I have been advised to dismiss twenty such children, rather than retain them by the above means; but if there be more joy in heaven over one sinner that repenteth, than over ninety and nine just persons who need no repentance, ought not such a feeling to be encouraged on earth, particularly when it can be done by means that are not injurious to the orderly, but, on the contrary, productive of the best effects? The child just mentioned afterwards went into the National School, with several others who had been nearly as bad as himself, but they scarcely ever failed to come and see me when they had a half holiday, and the master of the school told me that not one of them had ever been absent without leave, and that he had no fault to find with them. I have further to observe that the moment I perceived a bad effect produced by any method of punishment, it was relinquished. But I feel it my duty here to caution the reader against the too frequent practice of many to object. It may cost a man many years to find out what may be desirable and workable; but to become an objector requires no thought, accordingly the most thoughtless are generally the greatest objectors.
I believe that there was not a child in the school who would not have been delightedto carry the broom, if I had called it play; the other children might have laughed as long as they pleased, for he would have laughed as heartily as any of them, and as soon as he had done, I should have had a dozen applicants, with "Please, sir, may I? please, sir, may I?" but it was called apunishment, and hence I had no applications whatever; they all dreaded it as much as they would a flogging. I am aware that this plan of punishment may appear ridiculous, and perhaps it would be so to use it for older children; but with such young children I have found it to answer well, and therefore I have no wish to dispense with it. I would, however, have care taken not to encourage the children to ridicule each other while undergoing this or any other punishment, except in extraordinary cases, such as the one I have mentioned; on the contrary, we should encourage them to sympathize with and comfort a child, as soon as the punishment is over, and I can truly add, that I do not recollect a single instance when any child has been undergoing the broom punishment, but some of the others have come, and attempted to beg him off, with "Please, sir, may he sit down now?" and when asked the reason why they wished the little delinquent to be forgiven, they have answered, "May be, sir, he will be a good boy." Their request has been complied with, and the culprit forgiven; and what have I seen follow? Why, that which has taught me an important lesson, and convinced me thatchildren can operate on each other's minds, and be the means of producing very often better effects than adult people can. I have seen them clasp the child round the neck, take him by the hand, lead him about the play-ground, comfort him in every possible way, wipe his eyes with their pinafores, and ask him if he was not sorry for what he had done. The answer has been, "Yes;" and they have flown to me with, "Master, he says he is sorry for it, and that he will not do it again." In short, they have done that which I could not do—they have so won the child over by kindness, that it has caused the offender not only to be fond of them, but equally as fond of his master and the school. To these things I attribute the reclaiming of the children I have mentioned, and so far from punishment being productive of the "worst effects," I have found it productive of the best.
The ill effects of expelling children as incorrigible may be seen in the case of Hartley, who was executed some years back. He confessed before his execution that he had been concerned in several murders, and upwards of two hundred burglaries; and by the newspaper account we learn that he was dismissed from school at nine years of age, there being no school master who would be troubled with him, when, finding himself at liberty, he immediately became a robber. "Hartley's father" (the account proceeds), "formerly kept the Sir John Falstaff inn at Hull in Yorkshire; he was put to school in that neighbourhood, but his conduct at school was so marked with depravity, and so continually did he play the truant, that he was dismissed as unmanageable. He then, although only nine years of age, began with pilfering and robbing gardens and orchards, till his friends were obliged to send him to sea. He soon contrived to run away from the ship in which he had been placed, and having regained the land, pursued his old habits, and got connected with many of the principal thieves in London, with whom he commenced business regularly as a house-breaker, which was almost always his line of robbery."
Should not every means have been resorted to with this child before proceeding to the dangerous mode of expulsion? for it is not the whole who need a physician, but those who are sick; and I strongly suspect that if judicious punishment had been resorted to, it would have had the desired effect. I can only say that there never was a child expelled from the infant school under my care as incorrigible.
In conclusion, I have to observe, that the broom punishment is only for extraordinary occasions, and I think we are justified in having recourse to any means that are consistent with duty and humanity, in preference to turning a child out into the wide world.
Of all the difficulties I ever had to encounter, to legislate for rewards and punishments, gave me the most trouble. How often have I seen one child laugh at that which would make another child cry. If any department in teaching requires knowledge of character more than another it is this. Many a fine child's spirits are broken through the ignorance of teachers and parents in this particular; but for me to lay downinvariable rulesto manageevery child, would be like a person undertaking to describe a voyage to the moon. Every person's own good sense must decide for them according to character and circumstances; and as to rewards, the same discrimination must be used. One child will set much value on a little book, whilst another will destroy it in a day; and though the book might be worth the sixpence, a half-penny worth of whattheycall good stuff would be much more valuable. I have had more business done sometimes for a plum than for a sixpenny book. It is never necessary to give the child badges ofdistinction, and to allow it as many orders and degrees as an Austrian field-marshal. Crosses at the button holes, and bits of ribbon on the shoulders are unnecessary; they throw an apple of discord between the young creatures, who have sense enough to see that these things are frequently given away with a wonderous lack of discrimination, and sometimes to please parents more than reward merit. A carraway comfit put into the mouth of an infant will do more good than all the badges of distinction that I have mentioned, as a reward; but with respect to punishment, more will be said on it in my larger work, when we come to treat of National Education. Each creation of the most High is truly wonderful, and worthy of our constant study. We may learn lessons of the truest wisdom from the meanest leaf or insect, if we would regard it as one of His works. But how much more may be learnt, and what an amount of useful instruction may be gained, by a study of the finite mind, the highest work in creation. Many have turned their attention to minerals, plants, and animals, and thus added to our stores of knowledge. If equal attention had been paid to the young mind, to mark the gradual germination of its intellectual and moral powers, how much more accurate would our knowledge be of the proper methods of dealing with it both in instruction, direction, and punishment. Thus to study it has been the aim of my life, and I have made observations on thousands of children. When this great and living book is more constantly read, the contents of this humble volume may have a better chance of being appreciated; and the utter absurdity of many things palmed upon the public for the education of infants made glaringly manifest.
Means for conveying instruction—Method of teaching the alphabet in connection with objects—Spelling—Reading—Developing lessons—Reading lessons in Natural History—The Arithmeticon—Brass letters—Their uses.
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"Without things, words, accumulated by misery in the memory, had far better die than drag out a miserable existence in the dark. Without words, theirs stay and support, things unaccountably disappear out of the storehouse, and may be lost for ever; but binda thing with a word, a strong link, stronger than any steel, and softer than any silk, and the captive remains for ever happy in its bright prison-house."—Wilson.
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The senses of children having revealed every object in its true light, they next desire to know its name, and then express their perceptions in words. This you have to gratify, and from the time you tell them the name of an object, it is the representative of the thing in the mind of the child; if the object be not present, but you mention the name, this suggests it to the infant mind. Had this been more frequently thought of by instructors, we should have found them less eager to make the child acquainted with the names of things of which it has no knowledge or perception. Sounds and signs which give rise to no idea in the mind, because the child has never seen or known the things represented, are of no use, and can only burden the memory. It is, therefore, the object of our system to give the children a knowledge of things, and then a knowledge of the words which represent those things. These remarks not only apply to the names of visible things, but more particularly to those which are abstract. If I would say, shew a childa horse, before you tell it the name of the animal, still more would I urge it on the teacher to let a child see what love, kindness, religion, &c. are, before it is told what names to designate those principles by. If our ignorance as to material things be the result of instructing the children in names, instead of enabling them to become acquainted with things, so, on the other hand, I believe we may account, in the same way to some extent, forvirtuebeing so frequently a mere word, an empty sound, amongst men, instead of an active principle.
