ADDITION 



IS 



ADDITION 



the sand table the transition is made easily to 

 columns on large paper or on blackboard; dots 

 or tally marks with pencil, charcoal or chalk 

 take place of stones. The paper or board ap- 

 pears like this: 



Then follows the use of the digits in the 

 columns also, thus: 



This is the natural course of progress, as we 

 trace it through the centuries, the mind of 

 the race using counters to perform simple or 

 difficult operations, and the symbols to ex- 

 press and hold the results. We find the Eu- 

 ropean far dow r n into modern history doing 

 this, and to-day we may watch the Chinese 

 and the Japanese using the counter (the 

 abacus) and setting down results with symbols. 

 (See ABACUS.) Finally comes the column idea, 

 without marks of separation, and with this the 

 need of some sign to show that a column is 

 empty. When he writes 6 tens and 4 ones he 

 has 64, but when he writes 6 tens and has no 

 ones, he must have some sign to hold the first 

 column. The zero may be given him immedi- 

 ately or he may invent something for himself. 

 The dot, the triangle and sometimes the poly- 

 gon were the devices used where zero (0) is 

 now used. Now the child' has "place value" 

 clear. For further discussion of this, see NO- 

 TATION. He now writes as follows and com- 

 bines, using the dot: 



46 

 24 

 12 



82 



He sees 4+6 as 10; he puts a dot or a small 

 1 in tens column for each 10 he finds in 

 units column, and puts 2 in units place in the 

 sum. He has 8 tons and 2 ones, or 82. Here 

 follow several similar problems: 



23 

 12 

 55 



"90 



17 

 23 

 38 

 12 



16 



4 



23 



is 



90 61 



They should also appear in this form: 



Here the digits are used only to show the _5 



10 

 4 



23 

 JL8 

 21 



J? 

 61 



16 

 1 

 23 



15 

 _21 

 61 



In the above the child adds either column 

 first and writes its sum, and then adds tht 

 other column and writes the sum, and adds 

 these sums. Through this comes a thorough 

 understanding of the meaning of each num- 

 ber, and of the meaning of a sum. There are 

 just so many tens and so many ones, and he 

 reduces and reads as ones; for example, prob- 

 lem 3 is 4 tens and 2 tens and 1, or 6 tens and 

 1, or 61. 



With older children this method of adding 

 the columns in any order and putting down 

 the partial sums and then getting the total is 

 an excellent help to good understanding of 

 number and a good method of testing one's 

 own work in addition. To illustrate: 



