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The late Dr. Thornton, who, for many years, presided over the Patent-Office at Washington, perceiving the absurdity of learning to read by the repetition of sounds having no similarity to those of the words, published, in 1790, a pamphlet, entitled, Cadmus, or a Treatise on Written Language,' in which he proposed that every letter should be named according to its power ; and, there being more sounds than letters in the English language, introduced a sufficient number of new characters to supply the deficiency. To carry out this design, however, an entire new system of orthography became necessary, which the Doctor seriously proposed should be immediately carried into effect, not perceiving, apparently, that its adoption would render useless all the English books now in existence, and force us all to go back to school to learn to read! For this extraordinary production, the Magellanic gold medal, and the title of CADMUS were awarded to the learned doctor, by the American Philosophical Society ! Had the author known, that reading could be learnt without the intervention of any names of letters, he might have saved his labor, and our wise philosophers might have elsewhere bestowed their gold.

Writing This important branch of education is generally abandoned to itinerant teachers, on the plea of its requiring too much of the time and attention of the teacher of the public school. This would undoubtedly be correct, if he had to rule and set all the copies, and make and mend all the pens. But, surely, this cannot be necessary. Ruled books might be procured, and printed models of calligraphy, large enough to be distinctly seen by the scholars, when hung on the walls; and it would be an excellent exercise for the larger pupils to assist, by turns, in the penmaking department.

But the child should be a good writer, before ever he takes pen

in hand. As soon as he enters school, he should be provided with a slate ; and he should commence written arithmetic and composition, as soon as he is able to form the necessary characters. Were this properly attended to, all would be good writers; for the chief difficulty, here, as well as in reading, lies in the breaking up of those bad habits, which ought never to have been formed.

Where writing is taught in the district school, the most important elements, viz., the manner of holding the pen, and the position of the body, arms, and hands, are sadly neglected. General instructions on these points are commonly given, but they are not sufficiently insisted on, and enforced. The consequence is, that a cramped, stiff manner of writing is acquired, and, if writing is much practised before a better school be resorted to, the pupil is exceedingly apt, in a very short time, to fall back into his old manner, which has become, as it were, a second nature.

Arithmetic. The same pernicious error, which was noticed in speaking of the mode of teaching reading and writing, prevails in this science, viz., a neglect of the foundation ; a hurrying of the initiatory steps. Without clear, distinct notions of numeration, no satisfactory progress can ever be made in arithmetic ; and yet there are schools, where it is not taught at all ; where the pupil commences with addition, and is left to acquire a knowledge of the local value of figures as best he may. And even in those schools where it is taught, the subject is passed over, too rapidly; valuable deductions, that might be drawn from it, being entirely omitted. What these are, will appear in their proper place.

The four fundamental processes, addition, subtraction, multiplication, and division, are by no means sufficiently practised. In addition, in particular, after a while, the columns ought to be long, such as the pupil will probably meet with, when he comes to practise them in stores, counting-houses, banks, and other public offices; and, instead of adding, by single figures at a time, he should be accustomed to take from two to five figures at once ; for, unless he can do this with ease, he will never be an expert accountant. This mode of adding will be found, after a little practice, to be more easy, than the formal, tedious mode of taking one at a time. A great many abbreviations ought to be pointed out in multiplication; and the Italian method of performing division, now in use over all the continent of Europe, which employs only half the number of figures used in the old-fashioned way, ought also to be adopted.

The subject of decimal fractions is treated of, separately from that of whole numbers, in all our treatises on arithmetic, and in an advanced section of the book. This arrangement is highly exceptionable ; and is, probably, the principal reason why so many complain of the difficulty of understanding decimals, when, in fact, the subject is so exceedingly simple. Many persons, who have gone through two or three courses of arithmetic, have declared, that they never could thoroughly understand decimals. Their extreme simplicity confuses them ; as, from their position in the work, they are led to imagine, there must be something, behind, which they do not see ; something beneath the surface, which their efforts fail to bring to light ; a notion, that confuses and mystifies the whole subject. Let us see whether any difficulty could possibly arise, if decimals were taught in connexion with whole numbers.

And, first, let us suppose that notation of whole numbers had been explained to the pupil, so that he understood that figures increased tenfold in value by being moved one place to the left, and decreased tenfold by being moved to the right; and that they were named accordingly, viz.

do Millions.
A H. Thous.
Co T. Thous.


o Hundreds.


2, 4 37, 8 9 5 What difficulty could any child have, in understanding, that, when we had to place figures still further to the right, it became necessary to use a dot, (.) to show the place of units, which no longer occupied the right-hand place; and that the same names were used for the numbers ten times, &c., less than units, as for those tenfold, &c., greater ; only that we added th to them; the one to the left of units being called tens, that to the right tenths ; the 2d to the left, hundreds, the 2d to the right, hundredths, &c.

If a number, containing decimals, were now written on the black board, say,

468,326.4589 the child would have no difficulty in naming the figures, if he were told, always to begin with units. For, proceeding to the left, as in whole numbers, he would have 6 units, 2 tens, 3 hundreds, &c.; or to the right, 6 units, 4 tenths, 5 hundredths, &c. It should also be explained, that he might either name them 4 tenths and 5 hundredths, or 45 hundredths ; 4 tenths, 5 hundredths, and 8 thousandths, or 458 thousandths, &c. It should then be shown to him, that, by moving the dot one, two, or more places to the right or left, he would change the unit's place, and, consequently, every figure in the number would be decreased or increased, tenfold, a hundredfold, a thousandfold, &c. Finally, the reason should be given, for calling the figures, to the right of the units, fractions, and decimal fractions. All this would be perfectly intelligible to a class of children about six years old, if shown on the black board. Here would be a convenient place to show the use of the 0, commonly called cipher, but more properly figure of place ; its sole use being, to show the place of the significant figures. Thus, let these four numbers be written on the board,

600 006 .600 .006 and let it be explained, that the character 0 is of no use, unless it intervenes between some significant figure and the unit's place. The class should then be called on to point out, in which of these four numbers the character was necessary, and in which it was useless.

The repetition of this lesson on the black board, for three or four days in succession, would fix the fact, thoroughly, in the mind of the class, that whole numbers and

decimal fractions were named on the same principle ; both, in fact, being decimals, or numbers reckoned by tens.

Let us next examine, in what consists the difference between addition, subtraction, multiplication, and division, of whole numbers and of decimals, so as to ascertain, whether it is better to teach them separately, or together.

In addition of integers, figures of the same denomination are placed over each other, because it is most convenient, as those differing in denomination cannot be added together. For instance, if it be proposed to add 234, 156, and 798 together, we should place them thus :


798 because the figures 4, 6, and 8, being of one kind, viz., units, could be put together ; and also, for the same reason 9, 5, and 3, tens, and 7, 1, and 2, hundreds. We do not place them thus :

234 156

798 because the 6 and the 3; and the 8, 5, and 2 ; and the 9 and 1, being of different denominations, make neither 9, nor 15, nor 10, of any denomination. The same holds true of decimals; and no intelligent child could, for a moment, be at a loss, how to place them, if he knew how to place integers, and the reason why. The process of adding is precisely the same, in both; and the tens of one denomination are considered as units in the next higher, also for the same reason ; viz., because ten of one denomination make one of the other. Why, then, should a distinction be made between addition of integers and of decimals, when there is no difference ?

Exactly the same remarks apply to subtraction. Let us, therefore, pass at once to multiplication, which should be elucidated by an example on the black board, like the following:

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