studies in Arithmetic, 1916-1917 



37 



Figures 9 to 12 depict the situation more clearly than by 

 means of words. In each figure the line for Group III (3,000 

 to 10,000) stands out distinctly above those for the other 

 groups. In subtraction the fifth grade in cities of Group 111 

 gets more examples right than those in Groups II and IV at- 

 tempt. In this same figure, however, Group II stands above 

 all others in the eighth grade in both attempts and rights. 

 The lines for Group I (less than 1,000) hold about an average 

 position in all figures, while those for Class IV (10,000 and 

 above) as a rule fall distinctly below. 



These results are in general agreement with the results 

 found in Iowa and Kansas, particularly Kansas. It appears 

 that the type of supervisory and instructional organization 

 which a city of 3,000 to 10,000 permits secures results supe- 

 rior to those now secured both in cities smaller and in cities 

 larger. If this inference is correct, it would be profitable 

 to study the supervisory organization in the schools in cities 

 of 3,000 to 10,000. 



Variability. Two types of variability are of particular in- 

 terest. One is a variability in achievements in the different 

 schools systems, a kind of variability that has been empha- 

 sized in other parts of this study. We have noticed not only 

 widely different scores in different cities, but we also found 

 widely different results within some of the individual sys- 

 tems. This marked variability cannot be justified satisfac- 

 torily on the grounds of difference in mental endowment, for 

 population of the state and of any city is too homogeneous for 

 that. It must be due rather to environmental conditions, to 

 differences in amount of time devoted to the subject, or to dif- 

 ferences in the quality of teaching or supervision. 



The second type of variability is that within a single class 

 itself. This is computed by the directions given in Folder D. 

 This rule is, "Multiply the median deviation (M.D.) by 100 

 and divide by the median." A low per cent of variability is 

 the result of having the most of the cases clustering around 

 ^the median of the distribution, whereas a high per cent is due 

 to a wide range represented by scores scattered at a great dis- 

 tance in either direction from the median. 



The teacher and supervisor of a class should strive then to 

 accomplish two things: to increase the median achievement 

 of the class, and to reduce the per cent of variability. Sev- 