Our next endeavour is to teach the children to express their thoughts upon things; and if they are not checked by injudicious treatment, they will have some on every subject. We first teach them to expresstheir notions, we then tell them ours, and truth will prevail even in the minds of children. On this plan, it will operate by its own strength, not by the power of coercion, which renders even truth disagreeable and repulsive; the children will adopt it from choice in preference to error, and it will be firmly established in their minds.
It will no doubt be perceived, that for the promotion of the course here recommended, it will be advisable to connect with ouralphabetical and reading lessons, as much information as we possibly can. By so doing, the tedium of the task to the child will be considerably lessened, as well as much knowledge attained. The means of doing this in a variety of ways will, no doubt, suggest themselves to the intelligent teacher; but as an illustration of what we mean, the following conversational plan may not be useless.
We have twenty-six cards, and each card has on it one letter of the alphabet, and some object in nature; the first, for instance, has the letter A on the top, and an apple painted on the bottom. The children are desired to go into the gallery, which is formed of seats, one above the other, at one end of the school. The master places himself before the children, so that they can see him, and he them, and being thus situated, proceeds in the following manner:—
Q. Where am I? A. Opposite to us. Q. What is on the right side of me? A. A lady. Q. What is on the left side of me? A. A chair. Q. What is before me? A. A desk. Q. Who is before me? A. We, children. Q. What do I hold up in my hand? A. A letter A.Q. What word begins with A? A. Apple. Q. Which hand do I hold it up with? A. With the right hand. Q. Spell apple.[A] A. A-p-p-l-e. Q. How is an apple produced? A. It grows on a tree. Q. What part of the tree is in the ground? A. The root. Q. What is that which comes out of the ground? A. The stem. Q. When the stem grows up straight, what would you call its position? A. Perpendicular. Q. What are on the stem? A. Branches. Q. What are on the branches? A. Leaves. Q. Of what colour are they? A. Green. Q. Is there any thing else beside leaves on the branches? A. Yes, apples. Q. What was it before it became an apple? A. Blossom. Q. What part of the blossom becomes fruit? A. The inside. Q. What becomes of the leaves of the blossom? A. They fall off the tree. Q. What was it before it became a blossom? A. A bud. Q. What caused the buds to become larger, and produce leaves and blossom? A. The sap. Q. What is sap? A. A juice. Q. How can the sap make the buds larger? A. It comes out of the root, and goes up the stem. Q. What next? A. Through the branches into the buds. Q. What do the buds produce? A. Some buds produce leaves, some blossoms, and some a shoot. Q. What do you mean by a shoot? A. A young branch, which is green at first, but becomes hard by age. Q. What part becomes hard first? A. The bottom.
[Footnote A: It is not supposed that all or many of the children will be able to spell this or many of the subsequent words, or give such answers as we have put down. Butsomeamong the older or more acute of them will soon be able to do so, and thus become instructors to the rest. It may be proper to mention also that the information in Natural History, &c. &c., displayed in some of the answers, is the result of the instructions in Natural History which the children simultaneously receive, and which is spoken of in a subsequent chapter. Mr. Golt's simple arrangement of the Alphabet I much approve of, and no doubt it will come into general use.]
Q. What is this? A. The letter B—the first letter in baker, butter, bacon, brewer, button, bell, &c., &e. [The teacher can take any of these names he pleases, for instance, the first:] Children, let me hear you spell baker. A. B-a-k-e-r. Q. What is a baker? A. A man who makes bread. Q. What is bread made of? A. It is made of flour, water, yeast, and a little salt. Q. What is flour made of? A. Wheat. Q. How is it made? A. Ground to powder in a mill. Q. What makes the mill go round? A. The wind, if it is a windmill. Q. Are there any other kinds of mills? A. Yes; mills that go by water, mills that are drawn round by horses, and mills that go by steam. Q. When the flour and water and yeast are mixed together, what does the baker do? A. Bake them in an oven. Q. What is the use of bread? A. For children to eat. Q. Who causes the corn to grow? A. Almighty God.
Q. What is this? A. It is letter C, the first letter in cow, c-o-w, and cat, &c. Q. What is the use of the cow? A. The cow gives us milk to put into the tea. Q. Is milk used for any other purpose besides putting it into tea? A. Yes; it is used to put into puddings, and for many other things. Q. Name some of the other things? A. It is used to make butter and cheese. Q. What part of it is made into butter? A. The cream which swims at the top of the milk. Q. How is it made into butter? A. It is put into a thing called a churn, in the shape of a barrel. Q. What is done next? A. The churn is turned round by means of a handle, and the motion turns the cream into butter. Q. What is the use of butter? A. To put on bread, and to put into pie-crust, and many other nice things. Q. Of what colour is butter? A. It is generally yellow. A. Are there any other things made of milk? A. Yes, many things; but the principal one is cheese. Q. How is cheese made? A. The milk is turned into curds and whey, which is done by putting a liquid into it called rennet. Q. What part of the curd and whey is made into cheese? A. The curd, which is put into a press; and when it has been in the press a few days it becomes cheese. Q. Is the flesh of the cow useful? A. Yes; it is eaten, and is called beef; and the flesh of the young calf is called veal. Q. Is the skin of the cow or calf of any use? A. Yes; the skin of the cow or calf of any use? A. Yes; the skin of the cow is manufactured into leather for the soles of shoes. Q. What is made with the calf skin? A. The top of the shoe, which is called the upper-leather. Q. Are there any other parts of the cow that are useful? A. Yes; the horns, which are made into combs, handles of knives, forks, and other things. Q. What is made of the hoofs that come off the cow's feet? A. Glue, to join boards together. Q. Who made the cow? A. Almighty God.
Q. What is this? A. Letter D, the first letter it dog, dove, draper, &c. Q. What is the use of the dog, A. To guard the house and keep thieves away. Q. How can a dog guard the house and keep thieves away? A. By barking to wake the persons who live in the house. Q. Is the dog of any other use? A. Yes; to draw under a truck. D. Does he do as his master bids him? A. Yes; and knows his master from any other person. Q. Is the dog a faithful animal? A. Yes, very faithful; he has been known to die of grief for the loss of his master. Q. Can you mention an instance of the dog's faithfulness? A. Yes; a dog waited at the gates of the Fleet prison for hours every day for nearly two years, because his master was confined in the prison. Q. Can you mention another instance of the dog's faithfulness? A. Yes; a dog lay down on his master's grave in a churchyard in London for many weeks. Q. How did the dog get food? A. The people who lived near noticed him, and brought him victuals. Q. Did the people do any thing besides giving him victuals A. Yes; they made a house for him for fear he should die with wet and cold. Q. How long did he stay there? A. Until the people took him away, because he howled dreadfully when the organ played on Sundays. Q. Is it right to beat a dog? A. No; it is very wrong to use any animal ill, because we do not like to be beaten ourselves. Q. Did Almighty God make the dog? A. Yes; and every thing else that has life.
Q. What letter is this? A. E, the first letter in egg. Q. What is the use of an egg? A. It is useful for many purposes; to put into puddings, and to eat by itself. Q. Should country children keep an egg if they find it in the hedge? A. No, it is thieving; they should find out the owner and take it home. Q. Do children ever throw stones at the fowls? A. Yes; but they are mischievous children, and perhaps do not go to school. Q. What ought children to learn by going to school? A. To be kind and good to every body, and every thing that has life.
