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The reader will not, of course, understand me as wishing to discard Mental arithmetic.
All that I mean to suggest is the inquiry, whether its advantages are not looked for in the wrong direction, whether they are not sometimes over-estimated, and whether this mode of teaching arithmetic, especially when pursued as a hobby, is not sometimes pushed too far, and made the means of curious display, rather than of solid and lasting benefit.
In teaching mental arithmetic, too, for I would certainly teach it to some extent, I would suggest the expediency of teaching children, in performing these mental operations, to think in figures, in other words, to form conceptions of the arithmetical figures and signs, which are visible objects, rather than of quantities and relations, which are mere abstractions.
Multiplication is a mere metaphysical entity.
The sign of multiplication is a simple, visible symbol, addressed to the eye, and capable of being conceived by the mind with unmistakable clearness and precision.
A child counting its fingers in the first steps of learning to add and to take away, is a pretty sight, doubtless.
But it is painful to see a person grown to man's estate, and in other respects well educated, as I have very often seen, still dependent upon the same infantile contrivance,--still counting fingers when required to add long columns of figures.
Count the fingers, if necessary, in order to get the child under way.
But the sooner the leading-string can be dropped, and the child can be made to picture in his mind the pure figures and signs, their combinations and results, without reference to fingers, or apples, or cakes, or tops, the better for his arithmetic, and the better for his mental cultivation.
The subject has a painful interest for the Sabbath-School Teacher.
The teacher of the infant school, indeed, has some opportunity for employing this principle of pictorial representation, in teaching the little ones of his charge.
The infant school-room usually has conveniences for maps and picture cards and diagrams, and even blackboards; and most infant school teachers wisely avail themselves of the opportunity afforded.
But go into the main school-room--what can the teacher do?
Twenty, thirty, forty classes huddled together into one room, compact as sheep in a pen, how can the individual teacher, if disposed, use adequate visible illustrations for the instruction of his class?
Where shall he place his blackboard?
where shall he hang up his maps?
where shall he suspend his models?
where shall he exhibit his specimens?
The utmost that can be done in most of our schools, as at present provided for, is to have a few maps on the distant walls of the room which the superintendent may refer to, whenever he chooses, and which all the children may see who can!
The time must come, however, when the teaching of religious truth will be considered of as much importance as the teaching of arithmetic or of chemistry, and the Sabbath-School will have the same facilities for imparting instruction as the week-day school.
But that time has not yet come.
In the meanwhile, let the teacher carefully avail himself of whatever subsidiary aids are within his reach.
No teacher should ever present himself before his class without a Bible Atlas and a Bible Dictionary in his hand.
Many of those things with which his class ought to be made acquainted, are here not only described, but delineated, with equal accuracy and beauty.
Thanks to the booksellers and the religious publication societies, the scenes of sacred history, and indeed religious topics generally, have been illustrated in cheap pictorial cards, both large and small, and with admirable fidelity and skill.
These form a part of the indispensable furniture of the Sunday-School teacher.
They are to him as necessary as are experiments, or a cabinet of specimens, to the lecturer on the physical sciences.
The Sabbath-School teacher should be continually on the look-out for publications of this kind, not only for instructing and furnishing his own mind with definite ideas, but for exhibition to his class.
A wise teacher will not only have something to say to his class, but also something to show.
The ideas which the child gets from looking at really instructive pictures and maps, never leave him.
How much also our intelligent apprehension of the scriptures is increased, by a knowledge of topography, and by associating each event in the sacred narration with the place in which it occurred?
It may be proper to say, too, in this connection, that it is with a view to the principle now under consideration, that in preparing books and papers for the young, authors and publishers feel justified in giving so much labor and space to pictorial illustration.
When, indeed, such illustrations are merely for display, they deserve the contempt which they often receive.
But when these pictorial illustrations have a definite meaning and design, when they teach something, when they connect in the child's mind sound religious truth with distinct and easily remembered visible forms, they are a really valuable aid in the inculcation of doctrine.
The power of attention, like all the mental powers, is by nature greater in some than in others.
Still, there is no power more susceptible of improvement.
The importance of its cultivation cannot well be over-stated.
