LECTURE XI. ON THE TEACHING OF ARITHMETIC. BY WARREN COLBURN. I HAVE been requested to address the Convention, on the subject of teaching arithmetic. I accepted the invitation with extreme diffidence, believing there would be many gentlemen present, much more competent to this task than myself. The subject is certainly an important one in every point of view; whether we consider its application to the affairs of life, or its effects as a discipline of the mind, or the time which is usually devoted to it. With regard to its application, there are very few persons, either male or female, arrived at years of discretion, who have not occasions daily to make use of arithmetic, in some form or other, in the ordinary routine of business. And the person the most ready in calculation, is much the most likely to succeed in business of any kind. As our country becomes more thickly peopled, and competition in the various branches of business becomes greater, and farther progress is made in the arts, and new arts are discovered,—knowledge of all kinds is brought into requisition; and none more so than that of arithmetic, and the higher branches of mathematics, of which arithmetic is the foundation. Arithmetic, when properly taught, is acknowledged by all to be very important as a discipline of the mind; so much so, that even if it had no practical application, which should render it valuable on its own account, it would still be well worth while to bestow a considerable portion of time on it for this purpose alone. This is a very important consideration, though a secondary one, compared with its practical utility. The fact that the study of arithmetic is allowed to occupy so large a portion of time in all our schools, shows sufficiently the degree of importance attached to the subject by all classes of people. And that it does occupy so large a portion of time, is another very strong reason for attention to the mode of teaching it, that the time may be employed to the best advantage. As the demand for all kinds of knowledge is increasing, and new branches of learning are almost daily brought within the compass of the ordinary means of education; it becomes highly important, that those kinds, which require considerable labor for their acquirement, should be made to occupy as little țime as may be consistently, without sacrificing the advantage of learning them well. It may not seem improper here to introduce a few remarks concerning the relative advantages of the old and new systems of teaching arithmetic. For though most teachers, at the present time, prefer the new system, and the majority of the community are decidedly in favor of it; yet there are persons, and some whose opinions are entitled to high respect, who strongly object to the new system, and give a decided preference to the old. To such we ought at least to be able to give a reason why we prefer the new system. For this we shall appeal to facts; they are stubborn things, and the side which they favor must prevail. It must be allowed by all, that previous to the introduction of the new system, fewer persons learned arithmetic than at present. At least, fewer made any considerable progress in it. Very few females pretended to study it at all, and the number of either sex, that advanced much beyond the four primary rules, was very |