244 



SCIENCE 



[N. S. Vol. XXVni. .\o. 712 



Professor Hall uses the marks AAA, AA, 

 A, BB, B, CC, C, D, and E; nine marks in 

 all. He does not tell us, however, how these 

 marks are to be defined. The mere reference 

 to a particular curve of distribution does not 

 define the marks unless the difference of 

 ability represented by each two adjoining 

 marks is identical. But Professor Hall tells 

 us that he does not regard them as identical. 

 AAA he regards as equivalent to 99 to 100 

 per cent. Per cent, of what? He does not 

 tell us. Of questions permitting only an 

 affirmative or a negative answer and answered 

 correctly in oral or written examinations? 

 I am not sure that he means this exactly and 

 exclusively, since he speaks also of the grading 

 of laboratory note books. But I shall assume 

 that he means the percentage of correctly 

 answered questions. AA is regarded as stand- 

 ing for 95 to 99 per cent. The distance be- 

 tween the centers of the abilities AAA and 

 AA is, therefore, 2.5. If we examine the other 

 distances in the same manner we find them to 

 be 4.5, 5, 5, 5, 5, 7.5 and 10. If the hori- 

 zontal coordinate is divided by a scale of such 

 unsymmetrical units, reference to a symmet- 

 rical curve has little meaning. It seems to 

 me that the chief fact brought out in Pro- 

 fessor Hall's paper is this : If a teacher, in 

 grading his students, proceeds on the prin- 

 ciple that the number receiving medium marks 

 should far exceed the number receiving high 

 or low marks, the accumulated results of his 

 grading are likely to agree with his principle. 

 But who would expect this to be otherwise? 

 No one, however, will expect uniformity of 

 grading in a wliole institution to result from 

 the fact that each teacher is guided by that 

 principle, unless the various marks are defined. 

 Is it possible to define the marks used, as 

 standing for definite percentages of right 

 answers? I do not believe, judging from my 

 own experience in teaching, that students can 

 be ranked by such a mechanical method. And 

 if a teacher insisted on ranking them by such 

 a method, he would often find that the result 

 does not agree with Professor Hall's binomial 

 curve. I tested the native musical ability of 

 seventy-one students. The nature of the test 



IF JP W W" 



Fig. 1. 



will be described elsewhere and its appropri- 

 ateness demonstrated. The accompanying 

 curve (Fig. 1) shows h jw the ability in ques- 

 tion was found to be distributed (continuous 

 line) and how it should be distributed accord- 

 ing to Professor Hall (dotted line). There 

 was in this ease no distortion of the curve by 

 either dishonesty of the students or any " per- 

 sonal equation " of the teacher. The grading 

 consisted in the mechanical process of count- 

 ing the right answers. Nothing is easier, of 

 course, than to distribute the students in ac- 

 cordance with Professor Hall's curve, if we do 

 what he has done and apply to the horizontal 

 coordinate a scale of unequal units. But what 

 is the use of it? Thus far I can not see any. 

 Five years ago the faculty of the University 

 of Missouri voted that the grades of the insti- 

 tution should be A, B, C, D and E. What 

 those grades should mean was left undefined, 

 except that D and E were both called failures, 

 with the distinction that D students were per- 

 mitted to prepare privately for a second ex- 

 amination, and E students were not. It is 

 highly interesting to see how the assumption 

 that every teacher would know what the dif- 

 ferent grades stood for, has worked out in 

 practise. I have collected the reports of forty 

 teachers of the university during the last five 

 years, all with two exceptions professors or 