It affects not one study only, but all studies; not one mode of study only, but every mode of study, by text-book or by lecture;
lessons to be recited by memory, or those by question and answer; not even study only, but conduct and manners, the regulation of the heart and the formation of the character.
The precise measure of a child's success, in every thing that pertains to his character and standing as a scholar, will in nine cases out of ten be his power and habit of attention.
There are indeed lamentable cases of wilful and intentional disorder.
Yet every teacher knows that by far the greater portion of the things which interrupt and disturb a school arise from thoughtlessness and inattention.
There are also equally undoubted cases of ignorance that is no crime.
Yet the great majority of those who fail in their studies, fail simply because they do not attend.
To attend, however, means something more than merely to be bodily present, more even than to have the ears open and the eyes fixed in the direction of the speaker, when a thing is said, or done.
An old lady used to sit in the same aisle with me in church, and unfortunately lived opposite me in the street, who was neither deaf nor blind, and who was never absent from church, and yet she sent over invariably on Sunday evenings to know what it was the minister said about that meeting on Wednesday night, or that meeting on Friday night,--she did not rightly understand!
But it is not necessary to go to church, to find those who "having eyes see not, and having ears hear not, neither do they understand," who look without seeing, and hear without comprehending.
Publish a notice in your school, making some change of hours or lessons, or giving any specific direction.
No matter how simple, or how plainly expressed, the notice may be, or how particularly attention may be called beforehand to the announcement about to be made, where is the happy teacher who has been able on such an occasion to make himself understood by all?
Teachers and preachers and speakers of every name have generally very little idea how much they are misunderstood.
Let me give some instances.
In my own Sunday-School, I had neglected one morning to bring with me the teacher's class-books.
After opening the school, I rang the bell as a signal for attention.
There was a general hush throughout the room.
All eyes were turned to the desk.
I said: "Your class-books unfortunately have been left behind this morning.
They have been sent for, however, and they will soon be here.
As soon as they come, I will bring them round to the several classes.
In the meantime, you may go on with your regular lessons."
The bell was then tapped again, and the routine of the school resumed.
In about a minute, a girl came up to the desk, with, "Sir, teacher says, will you please to send her class-book;
it was not brought round, as usual, this morning, before school opened!"
Here was a class of ten girls, averaging twelve years of age, and not one of them, nor their teacher, had heard or understood the notice which I thought I had made so plain!
Here is another instance.
At the examination for admission to the Philadelphia High School, as a means of testing among other things how far this very faculty of hearing and of attention has been cultivated, the candidates are required to copy a passage from dictation.
These exercises are always preserved for reference, and in order to show the fairness of the examination.
On one occasion, when I was Principal of the School, I took the pains to copy out a few of the exercises, in order to show the singular freaks into which an uncultivated ear may be led.
One or two specimens will serve to illustrate the point.
The first clause with its variations, was as follows:-- Every breach of veracity indicates some latent vice.
" bridge " rascality " " latest vice.
" breech " feracity " " latinet vice.
" preach " eracity " " late device.
" branch " vivacity " " great advice.
" " " veracity " " late advice.
" " " " " " ladovice.
" " " " " " ladened vice.
Every branch of veracity in the next some latent vice.
Every reach of their ascidity indicates some advice.
In another part of the passage occurred the following: Petty operations.
Petty alterations.
Petty observations.
Patriarchal occupations.
Petty oblations.
Now of what use is it to a boy who mistakes "petty" for "patriarchal," "latent vice" for "great advice," "breach of veracity" for "reach of their ascidity," who is so untrained that he really cannot hear what is said, or see what is done,--of what use is it to such a boy, merely because he has gone through a prescribed routine of books and classes, or perchance because he has attained a certain amount of years and of pounds avoirdupois, to be pushed forward into a higher department to attend lectures on chemistry, or anatomy, or morals, or history, or literature?
It is preposterous.
It is an insult to the Professor, and an injury to the boy.
This, then, is the burden of my song.
We cannot take too much pains in early life in rousing this power of attention.
Depend upon it, no matter how much learning, so called, is crammed into a youth, his intellectual development has not begun until this power is roused.
