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in the exercises assigned to him. His memory is then not the 

 only faculty brought into play ; he reasons and draws conclus- 

 ions ; his good sense develops, he acquires correct language, 

 acquires a taste for what he does, and gains strength for greater 

 difficulties. Arithmetic has its principles and its axioms, just 

 as geometry has, and it is by setting them forth, by develop- 

 ing them logically that the pupil's intellect is sharpened and 

 his judgment exercised and himself fitted for the intelligent 

 practice of calculation. [The following American methods 

 recommended to French educators, need to be more generally 

 applied by our teachers. 



I. To prepare children for the study of arithmetic hy the use of 

 the abacus^ without prolonging this exercise too much. 



II. To extend the me of mental calculation^ as well in the form 

 of operations carried on in the head as in that of the rapid solution 

 of such problems. 



III. Not to he afraid of practicing children from an early age in 

 mental calculation^ fractions^ complex mimhers^ the metric system — 

 the whole presented not in the rigorous and definitive order of ulterior 

 instruction^ hut under the common^ elementally^ analogical^ and^ so 

 to speak, provisional form suited to a first survey of the suhject. 



Drawing in the Public Schools. — Six year«s ago drawing was 

 taught only in certain special schools, and that in a very imper- 

 fect manner : there were no models, no methods, no materials, 

 no masters. A committee was formed, and in a few years a 

 whole system of instruction was devised. In some states, Draw- 

 ing has been made obligatory ; four methods, strictly graded 

 and completing one another, bring the arts of designing within 

 the reach of pupils of all ages ; public expositions are increas- 

 ing ; all regular teachers are put in the way of teaching this 

 branch of education ; a normal school of art, to which flock 

 pupils from all parts, has been founded and a fruitful emulation 

 has arisen among various cities. If we take into account that 

 these are the fruits of a few years of trial, it must be acknowl- 

 edged that such remarkable results were never before obtained 

 in so short a time. The following are the recommendations 

 made on the subject of drawing : 



I. To commence drawing as soon as the child enters school, hy 

 slate or blackboard exercises, using the aid of squares or better style 