Q. What letter is this? A. Letter F, the first letter in frying-pan, father, &c. Q. Let me hear you spell frying-pan. A. F-r-y-i-n-g-p-a-n. Q. What is the use of the frying-pan? A. To fry meat and pan-cakes. Q. Spell me the names of the different kinds of meat. A. B-e-e-f, p-o-r-k, m-u-t-t-o-n, l-a-m-b, h-a-m, &c. Q. Of what shape are frying-pans? A. Some circular, and some are like an ellipsis.[A] Q. Are there any other utensils into which meat is put that are circular? A. Yes, please, sir, my mother has some circular plates; and, please, sir, my mother has some elliptical dishes. Q. Any thing besides? A. Yes, please, sir, my mother has a circular table; and, please, sir, my mother has a rectangular one, and it is made of deal.
[Footnote A: It may possibly strike some of my readers as strange that a geometrical question should be put in a conversation on the alphabet, but it should be remembered that, according to the Infant School system,languageis not taught exclusively, but in connection withnumberandform;—questions like the above, therefore are calculated to excite their memories, and induce an application of their geometrical knowledge.]
Q. What letter is this? A. Letter G, the first letter in goat, good, girl, &c. Q. Spell goat. A. G-o-a-t. Q. What is the use of the goat'? A. In some countries people drink the goat's milk; and the skin is useful to make the upper-leather of shoes. Q. Are goats fond of going into the valleys and low places? A. No; they are fond of going up hills and high places. Q. If a goat is coming down a hill which has only one narrow path merely wide enough for one goat to walk on without falling down, and another goat is coming up the same path, what do they do? A. The goat that is coming up lies down and lets the other goat walk over him. Q. Why does not one of the goats turn round and go back again? A. Because there would not be room, and the one which should try to turn round would fall down and be killed.
Q. What letter is this? A. Letter H, the first letter in horse, house, &c. Q. What is the use of the horse? A. To draw carts, coaches, stages, waggons, fire-engines, &c. Q. Spell horse, and cart, and coach. A. H-o-r-s-e, c-a-r-t, c-o-a-c-h. Q. What is the difference between a cart and coach? A. A cart has two wheels, and a coach has four. Q. Tell me some other difference. A. The horses in a cart go before each other, but the horses in a coach go side by side. Q. What is the use of a fire-engine? A. To put the fire out when the house is on fire. Q. Is it right for children to play with the fire? A. No, very wrong; as many children are burnt to death, and many houses burnt down from it. Q. Should the horse be cruelly used? A. No; he should be kindly treated, as he is the most useful animal we have. Q. Who created him? A. Almighty God.
Q. What letter is this? A. Letter I, the first letter in iron, idleness, &c. Q. Spell iron. A. I-r-o-n. Q. What is the use of an iron? A. To iron the clothes after they are washed, and to make them smooth. Q. How do they iron the clothes? A. Make the iron hot, and then work it backwards and forwards on the clothes. Q. Should little children come with clean clothes to school? A. Yes; and clean hands and faces too. Q. Is not iron used for other purposes? A. Oh, yes; for a great many things, as knives, forks, &c.
Q. What is this letter? A. J, the first letter in jug, John, &c. Q. What is the use of the jug? A. To hold water, or beer, or any other liquid. Q. What is a jug made of? A. Of clay, which is worked round into the shape of a jug, and then burnt, and that hardens it. Q. Should children be careful when they are carrying a jug? A. Yes; or else they will let it fall and break it. Q. Then it is necessary for children to be careful? A. Yes, every body should be careful.
Q. What letter is this? A. Letter K, the first letter in kite, &c. Q. What is the use of the kite? A. For little children to fly. Please, sir, my big brother has got a kite. Q. What does your brother do with his kite? A. Please, sir, he goes into the fields when he has got time, and flies it. Q. How does he fly it? A. Please, sir, he has got a long string, which he fixes to another called a loop, and then he unwinds the string, and gets some boy to hold it up. Q. What then? A. Please, sir, then he runs against the wind, and the kite goes up. Q. What is the use of the tail of the kite? A. Please, sir, it will not fly without a tail. Q. Why not? A. Please, sir, it goes round and round without a tail, and comes down. Q. Then what do you suppose is the use of the tail? Please, sir, I don't know. Another child will probably supply the answer. Please, sir, to balance it.
Q. What letter is this? A. Letter L, the first letter in lion, &c. Q. Spell lion. A. L-i-o-n. Q. What is the size of a full grown lion? A. A full grown lion stands four feet and a half high, and is eight feet long. Q. How high do you stand? A. Please, sir, some of us stand two feet, and none of us above three. Q. Has the lion any particular character among beasts? A. Yes, he is called the king of beasts on account of his great strength. Q. When he seizes his prey, how far can he leap? A. To the distance of twenty feet. Q. Describe some other particulars concerning the lion. A. The lion has a shaggy mane, which the lioness has not. Q. What other particulars? A. The lion's roar is so loud that other animals run away when they hear it. Q. Where are lions found? A. In most hot countries: the largest are found in Asia and Africa.
Q. What letter is this? A. Letter M, the first letter in Monday, mouse, &c. Q. What is the use of the mouse? A. To make the servants diligent and put the things out of the way. Q. How can mice make servants diligent? A. If people do not put their candles in a proper place the mice will gnaw them. Q. Are mice of any other service? A. Please, sir, if the mice did not make a smell, some people would never clean their cupboards out.[A]
[Footnote A: This answer was given by a child four years old; and immediately afterwards another child called out, "Please, sir, if it were not for bugs, some people would not clean their bedsteads."]
Q. What letter is this? A. Letter N, the first letter in nut, &c. Q. What is a nut? A. A thing that is hard, and it grows on a tree. Q. What shape is it? A. Something in the shape of a marble. Q. How can it be eaten, if it is like a marble? A. Please, air, it is the kernel that we eat. Q. flow are nuts produced? A. They grow on trees.
Q. What letter is this? A. Letter O, the first letter in orange. Q. Of what colour is an orange? A. An orange is green at first, but afterwards becomes of a colour called orange-red. Q. Do they grow in the ground like potatoes? A. No, they grow on trees like apples. Q. Can you tell me anything in the shape of an orange? A. Yes, the earth on which we live is nearly of that shape. Q. On what part of the earth do we live? A. The surface. Q. What do you mean by the surface? A. The outside. Q. Who formed the earth, and preserves it in its proper motions? A. Almighty God.
Q. What letter is this? A. Letter P, the first letter in pig, plum-pudding, &c. Q. What is the use of the pig? A. Its flesh is eaten, and is called pork. Q. What is the use of the hair or bristles? A. To make brushes or brooms. Q. What is the use of a brush? A. Some brushes are to brush the clothes, and others to brush the dirt out of the corners of the room. Q. Does a good servant ever leave the dirt in the corners? A. No, never; a good servant or any clean little girl would be ashamed of it.
Q. What letter is this? A. Letter Q, the first letter in quill, &c. Q. How are quills produced? A. From the wings of geese and other large birds. Q. What is the use of the quill? A. To form into pens and many other things. Q. What is the use of the pen? A. To dip into ink and write with it. Q. What do you write upon? A. Paper. Q. What is paper made of? A. Rags.
Q. What letter is this? A. Letter R, the first letter in rabbit, &c. Q. What is the use of the rabbit? A. The flesh of the rabbit is eaten, and is very nice. Q. What does the rabbit eat? A. Corn, grass, cabbage-leaves, and many different herbs. Q. What is the use of the skin? A. To make hats, and to trim boys' caps. Q. Are they very numerous? A. They are to be found in almost all countries.
