emanating from such associations give evidence of the impulse which is imparted by those meetings. Sometimes the schoolmasters of many districts assemble for similar purposes ; and of late regular festivals have taken place, chiefly for the cultivation of singing ; and on such occasions a large concourse of people takes place to listen to well-executed performances.

The administration and immediate surveillance of a parish school devolves, in the first instance, upon a local committee, consisting of the clergyman as chairman, the mayor, and two or more of the more influential resident heads of families. With them rests the election of three candidates for each vacation,—the final nomination depending on the decision of a higher authority. They also once or twice a year call together the new pupils, or occasionally dispense them from school-going for a certain time, and finally dismiss them after an examination. They take care that everything which is wanted in school be properly provided, and the general regulations observed. The next superior is the Inspector, already mentioned as president of the regular ineetings, who every half-year visits all the schools of his district, and generally serves as mediator between the local authorities and higher boards. Each regency-the civil administrative body for about half a million of inhabitants-has one special member or counsellor for school affairs, who likewise occasionally takes a tour of visitation ; but even the highest functionaries do not omit to visit sometimes an humble village school on their road.

The social position of national schoolmasters, as may be easily inferred from the whole of the foregoing statements, is superior to a similar situation in England. Besides a more suitable education and higher duties, the greater consideration they enjoy is owing to the intercourse they necessarily have with all the families, even the wealthier ones, in a town or village ; and in many cases they derive additional claim thereto from special causes, as leader or member of a choir or musical society, and from similar occupations. The pecuniary situation leaves much to be wished for, although government does as much as possible to make salaries more agree with the acknowledged importance of the duties and exertions. Positive numbers, however, might easily mislead those who are not acquainted with the respective value of money in the different countries.

The results of this system of public education are generally quite satisfactory. Not only is scarcely a young person to be found who cannot read and write, but no one will deny that the great improvement in the intellectual and social condition of the lower classes is, in a great measure, attributable to the direct or indirect influence of this universal training. There are, of course, different degrees in the accomplishments attained by the parish schools, according to the number of classes, that of pupils in each, the time and regularity of attending school, and many minor causes. In lower country schools and manufacturing districts, where insurmountable obstacles render a relaxation of the stricter rules necessary, the lessons are limited to the most requisite objects, including reading, writing, arithmetic, elements of grammar and compositionsinging, with so much knowledge of national history, geography, and other useful knowledge as the general reading-book offers. In more favoured establishments in towns or large country-places, where several masters are engaged at the same school, the above limits are considerably extended ; in the upper classes a regular course of sacred and national history, geography, arithmetic, with the elements of geometry, natural sciences, grammar, letter-writing and other compositions occurring in common life, singing (part-songs), is gone through ; whilst carefully elaborated reading-compendiums in verse and prose introduce a great many other objects, and are intended, under an experienced master, to open the mind to higher ideas, and dispose the heart for everything that is noble and elevated. Such instruction is quite sufficient for the respective classes of inhabitants in town and country. Tradesmen of all descriptions, merchants and their clerks, who do not require the knowledge of foreign languages, and all persons standing on a level with them in the social scale, before they enter into business, frequent no other but parish schools ; and besides this the latter also supply well-prepared pupils to the Latin colleges and commercial establishments.

The due influence of religion and church-authority upon education is secured by those dispositions of the law which grant to the clergy an important part, especially in the immediate or local administration of parish schools. One difficulty, which in England arises from the claims of so many different persuasions, does not exist to the same extent in Prussia and the adjoining States. Entire liberty of conscience is an acknowledged principle, but two persuasions—the Evangelical or Protestant, and the Roman Catholic,—are recognized as being entitled to equal rights and support from government. But as no fixed dogmas are strictly enjoined by the established Protestant Church, a much greater liberty and variety of opinion exists between its members than is possible in England without one party being compelled to separate and form a distinct community of dissenters. Therefore schools of the said two denominations suffice for almost all places; and wherever it can be possibly done, one of each persuasion is established. If a family, through isolation, is obliged to send its children to a school of different persuasion, little inconvenience is to be feared from such a circumstance; partly on account of a general spirit of toleration, partly because the strictly religious instruction is seldom given during regular school-hours, very often in church, and of course without any compulsion for parents who object to it.