He may have a vague, dreamy sort of knowledge; he may do sums by rule, and he may parse by rote, and do many other wondrous things; but his powers are not invigorated, he does not grow, until he begins really to see and hear, and feel _terra firma_ under his feet.
The principle which I am illustrating applies with special force to that part of a child's education which consists in learning the meaning of words.
I have serious doubts whether children ordinarily learn much of the real meaning of words by committing definitions to memory.
What is a definition?
It is only expressing the meaning of one word by the use of another word as nearly as possible synonymous.
Now, in the case of a child, it is at least an even chance that that other word is just as unknown as the one it is intended to explain.
It is like, in algebra, solving an equation with two unknown quantities, by giving the value of one unknown quantity in terms of the other.
A child, for instance, is told that "potent" means "efficacious," that "power" means "ability," that "potion" means a "physical draught," that "potential" means "existing in possibility, not in act."
These are definitions taken at random from a book in common use in our public schools.
The definitions possibly are good enough for the purpose for which they were designed.
I
am not quarrelling with the definitions.
But, surely, it is not by these that a child is to learn the meaning of the words.
Whether he is told that "power" means "ability," or "ability" means "power," that "potent" means "efficacious," or "efficacious" means "potent," in neither case, nine times out of ten, is any addition made to his stock of knowledge.
It is not until much later in life,--until in fact our knowledge of words is already very much extended, that we profit much by learning formal definitions.
But in childhood, we must learn the meaning and power of words, just as the mechanic becomes acquainted with his tools, by observing their use.
A boy, for instance, reads this sentence.
"The drug was very _efficacious_."
If the word is quite new to him, and there is nothing in the clause preceding or following to indicate its meaning, it is not at all unlikely that he may suppose it to mean "poisonous."
If, however, from the context, he finds that a person who had been sick, was made suddenly well, and this statement followed by the remark, that "the drug was very _efficacious_," he will probably get the idea that the word means "healing," or "curative."
He reads again, in another place, that a certain mode of teaching penmanship was found to be very "efficacious."
Here is a new use of the word, quite different from the other, and he is obliged to exclude from his idea of its meaning every thing like "healing."
So he goes on, every fresh example cutting off some extraneous idea which the previous examples had led him to attach to the word, and every step onward coming nearer to the general idea, though he may never express it in words, of something which accomplished its object, whatever that object may be.
It is, I believe, chiefly by observing in this way the manner in which words are used, that children do and must learn their meaning.
It is, in other words, by quickening and cultivating the habit of attention to the meaning,--by training a child, when he is reading, to imagine, not that he is reading the words, but that he is reading the sense, by accustoming him to look through the word, to the sense, just as he would look at objects out of doors through the window, and to consider the words, as he would consider the glass, merely as a medium, through which, and unmindful of it, he looks at something beyond,--_which something is the meaning_.
Let me not be misunderstood in regard to this matter of definitions.
I
believe it to be of the utmost importance that children should be constantly required to give definitions or explanations of the words whose meaning they have acquired.
All I mean to call in question is, whether that meaning to any considerable extent is acquired by committing to memory formal definitions prepared by others.
When they have once learned the meaning of a word, which is to be done mainly, if not only, by observing its use, then by all means let them be required to express that meaning by other words which they know.
Such an exercise cannot be too much insisted on.
It is one of the best means of securing that attention to the signification of words, which is so much wanted.
It requires the child, moreover, to bring his knowledge continually to the test.
It cultivates at once accuracy of thought, and accuracy of language, which is the vehicle of thought.
Train a child, therefore, to the habit of attention, first to the meaning of words as gathered from observation of their use, and secondly to the expression of that meaning in language appropriate and intelligible to others.
I have dwelt a little on this subject, because, as in the matter of hearing, I doubt whether people generally are aware how little children understand what they read.
Nor is this ignorance confined to children.
In our acts of devotion, we are all in the habit of using certain stereotyped phrases, without attaching to them any definite meaning, without perhaps so much as having even thought whether they had a meaning.
This same pernicious habit is seen also in our reading of the Scriptures.
We have read the phrases over from childhood, until we have become so familiar with them, that we are obliged often to stop, and by a sort of compulsory process to challenge each word as it passes, and see whether it really conveys any meaning to our mind.