Q. What is this? A. Letter S, the first letter in shoe, &c. Q. What is the use of shoes? A. To keep the feet warm and dry. Q. Should children walk in the mud or in the kennel? A. No, because that would spoil the shoes, and wear them out too soon. Q. And why should little children be careful not to wear them out any more than they can help? A. Because our parents must work harder to buy us more.
Q. What letter is this? A. Letter T, the first letter in tea-kettle. Q. What are tea-kettles made of? A. Some are made of tin, and some of copper, and some of iron. Q. Why are they not made of wood? A. Because the wood would burn. Q. What thing is that at the top? A. The handle. Q. What is underneath the handle? A. The lid. Q. What is in the front of it? A. The spout. Q. What is the use of the spout? A. For the water to come out. Q. What is the use of the handle? A. To take hold of. Q. Why do they not take hold of the spout? A. Because it is the wrong way.
Q. What letter is this? A. Letter U, the first letter in umbrella, &c. Q. Is letter U a vowel or consonant? A. A vowel. Q. What is the use of the umbrella? A. To keep the rain off any body. Q. What are umbrellas made of? A. Some of silk and some of cotton. Q. Which are the best? A. Those that are made of silk. Q. Is there any thing else in an umbrella? A. Yes; whalebone. Q. Where does whalebone come from? A. Out of a large fish called a whale. Q. Who made the whale? A. Almighty God.
Q. What letter is this? A. Letter V, the first letter in vine, &c. Q. What is a vine? A. A thing that grows against the wall and produces grapes. Q. Why does it not grow like another tree, and support its own weight? A. Because it is not strong enough. Q. Then it cannot grow and become fruitful in this country without man's assistance? A. No; and, please, sir, we cannot grow and become fruitful without the assistance of Almighty God.[A]
[Footnote A: This answer was given by a child five-years of age.]
Q. What letter is this? A. It is Letter W, the first letter in wheel. Q. Spell wheel. A. W-h-e-e-l. Q. What is the use of wheels? A. To make it easier for horses to draw. Q. How do you know that? A. Please, sir, I had a little cart full of stones, and the wheel came off; and, please, sir, I found it much harder to draw. Q. Then if it was not for wheels, the horses could not draw so great a weight? A. No, and, please, sir, people could not go into the country so quick as they do. Q. What trade do they call the persons that make wheels? A. Wheel-wrights.
Q. What letter is this? A. Letter X, the first letter in Xenophon, a man's name. Q. What was the particular character of Xenophon? A. He was very courageous. Q. What does courageous mean? A. To be afraid to do harm, but not to be afraid to do good, or anything that is right. Q. What is the greatest courage? A. To conquer our own bad passions and bad inclinations. Q. Is he a courageous man that can conquer his bad passions? A. Yes; because they are the most difficult to conquer.
Q. What letter is this? A. Letter Y, the first letter in yoke, &c. Q. Is it a vowel or consonant? A. When it begins a word it is called a consonant, but if not, a vowel. Q. What is a yoke? A. Please, sir, what the milk people carry the milk pails on. Q. What is the use of the yoke? A. To enable the people to carry the milk easier.
Q. What letter is this? A. Letter Z, the first letter in Zealander. Q.What is a Zealander? A. A man that lives on an island in the SouthernOcean, called Zealand. Q. How do they live? A. Principally by huntingand fishing. Q. What is hunting? A. Following animals to catch them.Q. Who made all the animals? A. Almighty God.
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The method above described is adapted to the large room, where the children may be taught all together; but it is necessary to change the scene even in this; for however novel and pleasing a thing may be at first, if it be not managed with prudence it will soon lose its effect. It is here to be observed, that the mode of teaching described, is not practised every day, but only twice or thrice a week. The children will take care that the teacher does not altogether forget to teach them in any way that they have been accustomed to. After letting the above plan lie by for a day or two, some of the children will come to the teacher, and say, "Please, sir, may we say the picture alphabet up in the gallery?" If the other children overhear the question, it will go through the school like lightning: "Oh yes—yes—yes, sir, if you please, do let us say the letters in the gallery." Thus a desire is created in the children's minds, and it is then especially that they may be taught with good effect.
Another planwhich we adopt, is in practice almost every day; but it is better adapted to what is called the class-room: we have the alphabet printed in large letters, both in Roman and Italic characters, on one sheet of paper: this paper is pasted on a board, or on pasteboard, and placed against the wall; the whole class then stand around it, but instead of one of the monitors pointing to the letters, the master or mistress does it; so that the children not only obtain instruction from each other, but every child has a lesson from the master or mistress twice every day.
Before they go to the reading lessons, they have the sounds of all the words in spelling: thus the sound of a—ball, call, fall, wall; then the reading-lesson is full of words of the same sound. In like manner they proceed with other letters, as i—the sound of which they learn from such words as five, drive, strive, until, by a series of lessons, they become acquainted with all the sounds; and are able to read any common book.
I have observed in some instances the most deplorable laxity in this particular. Cases have occurred in which children have been for two years at school, and yet scarcely knew the whole alphabet; and I have known others to be four years in an infant school, without being able to read. I hesitate not to say that the fault rests exclusively with the teachers, who, finding this department of their work more troublesome than others which are attractive to visitors, have sometimes neglected it, and even thrown it entirely aside, affirming that reading is not a part of the infant system at all! Such a declaration is, however, only to be accounted for from the most lamentable ignorance, preverseness, or both. Had it been true, we should not have had a single infant school in Scotland, and throughout that country the children read delightfully.
The great importance of full instruction in reading will be apparent from the following considerations.
1. If the parents do not find the children learn to read, they will discontinue sending them. This they consider essential, and nothing else will be deemed by them an adequate substitute.
2. Children cannot make desirable progress in other schools which they may enter, unless they obtain an ability to read at least simple lessons.
3. Neglect in this respect impedes the progress of the infant system. Such an obstacle ought not to exist, and should at once be removed.
4. In manufacturing districts children go to work very soon; and if they are not able to read before, there is reason to fear they will not afterwards acquire the power; but if they have this, Sunday schools may supply other deficiencies.
5. Want of ability to read prevents, of course, a knowledge of the Word of God.
To prevent this evil, I have arranged a series, denominated "Developing Lessons," the great object of which is to induce children to think and reflect on what they see. They are thus formed: at the top is a coloured picture, or series of coloured pictures of insects, quadrupeds, and general objects. For instance, there is one containing the poplar, hawk-moth, and wasp. The lesson is as follows: "The wasp can sting, and fly as well as the moth, which does not sting. I hope no wasp will sting me; he is small, but the hawk-moth is large. The moth eats leaves, but the wasp loves sweet things, and makes a round nest. If boys take the nest they may be stung: the fish like the wasp-grubs." On this, questions are proposed: Which stings? Which is small and which large? Which eats leaves? Which makes a round nest? &c. &c.
To take another instance. There is a figure of an Italian, to which is appended the following: "The Italian has got a flask of oil and a fish in his hand, and something else in his hand which the little child who reads this must find out. Any child can tell who makes use of the sense of seeing. In Italy they make a good deal of wine; big grapes grow there that they make it with. Italians can sing very well, and so can little children when they are taught." Questions are likewise proposed on this, as before.
Of these lessons, however, there is a great variety. All schools should possess them: they will effectually prevent the evil alluded to, by checking the apathy of children in learning to read, and calling the teacher's powers into full exercise. They are equally adapted to spelling and reading.
I will give several specimens of reading lessons in natural history, each of which has a large, well-engraved and coloured plate at the top, copied from nature.
