Chapter VIII: Reports of Cases (2)

A teacher, by adopting the following plan, succeeded in awakening a great degree of interest on the subject, and, consequently, of promoting rapid improvement. The plan was this: he prepared, on a large sheet of paper, a series of lessons in coarse-hand, beginning with straight lines, and proceeding to the elementary parts of the various letters, and finally to the letters themselves. This paper was posted up in a part of the room accessible to all.

The writing-books were made of three sheets of foolscap paper, folded into a convenient size, making twenty-four pages in the book. The books were to be ruled by the pupil, for it was thought important that each should learn this art. Every pupil in school, then, being furnished with one of these writing-books, was required to commence this series, and to practice each lesson until he could write it well; then, and not till then, he was permitted to pass to the next. A few brief directions were given under each lesson on the large sheet. For example, under the line of straight marks, which constituted the first lesson, was written as follows:

_Straight, equidistant, parallel, smooth, well-terminated._

These directions were to call the attention of the pupil to the excellences which he must aim at, and when he supposed he had secured them, his book was to be presented to the teacher for examination. If approved, the word _Passed_, or, afterward, simply _P_., was written under the line, and he could then proceed to the next lesson. Other requisites were necessary, besides the correct formation of the letters, to enable one to pass; for example, the page must not be soiled or blotted, no paper must be wasted, and, in no case, a leaf torn out. As soon as _one line_ was written in the manner required, the scholar was allowed to pass. In a majority of cases, however, not less than a page would be practiced, and in many instances a sheet would be covered, before one line could be produced which would be approved.

One peculiar excellency of this method was, that although the whole school were working under a regular and systematic plan, individuals could go on independently; that is, the progress of no scholar was retarded by that of his companion; the one more advanced might easily pass the earlier lessons in a few days, while the others would require weeks of practice to acquire the same degree of skill.

During the writing-hour the scholars would practice each at the lesson where he left off before, and at a particular time each day the books were brought from the regular place of deposit and laid before the teacher for examination. Without some arrangement for an examination of all the books together, the teacher would be liable to interruption at any time from individual questions and requests, which would consume much time, and benefit only a few.

When a page of writing could not pass, a brief remark, calling the attention of the pupil to the faults which prevented it, was sometimes made in pencil at the bottom of the page. In other cases, the fault was of such a character as to require full and minute oral directions to the pupil. At last, to facilitate the criticism of the writing, a set of arbitrary marks, indicative of the various faults, was devised and applied, as occasion might require, to the writing-books, by means of red ink.

These marks, which were very simple in their character, were easily remembered, for there was generally some connection between the sign and the thing signified. For example, the mark denoting that letters were too short was simply lengthening them in red ink; a faulty curve was denoted by making a new curve over the old one, &c. The following are the principal criticisms and directions for which marks were contrived:

Strokes rough. Too tall or too short.
Curve wrong. Stems not straight.
Bad termination Careless work.
Too slanting, and the reverse. Paper wasted.
Too broad, and the reverse. Almost well enough to pass.
Not parallel. Bring your book to the teacher.
Form of the letter bad. Former fault not corrected.
Large stroke made too fine, and the reverse.

A catalogue of these marks, with an explanation, was made out and placed where it was accessible to all, and by means of them the books could be very easily and rapidly, but thoroughly criticised.

After the plan had gone on for some time, and its operation was fully understood, the teacher gave up the business of examining the books into the hands of a committee, appointed by him from among the older and more advanced pupils. That the committee might be unbiased in their judgment, they were required to examine and decide upon the books without knowing the names of the writers. Each scholar was, indeed, required to place her name on the right hand upper corner of every page of her writing-book, for the convenience of the distributors; but this corner was turned down when the book was brought in, that it might not be seen by the committee.

This committee was invested with plenary powers, and there was no appeal from their decision. In case they exercised their authority in an improper way, or failed on any account to give satisfaction, they were liable to impeachment, but while they continued in office they were to be strictly obeyed.