OUR GOOD QUALITIES. It is generally admitted, and very frequently proved, that virtue and genius, and all the natural good qualities which men possess, are derived from their mothers.Theodore Hook.

CONSOLATION FOR THE DULL.—There is no talent so useful towards rising in the world, or which puts men more out of the reach of Fortune, than that quality generally possessed by the dullest sort of people, and in common speech called discretion—a species of lower prudence, by the assistance of which people of the meanest intellect, without any other qualification, pass through the world in great tranquillity, and with unusual good treatment, neither giving nor taking offence.-Swift.



SORE than a hundred different works on Common Arith-

metic were printed in England since the beginning of
this century; nevertheless, the following little essay
claims admission on account of several characteristics

which essentially distinguish it amongst so largea number.

3 The great majority of the above-mentioned books are intended for the use of the pupil, and merely contain the necessary mechanical rule for each arithmetical operation, with more or less copious and variegated examples, these latter to be solved by applying, quite mechanically, the given rule. It is evident, and many authors openly avow, that their only aim is to impart a certain practical skill, to enable the pupil to solve easily and quickly those arithmetical problems which may occur in common life. There is no pretension to look upon this branch of instruction from a higher point of view, and treat the subject, besides imparting that desirable practical skill, at the same time as a most suitable means of developing the mental faculties of a child. Some few writers acknowledge the eminent usefulness of mathematical subjects for that purpose ; but although they prefix to the title of their book the words “Intellectual,” “Rational,” or other such-like expressions, they either confine themselves to problems to be solved by Mental Arithmetic, only, or, seeking the great point in the different arrangement and selection of the problems, make at least no attempt to introduce a rational method into the very act of teaching this science. Even the most explicit, as far as method is concerned, of modern writers on Arithmetic, give comparatively few hints to the teacher, how he may bring his pupils to think about their operations, find out for themselves and thoroughly understand the rules, and be convinced of their correctness. Again, with the exception of two or three, who shortly mention the use of strokes on the black-board, or balls and other material objects, for illustrating the primary arithmetical notions and operations, all books on arithmetic suppose, in their beginning, a previous knowledge of numbers, and the original operations of adding, subtracting, &c. There may, perhaps, be amongst the number of books above given, one or another which more approaches to the form I have in view ; but if I pass it over unnoticed, I do so unintentionally. Besides a great many school-books on Arithmetic, which I had known before, I lately examined for a long time, and with much trouble, those which were to be found at the British Museum, but was very often disappointed by looking in vain for a copy which ought to have been there. However that may be, it is certain that a rational method of teaching the first principles of Arithmetic is far from being generally used, or even thought of, in most schools; and a great many guides for the teacher may be published yet to promote that more effectual primary instruction which forms now the object of so many claims and efforts.

The form in which the following sketches appear, that of dialogues, is undoubtedly the most natural, and best adapted to give a correct idea of that rational method which awakens and exerts the mental faculties, and only considers those acquirements as lasting and reliable which were obtained by self-activity of the mind. It is evident, that in a book only outlines or sketches for lessons can be given; a great many incidental questions and observations will suggest themselves during the course of a conversation ; and a mother who has once begun to try these instructions, will soon find that she requires very few hints as to the order and general character of her instructions, and that she does best not to bind herself too strictly to the models here given.

