con- 

 ditions into account, I am inclined to prefer 

 50 per cent, for the central group. 



More advisable than a division of the me- 

 dium group of students seems a subdivision 

 in the group of superior students. To belong 

 to the group of the 25 per cent, best is not a 

 great distinction. It would be well, therefore, 

 to separate from the group those who possess 

 unusual ability. The manner of subdividing 

 the group is a matter of convenience. We 

 may proceed in the following way. In the 

 probability curve (Fig. 2) the point of ex- 

 treme ability, where the height of the curve is 

 practically zero, is chosen as 3. The point of 

 the vertical line which separates the superior 

 from the medium students is then .68, as can 

 be read off from any table containing the 

 values of the probability integral. It sug- 

 gests itself to divide the ability-difference be- 

 tween this point and the extreme point, 3, 

 into two equal parts. The result of this divi- 

 sion is the point 1.84. To the left of this 

 point are then found 3 per cent, of all the 

 etudents, as can again be read off from any 

 table of the probability integral. We have 

 thus divided the group into two parts in such 

 a way that the best possible student is as much 

 better than the best student of the second 

 class, as this one is better than the best of the 

 medium, class. Let us, then, call the 3 per 

 cent, just separated by the name of " excel- 

 lent " and retain the name of " superior " for 

 the 22 per cent, following. 



In the same manner we may subdivide the 

 group of inferior students, calling the 3 per 

 cent, worst " failures " and retaining the name 

 of " inferior " for the other 22 per cent. 



I expect to meet with opposition when I 

 restrict failures to such a small percentage. 

 But I believe that 3 per cent, is a sufficient 

 number in order to weed out those who have 

 succeeded in entering college, but are entirely 

 unable to do the work which they have chosen. 

 I can not regard it as just to grade the other 

 22 per cent, as failures. But I do not mean 

 by this that they ought to be permitted to 

 take advanced work in the same line of study 

 or to enter courses of other departments for 

 which this particular study is required, or 

 that they should receive credit for the whole 

 number of hours. The teacher who gives 

 these advanced courses and the teacher who 

 gives the course of the other department must 

 have the power to admit or to exclude these 22 

 per cent, students as he deems best. And the 

 faculty should decide what fraction of the 

 regular number of hours of credit they should 

 receive. Similarly, the faculty should, as 

 Professor Cattell has proposed, give more than 

 the usual number of hours of credit to those 

 students who have excelled the medium 50 

 per cent. To make aU this possible the teacher 

 must place each student in the group to which 

 he belongs according to his rank. But those 

 whose rank puts them in the fourth group 

 should not be called failures in every possible 

 sense, should not be regarded as having ac- 

 complished nothing. If a teacher instructs 

 his class in such a manner that according to 

 his own judgment 25 per cent, of them accom- 

 plish nothing, then the conclusion is justifiable 

 that the teacher as a teacher has not accom- 

 plished anything, either. 



The University of Missouri, as mentioned 

 above, has two grades, D and E, both of which 

 mean failure, but with this difference, that 

 students who may be permitted to make up 

 their deficiency by private work are graded 

 D, whereas those who can receive subsequent 

 credit for the course only by taking it over 

 in class are graded E. To the present writer 



