Show B Y COLLEG I 1 the work of the first year embraces tile the deachin teaching of oatlie tile numbers from one to ten I 1 in ll 11 the beginning objects should be used and continued as ion long as the child absolutely requires them but as boon as possible discard them 1 each ach number is taken by itself measured by those that precede i it L and compared arid and studied in all its possible operations in teaching a number three steps are required qu ire d first the pure number second the sign of the number third the number applied under puro pure number the idea of number is given to the child by the use of objects which are placed before him to see eee have objects of uniform haic and size ak questions about the objects and when they understand the number the number of objects jon on the blackboard black board 1 then I hen teach and write on oil tile the board tile the I 1 si sin sign 0 n of the number it can caa now b be e applied by means of examples example the tee number from ten tell to one hundred occupy the second year anufrom and from one hundred to one thousand andi the first half of the third year is much the same saine as the first year except that eliat objects are not used after the ten aud ruay may be laid aside before if the child can understand and without them in ili the file second half of the third year the four fundamental rules in abstract and concrete numbers are introduced in unlimited range mental arid and written work should never be separated tellas as mental arithmetic is the foundation lit in numeration and notation the units tens hundreds etc are taught and also the place where they belong beloi ig teach the orders and provide thoroughly and no difficulty vi v ill be experienced in addition subtraction multiplication and davison Di vison in all the parts of arithmetic give plenty of drill average may may be ba taught 0 by means of various examples for instance r give the age 11 of the members b ars of the class and have them average the age of the class the next subject taken up is that of fraction teach the relation of the parts to the whole this can be done by the use of objects by dividing them into 12 1 2 13 1 3 11 14 1 4 1 etc ill ili decimal fractions show their relation to the common coi number ahio al of I 1 to 10 jf the lie subject of decimals is thoroughly understood percentage will conic come perfectly natural in ili teaching 4 this allow the students to give the their 1 r notes to one another measurements should be tau taught lit objectively and practically 11 have a ve the students measure the th e school room tile the floor and walls deduct abduct ins fur the doors abild windows take the class to a lumber y yard ard after school and let them measure iuca sure gome come of tile the pieces and bring their work to school next day visit with them buildings in ili i ourse course of construction wood piles exava tion etc this will do more good than twice tile the time spent ia imaginary examples Por portion this is ia a very verv difficult subject to present to cl children ildren an and d unless the reasoning considerably devo developed loped tile they will not understand it longitude and time may be taught by the use nee of the globe compound numbers should not be taught until after fractions have bavo i been cell Plesent presented ed the metric s system ys t cornea corn Cs after powers and roots r a introduce the subject as 0 ordinary rd i nary numbers decimal fractions fraction 11 S and ana U S lioney money IDLA EDIA CH apo TEACHING oi 01 Pert alizzi laid down tile the principle that all mathematical knowledge knowledg know led e is is founded on hoine immediate diate observation and therefore must proceed from the concrete to the abstract by means of innumerable examples the general principles are arc I 1 A method of teaching numbers to be successful must reco bocog alize nize the psychological fact that nearly ill knowledge obtained by children eh ildren in their earlier years yeara is is i obtained by means of the tens elementary teaching 0 of numbers should begin with th things ingIs IT IL figures are but tile the symbols of numbers and the child should become acquainted with the former through the latter III the progress pr oress of the child should be gradual and natural proceeding from the known to the unknown from the simple to the complex from fram the concrete tu to the abstract IV A child should not be deprived of the pleasures of finding find irli out a truth and in hi order that he lie may got get its full value lead him to discover it teach him to express it and train him to apply it V objects should be discarded as soon as the child is able to proceed without them for when that point is re reached objects retard rather than aid advancement VI by bv the ded deductive liati ve method ta the ie rule is stated slated proved to 10 be correct and then applied but by the inductive method the student is led gradually to discover arid and formulate late his own rules VII in tile the solution of an example c x the student inus must t first be able to see clearly what is given second what is required third hoir bow to find it ile ho must see sec ali all this before lie attempts a solution lution Fo there shoud shou d be a careful arrangement ran rani gement of work on slate notebook book or board plain figures and a 1 name for each result when a student can say eay 1 I see what IS is 0 given alren and required 1 I know how ho t to 0 solve the problem 1 I can prove it lie he has solved the example CA lIOtINE LARSEN |