Show fL l tt- tt i i fit i f ED EDUCATIONAL C A t I I 1 JiL 1 i I. I r NOTES IN P PROFESSOR STEWARTS STEWART'S CLASS LA S iN IN S 'S SPECIAL E L M METHODS IN ARiTH ARITHMETIC C. C Before the child enters eaters school he lie has acquired indefinite ideas of volume area distance weight time and value And has also lea learned ed to count or enumerate The purpose of arithmetic is to make definite e these ideas This is done dune by oy establishing artificial standard of me measurement meas s. s and comparing comparing- the indefinite quantity w with ith the definite stan stan- dard The first work of the child then at school is to become familiar by actual experience and use with these definite mea measuring units I His quantitative experience is to be measured by these definite standards The pedagogical order which is is to be followed by the teacher must be primarily determined by the childs child's experiences He knows something of time weight distance value and they are now to be made definite the application of the standards of measure The old method of arithmetic based upon the how many idea of number fixed in the mind of the child once as the invariable unit so that it was almost im impossible to to jJ pass pass from rr from m 47 unity to the fra fractional t i- i v part dart without confusion c n If the ratio idea of number is is developed from the first the child will r regard regard re re- i gard any quantity represented either by one or more than one or or a fraction of one as just or much a unit or standard of measurement as as s sI I f one itself itsell It is is im important that the measuring unit be a flexible quantity from the first Integers and decimal fractions may be regarded as regular reg- reg re regY Y ular varying units while the common common fractions are irregular flexible units There sho ild pra practically be h no bre break k in in passing from units unit to o tenths any more tl than p in passing p s from units to tens Common fractions fractions s decimals and pe percentage G It are arff rent forms of f notation n t tion The fraction i may b be expressed a as as' as 25 5 or 25 per cent There should be no break between these topics s' s of f arithmetic Every mathematical question pr presents sent data ata as quantities to be com compared co corn corn- pared to find fino ratios or as ratios and arid quantities to find quantities 1 1 I he he pe multiplier and quotient are arc c always r while e t the product multiplicand cand dividend and divis divisor or orare are are always quantities This should be he constantly constantly con con- con con- 1 kept in in mind by the teachers of f arithmetic tic The following explanation explanation ex- ex 5 from the pupil will enable the teacher to determine the pupils pupil's j knowledge of this fact If five oranges cost 25 cents what will one Orange drange orange or- or ange cost Explanation If If five oranges cost 25 cents one orange will wll f cost is as s many times 25 cents as the ratio of one orange to five orang oranges oranges s. s 1 The ratio of one orange to tau five oranges is one fifth One fifth times 25 cents is is the cost of one orange Problem At At 7 cents each how many melons can be bought for 56 cents Explanation As As the ratio of 56 5 cents to 7 cents which is is seven Seven times one orange can be bought In the above problems it will be seen that quantities to be compared and the ratios are all made distinct This form of explanation can be made as ai a test of a pupils pupil's knowledge of any problem It is is often convenient to express the solution in in the form thus if seven men working 18 days at nine nine hours a day can dig a ditch long what equals the number of days required by fourteen men working 8 hours a aday aday aday day to dig a ditch ft long Solution would be stated thus thus 7 7 14 of 8 Q of 26 of 18 davs days |