And well might Mrs George Sedley be delighted. Would not many a mother to-day triumph in such a literary effort? What can Thackeray be laughing at? Or does he, in truth, give us this little ‘theme’ as a tour de force?

An Educational Futility.—​I think this great moral teacher here throws down the gauntlet in challenge of an educational futility which is practised, and an educational fallacy which is accepted, even in the twentieth century. That futility is the exaction of original composition from schoolboys and schoolgirls. The proper function of the mind of the young scholar is to collect material for the generalisations of after-life. If a child is asked to generalise, that is, to write an essay upon some abstract theme, a double wrong is done him. He is brought up before a stone wall by being asked to do what is impossible to him, and that is discouraging. But a worse moral injury happens to him in that, having no thought of his own to offer on the subject, he puts together such tags of commonplace thought as have come in his way and offers the whole as his ‘composition,’ an effort which puts a strain upon his conscience while it piques his vanity. In these days masters do not consciously put their hand to the work of their pupils as did that ‘prodigiously well-read and delightful’ master who had the educating of George Osborne. But, perhaps without knowing it, they give the ideas which the cunning schoolboy seizes to ‘stick’ into the ‘essay’ he hates. Sometimes they do more. They deliberately teach children how to ‘build a sentence’ and how to ‘bind sentences’ together.

Lessons in Composition.—​Here is a series of preliminary exercises (or rather a part of the series, which numbers 40) intended to help a child to write an essay on ‘An Umbrella,’ from a book of the hour proceeding from one of our best publishing houses:—

“Step I.

“1. What are you?

“2. How did you get your name?

“3. Who uses you?

“4. What were you once?

“5. What were you like then?

“6. Where were you obtained or found?

“7. Of what stuff or materials are you made?

“8. From what sources do you come?

“9. What are your parts?

“10. Are you made, grown, or fitted together?

*  *  *  *  *

“Step II.

“I am an umbrella, and am used by many people, young and old.

“I get my name from a word which means a shade.

“The stick came perhaps from America, and is quite smooth, even, and polished, so that the metal ring may slide easily up and down the stick.

“My parts are a frame and a cover. My frame consists of a stick about a yard long, wires, and a sliding metal band. At the lower end of the stick is a steel ferrule or ring. This keeps the end from wearing away when I am used in walking.

“Step III.

“Now use it, is, are, and was, instead of I, have, my, and am.

*  *  *  *  *

“Exercise.

“Now write out your own description of it.”

Such Teaching a Public Danger.—​And this is work intended for Standards VI. and VII.! That is to say, this kind of thing is the final literary effort to be exacted from children in our elementary schools!

The two volumes (I quote from near the end of the second and more advanced volume) are not to be gibbeted as exceptionally bad. A few years ago the appalling discovery was made that, both in secondary and elementary schools, ‘composition’ was dreadfully defective, and, therefore, badly taught. Since then many volumes have been produced, more or less on the lines indicated in the above citation, and distinguished publishers have not perceived that to offer to the public, with the sanction of their name, works of this sterilising and injurious character, is an offence against society. The body of a child is sacred in the eye of the law, but his intellectual powers may be annihilated on such starvation diet as this, and nothing said! The worst of it is, both authors and publishers in every case act upon the fallacy that well-intentioned effort is always excusable, if not praiseworthy. They do not perceive that no effort is permissible towards the education of children without an intelligent conception, both of children, and of what is meant by education.

‘Composition’ comes by Nature.—​In fact, lessons on ‘composition’ should follow the model of that famous essay on “Snakes in Ireland”—“There are none.” For children under nine, the question of composition resolves itself into that of narration, varied by some such simple exercise as to write a part and narrate a part, or write the whole account of a walk they have taken, a lesson they have studied, or of some simple matter that they know. Before they are ten, children who have been in the habit of using books will write good, vigorous English with ease and freedom; that is, if they have not been hampered by instructions. It is well for them not even to learn rules for the placing of full stops and capitals until they notice how these things occur in their books. Our business is to provide children with material in their lessons, and, leave the handling of such material to themselves. If we would believe it, composition is as natural as jumping and running to children who have been allowed due use of books. They should narrate in the first place, and they will compose, later, readily enough; but they should not be taught ‘composition.’

XIV.—BIBLE LESSONS

Children enjoy the Bible.—​We are apt to believe that children cannot be interested in the Bible unless its pages be watered down—turned into the slipshod English we prefer to offer them. Here is a suggestive anecdote of the childhood of Mrs Harrison, one of the pair of little Quaker maidens introduced to us in the Autobiography of Mary Howitt, the better known of the sisters. “One day she found her way into a lumber room. There she caught sight of an old Bible, and turning over its yellow leaves she came upon words that she had not heard at the usual morning readings, the opening chapters of St Luke—which her father objected to read aloud—and the closing chapter of Revelation. The exquisite picture of the Great Child’s birth in the one chapter, and the beauty of the description of the New Jerusalem in the other, were seized upon by the eager little girl of six years old with a rapture which, she used to say, no novel in after years ever produced.”

And here is a mention of a child of five. “The little ones read every day the events of Holy Week with me. Z. is inexpressibly interesting in his deep, reverent interest, almost excitement.”

We are probably quite incapable of measuring the religious receptivity of children. Nevertheless, their fitness to apprehend the deep things of God is a fact with which we are called to ‘deal prudently,’ and to deal reverently. And that, because, as none can appreciate more fully than the ‘Darwinian,’ the attitude of thought and feeling in which you place a child is the vital factor in his education.

