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“ It is told that in the art of education he (Milton) performed wonders, and a formidable list is given of the authors, Greek and Latin, that were read in Aldersgate Street, by youth between ten and fifteen or sixteen years of age. Those who tell or receive these stories, should consider, that nobody can be taught faster than he can learn. The speed of the horseman must be limited by the power of the horse. Every man, that has ever undertaken to instruct others, can tell what slow advances he has been able to make, and how much patience it requires to recall vagrant inattention, to stimulate sluggish indifference, and to rectify absurd misapprehension.
“The purpose of Milton, as it seems, was to teach something more solid than the common literature of schools, by reading those authors that treat of physical subjects : such as the georgick, and astronomical treatises of the ancients. This was a scheme of improvement which seems to have busied many literary projectors of that age. Cowley, who had more means than Milton, of knowing what was wanting to the embellishments of life, formed the same plan of education in his imaginary college.
“But the truth is, that the knowledge of external nature, and the sciences which that knowledge requires or includes, are not the great or the frequent business of the human mind. Whether we provide for action or conversation, whether we wish to be useful or pleasing, the first requisite is the religious and moral knowledge of right and wrong; the next is an acquaintance with the history of mankind, and with these examples which may be said to embody truth, and prove, by events, the reasonableness of opinion. Prudence and justice are virtues and excellencies of all times and of all places; we are perpetually moralists, but we are geometricians only by chance. Our intercourse with intellectual nature is necessary; our speculations upon matter are voluntary, and at leisure. Physiological learning is of such rare emergence, that one may know another half his life, without being able to estimate his skill in hydrostatics or astronomy; but his moral and prudential character immediately appears.
“Those authors, therefore, are to be read at schools that supply most axioms of prudence, most principles of moral truth, and most materials for conversation; and these purposes are best served by poets, orators, and historians.
“Let me not be censured for this digression, as pedantic or paradoxical, for if I have Milton against me, I have Socrates on my side. It was his labour to turn philosophy from the study of nature to speculations upon life ; but the innovators whom I oppose are turning off attention from life to nature. They seem to think, that we are placed here to watch the growth of plants, or the motions of the stars. Socrates was rather of opinion, that what we had to learn was, how to do good, and avoid evil:
"Οτι τοι εν μεγάροισι κακόν τ' αγαθόν τε τέτυκται. “Of institutions we may judge by their effects. From this wonder-working academy, I do not know that there ever proceeded any man very eminent for knowledge : its only genuine product, I believe, is a small history of poetry, written in Latin, by his nephew Philips, of which, perhaps, none of my readers has ever heard.”
FIRST LESSONS IN ARITHMETIC.
My dear Sir,- If your Journal is ever to become generally useful to the cause of Education, it must provide not only essays for those who are able to guide the course of National instruction, but must furnish to those who are carrying on the details, such a portion of elementary information as shall enable them to improve themselves, and to convey the knowledge which they already possess in a better manner.
I have been much struck with some observations in your first Num. ber, in an article designated, “ Principles better than rules in teaching Arithmetic,” and which agree with my own experience so fully, that I shall endeavour to show what a teacher should do in teaching Arithmetic, rather than point out what they should not do.
The rules to be universally attended to are these.
1. Every sum should be set, by proposing to the children a question which might naturally arise, and which is so easy that the majority of the class must be fairly expected to solve it.
2. Each child should be allowed to solve it by themselves, and those who have done it correctly, should be placed at the head of the class.
3. Those who have answered it incorrectly, being now at the bottom of the class, should do the same sum aloud.
4. The children should never be told what rule they are to employ, but having heard the question, are to answer it as they can.
5. The question if rightly chosen will involve alternately correlative rules, i.e. addition and subtraction, or multiplication and division,
E.g. “ In the first class there were twenty-four children, in the second seventeen-how many were there in all ? ” We will suppose that of twenty children in the class, thirteen do this sum correctly. There will remain therefore seven who are standing at the bottom of the class, and who are to be instructed. The questions proposed are as follows.
In what rule is this sum ? Why? What do you do first? What stands for twenty-four ?*
What do you do next? Why? What stands for seventeen ? What next? How many are seven and four? What do you put down ? And when do you put it down ? How many do you carry? Why?
The teacher should at the same time display the working on a slate or a blank board, with chalk, and those children who have answered the question correctly, should be cross-examined as to the reason of everything.
The next question may be this :
“ Mary Thompson was nine years old when her mother was thirtytwo, how old was the mother when Mary was born ?”.
If the same process be here pursued, it is very probable that some of the children will add, instead of subtract, the nine years, which may be explained by asking, How many years ago was Mary born? Was the mother older or younger nine years ago ?
The whole of these observations may at first sight appear childish, but the actual state of the arithmetical teaching in the majority of girl schools throughout the kingdom, render it necessary that any real reform should take place from the very beginning.
The majority of National School mistresses know very little of Arithmetic, and they know less of the art of teaching Arithmetic. Obser. vations corresponding with these, have been long ago published, and are in the hands of many of the mistresses ; but most of those who have the book (Instructions for teaching Arithmetic to very little children,) and who use the questions, either never read the instructions, or never follow them.
* The children would generally answer two and four. They should always be accustomed to say two tens and four, and may be asked, Why does the two stand for two tens ? and they should be instructed to answer, Because it is in the place of tens.
My object to-day, therefore, is to send some questions without answers, which mistresses may propose to the children; and if they will only allow the children in each case, first to try whether they can work out the answer, each by himself, and then instruct those who do not succeed in the attempt, according to the plan before laid down, they will find that their pupils will soon advance in the knowledge of what they are doing.
In a school there were fifty-three children who had bonnets, and nineteen who had none-How many children were there?