How glad some poor children would be if they could read about the eagle. He is a big strong bird, and has such great wings, and such long sharp claws, that he can dig them into the lamb, hare, rabbit, and other animals, and thus fly away with them to feed his young ones, and to eat them himself. Eagles make such a large nest on the side of some high rock, where nobody can get at it. There used to be eagles in Wales, and there are some now in Scotland, but very few in England, for they do not like to be where there are many people.The Almighty gave man dominion over the birds of the air, as well as over the other animals, and as he gave man power tothink, if the eagles become troublesome, men catch them, though they can fly so high; and as the eagle knows this, he likes to keep out of our way, and go into parts of the world where there are not so many people. There are many sorts of eagles: the black eagle, the sea eagle, the bald eagle, and others. They have all strong bills bent down in front, and strong claws. This bird is mentioned in the Bible.
Questions are proposed after this is read, and thus the examination proceeds:—Q. What is that? A. An eagle. Q. What sort of a bird is he? A. He is big and strong. Q. What are those? A. His feathers. Q. What else are they called? A. His plumage. Q. Is the eagle a small bird? A. No, very large. Q. Are his claws long and sharp? A. Yes. Q. What animals could he carry away? A. A lamb, a hare, a rabbit, or other small animals. Q. What does he do with those? A. Feed his young ones. Q. Where does the eagle make his nest? A. On the side of some rock. Q. Why does he make it there? A. That no one may get at it. Q. Used there to be eagles in Wales? A. Yes. Q. Where are there a few still? A. In England, Scotland, and Ireland. Q. Why are they not as plentiful as they were? A. Because they do not like to be where many men live. Q. Did the Almighty give man dominion over the birds of the air? A. Yes. Q. What other power did he give man? A. Power to think. Q. As men can think, when the eagles became troublesome, what did they do? A. They caught them. Q. And what did the eagles that were not caught do? A. They went to places where men were not so plenty. Q. Are, there many different kinds of eagles? A. Yes. Q. Name some. A. The black eagle, the bald eagle, the sea eagle, and others.
The vulture is like the eagle in size, and some of its habits; but it is so very different from it in many ways, that there is little danger of confusing the two together: the greatest distinction between them is, that the head of the vulture is either quite naked, or covered only with a short down, while the eagle's is well feathered. This is the chief difference in appearance, but in their habits there is a much greater. Instead of flying over hills and valleys in pursuit of living game, the vultures only search for dead carcasses, which they prefer, although they may have been a long time dead, and therefore very bad, and smelling very offensively. They generally live in very warm countries, and are useful in clearing away those dead carcasses which, but for them, would cause many dreadful diseases. In some countries, indeed, on account of this, the inhabitants will not allow any one to injure them, and they are called for this reason scavengers, which means that they do the business for which scavengers are employed. Vultures are very greedy and ravenous; they will often eat so much that they are not able to move or fly, but sit quite stupidly and insensible. One of them will often, at a single meal, devour the entire body of an albatross (bones and all), which is a bird nearly as large as the vulture itself. They will smell a dead carcass at a very great distance, and will soon surround and devour it.
Vultures lay two eggs at a time and only once a year: they build their nests on the same kind of places as eagles do, so that it is very hard to find them.
What does the vulture resemble the eagle in? A. In size and in some of its habits. Q. In what does it differ from the eagle? A. In having a neck and head either naked or covered with short down. Q. What is the difference in the manner in which they feed? A. The eagle seeks its food over hill and valley, and lives entirely on prey which he takes alive, while the vulture seeks out dead and putrid carcasses. Q. For what reason do you suppose is the vulture's neck not covered with feathers as the eagle's is? A. If they had feathers on their necks, like eagles and hawks, they would soon become clotted with blood. Q. Why would this happen? A. Because they are continually plunging their necks into decayed flesh and bloody carcasses. Q. How do vultures sit? A. In a dull, mopeing manner. Q. Where do they generally sit? A. On tall dead trees. Q. Do they continue thus long? A. Yes, for several hours. Q. What is the cause of their thus sitting so dull and inactive? A. The great quantity of food they have eaten. Q. Is there any description of vulture forming an exception to the general character of those birds? A. Yes, that particular kind called the snake eater. Q. Where is this bird a native of? A. Of Africa. Q. Why is it called the snake eater? A. On account of its singular manner of destroying serpents, on which it feeds. Q. Describe the manner in which this bird kills its prey. A. He waits until the serpent raises its head, and then strikes him with his wing, and repeats the blow until the serpent is killed. Q. What do the natives of Asia and Africa call the vulture? A. The scavenger. Q. Why? A. Because they are so useful in eating dead carcasses. Q. How is this useful? A. It clears the ground of them; otherwise, in those warm places, they would be the cause of much disease. Q. What does this shew us? A. That the good God has created nothing without its use. Q. What is the largest bird of the vulture kind? A. The great condor of South America. Q. What does its wing often measure from tip to tip? A. Twelve feet when spread out. Q. How do the natives of South America often catch the vulture? A. The dead carcass of a cow or horse is set for a bait, on which they feed so ravenously that they become stupid, and are easily taken.
I hope you will not put your dirty hands on this picture of the crocodile. The live ones have hard scales on their backs, and such a many teeth, that they could bite a man's leg off; but there are none in our land, only young ones that sailors bring home with them. The crocodile can run fast; those are best off who are out of his way. He lives by the water; he goes much in it; and he can swim well. Young ones come out of eggs, which the old ones lay in the sand. Some beasts eat the eggs, or else there would be too many crocodiles. The crocodile can run fast if he runs straight, and those who wish to get out of his way run zigzag, and he takes some time to turn; the poor black men know this, and can get out of his way; but some of them can fight and kill him on the land or in the water. I think the crocodile is mentioned inScripture. Ask your teacher what Scripture means. When you learn geography you will know where many of the places are that are mentioned in the Bible, and you will see where the river Nile is. There are such a many crocodiles on the banks of that river that the people are afraid to go alone. What a many wonderful animals our great Creator has made! How humble and thankful we should be to see so many great wonders!
Q. What have crocodiles on their backs? A. Hard scales. Q. Have they many teeth? A. Yes, a great many. Q. Could they bite off a man's leg? A. They could. Q. Are there any in our country? A. None wild, but a few that sailors bring in ships. Q. Can the crocodile run fast? A. Yes. Q. Where does he live? A. In the water. Q. What do their young ones come out of? A. Out of eggs, which the old one lays in the sand. Q. How do people run that wish to get out of the crocodile's way? A. Zigzag, like the waved line in our lesson. Q. What do some men do? A. Fight and kill them in the water. Q. Where do most of those animals live? A. In the river Nile. Q. Where is this river? A. In Egypt.
The spelling lessons contain words capable of explanation, such as white, black, round, square; others are classed as fleet, ship, brig, sloop, &c.; and others are in contrast, as hot, cold, dark, light, wet, dry, &c.
In this department we use the tablet placed beneath the arithmeticon, the invention and improvement of which are described in the volume entitled "Early Discipline Illustrated, or the Infant System Successful and Progressing." A clear idea of the whole apparatus is given by the wood-cut on the next page, and it ought certainly to be found in every infant school. The sense of sight is then brought into full action to aid the mind, and that with results which would not easily be conceived. We shall take another opportunity of explaining the use of the upper part of the apparatus, the lower demanding our present attention.
