72 THE THIRD YEARBOOK 



3. Fractions : common and decimal ; fundamental operations. 



4. Percentage : all the processes or " cases." 



5. Square measure, units : acre, square rod, square yard, square 

 foot, square mile. 



6. Linear measure : inch, foot, yard, rod, mile. 



7. Volume: pint, quart, gallon, barrel. 



A word further must be said as to the method of teaching 

 these forms and processes in connection with the actual image- 

 development. Most teachers are so overconscientious about the 

 matter, to put it charitably, that when a pupil fails to learn the 

 processes at once, he forthwith drops everything else and proceeds 

 to belabor him so that "he will never have to learn that particular 

 fact again." The teacher who does this is not thinking of what he is 

 doing. He is merely trying with his eyes shut to make a reputation 

 for being " thorough." Such a teacher pays no attention whatever 

 to the way in which we naturally learn all those things in child- 

 hood that we never, never forget. A child never learns anything 

 thoroughly the " first time ; " neither does an adult. But he comes 

 back to it again and again as he needs it ; its function becomes all 

 the while clearer and clearer, and finally we have the astonishing 

 result that neither the worries of active life, nor the ravages of 

 disease nor length of years, can efface the picture from memory. It 

 is probably not without the deepest significance that teachers would 

 do well to heed that, when in old age all the experiences of an entire 

 middle life fade, there remain those vivid memories of childhood 

 that were garnered up in nature's own deliberate way. In the 

 delight of those visions of a long-ago youth, it is doubtful if the 

 multiplication table or the division of fractions ever plays an impor- 

 tant part. The pupil should not be belabored into mathematical 

 processes any more than he should be belabored into words in his 

 reading. In the latter subject the principles of the kindergarten 

 are beginning to be appreciated ; in the former, the methods of the 

 penitentiary still prevail. 



