Haggerty: Study ix Arithmetic 



445 



Specific Character of Habits 



The variability of rankings shown by this table emphasizes a 

 fundamental fact in educational psychology, a fact very generally 

 neglected by educational theorists. This fact is the very specific 

 character of the habits formed in the learning of any one of the 

 skills measured in these tests. A study of this table will show 

 that efficiency in one process does not necessarily mean efficiency 

 in any other process. Children may add well and subtract poorly 

 as in the case of city 20, fifth grade, or may multiply well and 

 add poorly as in city 5. seventh grade, or may divide well and 

 subtract poorly as in city 19, eighth grade. What does this mean 

 except that children learn those skills in which they are effectively 

 trained? The others they do not learn. 



One does not learn subtraction by learning addition, nor does 

 he learn division by drill on multiplication. To be sure there 

 must be some overlapping from one process to another. There is 

 some addition in multiplication and in long division both multi- 

 plication and subtraction function. But apart from these evident 

 overlappings there are habits quite specifically characteristic of 

 each process which are learned only by drill in that process alone. 

 The almost anarchic tendency shown in these tables for children 

 to be strong in one thing and weak in another is doubtless to be 

 accounted for by the specific nature of the habits demanded in 

 each case. To learn addition is not to learn subtraction, and to 

 learn subtraction is not to learn multiplication, and so on. To 

 extend the argument one could say that to learn any one or all 

 of the processes is certainly not to learn the whole of arithmetic 

 or the whole of mathematics, nor is the learning of mathematics, 

 however thorough, anything more than the acquisition of skills 

 and habits thoroughly specific and limited. It is not '"the train- 

 ing of the mind" in any other sense. The virtue of such specific 

 training is, of course, to be determined by the degree to which such 

 specific habits function practically in the life of the individual. 



, Variability 



Just as the median is a better measure of group achievement 

 than the mode, so the per cent of variability is a better measure 

 of the distribution of ability than are the minimum and maximum 

 scores. In the tables the per cent of variability is given to the 

 right of the median. In Table II it ranges from 24 in cities 7, 

 10, 13, and 15 to 30 in city 4, and 33 in city 5. The desideratum 



