"The amount of time now expended upon the study of arithmetic in the schools appears to be nearly 4 1-2 hours a week, or almost exactly one-fifth of the entire school time, are devoted to the study of arithmetic, on the average, during the nine years of school life according to the prescribed courses.
At the present time the results in accuracy, if not in facility, of arithmetical work leave very much to be desired. Scarcely has the child been taught to count as high as 10, when he is put at technical applications of arithmetic, to money coins, to divisions of time, space, etc.; and these technical applications are increased in number and in difficulty through the successive years of the grammar school, until for a large amount of so-called arithmetic the pupil gets comparatively little practice in the art of numbers. I am far from saying that the pupils of our public schools should not acquire a certain amount of useful information. The most familiar "tables" of lengths, weights, measures and coins may properly be given them, and they may advantageously be practiced in simple operations thereunder. But this whole matter of the technical applications of arithmetic should be treated in a highly conservative spirit. Of late years there has been some reform in this particular, and a few of the monstrosities of the old curriculum, notably our old ancient enemy, duodecimals, have been thrown overboard. But there still remains many things, as taught in our schools, which occupy time which could better be devoted to the study of other subjects; or at least, to a greater degree of practice in simple operations. Who of us has not seen, in the hands of children of 11, 12 and 13 years of age, examples in "compound and complex fractions" which were more difficult than any operation which any bank cashier in the city of Boston has occasion to perform, in the course of his business, from January to December? The most jagged fractions, such as would hardly ever be found in actual business operations, e. g. 11-29 or 13-27, are piled one on top of another, to produce unreal and impossible difficulty; and the child, having been furnished with such an arithmetical monstrosity, is set to multiplying or dividing it by another "compound and complex fraction" as unreal and ridiculous as itself. All this sort of thing in the teaching of young children is careless and mischievous.
It is bad psychology, bad physiology and bad pedagogics.
To smuggle exercises of this character into instruction given in the name of arithmetic, is an abuse. By it has has been created a bastard arithmetic which fails to perform the true function of that study in our public schools - namely, to produce accuracy and a reasonable degree of facility in numerical operations, while wasting the time of the pupils, perplexing their minds, worrying their tempers, rasping their nerves, and, in case of total or partial failure, unnecessarily and unrighteously shocking and impairing their self-respect and scholarly ambition."