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questions, practical and unpractical, arithmetical, geometrical, algebraic, and nondescript. It is just to say that a vast improvement has been made, within a few years, in the manner of teaching arithmetic. More of the science of numbers is learned, along with the art; and as a consequence, more of both knowledge and discipline is derived from the study. Still it is true that a great part of the time spent over the slate and arithmetic contributes to neither so much as it ought. More of mental arithmetic should be insisted upon, with reference both to training the powers of memory and analysis, and to the practical uses of arithmetic in every-day business. And written arithmetic might well be confined, in ordinary cases, to a thorough explanation of its principles, and a sufficient number of examples for illustration. Arithmetic thus studied would contribute its fair proportion to the two purposes named above. It is doubted whether the mere intellectual puzzles, the extraneous and super-arithmetical matter, contained in some of our text-books, are of much worth in promoting healthful and symmetrical discipline, while as an addition to our practical knowledge they are of none at all.
But allowing that this long dwelling upon arithmetical difficulties may add something of intellectual sharpness to our Yankee boys, would it not add much more to their respectability as scholars and their usefulness as citizens to spend a portion of the time thus devoted, in learning to read and spell, and speak and write, their mother tongue with more propriety? I claim that the thorough and careful study of language may impart as much of mental discipline as the study of arithmetic; and if there is a difference in the kind of training secured by the two, it is not in favor of the latter. But when we consider the value of the two as means of practical usefulness and personal accomplishment, it falls far below that of language.
To read well is an elegant art, rarely attained by our young people. . How few of them can take up an evening journal, and read the news of the day, especially from the telegraphic columns, intelligently and without hesitation! This would not be so if half the time consumed upon the less useful portions of arithmetic were given to the study of reading, – newspaper reading with the rest, — with dictionary and gazetteer in hand. Then, again, how few of our children, on finishing their course at school, can express themselves with grammatical propriety in ordinary conversation! And how few of our young men can present their opinions in an address or a public debate with fitness and force ! simply because they have not learned the ready and accurate use of their mother tongue. Still, again, if called upon to communicate their thoughts on any subject through
the press, or to draw up a business document, or a series of resolutions, or to indite an important epistle, to what “ lame and impotent conclusions ” do they often suddenly come, to their utter confusion! And this want of early training in the grammar and composition of the language is felt in after-life much more seriously than any want of skill in solving arithmetical enigmas. I hope not to be misunderstood. Arithmetic is one of the most valuable and beautiful studies ; beautiful in its place and season, but not when it overshadows and dwarfs all other branches of the tree of knowledge. Our conclusion, then, seems a very safe one, that as compared with reading, spelling, and grammar, arithmetic has received a disproportionate attention.
From the matter of the instruction given in our school-rooms I pass to the methods of imparting it. And here I find the same tendency to extremes.
In the first place, I find a strong leaning in some minds to that which is old, — the old style and methods familiar to their boyhood. In other minds, there is an equally unfortunate tendency to be satisfied with only the latest inventions in the art of education. I need not endeavor to prove that the truth lies between these extremes ; requiring us to reject nothing, and to accept nothing, because of its newness or its antiquity; but to receive all and only that which commends itself to our judgment, whether new or old. While asking for the old paths with a just reverence for the past, let us not mistake its hoary errors for grayhaired wisdom. And while we listen candidly to the claims of new discoverers, let us not catch too eagerly at every novelty that may cross our way.
In the practical instruction of the school-room, I would frequently introduce to the attention of pupils something essentially new. I would present something fresh in matter or manner, to stimulate their flagging interest, and to give them new views of truth. Why should not our pupils in school, as well as their older friends out of school, be gratified with occasional varieties and novelties? But I would not allow this desire for new things to interfere with the systematic pursuit of the old and established courses and methods, proved by long experience to be well suited to their end. The teacher who invents nothing new for the entertainment and instruction of his pupils, and he who devotes very much time to new discoveries and novel methods, are alike unwise.
This tendency to extremes is seen, again, in the matter of analytic and formulary instruction. Arithmetic, for example, was taught, only a generation since, by certain prescribed rules given in the old text-books, such as Pike and Walsh and Welch, without the least hint that the learner should know or could know any reason for those rules. And there are persons of the old-school pattern of the present day, who believe that the rule, and the corresponding practice, are all that is necessary for the scholar to learn. What he will need in the business of life, say they, is the definite rule, — the sure method of reaching the result; a fig for “the why and the wherefore !”
The publication of Colburn's First Lessons introduced a new era in the study of arithmetic. Analysis took the place of formal rules. A great step was gained. But when Colburn's Sequel was published, and the whole system of arithmetic was proposed to be conducted upon the merely analytic plan, excluding all rules, then the opposite extreme was reached. We need in this important branch of study, as in others, a thorough analysis of principles and processes for discipline and instruction, and the convenient formula, or rule, for future use; a form of words clearly arranged and compactly stated, in which the principle once developed and explained may be retained in memory and applied to practical purposes. Very naturally, therefore, there was a reaction from the methods of Colburn's Sequel, and a new style of text-books in arithmetic was introduced, combining the two methods. Thus the best wisdom of our practical educators has decisively settled the point, that while the analytic process is necessary, to unfold the principles of arithmetic and the philosophy of its methods, it is convenient at the same time to