Should know the Bible Text.—​Children between the ages of six and nine should get a considerable knowledge of the Bible text. By nine they should have read the simple (and suitable) narrative portions of the Old Testament, and, say, two of the gospels. The Old Testament should, for various reasons, be read to children. The gospel stories, they might read for themselves as soon as they can read them beautifully. It is a mistake to use paraphrases of the text; the fine roll of Bible English appeals to children with a compelling music, and they will probably retain through life their first conception of the Bible scenes, and, also, the very words in which these scenes are portrayed. This is a great possession. Half the clever talk we hear to-day, and half the uneasiness which underlies this talk, are due to a thorough and perfect ignorance of the Bible text. The points of assault are presented to men’s minds naked and jagged, without atmosphere, perspective, proportion; until the Bible comes to mean for many, the speaking of Balaam’s ass or the standing still of the sun at Joshua’s bidding.

But let the imaginations of children be stored with the pictures, their minds nourished upon the words, of the gradually unfolding story of the Scriptures, and they will come to look out upon a wide horizon within which persons and events take shape in their due place and in due proportion. By degrees, they will see that the world is a stage whereon the goodness of God is continually striving with the wilfulness of man; that some heroic men take sides with God; and that others, foolish and headstrong, oppose themselves to Him. The fire of enthusiasm will kindle in their breast, and the children, too, will take their side, without much exhortation, or any thought or talk of spiritual experience.

Essential and Accidental Truth.—​As for whether such and such a narrative be a myth, or a parable, or a circumstance that has actually occurred, such questions do not affect the sincere mind of a child, because they have nothing to do with the main issues. It is quite well to bring before children, in the course of their Bible readings, whatever new light modern research puts in our way; the more we can help them in this way, the more vivid and real will Bible teaching become to them. But this grace, at any rate, the children may claim at our hands, that they shall not be disturbed by questions of authenticity in their Bible reading any more than in their reading of English history. Let them hear the story of the Garden of Eden, for example, as it stands; just so, we might even let them have the story of the man who went fishing and found a goodly pearl; and this, because the thing that matters in both stories is the essential truths they embody, and not the mere accidents of time and place. It is conceivable that the ‘pearl of great price’ was matter of current talk at the time; a so-called ‘fact’ seized upon by our Lord to make of it the vehicle for essential truth. If we will believe it, the minds of children are, perhaps, more fit than our own to appropriate and deal with truth. By-and-by they will perceive, and discard, if necessary, the accidental circumstances with which the truth is clothed upon; but let us be very chary of our own action. Let us remember that neither we nor the children can bear the white light of naked truth; that if, for example, we succeed in destroying the clothing that covers the story of the first fall—the tree and its fruit, the tempting serpent, the yielding woman—we have no other clothing at hand for the fundamental truths of responsibility, temptation, sin; and, once uncovered, with no vesture which we can lay hold upon, the truths themselves will assuredly slip from our grasp.

We need not be at the pains to discriminate, in teaching children Bible narratives, between essential and accidental truth—the truth which interprets our own lives, and that which concerns only the time, place, and circumstances proper to the narrative. The children themselves will discern and keep fast hold of the essential, while the merely accidental slips from their memory as from ours. Therefore, let the minds of young children be well stored with the beautiful narratives of the earlier portions of the Old Testament and of the gospels; but, in order that these stories may be always fresh and delightful to them, care must be taken lest Bible teaching stale upon their minds. Children are more capable of being bored than even we ourselves, and many a revolt has been brought about by the undue rubbing-in of the Bible, in season and out of season, even in nursery days. But we are considering, not the religious life of children, but their education by lessons; and their Bible lessons should help them to realise in early days that the knowledge of God is the principal knowledge, and, therefore, that their Bible lessons are their chief lessons.

Method of Bible Lessons.—​The method of such lessons is very simple. Read aloud to the children a few verses covering, if possible, an episode. Read reverently, carefully, and with just expression. Then require the children to narrate what they have listened to as nearly as possible in the words of the Bible. It is curious how readily they catch the rhythm of the majestic and simple Bible English. Then, talk the narrative over with them in the light of research and criticism. Let the teaching, moral and spiritual, reach them without much personal application. I know of no better help in the teaching of young children than we get in Canon Paterson Smyth’s Bible for the Young. Mr Smyth brings both modern criticism and research to bear, so that children taught from his little manuals will not be startled to be told later that the world was not made in six days; and, at the same time, they will be very sure that the world was made by God. The moral and spiritual teaching in these manuals is on broad and convincing lines. It is rather a good plan occasionally to read aloud Mr Smyth’s lesson on the subject after the Bible passage has been narrated. Children are more ready to appropriate lessons that are not directly levelled at themselves; while the teacher makes the teaching her own by the interest with which she reads, the pictures and other illustrations she shows, and her conversational remarks.

Picture Illustrations.—​The pictures in the Illustrated New Testament are, at the same time, reverent and actual, an unusual combination, and children enjoy them greatly. It would be well for them to have only the penny gospel they are reading, but it should perhaps be protected (and honoured) by an embroidered cover. A tattered Bible is not a wholesome sight for children. The Holy Gospels with Illustrations from the Old Masters,[23] published by the S.P.C.K., is admirable. The study of such pictures as are here reproduced should be a valuable part of a child’s education; it is no slight thing to realise how the Nativity and the visit of the Wise Men filled the imagination of the early Masters, and with what exceeding reverence and delight they dwelt upon every detail of the sacred story. This sort of impression is not to be had from any up-to-date treatment, or up-to-date illustrations; and the child who gets it in early days, will have a substratum of reverent feeling upon which should rest his faith. But it is well to let the pictures tell their own tale. The children should study a subject quietly for a few minutes; and then, the picture being removed, say what they have seen in it. It will be found that they miss no little reverent or suggestive detail which the artist has thought well to include.

