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First Lessons in Arithmetic.

to count fifty or one hundred; for the art of counting as far at least as twenty, if not fifty, should, as it appears to me, be one of the child's earliest lessons.

This being premised, I say, the children are all asked to judge how many pints the vessel will hold. In doing this, care is taken, usually, to begin with one of the youngest, that their opinion may be as unbiassed and unprejudiced as possible. Great care ought also to be taken that those who judge best do not indulge in triumphing over those whose judgment is less perfect.

Mrs T. found no difficulty of securing the attention of her children, and indeed the action of all their faculties, during these exercises; but she sometimes wondered at the apparent obtuseness of perception in some of them. The progress of the latter faculty was exceedingly slow. However, it was always evident to her that there was progress; and this was a sufficient encouragement to her to persevere.

She had never yet had a son or daughter who could not, at the age of six, judge with far greater accuracy of the capacity of all sorts of vessels presented to the eye, than most adults can who have never been subjected to any such discipline. Even the youngest, who is not yet quite six, and whose progress has been slower than either of the others, will tell, with surpris ing accuracy, how much a large or small vessel of the most uncouth shape will hold-such as a demijohn, or a cask, or a wooden bottle.

It is in the progress of exercises like these, that they are taught how much a pint is; and also how much a gallon is. None of these names are indeed presented at first, except the standard name; a pint. After some time, however, when they become familiar with pints, they are taught that a quart is two of these pints; and that a gallon is eight of them, or four quarts.

They are also shown the component parts of a pint; and taught to judge of these too with accuracy. In this process, they learn the name of gill; and that a pint is four gills. They are also le i to observe that two gills make half a pint, and two half gills make make one gill.

These exercises, suitably managed, are an introduction to arithmetic, as well as a discipline to the mental faculties. Who does not see that every one of them is an arithmetical lesson ? You pour two pints of water into a quart measure. Here is tangible evidence, to the child, that one pint and one pint make two pints. You empty the quart measure four times into the gallon measure; and what is this but the adding together of several smaller sums to make a larger one, or a sum total? And the same remark might be made of every lesson which is given on

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the above principles. It is, in effect, the teaching of arithmetic by means of sensible objects.

For not only may the pupil acquire here, the elements of addition; those too of substraction, multiplication and division will be taught by the same exercises suitably extended and varied. Thus in asking a child to judge how many pints or gallons a given vessel will hold, is it not obvious that we require him to carry on both the multiplying and dividing processes?

It is, moreover, an exercise in language. Multitudes of the young, and not a few to whom the term young would hardly apply, pass through life without having any definite notions what is meant by the words gill, pint, quart, gallon, barrel, hogshead, peck, bushel, &c., or at least of more than one or two of them. Perhaps most persons have some sort of an idea-though usually inadequate—of a pint, a quart, or a gallon. But beyond this, few can go. Now if this is so, not only their notions of things must want accuracy, but so must their language.

This leads us naturally to the remark-for it is little more than to repeat the sentiments of the preceding paragraph-that such exercises as I have been describing, are valuable as lessons in defining. Of all things which are necessary, both as preliminary to school instruction and during school hours, I know of nothing more neglected, in proportion to its value both as a means of mental discipline and as a key to knowledge itself, than the practice of defining. Now the child who is pursuing such exercises as it is the object of this chapter to encourage, is doing not a little in the way of getting correct definitions of a large number of words.

I ought to remark here, however, that it is highly indispensable to connect with these exercises, another; or rather to apply to it the results of another. By previous exercises, for example, conducted on the same principles and in the same spirit, he is supposed to have learned how much an inch is-how much a foothow much a yard, &c.; and to have obtained by means of little cubes of wood, or some other material, a perfect idea of a solid or cubic inch-of four, eight, twelve, sixteen, &c., solid or cubic inches; of a cubic foot, &c. This being premised, it is highly desirable to lead him gradually to the conception of the size of a pint, a quart, a gallon, a bushel, &c., in solid or cubic inches; so that when the word pint is mentioned it may suggest to him a certain number of cubic inches of something. It is indeed true that there is room here for error. For since a solid or cubic pint cannot be represented by an even number of solid inches, the child's idea may, after all, be somewhat confused by a block of wood three inches square, and four high; and it is quite

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Letter to Mr Brooks.

obvious that a pint could not well be represented by any even number of inches. Still the difficulty would be sufficiently obviated by making a gallon, the standard. A gallon is 2771 cubic inches; which are represented with sufficient accuracy for common purposes, by a block measuring six and a half inches in every direction. Of this, the child should have a most perfect idea, by becoming familiar with a block exactly of this size. He should, indeed, be told that it falls short of a gallon, by a very little ; but that the deficiency is not great.

Now let a person once have a clear idea of a gallon in this way, and at the same time let him be accustomed to such exercises as those which I have described above, as being practised by Mrs T. in her family, and it is surprising to see what an effect it will have in his subsequent progress in the study not only of the exact sciences, but of almost all others. Thousands-I hardly need to repeat the sentiment-blunder through the world, as utterly ignorant on some of these preliminary points as they are of what is going on in the moon.