The idea of publishing the present treatise gradually presented itself to me. Being engaged in schools, as well as in private families, in England ever since 1851, I had ample opportunity of observing the deficient knowledge and surety of my pupils in Arithmetic, owing chiefly to the want of a rational system in their first instruction. But, as Mathematics were not my particular department, I took no further notice of it until, from changed circumstances, I became more lively interested in the general proficiency of my pupils. I then undertook one special branch of that science—the fractions; and being myself, as well as my friends and pupils, well satisfied with the result of my teaching, wrote down a sketch of the method I followed, and published it in the JOURNAL OF EDUCATION. But even during those lessons in fractions, I was very often checked and unpleasantly disappointed by finding that the original foundations of my pupils' knowledge and skill in Arithmetic were so very loose and unsatisfactory; their science and ability were strictly limited by a certain number; the common operations of adding, subtracting, and multiplying, by mental Arithmetic, went up to a given number; beyond that, pen and ink were absolutely necessary, and then even the slightest deviation from a mechanical rule put them out. Thus it often happened that an otherwise satisfactory demonstration or solution of a problem was impeded by such common-place difficulties. I now inquired more closely into the matter, examined the respective schoolbooks, attended lessons, and had conversations with masters and parents about the subject. The result of my studying the books generally used in schools, I have already given ; I did not find one intended for the teacher himself, containing an exposition of the method to be followed in teaching. As for the lessons, it may be easily inferred, from the want of proper guides for the masters, and the generally acknowledged deficiency of systematical training of teachers in public as well as private establishments, that they do not materially differ from the mere mechanical treatment of the subject in the respective books. What I heard from parents and tutors, only confirmed me in my idea that nothing more beneficial for this branch of education could be done than to write some explicit models of lessons, such as they ought to be given in schools or private families. It had been my particular good fortune to meet with many pupils who had received their first instruction from their own mother, and, as is always the case, turned out very intelligent pupils. The only reason why those mothers had entirely neglected Arithmetic was, that they considered the subject too dry for little children; they did not know themselves much about it, and had no idea how to give those lessons. The following pages are especially also intended for such mothers; if they only try, they will soon find that it is not so difficult after all, and their efforts will certainly have a most beneficial effect upon the intellectual development of their children.

First Notions. The Numbers from 1 to 10. Master. (Having placed the whole class before him in front of the black-board.) What do I hold here in my hand ?-Answer. A pen.

M. Say : That is a pen. How many pens are there -A. One pen. M. Say again : That is one pen.

[We observe here in the beginning, that it is very important to insist always upon full sentences. Such complete answers not only prove that the question has been well understood, but also induce the pupil to think more distinctly, and express himself more correctly.]

M. Now say all together : That is one pen. (Taking another pen into his left hand :) How many pens have I here -A. That is also one pen.

M. Say so all together. Now listen to what I say, and we shall afterwards see who can repeat it (putting the two pens together): One pen and one pen are two pens. Who can say the same ? (Several children do so.)

M. Say so all together.

M. Who can lift up one finger ? Do all so. Henry, show me two pens—lift up two fingers. What is more, one shilling or two shillings ? -A. Two shillings are more than one shilling.

M. How much more ?A. One shilling more. Or better: Two shillings are one shilling more than one shilling.

M. How many tables, fireplaces, &c. are in this room ?-A. In this room there is one table, &c.

M. (Naming an object which is twice in the room :) How many maps are in this room I-A. There are two maps in this room.

M. Name other objects of which there two in this room.-A. We have here two black-boards, two windows, &c.

M. What have you once on your body ?-1. I have one head, one mouth, one forehead, &c.

M. What have you twice on your body?-A. I have two eyes, two arms, two hands, &c.

M. What is only once in this town ?-A. In our town there is one market-place, one town-hall, one inayor, &c.

M. Now look here; I make one stroke on the black-board, now two more beneath the first. Take this piece of chalk and do the same; try to make your strokes straight, and equally long and thick.

[For a first regular lesson with little children the preceding exercises are sufficient. With all preparations, getting them in order, corrections, additional questions which may suggest themselves during its course, it will take nearly half an hour; and as uninterrupted attention is required, that time must not be exceeded. The next lesson begins with a repetition of the preceding one, particularly of its first questions. Then the master continues.

M. How many pencils do I hold here ?- A. There are two pencils.

M. (Taking another pencil) How many pencils have I here ?-A. That is one pencil.

M. Now listen to me : Two pencils and one pencil are called three pencils. John, say the same ; now Henry ; now all together. Give me one pencil, now two, now three ; always say at the same time how many you give me. What is three times in this room ? Take the chalk and

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