The various R.T.S. publications issued in the series of Bypaths of Bible Knowledge will be found very helpful by the teacher, as illustrating modern research; notably, Professor Sayce’s Fresh Light from Ancient Monuments, and Budge’s Dwellers on the Nile.[24]

Bible Recitations.—​The learning by heart of Bible passages should begin while the children are quite young, six or seven. It is a delightful thing to have the memory stored with beautiful, comforting, and inspiring passages, and we cannot tell when and how this manner of seed may spring up, grow, and bear fruit; but the learning of the parable of the Prodigal Son, for example, should not be laid on the children as a burden. The whole parable should be read to them in a way to bring out its beauty and tenderness; and then, day by day, the teacher should recite a short passage, perhaps two or three verses, saying it over some three or four times until the children think they know it. Then, but not before, let them recite the passage. Next day the children will recite what they have already learned, and so on, until they are able to say the whole parable.

XV.—ARITHMETIC

Educative Value of Arithmetic.—​Of all his early studies, perhaps none is more important to the child as a means of education than that of arithmetic. That he should do sums is of comparatively small importance; but the use of those functions which ‘summing’ calls into play is a great part of education; so much so, that the advocates of mathematics and of language as instruments of education have, until recently, divided the field pretty equally between them.

The practical value of arithmetic to persons in every class of life goes without remark. But the use of the study in practical life is the least of its uses. The chief value of arithmetic, like that of the higher mathematics, lies in the training it affords to the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders. There is no one subject in which good teaching effects more, as there is none in which slovenly teaching has more mischievous results. Multiplication does not produce the ‘right answer,’ so the boy tries division; that again fails, but subtraction may get him out of the bog. There is no must be to him; he does not see that one process, and one process only, can give the required result. Now, a child who does not know what rule to apply to a simple problem within his grasp, has been ill taught from the first, although he may produce slatefuls of quite right sums in multiplication or long division.

Problems within the Child’s Grasp.—​How is this insight, this exercise of the reasoning powers, to be secured? Engage the child upon little problems within his comprehension from the first, rather than upon set sums. The young governess delights to set a noble ‘long division sum,’—953,783,465 ÷ 873—which shall fill the child’s slate, and keep him occupied for a good half-hour; and when it is finished, and the child is finished too, done up with the unprofitable labour, the sum is not right after all: the two last figures in the quotient are wrong, and the remainder is false. But he cannot do it again—he must not be discouraged by being told it is wrong; so, ‘nearly right’ is the verdict, a judgment inadmissible in arithmetic. Instead of this laborious task, which gives no scope for mental effort, and in which he goes to sea at last from sheer want of attention, say to him—

“Mr Jones sent six hundred and seven, and Mr Stevens eight hundred and nineteen, apples to be divided amongst the twenty-seven boys at school on Monday. How many apples apiece did they get?”

Here he must ask himself certain questions. ‘How many apples altogether? How shall I find out? Then I must divide the apples into twenty-seven heaps to find out each boy’s share.’ That is to say, the child perceives what rules he must apply to get the required information. He is interested; the work goes on briskly: the sum is done in no time, and is probably right, because the attention of the child is concentrated on his work. Care must be taken to give the child such problems as he can work, but yet which are difficult enough to cause him some little mental effort.

Demonstrate.—​The next point is to demonstrate everything demonstrable. The child may learn the multiplication-table and do a subtraction sum without any insight into the rationale of either. He may even become a good arithmetician, applying rules aptly, without seeing the reason of them; but arithmetic becomes an elementary mathematical training only in so far as the reason why of every process is clear to the child. 2 + 2 = 4, is a self-evident fact, admitting of little demonstration; but 4 × 7 = 28 may be proved.

He has a bag of beans; places four rows with seven beans in a row; adds the rows, thus: 7 and 7 are 14, and 7 are 21, and 7 are 28; how many sevens in 28? 4. Therefore it is right to say 4 × 7 = 28; and the child sees that multiplication is only a short way of doing addition.

A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to ‘do sums’ on his slate.

He may arrange an addition table with his beans, thus—

⬭⬭	⬭	= 3 beans
⬭⬭	⬭⬭	= 4 ”
⬭⬭	⬭⬭⬭	= 5 ”

and be exercised upon it until he can tell, first without counting, and then without looking at the beans, that 2 + 7 = 9, etc.

Thus with 3, 4, 5,—each of the digits: as he learns each line of his addition table, he is exercised upon imaginary objects, ‘4 apples and 9 apples,’ ‘4 nuts and 6 nuts,’ etc.; and lastly, with abstract numbers—6 + 5, 6 + 8.

A subtraction table is worked out simultaneously with the addition table. As he works out each line of additions, he goes over the same ground, only taking away one bean, or two beans, instead of adding, until he is able to answer quite readily, 2 from 7? 2 from 5? After working out each line of addition or subtraction, he may put it on his slate with the proper signs, that is, if he have learned to make figures. It will be found that it requires a much greater mental effort on the child’s part to grasp the idea of subtraction than that of addition, and the teacher must be content to go slowly—one finger from four fingers, one nut from three nuts, and so forth, until he knows what he is about.

