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tion to the next higher grade, and from that up to the highest 

 or High School, and the programme is planned for those who 

 complete the full curriculum, rather than for the majority who 

 withdraw early for work or business. It is worthy of inquiry 

 whether at each successive step the conditions of promotion 

 may not wisely include the same studies and attainments 

 which constitute the best preparation for the business of life, 

 as well as for higher grades in school. 



How to secure the best results with the least cost of time as 

 well as money, is a problem not yet fully solved. Our text 

 books, now too voluminous, should comprise less of minute 

 details and more of practical methods and principles. Such 

 topics in arithmetic as the least common multiple of common 

 fractions, casting out of nines in multiplication and division, 

 alligation medial and alternate, and commutation of radix, may 

 well be omitted in a common school course, or briefly noticed 

 in the appendix. Those and kindred topics, of no use in 

 ordinary business, fill a large space in nearly all the arithmetics. 

 They have a traditionary sanction. In continuing them the 

 authors have consulted usage more than utility. Like the 

 titled scions of rank in the old world, they have come down by 

 so long a literary descent that no one disputes their right to 

 their honored place. Worth m^ore than all these complicated 

 processes is the thorough mastery of the ground rules. In all 

 our schools rapid mental combinations should be daily prac- 

 ticed till pupils can add, multiply and divide with the utmost 

 facility and accuracy. This done, the rest of arithmetic will be 

 comparatively easy and pleasant. 



Ex-President Thomas Hill justly complains that our Arith- 

 metics have been expanded until the unfortunate pupil is lost 

 in a wilderness of words, and does not find his way through, in 

 time to learn to cipher. The science of arithmetic receives so 

 much attention that the art is neglected. Life is not long 

 enough to spend so long a proportion of it on arithmetic as is 

 spent in the modern system of teaching it, and arithmetic is too 

 valuable an art to have our children neglect to acquire facility 

 in it, instead of being stupefied and disgusted with premature 

 attempts to understand it as a science." It is certainly a use- 

 less repetition to require children to learn, for example, explana- 