[Illustration]
To use thetablet, let the followings things be observed. It is supposed the children know well there are twenty-six letters in the alphabet; that twenty are called consonants, and that six are vowels. We take first one perpendicular row of letters in the figure. Now point to D, and say, What is that'? and the answer will be, D. Ask, Is it a vowel or consonant, and they will reply, A consonant; but ask, Why do you know it is D, and the answer will probably be, It is so because it is. Hide the circular part of the letter, and ask, What is the position of the other part, and they will say, having previously learnt the elements of form which will shortly be explained, A perpendicular line; hide that, and ask them what the other part is, telling them to bend one of their fore-fingers in the same form, and they will say, A curved line. If they are then asked how they may know it is D, they will say, Because it is made of a perpendicular line and has a curved line behind. Further information may then be given. Turn the D letter up thus [Illustration: The character D turned on its side], and say, I want to teach you the difference between concave and convex: the under part of the curve is concave and the upper part of it is convex. Then say, I shall now take the letter away, and wish you to shew me concave and convex on one of your fingers; when they will bend the forefinger and point them both out on it. Go on with the other letters in the same way: shew them the vowels after the consonants and analyze each one. For example, A is formed of two inclined lines and a horizontal line to join them in the centre; and the top of that letter is an acute angle, and were a line placed at the bottom it would be a triangle. A brass letter may be moreover shewn to be a substance: its properties may be described as hard, smooth, bright, &c., and its coming from the mineral kingdom may be noticed, and thus the instruction may be indefinitely varied.
Thepowerof letters may then be pointed out. Ask them to spell M R, and they will give you the sound of R, or something like it, and so in reference to other letters. But place the A against the M as it appears in the figure, and you may teach them to say A, M, AM; and thus all the way down the left side of the row of consonants. If then you carry the vowel down on the other side of them, you will change the lesson, and by such means go on almostad infinitum. Double rows of consonants may be placed with a vowel between them, and when well practiced in this, they will ask for the vowel to be omitted that they may supply it, which they will do very readily and with great pleasure, while there is a tasking of the mind which cannot but prove beneficial.
Again, turn the frame with the balls round, so that the wires are perpendicular instead of horizontal, raise a ball gently, and say, To ascend, ascending, ascended; let it fall gently, saying, to descend, descending, descended; with a little explanation these words will then be understood, and others may be taught in the same way. To fall, falling, fallen; to rise, rising, risen; to go, going, gone, will readily occur, and others will easily be supplied by the ingenuity of the instructor. The frame may also be applied togrammar.
It is to be used as follows:—Move one of the balls to a part of the frame distinct from the rest. The children will then repeat, "Thereitis, thereitis." Apply your finger to the ball, and set it running round. The children will immediately change from saying, "Thereitis," to "Thereitgoes, thereitgoes."
When they have repeated "There it goes" long enough to impress it on their memory, stop the ball; the children will probably say, "Nowitstops, nowitstops." When that is the case, move another ball to it, and then explain to the children the difference between singular and plural, desiring them to call out, "Theretheyare, theretheyare;" and when they have done that as long as may be proper, set both balls moving, and it is likely they will call out, "Theretheygo, theretheygo." I do not particularize further, because I know that good teachers will at once see the principle aimed at, and supply the other requisite lessons: the object of this book being rather to shew the principle of the thing, than to go into detail.
The arithmeticon—How applied—Numeration—Addition—Subtraction— Multiplication—Division—Fraction—Arithmetical tables—Arithmetical Songs—Observations.
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"In arithmetic, as in every other branch of education, the principal object should be to preserve the understanding from implicit belief, to invigorate its powers, and to induce the laudable ambition of progressive improvement."—Edgeworth
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The advantage of a knowledge of arithmetic has never been disputed. Its universal application to the business of life renders it an important acquisition to all ranks and conditions of men. The practicability of imparting the rudiments of arithmetic to very young children has been satisfactorily shewn by the Infant-school System; and it has been found, likewise, that it is the readiest and surest way of developing the thinking faculties of the infant mind. Since the most complicated and difficult questions of arithmetic, as well as the most simple, are all solvable by the same rules, and on the same principles, it is of the utmost importance to give children a clear insight into the primary principles of number. For this purpose we take care to shew them, by visible objects, that all numbers are combinations of unity; and that all changes of number must arise either from adding to or taking from a certain stated number. After this, or rather, perhaps I should say, in conjunction with this instruction, we exhibit to the children thesignsof number, and make them acquainted with their various combinations; and lastly, we bring them to the abstract consideration of number; or what may be termedmental arithmetic. If you reverse this, which has generally been the system of instruction pursued—if you set a child to learn its multiplication, pence, and other tables, before you have shewn it byrealities, the combinations of unity which these tables express in words—you are rendering the whole abstruse, difficult, and uninteresting; and, in short, are giving it knowledge which it is unable to apply.
As far as regards the general principles of numerical tuition, it may be sufficient to state, that we should begin with unity, and proceed very gradually, by slow and sure steps, through the simplest forms of combinations to the more comprehensive. Trace and retrace your first steps—the children can never be too thoroughly familiar with the first principles or facts of number.
We have various ways of teaching arithmetic, in use in the schools; I shall speak of them all, beginning with a description of the arithmeticon, which is of great utility.
[Illustration]
I have thought it necessary in this edition to give the original woodcut of the arithmeticon, which it will be seen contains twelve wires, with one ball on the first wire, two on the second, and so progressing up to twelve. The improvement is, that each wire should contain twelve balls, so that the whole of the multiplication table may be done by it, up to 12 times 12 are 144. The next step was having the balls painted black and white alternately, to assist the sense of seeing, it being certain that an uneducated eye cannot distinguish the combinations of colour, any more than an uneducated ear can distinguish the combinations of sounds. So far the thing succeeded with respect to the sense of seeing; but there was yet another thing to be legislated for, and that was to prevent the children's attention being drawn off from the objects to which it was to be directed, viz. the smaller number of balls as separated from the greater. This object could only be attained by inventing a board to slide in and hide the greater number from their view, and so far we succeeded in gaining their undivided attention to the balls we thought necessary to move out. Time and experience only could shew that there was another thing wanting, and that was a tablet, as represented in the second woodcut, which had a tendency to teach the children the difference between real numbers and representative characters, therefore the necessity of brass figures, as represented on the tablet; hence the children would call figure seven No. 1, it being but one object, and each figure they would only count as one, thus making 937, which are the representative characters, only three, which is the real fact, there being only three objects. It was therefore found necessary to teach the children that the figure seven would represent 7 ones, 7 tens, 7 hundreds, 7 thousands, or 7 millions, according to where it might be placed in connection with the other figures; and as this has already been described, I feel it unnecessary to enlarge upon the subject.
[Illustration]
It will be seen that on the twelve parallel wires there are 144 balls, alternately black and white. By these the elements of arithmetic may be taught as follows:—
Numeration.—Take one ball from the lowest wire, and say units,one, two from the next, and say tens,two; three from the third, and say hundreds,three; four from the fourth, and say thousands,four; five from the fifth, and say tens of thousands,five; six from the sixth, and say hundreds of thousands,six; seven from the seventh, and say millions,seven; eight from the eighth, and say tens of millions,eight; nine from the ninth, and say hundreds of millions,nine; ten from the tenth, and say thousands of millions,ten; eleven from the eleventh, and say tens of thousands of millions,eleven; twelve from the twelfth, and say hundreds of thousands of millions,twelve.
