ARITHMETIC 352 



Practical Problems. Drill pupils on simple, 

 modern, business forms such as: notes, checks, 

 money orders, receipts, drafts, etc. ; taxes, insur- 



ARITHMETIC 



ance, commercial discount, stocks and bonds. See 

 DISCOUNT ; INSURANCE ; TAXES ; CHECKS ; NOTES ; 

 DRAFTS, and the like. 



History of Arithmetic 



FINGERS AS COUNTERS 



Arithmetic is the science of number, the 

 scientific formulation of number relations. The 

 savage formulates his number concepts in a 

 crude way, using his fingers as counters and 

 when all are used 

 says "a hand," 

 meaning 5, "two 

 hands," meaning 

 10. 



In Madagascar 

 a chief has been 

 observed count- 

 ing his army as 

 follows: The sol- 

 diers pass before 

 the chief and a 

 pebble is dropped 

 as a counter as 

 each one passes. 

 When ten peb- 

 bles have been 

 dropped, one peb- 

 ble is set aside 

 and a new pile 

 begun, and again when the pile has grown to 

 ten, one is set aside and so on until ten have 

 been set aside, when one is set aside to mean 

 one hundred. The 

 Aztecs indicated 

 10 by a picture 

 of the "upper 

 half of man" 

 and their word 

 for 10 was 

 matlactli, or 

 hand-half. Some 

 Indian tribes in 

 the North express 

 twenty thus: "A 

 man come to an 

 end." Another THE AZTEC "TEN" 

 tribe calls it "One Indian ended." 



These few illustrations taken from thousands 

 that travelers have brought to us from among 

 the tribes indicate the attempt of the low races 

 to formulate number relations so that they 

 may have some control over this important 

 element of number in the life about them by 

 which they count and to estimate their pos- 

 sessions and carry on trade and compare the 

 wealth and strength of different tribes. The 



same need that leads to this crude formulation 

 on the part of the savage leads to the finer 

 formulation and study of arithmetic as it is 

 found among the more civilized peoples of the 

 world, and indeed 

 largely to our 

 study of it to- 

 day. Of course 

 the culture value 

 of arithmetic is 

 more or less to 

 the front in the 

 higher civiliza- 

 tion, but empha- 

 sis on the culture 

 value is much INDICATING "TWENTY" 



criticized; especially at the present time when 

 technical and vocational work is attracting the 

 attention and receiving the approval of a large 

 part of schoolmen and laymen, there is a 

 tendency to teach arithmetic for its utilitarian 

 value. 



Far back in the centuries we find it taught 

 in the schools of the far East only for its 

 utility, and therefore only those parts of it 

 that were useful to the people and answered 

 their vital needs were taught. Among the 

 great traders of Southwestern Asia, the Phoe- 

 nicians, Babylonians and others, we find that 

 arithmetic was taught extensively, as is seen 

 by the tablets found by excavation in that 

 part of the world. The tablets show compre- 

 hensive bank accounts, and some recently 

 found show work of school children. Among 

 some of the Semitic people arithmetic occu- 

 pied from one-third to one-half of all the 

 school time during the years corresponding to 

 our later grade and high school years. In the 

 commercial cities arithmetic was taught en- 

 tirely for its utility. Italy as a commercial 

 nation gave to the world mercantile arith- 

 metic. During the time of the Hanseatic 

 League the merchants throughout the com- 

 mercial cities and all along the routes of trade 

 demanded that the arithmetic of trade and 

 commerce be taught, and when the products 

 of the church school did not satisfy them they 

 set up schools of their own for the study of 

 arithmetic under control of a Rechenmeister, 

 who was usually the city sealer of weights and 

 measures. Indeed, arithmetic was so com- 