If I were to say to a class, "The Bible tells us of a man who was older than his father," or some such apparent contradiction in terms, the sharp antithesis would doubtless arrest their attention, and I would at least be asked to explain myself.
Yet, ten to one, they have read, hundreds of times, of him who is "the _root_ and the _offspring_ of David, the bright and morning star," without noticing anything at all remarkable in the expression.
It is to them merely something good and pious, couched in a very pleasant and sonorous flow of words, and meaning doubtless something very comforting and edifying.
I was once teaching temporarily a young ladies' Bible Class.
The average age of the members was at least seventeen.
They were the pick from a large city school, and had been selected for their superior educational advantages and attainments.
Most of them were attending expensive private schools during the week.
Wishing to satisfy myself as to the general knowledge and the intellectual habits of the members, I took the plan of simply reading verse about, stopping from time to time to talk familiarly about anything which might happen to suggest itself.
This verse among others was read: it is from the account of the miracle on the day of Pentecost: "And there appeared unto them cloven tongues like as of fire, and it sat upon each of them."
I found, upon inquiring, that _not one_ in that large class had the remotest idea of what was meant by the word "cloven."
One young lady thought it meant "fiery," another "flaming," another "winged," and so on.
Most of them, however, said that they really had never thought of the matter before.
Probably every one of them had read the passage hundreds of times; and when we began talking about it, no one of them seemed to have an idea that there was anything in the verse which she did not understand.
It was not until I took it up, word by word, and challenged a peremptory and sharp scrutiny into the meaning attached to each word, that the remarkable fact came out which I have stated.
One or two more leaves from my professional experience will be given.
During the greater part of my professional life, it has been a part of my duty to examine candidates for the office of teacher in the public schools.
Out of ninety-eight candidates for the office of assistant teacher, whom I examined on one occasion, only one knew the meaning of the word "sumptuary," although in the public discussion then going on about the license law, the word was in daily use in the public papers;
in fact, I took it out of the newspaper of that morning.
On another occasion, out of fourteen candidates for the office of Principal teacher of a boys' Grammar school, four defined "friable" as that which can be fried; several did not know at all the meaning of "hibernating," and one, the successful candidate, said it meant "relating to Ireland."
By "successful" candidate, I mean the one who got the vote of the Directors!
This sober scrutiny into any one's knowledge of the meaning of words in common use, is one of the most reliable tests of his general intellectual progress and cultivation.
It is one of the means by which in many city schools it is customary to test a candidate's fitness for promotion.
To show how little people generally, and even teachers, are aware of the extent to which children misconceive the meaning of words in common use, I have transcribed a few examples from an examination of the kind which I once held.
The definitions which I am about to quote were not the work of oral confusion and haste, but were given in writing, in circumstances of entire quietude and ample deliberation.
The average age of the candidates, on the occasion referred to, was fourteen years and ten months, and no one of them was by law under thirteen years.
_Stature_--A picture; "I saw a stature of Washington."
_Fabulous_--Full of threads; "Silk is fabulous."
_Accession_--The act of eating a great deal; "John got very sick after dinner by accession."
_Atonement_--A small insect; "Queen Mab was pulled by little atonements."
Sound, [orthodox]; "They went to the church of the Atonement."
_Auxiliary_--To form; "The gardener did auxiliary his garden."
_Ingredient_--A native-born; "Tobacco is an ingredient of this country."
_Fragment_--Sweetmeats; "It was a fragment."
_Develop_--To swallow up; "God sent a whale to develop Jonah."
_Exotic_--Relating to a government; "Some countries have a very exotic government."
Patriotic; "He was exotic in the cause of Independence."
Absolute; "The government of Turkey is exotic."
Standing out; "The company were exotic."
_Circumference_--Distance through the middle.
Distance around the middle of the outside.
_Callous_--Something which cannot be effected; "That America should gain her independence was supposed to be callous."
_Mobility_--Belonging to the people; "The mobility of St. Louis has greatly increased."
_Anomalous_--Powerful; "His speech was considered anomalous."
_Adequate_--A land animal; "An elephant is an adequate."