When the child can add and subtract numbers pretty freely up to twenty, the multiplication and division tables may be worked out with beans, as far as 6 × 12; that is, ‘twice 6 are 12’ will be ascertained by means of two rows of beans, six beans in a row.

When the child can say readily, without even a glance at his beans, 2 × 8 = 16, 2 × 7 = 14, etc., he will take 4, 6, 8, 10, 12 beans, and divide them into groups of two: then, how many twos in 10, in 12, in 20? And so on, with each line of the multiplication table that he works out.

Problems.—​Now he is ready for more ambitious problems: thus, ‘A boy had twice ten apples; how many heaps of 4 could he make?’ He will be able to work with promiscuous numbers, as 7 + 5 - 3. If he must use beans to get his answer, let him; but encourage him to work with imaginary beans, as a step towards working with abstract numbers. Carefully graduated teaching and daily mental effort on the child’s part at this early stage may be the means of developing real mathematical power, and will certainly promote the habits of concentration and effort of mind.

Notation.—​When the child is able to work pretty freely with small numbers, a serious difficulty must be faced, upon his thorough mastery of which will depend his apprehension of arithmetic as a science; in other words, will depend the educational value of all the sums he may henceforth do. He must be made to understand our system of notation. Here, as before, it is best to begin with the concrete: let the child get the idea of ten units in one ten after he has mastered the more easily demonstrable idea of twelve pence in one shilling.

Let him have a heap of pennies, say fifty: point out the inconvenience of carrying such weighty money to shops. Lighter money is used—shillings. How many pennies is a shilling worth? How many shillings, then, might he have for his fifty pennies? He divides them into heaps of twelve, and finds that he has four such heaps, and two pennies over; that is to say, fifty pence are (or are worth) four shillings and twopence. I buy ten pounds of biscuits at fivepence a pound; they cost fifty pence, but the shopman gives me a bill for 4s. 2d.; show the child how put down: the pennies, which are worth least, to the right; the shillings, which are worth more, to the left.

When the child is able to work freely with shillings and pence, and to understand that 2 in the right-hand column of figures is pence, 2 in the left-hand column, shillings, introduce him to the notion of tens and units, being content to work very gradually. Tell him of uncivilised peoples who can only count so far as five—who say ‘five-five beasts in the forest,’ ‘five-five fish in the river,’ when they wish to express an immense number. We can count so far that we might count all day long for years without coming to the end of the numbers we might name; but after all, we have very few numbers to count with, and very few figures to express them by. We have but nine figures and a nought: we take the first figure and the nought to express another number, ten; but after that we must begin again until we get two tens, then, again, till we reach three tens, and so on. We call two tens, twenty, three tens, thirty, because ‘ty’ (tig) means ten.

But if I see figure 4, how am I to know whether it means four tens or four ones? By a very simple plan. The tens have a place of their own; if you see figure 6 in the ten-place, you know it means sixty. The tens are always put behind the units: when you see two figures standing side by side, thus, ‘55,’ the left-hand figure stands for so many tens; that is, the second 5 stands for ten times as many as the first.

Let the child work with tens and units only until he has mastered the idea of the tenfold value of the second figure to the left, and would laugh at the folly of writing 7 in the second column of figures, knowing that thereby it becomes seventy. Then he is ready for the same sort of drill in hundreds, and picks up the new idea readily if the principle have been made clear to him, that each remove to the left means a tenfold increase in the value of a number. Meantime, ‘set’ him no sums. Let him never work with figures the notation of which is beyond him, and when he comes to ‘carry’ in an addition or multiplication sum, let him not say he carries ‘two,’ or ‘three,’ but ‘two tens,’ or ‘three hundreds,’ as the case may be.

Weighing and Measuring.—​If the child do not get the ground under his feet at this stage, he works arithmetic ever after by rule of thumb. On the same principle, let him learn ‘weights and measures’ by measuring and weighing; let him have scales and weights, sand or rice, paper and twine, and weigh, and do up, in perfectly made parcels, ounces, pounds, etc. The parcels, though they are not arithmetic, are educative, and afford considerable exercise of judgment as well as of neatness, deftness, and quickness. In like manner, let him work with foot-rule and yard measure, and draw up his tables for himself. Let him not only measure and weigh everything about him that admits of such treatment, but let him use his judgment on questions of measure and weight. How many yards long is the tablecloth? how many feet long and broad a map, or picture? What does he suppose a book weighs that is to go by parcel post? The sort of readiness to be gained thus is valuable in the affairs of life, and, if only for that reason, should be cultivated in the child. While engaged in measuring and weighing concrete quantities, the scholar is prepared to take in his first idea of a ‘fraction,’ half a pound, a quarter of a yard, etc.

Arithmetic a Means of Training.—​Arithmetic is valuable as a means of training children in habits of strict accuracy, but the ingenuity which makes this exact science tend to foster slipshod habits of mind, a disregard of truth and common honesty, is worthy of admiration! The copying, prompting, telling, helping over difficulties, working with an eye to the answer which he knows, that are allowed in the arithmetic lesson, under an inferior teacher, are enough to vitiate any child; and quite as bad as these is the habit of allowing that a sum is nearly right, two figures wrong, and so on, and letting the child work it over again. Pronounce a sum wrong, or right—it cannot be something between the two. That which is wrong must remain wrong: the child must not be let run away with the notion that wrong can be mended into right. The future is before him: he may get the next sum right, and the wise teacher will make it her business to see that he does, and that he starts with new hope. But the wrong sum must just be let alone. Therefore his progress must be carefully graduated; but there is no subject in which the teacher has a more delightful consciousness of drawing out from day to day new power in the child. Do not offer him a crutch: it is in his own power he must go. Give him short sums, in words rather than in figures, and excite in him the enthusiasm which produces concentrated attention and rapid work. Let his arithmetic lesson be to the child a daily exercise in clear thinking and rapid, careful execution, and his mental growth will be as obvious as the sprouting of seedlings in the spring.