The tablet beneath the balls has six spaces for the insertion of brass letters and figures, a box of which accompanies the frame. Suppose then the only figure inserted is the 7 in the second space from the top: now were the children asked what it was, they would all say, without instruction, "It is one." If, however, you tell them that an object of such a form stands instead of seven ones, and place seven balls together on a wire, they will at once see the use and power of the number. Place a 3 next the seven, merely ask what it is, and they will reply, "We don't know;" but if you put out three balls on a wire, they will say instantly, "O it is three ones, or three;" and that they may have the proper name they may be told that they have before themfigure 7andfigure 3. Put a 9 to these figures, and their attention will be arrested: say, Do you think you can tell me what this is? and, while you are speaking, move the balls gently out, and, as soon as they see them, they will immediately cry out "Nine;" and in this way they may acquire a knowledge of all the figures separately. Then you may proceed thus: Units 7, tens 3; place three balls on the top wire and seven on the second, and say, Thirty-seven, as you point to the figures, and thirty-seven as you point to the balls. Then go on, units 7, tens, 3, hundreds 9, place nine balls on the top wire, three on the second, and seven on the third, and say, pointing to each, Nine hundred and thirty-seven. And so onwards.
To assist the understanding and exercise the judgment, slide a figure in the frame, and say, Figure 8. Q. What is this? A. No. 8. Q. If No. 1 be put on the left side of the 8, what will it be? A. 81. Q. If the 1 be put on the right side, then what will it be? A. 18. Q. If the figure 4 be put before the 1, then what will the number be? A. 418. Q. Shift the figure 4, and put it on the left side of the 8, then ask the children to tell the number, the answer is 184. The teacher can keep adding and shifting as he pleases, according to the capacity of his pupils, taking care to explain as he goes on, and to satisfy himself that his little flock perfectly understand him. Suppose figures 5476953821 are in the frame; then let the children begin at the left hand, saying, units, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, tens of millions, hundreds of millions, thousands of millions. After which, begin at the right side, and they will say, Five thousand four hundred and seventy-six million, nine hundred and fifty-three thousand, eight hundred and twenty-one. If the children are practised in this way, they will soon learn numeration.
The frame was employed for this purpose long before its application to others was perceived; but at length I found we might proceed to
Addition.—We proceed as follows:—1 and 2 are 3, and 3 are 6, and 4 are 10, and 5 are 15, and 6 are 21, and 7 are 28, and 8 are 36, and 9 are 45, and 10 are 55, and 11 are 66, and 12 are 78.
Then the master may exercise them backwards, saying, 12 and 11 are 23, and 10 are 33, and 9 are 42, and 8 are 50, and 7 are 57, and 6 are 63, and 5 are 68, and 4 are 72, and 3 are 75, and 2 are 77, and 1 is 78, and so on in great variety.
Again: place seven balls on one wire, and two on the next, and ask them how many 7 and 2 are; to this they will soon answer, Nine: then put the brass figure 9 on the tablet beneath, and they will see how the amount is marked: then take eight balls and three, when they will see that eight and three are eleven. Explain to them that they cannot put underneath two figure ones which mean 11, but they must put 1 under the 8, and carry 1 to the 4, when you must place one ball under the four, and, asking them what that makes, they will say, Five. Proceed by saying, How much are five and nine? put out the proper number of balls, and they will say, Five and nine are fourteen. Put a four underneath, and tell them, as there is no figure to put the 1 under, it must be placed next to it: hence they see that 937 added to 482, make a total of 1419.
Subtractionmay be taught in as many ways by this instrument. Thus: take 1 from 1, nothing remains; moving the first ball at the same time to the other end of the frame. Then remove one from the second wire, and say, take one from 2, the children will instantly perceive that only 1 remains; then 1 from 3, and 2 remain; 1 from 4, 3 remain; 1 from 5, 4 remain; 1 from 6, 5 remain; 1 from 7, 6 remain; 1 from 8, 7 remain; 1 from 9, 8 remain; 1 from 10, 9 remain; 1 from 11, 10 remain; 1 from 12, 11 remain.
Then the balls may be worked backwards, beginning at the wire containing 12 balls, saying, take 2 from 12, 10 remain; 2 from 11, 9 remain; 2 from 10, 8 remain; 2 from 9, 7 remain; 2 from 8, 6 remain; 2 from 7, 5 remain; 2 from 6, 4 remain; 2 from 5, 3 remain; 2 from 4, 2 remain; 2 from 3, 1 remains.
The brass figure should be used for the remainder in each case. Say, then, can you take 8 from 3 as you point to the figures, and they will say "Yes;" but skew them 3 balls on a wire and ask them to deduct 8 from them, when they will perceive their error. Explain that in such a case they mustborrowone; then say take 8 from 13, placing 12 balls on the top wire, borrow one from the second, and take away eight and they will see the remainder is five; and so on through the sum, and others of the same kind.
InMultiplication, the lessons are performed as follows. The teacher moves the first ball, and immediately after the two balls on the second wire, placing them underneath the first, saying at the same time, twice one are two, which the children will readily perceive. We next remove the two balls on the second wire for a multiplier, and then remove two balls from the third wire, placing them exactly under the first two, which forms a square, and then say twice two are four, which every child will discern for himself, as he plainly perceives there are no more. We then move three on the third wire, and place three from the fourth wire underneath them saying, twice three are six. Remove the four on the fourth wire, and four on the fifth, place them as before and say, twice four are eight. Remove five from the fifth wire, and five from the sixth wire underneath them, saying twice five are ten. Remove six from the sixth wire, and six from the seventh wire underneath them and say, twice six are twelve. Remove seven from the seventh wire, and seven from the eighth wire underneath them, saying, twice seven are fourteen. Remove eight from the eighth wire, and eight from the ninth, saying, twice eight are sixteen. Remove nine on the ninth wire, and nine on the tenth wire, saying twice nine are eighteen. Remove ten on the tenth wire, and ten on the eleventh underneath them, saying, twice ten are twenty. Remove eleven on the eleventh wire, and eleven on the twelfth, saying, twice eleven are twenty-two. Remove one from the tenth wire to add to the eleven on the eleventh wire, afterwards the remaining ball on the twelfth wire, saying, twice twelve are twenty-four.
Next proceed backwards, saying, 12 times 2 are 24, 11 times 2 are 22, 10 times 2 are 20, &c.
ForDivision, suppose you take from the 144 balls gathered together at one end, one from each row, and place the 12 at the other end, thus making a perpendicular row of ones: then make four perpendicular rows of three each and the children will see there are 4 3's in 12. Divide the 12 into six parcels, and they will see there are. 6 2's in 12. Leave only two out, and they will see, at your direction, that 2 is the sixth part of 12. Take away one of these and they will see one is the twelfth part of 12, and that 12 1's are twelve.
To explain the state of the frame as it appears in the cut, we must first suppose that the twenty-four balls which appear in four lots, are gathered together at thefigured side: when the children will see there are three perpendicular 8's, and as easily that there are 8 horizontal 3's. If then the teacher wishes them to tell how many 6's there are in twenty-four, he moves them out as they appear in the cut, and they see there are four; and the same principle is acted on throughout.
The only remaining branch of numerical knowledge, which consists in an ability to comprehend the powers of numbers, without either visible objects or signs—is imparted as follows:
Addition.
One of the children is placed before the gallery, and repeats aloud, in a kind of chaunt, the whole of the school repeating after him; One and one are two; two and one are three; three and one are four, &c. up to twelve.
Two and two are four; four and two are six; six and two are eight, &c. to twenty-four.
Three and three are six; six and three are nine; nine and three are twelve, &c. to thirty-six.
Subtraction.
One from twelve leaves eleven; one from eleven leaves ten, &c.
Two from twenty-four leave twenty-two; two from twenty-two leave twenty, &c.
Multiplication.
