studies in Arithmetic, 1916-1917 



23 



example, gives the per cent of pupils in each of the grades 

 scoring each number of attempts. It gives the rate distribu- 

 tion in addition and should be read as follows : .2 per cent of 

 the 1,011 fourth grade pupils finished 0 examples in the al- 

 lotted time; 2.2 per cent finished 1 example; 8.5 per cent fin- 

 ished 2 examples, etc. The mode, that is, the largest single 

 group, is given in bold-faced type. The speed distributions 

 for all grades are read in the same manner. Table VII i? 

 gives the accuracy distribution for addition and should be 

 read thus : 48.3 per cent of the 1,011 fourth grade pupils made 

 an accuracy score of 0-49 per cent; 10.3 per cent made score 

 of 50-59 per cent; 11.5 per cent made score of 60-69 per cent, 

 etc. ; 12.4 per cent made a perfect score in examples at- 

 tempted. Here again the mode is given in bold type. 



Tables VIII A to X 5 give the speed and accuracy distri- 

 butions in subtraction, multiplication, and division, and are 

 read in the same manner as Tables VII A and VII B for addi- 

 tion. 



Further examination of Table VII A shows a wide range in 

 adding ability. In all five grades there are some pupils who 

 attempted as few as 0 or 1 example. In the fourth grade one 

 pupil attempted 13 examples, in the fifth one pupil attempted 

 21 examples, in the sixth two attempted 17, in the seventh 

 one attempted 18, and in the eighth there were pupils who at- 

 tempted from 20 to 24 examples. In the eighth grade .2 per 

 cent finished 0 examples and .1 per cent attempted 24 ex- 

 amples, and 22 different rates of speed were shown. 



The data in Table VII A are not subject to adverse criti- 

 cism only. They reveal the fact that there is a gradual 

 growth in rate of work from the fourth to the eighth grade. 

 Refer, for example, to the third column. They decrease grad- 

 ually from 8.5 per cent to .15 ; i.e. there is a gradual decrease 

 from the fourth to the eighth in the number of pupils who at- 

 tempted so few as 2 examples. The same thing may be said 

 of all the columns up to the modes. Now note the column to 

 the right of the modes. The same growth is revealed. Here, 

 however, the per cents naturally increase from the fourth to 

 the eighth grade. Thus, in the column headed 9, we find that 

 1.5 per cent in the fifth attempted 9 examples and so on until 

 in the eighth we have 15.4 per cent attempting the same num- 

 ber. This evidence of growth characterizes the columns to 

 the right of the one in question. 



