880 



SCIENCE 



[N. S. Vol. XXXIX. No. 1015 



tion to which lies mainly in the fact that it is 

 new. But this scale is the most scientific yet 

 proposed. It is based on careful, statistical 

 theory. 



The mode of distribution of mental abilities, 

 exhibited in the normal curve, suggests that 

 the scale be subdivided into an odd number 

 of parts, so that there may be a central group, 

 representing average students, which is the 

 most common type of students. The other 

 groups are placed symmetrically above and 

 below this central group. What should be the 

 total number of groups? Experience shows 

 that three groups are hardly sufficient, that 

 seven groups are excessive. The five-group 

 system is altogether in nearest accord with 

 experience. Accordingly, we shall use the 

 terms " Excellent," " Superior," " Medium," 

 "Inferior," " Poor," and define their positions 

 on the Pearson scale, thus: 



Poor 

 Below — 1.5 



Inferior Medium 



— 1.5 to —.5+ —.5 to + .5 



Superior 

 .5 + to +1.5 



Excellent 

 Above + 1.5 



When a class of 20, 30 or 40 pupils has to 

 be marked, we first determine the ranks of the 

 pupils. Then the numerical values of these 

 tables are a suggestion as to the probable marks 

 to be assigned. Eor any one class of 20 these 

 tabular figures are, of course, not binding. 

 If a large number of different classes of 20 

 could be marked with absolute accuracy, th« 

 averages of the marks of all the pupils that 

 take the rank n in the lists of twenties would 

 yield the values given in the tables. Thus the 

 averages of the students ranked fifth in differ- 

 ent classes of twenty students each, is .8. 

 What deviation from the tabular marks should 

 be made in the case of any particular class 

 because of its individual variation or its devia- 

 tion from a " fair sample " must lie with the 

 judgment of the instructor. The position of 

 the exact line of cleavage between pupils 

 " passing " and those " not passing " must rest 

 with him. It is my own judgment that, if 

 teachers were to follow very closely the tabular 

 marhs, and were to modify them in only ex- 



ceptional cases, and then only slightly, that 

 a great stride would be taJcen toward a scien^ 

 tific and absolute method of marJcing. Gross 

 irregularities in marking, such as Finkelstein 

 has found in Cornell, and such as we know 

 to exist in schools with which we are con- 

 nected — irregularities working great injustice 

 to pupils aspiring to honors and to scholar- 

 ships — would be eliminated by the adoption 

 of a plan as herein set forth. Every one knows 

 that the marking system as carried on at pres- 

 ent in high schools and colleges is a farce. 

 But the adoption of a scheme of marking as 

 here proposed would show that a mark of 

 places the pupil in a modal position, as a 

 mediocre student. A mark above 1.5 places 

 him in the list of the very few branded " ex- 

 cellent." A mark below — 1.5 places him near 

 the line of students marked " not passed." 

 In nearly all the marking systems that 

 have been suggested in recent years, the 

 recommendation is made that, under normal 

 conditions, a certain percentage of the class 

 be marked " excellent," another percentage 

 " superior," etc. The Missouri plan involves 

 the same idea by dividing each class of 100 

 into four groups of 25 students each, and then 

 subdividing the first and last groups again into 

 two classes. I have never seen it pointed out 

 that such a procedure, as a matter of fact, 

 rests upon an unsound basis. The tabular 

 data computed from Pearson's formulas show 

 that if, for instance, we mark 7 per cent, of a 

 class of 100 " excellent," we have a different 

 standard of "excellence " from what we have 

 when 7 per cent, of a class of 50 is marked 

 " excellent." The difference in standard is 

 slight, but it exists, and therefore renders the 

 percentage basis scientifically objectionable. 

 To illustrate : When 7 per cent, of the class 

 are marked " excellent," the lower limit for 

 this mark on the Pearson scale is (using more 

 accurate results than those in our table) 1.4390 

 for a class of 100, 1.4045 for a class of 50, 

 1.3951 for a class of 40, 1.3529 for a class of 

 30, and 1.3080 for a class of 20. Seven per 

 cent, of a class of 41 members is four, but only 

 three of the four stand above the point 1.4390 



