NUMBER- WORK IN NA TURE-STUD V 67 



of number with nature-study materials is as bad as the present 

 sterile array of problems in the ordinary text-book in arithmetic. 

 There will never be any such thing as rational mathematical work 

 until it is confined to the appropriate part it plays in the development 

 of an image. 



One of the chief obstacles to intelligent number-work is the 

 deep-seated feeling in the minds of most teachers that a large 

 amount of drill-work is necessary in order to fix the process. That 

 much repetition may be necessary does not imply, however, that 

 it shall take the nature of drill on empty and meaningless forms. 

 The same principles apply here that apply to reading. It would 

 be just as senseless to isolate the words of a lesson and require the 

 pupil to learn them all by rote before learning to read, as it is to 

 isolate a lot of facts in the form of the multiplication table or the 

 tables of compound numbers and require the pupils to memorize 

 them. That both words and certain results in arithmetic must be 

 memorized no one will dispute, but there is no reason for doing 

 one thing with words in reading and another thing with number. 



The tables of various kinds in arithmetic should be built up just 

 as a vocabulary is formed. When a word is used by the pupil in 

 the development of an image, the teacher usually, as she should do, 

 makes an effort to fix the word in the mind. If the child fully 

 understands its function in the development of his image, it is 

 comparatively easy to do this ; otherwise it is not readily done. So 

 in number, if the development of the image requires that the pupil 

 get the product of 6 times 8, when the result, 48, is obtained the 

 operation should be fixed in the same way that the word is memo- 

 rized. In fact, this part of the work is nothing but a language 

 lesson, and it should be treated as such. If from day to day these 

 operations are all gathered up and tabulated as they occur, the 

 tables will take care of themselves. 



The real point of importance that is involved here is a moral one. 

 No one has yet been able to calculate the evil done to the pupil 

 by enforcing the current drill methods in arithmetic. By this prac- 

 tice it habituates the pupils to dealing with forms without meaning 

 — to blindly doing things from which they expect no intelligible 

 result. If we were to practice the same methods in teaching read- 

 ing, if we were to " drill " the pupils upon words without meaning 

 for year after year, as we now drill them year after year upon 