The A B C Arithmetic.—​Instead of entering further into the subject of the teaching of elementary arithmetic, I should like to refer the reader to the A B C Arithmetic by Messrs Sonnenschein & Nesbit.

The authors found their method upon the following passage from Mill’s Logic:—“The fundamental truths of the science of Number all rest on the evidence of sense; they are proved by showing to our eyes and our fingers that any given number of objects, ten balls for example, may by separation and re-arrangement exhibit to our senses all the different sets of numbers the sum of which is equal to ten. All the improved methods of teaching arithmetic to children proceed on a knowledge of this fact. All who wish to carry the child’s mind along with them in learning arithmetic, all who wish to teach numbers and not mere ciphers, now teach it through the evidence of the senses in the manner we have described.”

Here we may, I think, trace the solitary source of weakness in a surpassingly excellent manual. It is quite true that the fundamental truths of the science of number all rest on the evidence of sense; but, having used eyes and fingers upon ten balls or twenty balls, upon ten nuts, or leaves, or sheep, or what not, the child has formed the association of a given number with objects, and is able to conceive of the association of various other numbers with objects. In fact, he begins to think in numbers and not in objects, that is, he begins mathematics. Therefore I incline to think that an elaborate system of staves, cubes, etc., instead of tens, hundreds, thousands, errs by embarrassing the child’s mind with too much teaching, and by making the illustration occupy a more prominent place than the thing illustrated.

Dominoes, beans, graphic figures drawn on the blackboard, and the like, are, on the other hand, aids to the child when it is necessary for him to conceive of a great number with the material of a small one; but to see a symbol of the great numbers and to work with such a symbol are quite different matters.

With the above trifling exception, which does not interfere at all with the use of the books, nothing can be more delightful than the careful analysis of numbers and the beautiful graduation of the work, “only one difficulty at a time being presented to the mind.” The examples and the little problems could only have been invented by writers in sympathy with children. I advise the reader who is interested in the teaching of arithmetic to turn to Mr Sonnenschein’s paper on ‘The Teaching of Arithmetic in Elementary Schools,’ in one of the volumes published by the Board of Education.[25]

Preparation for Mathematics.—​In the ‘forties’ and ‘fifties’ it was currently held that the continual sight of the outward and visible signs (geometrical forms and figures) should beget the inward and spiritual grace of mathematical genius, or, at any rate, of an inclination to mathematics. But the educationalists of those days forgot, when they gave children boxes of ‘form’ and stuck up cubes, hexagons, pentagons, and what not, in every available schoolroom space, the immense capacity for being bored which is common to us all, and is far more strongly developed in children than in grown-up people. The objects which bore us, or the persons who bore us, appear to wear a bald place in the mind, and thought turns from them with sick aversion. Dickens showed us the pathos of it in the schoolroom of the little Gradgrinds, which was bountifully supplied with objects of uncompromising outline. Ruskin, more genially, exposes the fallacy. No doubt geometric forms abound,—the skeletons of which living beauty, in contour and gesture, in hill and plant, is the covering; and the skeleton is beautiful and wonderful to the mind which has already entered within the portals of geometry. But children should not be presented with the skeleton, but with the living forms which clothe it. Besides, is it not an inverse method to familiarise the child’s eye with patterns made by his compasses, or stitched upon his card, in the hope that the form will beget the idea? For the novice, it is probably the rule that the idea must beget the form, and any suggestion of an idea from a form comes only to the initiated. I do not think that any direct preparation for mathematics is desirable. The child, who has been allowed to think and not compelled to cram, hails the new study with delight when the due time for it arrives. The reason why mathematics are a great study is because there exists in the normal mind an affinity and capacity for this study; and too great an elaboration, whether of teaching or of preparation, has, I think, a tendency to take the edge off this manner of intellectual interest.

XVI.—NATURAL PHILOSOPHY

A Basis of Facts.—​Of the teaching of Natural Philosophy, I will only remind the reader of what was said in an earlier chapter—that there is no part of a child’s education more important than that he should lay, by his own observation, a wide basis of facts towards scientific knowledge in the future. He must live hours daily in the open air, and, as far as possible, in the country; must look and touch and listen; must be quick to note, consciously, every peculiarity of habit or structure, in beast, bird, or insect; the manner of growth and fructification of every plant. He must be accustomed to ask why—Why does the wind blow? Why does the river flow? Why is a leaf-bud sticky? And do not hurry to answer his questions for him; let him think his difficulties out so far as his small experience will carry him. Above all, when you come to the rescue, let it not be in the ‘cut and dried’ formula of some miserable little text-book; let him have all the insight available, and you will find that on many scientific questions the child may be brought at once to the level of modern thought. Do not embarrass him with too much scientific nomenclature. If he discover for himself (helped, perhaps, by a leading question or two), by comparing an oyster and his cat, that some animals have backbones and some have not, it is less important that he should learn the terms vertebrate and invertebrate than that he should class the animals he meets with according to this difference.