_Transition_--The act of transcribing; "The transition of that book was gaining ground in the public mind."
_Gregarious_--Pertaining to idols; "The Sandwich Islands worship gregarious."
Pertaining to an oak; "The Druids were noted for their gregarious exercises."
Consisting of grain.
Grass-eating.
Full of talk.
Full of color.
_Propensity_--Dislike; "He had a propensity to study."
_Artificially_--Belonging to flowers.
_Fluctuation_--coming in great numbers; "There was a great fluctuation of emigrants."
Setting on fire.
Beating.
_Odium_--That you have a great tact at anything; "Your odium is very great."
A poisonous herb.
Pertaining to song; "He was an odium writer."
A sweet smell; "The odium of new-mown hay."
_Transverse_--To turn over; "Transverse that bucket and see what is in it."
To change from verse; "Some writers change books from transverse to verse."
To verse again; "He transversed his copy."
To spread abroad; "They transverse the Bible."
_Utility_--Relating to the soil; "The ground it remarkable for its utility."
_Quadruple_--Relating to birds; "There was a number of quadruple."
_Alternate_--Not ternate.
_Menace_--A tare in the flesh; "The dog caused a menace in John's arm."
_Vital_--Relating to death; "Vital spark of heavenly flame."
_Intrinsic_--not trinsic.
Weak, feeble; "He was a very intrinsic old man."
_Subservient_--One opposed to the upholding of servants.
Stubborn;
"On account of the boy being subservient he was turned out of school."
_Perfidy_--Trust; not to cheat; "Such a man is perfidy; that is, everything can be trusted to him."
Accessible; "Some persons have a great deal of perfidy."
_Access_--Intermission; "Joseph had access of his teacher to go into the room."
_Vicinity_--In the same direction; "Pekin is in the vicinity of Philadelphia."
_Subsequent_--Preceding; "The subsequent chapter."
_Infectious_--To make fectious.
_Exquisite_--To be in a quisitive manner.
To help.
To find out.
Talkative.
Not required.
_Mingle_--To tear in pieces.
_Deride_--To ride down.
_Manifold_--Made by the hand.
Pertaining to man; "Forgive our manifold sins."
I have failed entirely in the general drift of this chapter, if I have not made it obvious that the principle which I have been attempting to illustrate is one of singularly pervading influence, and of most various and manifold applications.
The subject is indeed eminently suggestive.
One single additional line of illustration, however, must suffice.
I
refer to the application of this principle to what may be called the incidentals of teaching and training.
A child, for instance, should not only "spell out of book," as it is called, but his attention should by some means be directed to the way in which words are spelled.
He should be accustomed to form, as it were, a mental image of each word, to think of it as having a particular form and appearance, so that his eye will detect instantly a wanting or an excrescent letter, just as he sees a wen, a defective limb, or a distorted feature on the person of an acquaintance.
Only fire his young ambition with the aim to spell well, and quicken his attention to the way in which words are spelled, and every time he reads a book he receives incidentally a lesson in spelling.
A child should have stated exercises and systematic instructions in the art of reading.
But quite as much improvement in this important and too much neglected accomplishment may be gained by not allowing children at any time to read in an improper manner.
Every demonstration at the blackboard, every text or hymn repeated from memory, every recitation in arithmetic, grammar, or geography, every exercise of every kind in which the voice is used and words are uttered, may be made an incidental lesson in reading.
By being never allowed to pronounce words incorrectly, to utter them in a low or drawling manner, or to crowd and overlap them, as it were, one upon the other, the ear becomes accustomed to the correct sounds of the language, and immediately detects any variation from its accustomed standard.
By thus insisting, in every vocal exercise, upon the full and correct pronunciation of the elementary sounds of the language, more may be done to make good readers and speakers than by all the pronouncing dictionaries and elocution books in print.
Let a child by all means take lessons in writing.
Let him learn plain text, German text, round hand, running hand, back hand, and the flourishes.
But if he is to become rapidly master of that truly beautiful and most useful accomplishment, let the teacher insist upon his always attending to his manner of writing, and always writing as well as he can.
