68 THE THIRD YEARBOOK 



processes which lead to senseless or meaningless results in arith- 

 metic, we should engender the same indifference, not to say hatred, 

 to literature that now exists in regard to mathematics. Why is it 

 that when pupils leave school they always have more or less taste 

 for their literary studies while not one in ten thousand even 

 attempts to "keep up" his mathematics? Why is it that at a 

 certain point in the academic course students have sometimes insti- 

 tuted the custom of publicly burning their calculus? Why is it 

 they have never thought of burning their Shakespeare, or Milton, 

 or Tennyson? There is no reasonable answer to these questions, 

 except that in the one case the study of literature has been made 

 to contribute something to their lives of real value which they are 

 able to appreciate, while in the other case they have got nothing. 

 Everybody clings to that which really helps him grow, and the fact 

 that the great majority of pupils who leave school either detest 

 mathematics or are in a state of helpless despair about the subject 

 is enough to make the philosophers who are inundating us with 

 volumes on the psychology and pedagogy of the subject stop to 

 think. They have surrounded the subject with so much mystery 

 that most teachers are no longer even curious about it, and they 

 have given up trying to penetrate it. There is no more mystery 

 about the psychology of number than there is about the psychology 

 of reading or drawing or any other subject. The fact is that there 

 is no psychology of any subject — it is all the psychology of thinking. 

 It is simply a question of finding out what image the pupil has that 

 is worth developing, and then of helping him to the use of tools, 

 as he needs them, in its growth. Mathematics plays a distinct part 

 in image-development which any teacher of ordinary sense can 

 recognize. It is nothing but the blindest slavery to tradition that 

 keeps the pupils from a rational use of number. It is due to the 

 general prevalence of the antiquated notion that in these early 

 stages of education it is necessary to isolate in a meaningless way 

 the process side of the subject for the purpose of drill. It has 

 been shown very clearly, both in theory and in practice, that the 

 pupil does not get by this method that mental discipline that is 

 supposed to come with the study of mathematics. It is evident 

 that this must be so because, as before pointed out, the drill is 

 necessarily much more a matter of language than of number; the 

 drill fails even as a linguistic exercise because the language is 