Eyes and No-eyes.—​The method of this sort of instruction is shown in Evenings at Home, where ‘Eyes and No-eyes’ go for a walk. No-eyes comes home bored; he has seen nothing, been interested in nothing: while Eyes is all agog to discuss a hundred things that have interested him. As I have already tried to point out, to get this sort of instruction for himself is simply the nature of a child: the business of the parent is to afford him abundant and varied opportunities, and to direct his observations, so that, knowing little of the principles of scientific classification, he is, unconsciously, furnishing himself with the materials for such classification. It is needless to repeat what has already been said on this subject; but, indeed, the future of the man or woman depends very largely on the store of real knowledge gathered, and the habits of intelligent observation acquired, by the child. “Think you,” says Mr Herbert Spencer, “that the rounded rock marked with parallel scratches calls up as much poetry in an ignorant mind as in the mind of the geologist, who knows that over this rock a glacier slid a million of years ago? The truth is, that those who have never entered on scientific pursuits are blind to most of the poetry by which they are surrounded. Whoever has not in youth collected plants and insects, knows not half the halo of interest which lanes and hedgerows can assume.”

Principles.—​In this connection I should like to recommend The Sciences, by Mr Holden. America comes to the fore with a schoolbook after my own heart. The Sciences is a forbidding title, but since the era of Joyce’s Scientific Dialogues I have met with nothing on the same lines which makes so fit an approach to the sensible and intelligent mind of a child. This is what we may call a ‘first-hand’ book. The knowledge has of course all been acquired; but then it has been assimilated, and Mr Holden writes freely out of his own knowledge both of his subject-matter and of his readers. The book has been thrown into the form of conversations between children—simple conversations without padding. About three hundred topics are treated of: Sand-dunes, Back-ice, Herculaneum, Dredging, Hurricanes, Echoes, the Prism, the Diving-bell, the Milky Way, and, shall I say, everything else? But the amazing skill of the author is shown in the fact that there is nothing scrappy and nothing hurried in the treatment of any topic, but each falls naturally and easily under the head of some principle which it elucidates. Many simple experiments are included, which the author insists shall be performed by the children themselves. I venture to quote from the singularly wise preface, a vade mecum for teachers:—

“The object of the present volume is to present chapters to be read in school or at home that shall materially widen the outlook of American schoolchildren in the domain of science, and of the applications of science to the arts and to daily life. It is in no sense a text-book, although the fundamental principles underlying the sciences treated are here laid down. Its main object is to help the child to understand the material world about him.”

To be Comprehended by Children.—“All natural phenomena are orderly; they are governed by law; they are not magical. They are comprehended by someone; why not by the child himself? It is not possible to explain every detail of a locomotive to a young pupil, but it is perfectly practicable to explain its principles so that this machine, like others, becomes a mere special case of certain well-understood general laws. The general plan of the book is to awaken the imagination; to convey useful knowledge; to open the doors towards wisdom. Its special aim is to stimulate observation and to excite a living and lasting interest in the world that lies about us.

“The sciences of astronomy, physics, chemistry, meteorology, and physiography are treated as fully and as deeply as the conditions permit; and the lessons that they teach are enforced by examples taken from familiar and important things. In astronomy, for example, emphasis is laid upon phenomena that the child himself can observe, and he is instructed how to go about it. The rising and setting of the stars, the phases of the moon, the uses of the telescope, are explained in simple words. The mystery of these and other matters is not magical, as the child at first supposes. It is to deeper mysteries that his attention is here directed. Mere phenomena are treated as special cases of very general laws. The same process is followed in the exposition of the other sciences.

“Familiar phenomena, like those of steam, of shadows, of reflected light, of musical instruments, of echoes, etc., are referred to their fundamental causes. Whenever it is desirable, simple experiments are described and fully illustrated, and all such experiments can very well be repeated in the schoolroom.... The volume is the result of a sincere belief that much can be done to aid young children to comprehend the material world in which they live, and of a desire to have a part in a work so very well worth doing.”

I cannot help quoting also in this connection from an article[26] by the Rev. H. H. Moore dealing with a forgotten pioneer of a rational education and his experiment. This pioneer was the Rev. Richard Dawes, at one time Rector of Kings Somborne parish, Hampshire, who, in 1841, worked out the problem of rational education in an agricultural village, in which he found the population unusually ignorant and debased. The whole story is of great interest, but our concern is with the question of Natural Philosophy, the staple of the teaching given in this school.

As taught in a Village School.—​Mr Dawes thus explained his object:—“I aimed at teaching what would be profitable and interesting to persons in the position in life which the children were likely to occupy. I aimed at their being taught what may be called the philosophy of common things—of everyday life. They were shown how much there is that is interesting, and which it is advantageous for them to know, in connection with the natural objects with which they are familiar; they had explained to them, and were made acquainted with, the principles of a variety of natural phenomena, as well as the principles and construction of various instruments of a useful kind. A practical turn was given to everything; the uses and fruits of the knowledge they were acquiring were never lost sight of.” A list of some of the subjects included in this kind of teaching will be the best commentary on Mr Dawes’ scheme:—

