Haggerty: Studies in Arithmetic 



9 



it means that city 7 has not learned how to teach addition as 

 effectively as the other subjects. The variability in median 

 scores probably indicates more o^' less accurately the differences 

 in teaching methods, and if any city is to secure a change in 

 score it will do so by changing its methods of instruction. 



Speed and Accuracy 



One of the common causes urged for a low dependability is 

 that the children work too rapidly. The evidence in this table 

 of medians is directly contrary to that argument. Twenty-four 

 grades which fall below 60 per cent in dependability have a 

 median score in attempts of 7.1, while 11 grades which scored 

 from 70 to 75 have a median score of 7.7, and the 7 cities which 

 score above 75 per cent in accuracy have a median of 9.8. These 

 figures would seem to justify the statement that the more rapid 

 the work the more accurate it is. Whether this extreme state- 

 ment could be justified may well be doubted. The ratio between 

 accuracy and speed is probably an individual matter, and there 

 are certain limits of speed within which an individual does his 

 best work. If he is pushed beyond this limit he loses in accuracy; 

 likewise if he is slowed down too much he tends to become in- 

 accurate. No one has yet determined for children in general 

 or for any individual child in particular the limits within which 

 he will do his best work in any subject. 



The value of speed in securing greater accuracy is doubtless 

 a function of attention. When the mental processes are rapid 

 their inhibitory power is greater and, hence, the subject is less 

 open to distraction from interfering stimuli. He has concentrated 

 attention. To slow down these processes weakens their resistance, 

 and contending neural impulses get the right of way with con- 

 sequent dispersed attention, providing the condition for in- 

 accurate work. For this reason many children would be rendered 

 more accurate if they were speeded up within certain limits. 



Standard Scores and Charts 



One cannot from the median score of a class judge the efficiency 

 of that class except in reference to a standard of achievement for 

 a class of that grade. In the 1914 study'^ we published a chart 

 which we called the Indiana Standard. The form of the chart was 



'M. E. Haggerty. Arithmetic: A Co-operative Study in Educational Measurements 

 {Indiana University Studies, No. 27). 