I will only add here, that Mrs T. varies her lessons, so as to have a never ceasing variety. She is not always engaged in the monotonous employment of pouring pints or gallons into a larger vessel. On the contrary, she so manages as to give freshness and interest to every successive exercise, and to ensure perpetual, though it should be slow progress.

ENCOURAGEMENT FROM COUSIN.

(Extracts from a Letter to Rev. Charles Brooks, of Hingham)

'PARIS, APRIL 20, 1837.

SIR-If you have met with difficulties in your efforts to disseminate in America, the principles of primary instruction, do not be discouraged; for no great good can be effected without difficulty and delay. I shall be delighted if I can be of any use to you in this good work, and you may say from me to the American Institute, that I am ready to give them any and every information they may wish. I see that you have a translation of my report on public instruction in Prussia. Is that translation Mrs Austin's? Her translation is excellent, but it comprises merely the primary instruction in Prussia, whereas the original work treats of that same instruction in countries less

Model Normal Schools.

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extensive than Prussia, and which would be more appropriate models for a State of the American Union. Perhaps it would be well to have a certain number of copies of that work, either at the library of the American Institute, or at the library of the primary normal schools which you propose to establish. I will thank you, Sir, to send me a copy of the translation of my report, which is used in America. I could then see what you have, and what you want; I would thank you, too, if you would have the kindness to add to the package all the documents which you can collect, on the public schools in Massachusettsthe laws, if there are any, the regulations of the private schools, reports, &c. I have the honor to know by correspondence, several gentlemen of Massachusetts.

I find in a Spanish work of Mr Ramon de la Sagra, entitled Five months in the United States,' information on the subject of primary instruction in Massachusetts, which interests me much, but which I do not know whether I ought to trust. What is Mr Alcott's school? Has the American Society of Education published any reports? Could I not obtain some numbers of the Annals of Education? If the government of Massachusetts desires my assistance, they will be kind enough to put me in possession of the exact state of affairs: otherwise I can do little more than send them some general maxims of very little utility. Thus, for the primary normal school which you propose, I am ready to offer you a plan. But in the first place, I must know how much money can be annually appropriated to it, and if the customs of the country require that this primary normal school should be a day school or a boarding school. For a boarding school you have several models in my report; for instance, the two great normal schools of Brutit and Pottsdam. If you wish a day school, take for model the normal school of Weimar. But Mrs Austin has not translated my report on Saxony. I therefore send you a detailed description of a Dutch normal school for yourself and the American Institute. I beg you would study this paper with the greatest attention, and make it known to all who are interested in popular instruction. I add another on the celebrated charity schools of Amsterdam, and another still on the primary day school of Rotterdam, and on the school of correction, of the same city. Allow me also to send you a pamphlet on the University of Utrecht, which you will please present from me to the University of Cambridge. These four papers are fragments of a journey that I took six months ago, into Holland, and an account of which I am now publishing. This last publication will perhaps be more useful to America, than my work on Prussia, inasmuch as Holland is

280

Proceedings of the American Lyceum.

an ancient commercial and industrious republic, whose manners and institutions bear a strong analogy to those of the United States. This work will appear in a few days. In the mean time, these four little pamphlets which I subjoin, may be of some service.

Accept, Sir, the assurance of the deep interest which I take in your honorable efforts.

I am wholly yours,

VICTOR COUSIN.'

MISCELLANY.

PROCEEDINGS OF THE AMERICAN LYCEUM.

THE Eighth Annual meeting of the American Lyceum was convened in the Free Church, at Hartford, Conn., May 15, 1838, at 10 o'clock, A. M. Rev. T. H. Gallaudet, of Hartford, was called to the chair, and prayer made by the Rev. Mr Putnam, of Middleborough, Mass.; after which the meeting was duly organized, by the appointment of General Nath' Terry, President, and Prof. Charles Davies, Secretary. Prof. Davies subsequently declining, Theodore Dwight, Jr., of New York, was chosen in his stead.

The credentials of the delegates from Lyceums, and other literary institutions having been examined, the reports of those delegates were called for, in the order of the various States of the Union to which they belonged. The reports were chiefly verbal; but a resolution was passed, early in the session, requesting the delegates to leave them, in writing, with the Secretary.

A report was made by Dr W. A. Alcott, of Boston, on the character and objects of the American Physiological Society. A brief account was also given of another Association with which he was acquainted in Boston the Social Institute.

A letter was read from Lewis G. Pray, Chairman of the Primary School Committee of Boston, on the Primary Schools of that city, which was referred to the Executive Committee for publication.

Reports were made either at this time or during the progress of the meeting, by the following individuals, from the societies respectively named; most of them, though not all, being delegates. By Prof. John Johnston, from the Cuvierian Society of Middletown, Conn.; by Mr