“Some of the properties of air, explaining how its pressure enables them to pump up water, to amuse themselves with squirts and popguns, to suck up water through a straw; explaining also the principles and construction of a barometer, the common pump, the diving-bell, a pair of bellows. That air expands by heat, shown by placing a half-blown bladder near the fire, when the wrinkles disappear. Why the chimney-smoke sometimes rises easily in the air, sometimes not. Why there is a draught up the chimney, and under the door, and towards the fire. Air as a vehicle of sound, and why the flash of a distant gun fired is seen before the report is heard; how to calculate the distance of a thunderstorm; the difference in the speeds at which different materials conduct sound. Water and its properties, its solid, fluid, and vaporous state; why water-pipes are burst by frost; why ice forms and floats on the surface of ponds, and not at the bottom; why the kettle-lid jumps up when the water is boiling on the fire; the uses to which the power of steam is applied; the gradual evolution of the steam-engine, shown by models and diagrams; how their clothes are dried, and why they feel cold sitting in damp clothes; why a damp bed is so dangerous; why one body floats in water, and another sinks; the different densities of sea and fresh water; why, on going into the school on a cold morning, they sometimes see a quantity of water on the glass, and why on the inside and not on the outside; why, on a frosty day, their breath is visible as vapour; the substances water holds in solution, and how their drinking water is affected by the kind of soil through which it has passed. Dew, its value, and the conditions necessary for its formation; placing equal portions of dry wool on gravel, glass, and the grass, and weighing them the next morning. Heat and its properties; how it is that the blacksmith can fit iron hoops so firmly on the wheels of carts and barrows; what precautions have to be taken in laying the iron rails of railways and in building iron bridges, etc.; what materials are good, and what bad, conductors of heat; why at the same temperature some feel colder to our touch than others; why a glass sometimes breaks when hot water is poured into it, and whether thick or thin glass would be more liable to crack; why water can be made to boil in a paper kettle or an eggshell without its being burned. The metals, their sources, properties, and uses; mode of separating from the ores. Light and its properties, illustrated by prisms, etc.; adaptation of the eye; causes of long- and short-sightedness. The mechanical principles of the tools more commonly used, the spade, the plough, the axe, the lever, etc.”

“It may surprise some who read carefully the above list that such subjects should have been taught to the children of a rural elementary school. But it is an undeniable fact that they were taught in Kings Somborne school, and so successfully that the children were both interested and benefited by the teaching. Mr Dawes, in answer to the objection that such subjects are above the comprehension of the young, said:—‘The distinguishing mark of Nature’s laws is their extreme simplicity. It may doubtless require intellect of a high order to make the discovery of these laws; yet, once evolved, they are within the capacity of a child,—in short, the principles of natural philosophy are the principles of common sense, and if taught in a simple and common-sense way, they will be speedily understood and eagerly attended to by children; and it will be found that with pupils of even from ten to twelve years of age much may be done towards forming habits of observation and inquiry.’ Such a fact, I think, suggests some valuable practical lessons for those who have the responsibility of deciding what subjects to include in an educational system for children.”

In reading of this remarkable experiment, we feel that we must at once secure a man, all-informed like the late Dean Dawes, to teach our own Jack and Elsie; but it is something to realise what these young persons should know, and Mr Holden has done a great deal for us. Some of the chapters in The Sciences may be beyond children under nine, but they will be able to master a good deal. One thing is to be borne in mind: nothing should be done without its due experiment. By the way, our old friend, Joyce’s Scientific Dialogues, if it is still to be had, describes a vast number of easy and interesting experiments which children can work for themselves.

XVII.—GEOGRAPHY

Geography is, to my mind, a subject of high educational value; though not because it affords the means of scientific training. Geography does present its problems, and these of the most interesting, and does afford materials for classification; but it is physical geography only which falls within the definition of a science, and even that is rather a compendium of the results of several sciences than a science itself. But the peculiar value of geography lies in its fitness to nourish the mind with ideas, and to furnish the imagination with pictures. Herein lies the educational value of geography.

As commonly Taught.—​Now, how is the subject commonly taught? The child learns the names of the capital cities of Europe, or of the rivers of England, or of the mountain-summits of Scotland, from some miserable text-book, with length in miles, and height in feet, and population, finding the names on his map or not, according as his teacher is more or less up to her work. Poor little fellow! the lesson is hard work to him; but as far as education goes—that is, the developing of power, the furnishing of the mind—he would be better employed in watching the progress of a fly across the windowpane. But, you will say, geography has a further use than this strictly educative one; everybody wants the sort of information which the geography lesson should afford. That is true, and is to be borne in mind in the schoolroom; the child’s geography lesson should furnish just the sort of information which grown-up people care to possess. Now, do think how unreasonable we are in this matter; nothing will persuade us to read a book of travel unless it be interesting, graphic, with a spice of personal adventure. Even when we are going about with Murray in hand, we skip the dry facts and figures, and read the suggestive pictorial scraps; these are the sorts of things we like to know, and remember with ease. But none of this pleasant padding for the poor child, if you please; do not let him have little pictorial sentences that he may dream over; facts and names and figures—these are the pabulum for him!

Geography should be Interesting.—​But, you say, this sort of knowledge, though it may be a labour to the child to acquire it, is useful in after life. Not a bit of it; and for this reason—it has never been really received by the brain at all; has never got further than the floating nebulæ of mere verbal memory of which I have already had occasion to speak. Most of us have gone through a good deal of drudgery in the way of ‘geography’ lessons, but how much do we remember? Just the pleasant bits we heard from travelled friends, about the Rhine, or Paris, or Venice, or bits from The Voyages of Captain Cook, or other pleasant tales of travel and adventure. We begin to see the lines we must go upon in teaching geography: for educative purposes, the child must learn such geography, and in such a way, that his mind shall thereby be stored with ideas, his imagination with images; for practical purposes he must learn such geography only as, the nature of his mind considered, he will able to remember; in other words, he must learn what interests him. The educative and the practical run in one groove, and the geography lesson becomes the most charming occupation of the child’s day.