There were one hundred and three names on the books, but one very wet day there were fifteen absent-How many were there present ?
In a school one half of the children had naked feet, seventeen had shoes, and nine, boots-How many children were there altogether ?
There were two hundred and fifteen people in a church, ninety-seven were males-How many females were there?
The Rector was born in 1792–How old is he now ? His wife, who was born the same year, died when she was thirtyfive-In what year did she die ?
How many days are there in January, February, and March?
In the year 1831 there were three hundred and forty-seven people in the parish; in 1841, there were four hundred-What was the increase ?
If the increase had been ninety-four, how many would there have been in 1841 ?
A woman had to walk one hundred and four miles; when she had gone seventeen, how many more had she to go?
A man had to carry a basket thirty-seven miles, and walk back again, in so doing he went out of his way five miles—How far did he walk in
In a class there were sixteen children-how many feet were there altogether?
There were thirty-seven children in a school, and they walked two and two to church—How many pair were there?
If they had walked three and three, how many lines would there have been ?
A man had five children, and some one gave them five shillings between them—How much had they each ?
How much must he have given that they might have sixpence each ?
Three feet make a yard—How many yards are there in twenty-six feet ?
How many fourpenny pieces are there in twenty-three shillings?
There was a family of a mother and three children. The mother had eightpence a day, and each of the children sixpence.--How much had
they altogether for each day? And how much would this amount to for three days ?
A gentleman gave three pounds among five children-How much had each?
I presume that two objections will arise to this method of beginning with children :
First, that what is here advanced must be known to every teacher.
Secondly, that the introduction of questions involving higher rules of arithmetic, will only tend to distract the minds of the children.
To this I would answer, that my object is to induce people to employ a method which practically teaches principles and not rules ; and that, in fact, the present method of teaching arithmetic does not answer; but that if they would confine every sum to a question thus solved by the children, and then openly teach those who did not solve the question, that the children would soon acquire a real knowledge of arithmetic. Secondly, as there are only in reality four rules, or rather two processes, converse to each other, by which all questions must be solved, I should first try to make the pupils understand how to add and subtract, and when to use the one or the other process, and then proceed to instruct them how to multiply and divide, and when to use the one or the other; and my method of doing this would be to lay before them such a question as they would all understand, and which some of them would be able to perform technically, and some would not; and when I had ascertained who could and who could not do this, I should display before them all the practical working of the question.
The point on which I insist, is, that every sum should be proposed in the shape of a rational question, and that each child should be allowed to try to do the sum by himself. I remain, &c., Feb. 18, 1843.
STUDY MADE EASY.—IS THIS WISE ?
Juvat ipse labor.-MART. The opinion of those persons who think that every thing is an improvement which renders study more easy, seems to be founded upon an erroneous notion of the principal design of early education, which is not so much the acquisition of certain branches of knowledge, as the forming in the young mind of habits of close application, the strengthening of the memory, and disciplining the other faculties, so as to be able hereafter to pursue with advantage any studies which may then be deemed necessary. They who learn gymnastics are aware, that its ultimate object is not to enable them to jump a certain distance, or to move the limbs in certain prescribed ways, but the acquisition of general activity, flexibility, and vigour. So studies have a general tendency to strengthen the mental powers, besides the specific advantages which it is their ostensible object to secure. “Ipsa denique utilissima est exercitationis difficultas." Quint.
Now, whatever tends to render literary or scientific attainments comparatively easy, defeats to the same extent this salutary intention. In this way, many branches of learning may be acquired, without the mind undergoing that wholesome discipline, which it is one great design of study to afford. Habits of close application, so essential to future eminence, will seldom be acquired where mental pursuits are so far facilitated, as to supersede the necessity of diligent and persevering exertion.
At a very tender age, perhaps, and in acquiring the earliest rudiments, some such contrivances may be safely allowed; but at a more advanced stage of education, the pupil should be accustomed to depend chiefly on his own resources ; and hence the various helps so often had recourse to, such as translations of works in the classical or foreign languages, keys to exercises, and to books 'on arithmetic, the mathematics, &c., should be very sparingly allowed ; even the assistance of a private tutor, if too lavishly bestowed, will have an unfavourable tendency, by dwarfing those habits of self-dependence, upon which eventual success so greatly depends.
The preceding remarks, it is perhaps scarcely necessary to state, are not intended to disparage the various methods referred to when discreetly used to accelerate literary pursuits, or to enable the student to keep pace with the rapid advance of knowledge in the present day, and to embrace a wider circle of scientific and literary subjects. When a demand is made upon the pupil in point of acquisition, proportionate to the facilities enjoyed, the evil consequences will not only be avoided, but a much greater amount of information will be the necessary result. It is only when these facilities are permitted to supply the place of close thought and personal effort, when they are rendered by their abuse little better than a præmium for idleness, that these strictures can be considered applicable. So long as a disposition to advance is manifested, a degree of impatience exhibited to surmount obstacles in his literary and scientific career, and a feeling of exultation at difficulties overcome, it is evident that whatever assistance the youthful student may have received, has had a beneficial effect, by exciting rather than satisfying the desire of improvement. Here, then, the preceptor has a wide and important field for the exercise of his discretion, in giving or withholding such assistance; nor should he ever forget, for his own as well as his pupil's sake, that
“Melius est discere quam doceri.” Winchmore Hill Academy, Feb, 9, 1843.
A CLASSIFICATION OF EDUCATIONAL BOOKS
REQUIRED FOR NATIONAL SCHOOLS. The books are required to be of an elementary kind, and adapted to the condition of the poor and industrious classes. The child is supposed to enter the National or Parochial School at seven years old in agricultural districts, at six years old in towns. He is ignorant of the first elements of education, and in many cases scarcely knows the alphabet. The