8 04 



POPULAR SCIENCE MONTHLY. 



ering up the twelve objects that represent the product. When 

 he has played at this for some time he may become acquainted with 

 all the products up to ten times ten or beyond without having to 

 make any abnormal effort of memory. 



The idea of numeration, which is usually put off till a later 

 period, should also be given at the beginning. Children soon under- 



FIG. 2. 



stand the decimal numeration and learn to write 10 for ten, and 

 other numbers composed of one of the nine ciphers and zero. But 

 the fact which, however, though quite essential to know, receives 

 very little attention is that there is nothing particular about this 

 number ten, and that systems of numeration can be devised resting 

 on any basis that may be taken; that the principle of every system of 

 numeration consists in taking a certain number of units and group- 

 ing them. Take, for example, a system having five as its basis. All 

 the numbers of such a system can be represented with the figures 

 1, 2, 3, and 4, the symbol 10 standing in this case for five. To con- 

 struct a number we have only to group the units by fives and ob- 

 serve the result. 



To learn decimal numeration by this process we put tens of ob- 

 jects into little boxes, tens of little boxes into larger ones, and so on. 

 The child can in this way acquire an exact idea of the units of suc- 

 cessive order in any system that may be desired. 



This method of teaching was developed in a remarkable way 