How to begin.—​But, how to begin? In the first place, the child gets his rudimentary notions of geography as he gets his first notions of natural science, in those long hours out of doors of which we have already seen the importance. A pool fed by a mere cutting in the fields will explain the nature of a lake, will carry the child to the lovely lakes of the Alps, to Livingstone’s great African lake, in which he delighted to see his children ‘paidling’—“his own children ‘paidling’ in his own lake.” In this connection will come in a great deal of pleasant talk about places, ‘pictorial geography,’ until the child knows by name and nature the great rivers and mountains, deserts and plains, the cities and countries of the world. At the same time, he gets his first notions of a map from a rude sketch, a mere few lines and dots, done with pencil and paper, or, better still, with a stick in the sand or gravel. ‘This crooked line is the Rhine; but you must imagine the rafts, and the island with the Mouse Tower, and the Nuns’ Island, and the rest. Here are the hills, with their ruined castles—now on this side, now on that. This dot is Cologne,’ etc. Especially, let these talks cover all the home scenery and interests you are acquainted with, so that, by-and-by, when he looks at the map of England, he finds a score of familiar names which suggest landscapes to him—places where ‘mother has been,’—the woody, flowery islets of the Thames; the smooth Sussex downs, delightful to run and roll upon, with soft carpet of turf and nodding harebells; the York or Devon moors, with bilberries and heather:—and always give him a rough sketch-map of the route you took in a given journey.

What next?—​Give him next intimate knowledge, with the fullest details, of any country or region of the world, any county or district of his own country. It is not necessary that he should learn at this stage what is called the ‘geography’ of the countries of Europe, the continents of the world—mere strings of names for the most part; he may learn these, but it is tolerably certain that he will not remember them. But let him be at home in any single region; let him see, with the mind’s eye, the people at their work and at their play, the flowers and fruits in their seasons, the beasts, each in its habitat; and let him see all sympathetically, that is, let him follow the adventures of a traveller; and he knows more, is better furnished with ideas, than if he had learnt all the names on all the maps. The ‘way’ of this kind of teaching is very simple and obvious; read to him, or read for him, that is, read bit by bit, and tell as you read, Hartwig’s Tropical World,[27] the same author’s Polar World,[27a] Livingstone’s missionary travels, Mrs Bishop’s Unbeaten Tracks in Japan[27a]—in fact, any interesting, well-written book of travel. It may be necessary to leave out a good deal, but every illustrative anecdote, every bit of description, is so much towards the child’s education. Here, as elsewhere, the question is, not how many things does he know, but how much does he know about each thing.

Maps.—Maps must be carefully used in this kind of work,—a sketch-map following the traveller’s progress, to be compared finally with a complete map of the region; and the teacher will exact a description of such and such a town, and such and such a district, marked on the map, by way of testing and confirming the child’s exact knowledge. In this way, too, he gets intelligent notions of physical geography; in the course of his readings he falls in with a description of a volcano, a glacier, a cañon, a hurricane; he hears all about, and asks and learns the how and the why, of such phenomena at the moment when his interest is excited. In other words, he learns as his elders elect to learn for themselves, though they rarely allow the children to tread in paths so pleasant.

What General Knowledge a Child of Nine should have.—​Supposing that between the child’s sixth and his ninth year half a dozen well-chosen standard books of travel have been read with him in this way, he has gained distinct ideas of the contours, the productions, and the manners of the people, of every great region of the world; has laid up a store of reliable, valuable knowledge, that will last his lifetime; and besides, has done something to acquire a taste for books and the habit of reading. Such books as Lady Brassey’s Voyage in the ‘Sunbeam’ should be avoided, as covering too much ground, and likely to breed some confusion of ideas.

Particular Knowledge.—​But we are considering lessons as ‘Instruments of Education’; and the sort of knowledge of the world I have indicated will be conveyed rather by readings in the ‘Children’s Hour’ and at other times than by way of lessons. I know of nothing so good as the old-fashioned World at Home (for lessons) for children between six and seven. As they hear, they wonder, admire, imagine, and can even ‘play at’ a hundred situations. The first ideas of geography, the lessons on place, which should make a child observant of local geography, of the features of his own neighbourhood, its heights and hollows, and level lands, its streams and ponds, should be gained, as we have seen, out of doors, and should prepare him for a certain amount of generalisation—that is, he should be able to discover definitions of river, island, lake, and so on, and should make these for himself in a tray of sand, or draw them on the blackboard.

Definitions.—​But definitions should come in the way of recording his experiences. Before he is taught what a river is, he must have watched a stream and observed that it flows; and so on with the rest.

Children easily simulate knowledge, and at this point the teacher will have to be careful that nothing which the child receives is mere verbiage, but that every generalisation is worked out somewhat in this way:—The child observes a fact, as, for example, a wide stretch of flat ground; the teacher amplifies. He reads in his book about Pampas, the flat countries of the north-west of Europe, the Holland of our own eastern coast, and, by degrees, he is prepared to receive the idea of a plain, and to show it on his tray of sand.

Fundamental Ideas.—​By the time he is seven, or before, he finds himself in need of further knowledge. He has read of hot countries and cold countries, has observed the seasons and the rising and setting of the sun, has said to himself—