studies in Arithmetic, 1916-1917 



17 



examples right from 4.4 attempts. Nine cities in the fifth 

 grade subtraction are inferior to City 12 in number of ex- 

 amples attempted in the fourth grade which has a median of 

 6.7. Fourteen of the 18 cities reporting fourth grade sub- 

 traction attempts are superior to City 10 in the fifth grade 

 subtraction attempts. Fifteen cities fail in the sixth grade 

 multiplication to reach the median score for attempts of City 

 12 in the fifth grade. The median accuracy for all cities in 

 the fifth grade is only 56 per cent, yet there are 6 cities in the 

 sixth, 10 in the seventh, and 7 in the eighth grade that fall 

 below this per cent of accuracy. In the eighth grade the range 

 of the median scores in addition attempts and in accuracy is 

 from 6.5 to 11.0 and 50 to 80 respectively; in subtraction it 

 is from 8.7 to 15.0 and 67 to 100; in multiplication, from 

 7.0 to 12.0 and 54 to 88.5 ; and in division from 6.8 to 11.0 and 

 70 to 100. 



The Significance of These Differences. These differences 

 are significant. They mean that different cities are obtain- 

 ing widely different products from the instruction in arith- 

 metic which is provided in their schools. If those cities whose 

 median scores are low are securing a product which is satis- 

 factory, then we may ask if the cities which have the high 

 medians are not placing too much emphasis upon the opera- 

 tions of arithmetic. On the other hand, if the higher median 

 scores represent a satisfactory product, then those cities which 

 have the lower median scores are allowing a majority of 

 their children to advance from grade to grade and even to 

 leave school without a satisfactory equipment in the funda- 

 mental operations of arithmetic. 



Whenever the median score of a class or a city differs more 

 than one example from the standard, the cause should be stud- 

 ied. It may be that there is some satisfactory explanation. 

 If not, an adjustment in the instruction should be made which 

 will bring the median scores within the ''zone of safety". It 

 should be noted that we are referring to the scores which 

 'are above standard as well as those which are below. Al- 

 tho the situation probably is not as serious, it should be rec- 

 ognized that median scores which are distinctly above stand- 

 ard are unsatisfactory as well as those which are below. 



Since 24 of the 27 cities gave these tests for the first time 

 in 1917, we have here an illustration of the need for measur- 