Whether he writes a composition, a sketch, a letter, whenever for any purpose he puts pen to paper, let him be required to form each letter distinctly, to write it gracefully, and to give to his exercise a neat and elegant appearance.
Teach him to think of a crooked line or a blotted page as of an untied shoe, or a dirty face.
By thus making every written exercise an exercise in writing, his progress will be increased beyond your expectations, and you will soon see him looking with pleasure at the clean and symmetrical forms which flow so gracefully from his pen, as he goes from line to line over the virgin page, no half-formed or misshapen letters to embarrass, but all in every part as elegantly written as it is easily read.
Grammar should no doubt be taught by text-book and in stated lessons.
The parts of speech, the conjugations and declensions, syntax and parsing, must all be systematically conned, the rules and definitions committed to memory, and the judgment exercised upon their application.
At the same time every recitation of a child, as well as all his conversation, ought to be made an incidental and unconscious lesson in grammar.
Only never allow him to use unchallenged an incorrect or ungrammatical expression, train his ear to detect and revolt at it, as at a discordant note in music, let him if possible hear nothing but sterling, honest English, and he will then learn grammar to some purpose.
If, on the contrary, he is allowed to recite and to talk in whatever language comes uppermost, and to hear continually those around him reciting and talking in a similar manner, he may parse till he is blind without learning "to speak and write the English language correctly."
Banish from the nursery, the school-room, and the play-ground, incorrect and ungrammatical expressions, and you do more than can be done in all other ways to preserve "the well of English undefiled."
Young persons need systematic instructions in the principles which should govern their conduct.
They need not indeed be troubled with the more abstruse questions in the theory of morals.
But the great obvious rules of duty should be taught them, in a systematic manner, by a competent instructor.
But that man would be thought little acquainted with the influences which go to mould and form the character, who should suppose the matter ended here.
The doctrines inculcated in the lesson, must be carried out and applied in all the petty incidents of the day.
Not an hour passes in a large family or a school, without an occurrence involving some principle in morals.
A boy of moderate talents, notwithstanding all his exertions, is eclipsed by one more gifted, and he is tempted to envy.
Imagining himself aggrieved or insulted by his fellows, he burns for revenge.
Overtaken in a fault and threatened with punishment, he is tempted to lie.
Misled by the opinion of others, or esteeming some rule of his teachers harsh and unnecessary, he is inclined to disobey.
These and a hundred other instances which might be named, will suggest to the thoughtful parent or teacher so many opportunities for giving incidentally the most important practical instruction in morals.
In these and the manifold other illustrations which might be given, the essential point is to quicken and keep alive the attention.
Whatever be the subject of study, and whether the instructions be direct or incidental, let children be preserved from attending to it in a sluggish, listless, indifferent manner.
The subject of study, in the case of young persons, is often of less importance than the manner of study.
I have been led sometimes to doubt the value of many of the inventions for facilitating the acquisition of knowledge by children.
That knowledge the acquisition of which costs no labor, will not be likely to make a deep impression, or to remain long upon the memory.
It is by labor that the mind strengthens and grows: and while care should be taken not to overtask it by exertions beyond its strength, yet let it never be forgotten that mere occupation of the mind, even with useful and proper objects, is not the precise aim of education.
The educator aims, not to make learned boys, but able men.
To do this, he must tax their powers.
He must rouse them to manly exertion.
He must teach them to think, to discriminate, to digest what they have received, to work.
Every day there must be the glow of hard work,--not the exhaustion and languor which arise from too protracted confinement to study,--which have the same debilitating effect upon the mind that a similar process has upon the body,--but vigorous and hardy labor, such as wakens the mind from its lethargy, summons up the resolution and the will, and puts the whole internal man into a state of determined and positive activity.
The boy in such a case feels that he is at work.
He feels, too, that he is gaining something more than knowledge.
He is gaining power.
He is growing in strength.
He grapples successfully to-day with a difficulty that would have staggered him yesterday.
There is no mistaking this process; and no matter what the subject of study, the intellectual development what it gives, is worth infinitely more than all that vague, floating kind of knowledge sometimes sought after, which seems to be imbibed somehow from the atmosphere of the school-room, as it certainly evaporates the moment a boy enters the atmosphere of men and of active life.
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