Twice one are two; twice two are four, &c. &c. Three times three are nine, three times four are twelve, &c. &c.
Twelve times two are twenty-four; eleven times two are twenty-two, &c. &c.
Twelve times three are thirty-six; eleven times three are thirty-three, &c. &c. until the whole of the multiplication table is gone through.
Division.
There are twelve twos in twenty-four.—There areeleven twos in twenty-two, &c. &c.There are twelve threes in thirty-six, &c.There are twelve fours in forty-eight, &c. &c.
Fractions.
Two are the half (1/2) of four. " " " third (1/3) of six. " " " fourth (1/2) of eight. " " " fifth (1/5) of ten. " " " sixth (1/6) of twelve. " " " seventh (1/7) of fourteen. " " " twelfth (1/12) of twenty-four; two are the eleventh (1/11) of twenty-two, &c. &c.
Three are the half (1/2) of six. " " " third (1/3) of nine. " " " fourth (1/4) of twelve.
Three are the twelfth (1/12) of thirty-six; three are the eleventh (1/11) of thirty-three, &c. &c.
Four are the half (1/2) of eight, &c.
In twenty-three are four times five, and three-fifths (3/5) of five; in thirty-five are four times eight, and three-eighths (3/8) of eight.
In twenty-two are seven times three, and one-third(1/3) of three.
In thirty-four are four times eight, and one-fourth(1/4) of eight.
The tables subjoined are repeated by the same method, each section being a distinct lesson. To give an idea to the reader, the boy in the rostrum says ten shillings the half (1/2) of a pound; six shillings and eightpence one-third (1/3) of a pound, &c.
Sixpence the half (1/2) of a shilling, &c. Always remembering, that whatever the boy says in the rostrum, the other children must repeat after him, but not till the monitor has ended his sentence; and before the monitor delivers the second sentence, he waits till the children have concluded the first, they waiting for him, and he for them; this prevents confusion, and is the means of enabling persons to understand perfectly what is going on in the school.
In a book lately published, which is a compilation by two London masters, it is stated, in the preface, that they were at a loss for proper lessons: had they used those in existence I cannot help thinking they were enough for the capacity of children under six years of age.
Numeration, Addition, Subtraction, Multiplication, Division, and PenceTables.
—————————————————————————————————- | ADDITION AND SUBTRACTION TABLE | | 1 & | 2 & | 3 & | 4 & | 5 & | 6 & | | 1 are 2 | 1 are 3 | 1 are 4 | 1 are 5 | 1 are 6 | 1 are 7 | | 2 — 3 | 2 — 4 | 2 — 5 | 2 — 6 | 2 — 7 | 2 — 8 | | 3 — 4 | 3 — 5 | 3 — 6 | 3 — 7 | 3 — 8 | 3 — 9 | | 4 — 5 | 4 — 6 | 4 — 7 | 4 — 8 | 4 — 9 | 4 — 10 | | 5 — 6 | 5 — 7 | 5 — 8 | 5 — 9 | 5 — 10 | 5 — 11 | | 6 — 7 | 6 — 8 | 6 — 9 | 6 — 10 | 6 — 11 | 6 — 12 | | 7 — 8 | 7 — 9 | 7 — l0 | 7 — 11 | 7 — 12 | 7 — 13 | | 8 — 9 | 8 — 10 | 8 — 11 | 8 — 12 | 8 — 13 | 8 — 14 | | 9 — 10 | 9 — 11 | 9 — 12 | 9 — 13 | 9 — 14 | 9 — 15 | | 10 — 11 | 10 — 12 | 10 — 13 | 10 — 14 | 10 — 15 | 10 — 16 | | 11 — l2 | 11 — 13 | 11 — 14 | 11 — 15 | 11 — 16 | 11 — 17 | | l2 — 13 | 12 — 14 | 12 — 14 | 12 — 16 | 12 — 17 | l2 — 18 | —————————————————————————————————- | 7 & | 8 & | 9 & | 10 & | 11 & | 12 & | | 1 are 8 | 1 are 9 | 1 are 10 | 1 are 11 | 1 are 12 | 1 are 13 | | 2 — 9 | 2 — 10 | 2 — 11 | 2 — 12 | 2 — 13 | 2 — 14 | | 3 — 10 | 3 — 11 | 3 — 12 | 3 — 13 | 3 — 14 | 3 — 15 | | 4 — 11 | 4 — 12 | 4 — 13 | 4 — 14 | 4 — 15 | 4 — 16 | | 5 — 12 | 5 — 13 | 5 — 14 | 5 — 15 | 5 — 16 | 5 — 17 | | 6 — 13 | 6 — 14 | 6 — 15 | 6 — 16 | 6 — 17 | 6 — 18 | | 7 — 14 | 7 — 15 | 7 — 16 | 7 — 17 | 7 — 18 | 7 — 19 | | 8 — 15 | 8 — 16 | 8 — 17 | 8 — 18 | 8 — 19 | 8 — 20 | | 9 — 16 | 9 — 17 | 9 — 18 | 9 — 19 | 9 — 20 | 9 — 21 | | 10 — 17 | 10 — 18 | 10 — 19 | 10 — 20 | 10 — 21 | 10 — 22 | | 11 — l8 | 11 — 19 | 11 — 20 | 11 — 21 | 11 — 22 | 11 — 23 | | 12 — 19 | 12 — 20 | 11 — 21 | l2 — 22 | 12 — 23 | 12 — 24 | =================================================================== | MULTIPLICATION AND DIVISION TABLE. || NUMERATION TABLE. | |——————————————————||—————————————-| |2—2 are 4|4—5 are 20| 6—12 are 72|| 1 Units. | | 3 — 6| 6 — 24| 7— 7 — 49|| 21 Tens. | | 4 — 8| 7 — 28| 8 — 56|| 321 Hundreds | | 5 — 10| 8 — 32| 9 — 63|| 4,321 Thousands. | | 6 — 12| 9 — 36| 10 — 70|| 54,321 X of Thousands.| | 7 — 14| 10 — 40| 11 — 77|| 654,321 C of Thousands.| | 8 — 16| 11 — 44| 12 — 84|| 7,654,321 Millions. | | 9 — 18| 12 — 48| 8— 8 — 64|| 87,654,321 X of Millions. | | 10 — 20|5—5 — 25| 9 — 72||987,654,321 C of Millions. | | 11 — 22| 6 — 30| 10 — 80||===========================| | 12 — 24| 7 — 35| 11 — 88|| | |3—3 — 9| 8 — 40| 12 — 96|| PENCE TABLE | | 4 — 12| 9 — 45| 9— 9 — 81|| | | 5 — 15| 10 — 50| 10 — 90||—————————————-| | 6 — 18| 11 — 55| 11 — 99||d.s. d.|d.s. d.| | 7 — 21| 12 — 60| 12 — 108|| 20 is 1 8 | 90 is 7 6 | | 8 — 24|6—6 — 36|10—10 — 100|| 30 — 2 6 |100 — 8 4 | | 9 — 27| 7 — 42| 11 — 110|| 40 — 3 4 |110 — 9 2 | | 10 — 30| 8 — 48| 12 — 120|| 50 — 4 2 |120 —10 0 | | 11 — 33| 9 — 54|11—11 — 121|| 60 — 5 0 |130 —10 10 | | 12 — 36| 10 — 60| 12 — 132|| 70 — 5 10 |140 —11 8 | |4—4 — 16| 11 — 66|12—12 — 144|| 80 — 6 8 |144 —12 0 | —————————————————————————————————-
Tables of Weights and Measures.
Shilling Tables