This plan went on successfully for three months, and with very little diminution of interest. The whole school went regularly through the lessons in coarse-hand, and afterward through a similar series in fine-hand, and improvement in this branch was thought to be greater than at any former period in the same length of time.

The same principle of arranging the several steps of an art or a study into a series of lessons, and requiring the pupil to pass regularly from one to the other, might easily be applied to other studies, and would afford an agreeable variety.

12. THE CORRESPONDENCE.--A master of a district school was walking through the room with a large rule in his hands, and as he came up behind two small boys, he observed that they were playing with some papers. He struck them once or twice, though not very severely, on the head with the rule which he had in his hand. Tears started from the eyes of one. They were called forth by a mingled feeling of grief, mortification, and pain. The other, who was of "sterner stuff," looked steadily into the master's face, and when his back was turned, shook his fist at him and laughed in defiance.

Another teacher, seeing a similar case, did nothing. The boys, when they saw him, hastily gathered up their playthings and put them away. An hour or two after, a little boy, who sat near the master, brought them a note addressed to them both. They opened it, and read as follows:

"To EDWARD AND JOHN,--I observed, when I passed you to-day, from your concerned looks, and your hurried manner of putting something into your desk, that you were doing something that you knew was wrong. When you attempt to do any thing whatever which conscience tells you is wrong, you only make yourself uneasy and anxious while you do it, and then you are forced to resort to concealment and deception when you see me coming. You would be a great deal happier if you would always be doing your duty, and then you would never be afraid. Your affectionate teacher,----."

As the teacher was arranging his papers in his desk at the close of school, he found a small piece of paper neatly folded up in the form of a note, and addressed to him. He read as follows:

"DEAR TEACHER,--We are very much obliged to you for writing us a note. We were making a paper box. We know it was wrong, and are determined not to do so any more. We hope you will forgive us.

"Your pupils, EDWARD, JOHN."

Which of these teachers understood human nature best?

13. WEEKLY REPORTS.--The plan described by the following article, which was furnished by a teacher for insertion here, was originally adopted, so far as I know, in a school on the Kennebec. I have adopted it with great advantage.

A teacher had one day been speaking to her scholars of certain cases of slight disorder in the school, which, she remarked, had been gradually creeping in, and which, as she thought, it devolved upon the scholars, by systematic efforts, to repress. She enumerated instances of disorder in the arrangement of the rooms, leaving the benches out of their places, throwing waste papers upon the floor, having the desk in disorder inside, spilling water upon the entry floor, irregular deportment, such as too loud talking or laughing in recess, or in the intermission at noon, or when coming to school, and making unnecessary noise in going to or returning from recitations.

"I have a plan to propose," said the teacher, "which I think may be the pleasantest way of promoting a reform in things of this kind. It is this. Let several of your number be chosen a committee to prepare statedly--perhaps as often as once a week--a written report of the state of the school. The report might be read before the school at the close of each week. The committee might consist, in the whole, of seven or eight, or even of eleven or twelve individuals, who should take the whole business into their hands. This committee might appoint individuals of their number to write in turn each week. By this arrangement, it would not be known to the school generally who are the writers of any particular report, if the individuals wish to be anonymous. Two individuals might be appointed at the beginning of the week, who should feel it their business to observe particularly the course of things from day to day with reference to the report. Individuals not members of the committee can render assistance by any suggestions they may present to this committee. These should, however, generally be made in writing.

"Subjects for such a report will be found to suggest themselves very abundantly, though you may not perhaps think so at first. The committee may be empowered not only to state the particulars in which things are going wrong, but the methods by which they may be made right. Let them present us with any suggestions they please. If we do not like them, we are not obliged to adopt them. For instance, it is generally the case, whenever a recitation is attended in the corner yonder, that an end of one of the benches is put against the door, so as to occasion a serious interruption to the exercises when a person wishes to come in or go out. It would come within the province of the committee to attend to such a case as this, that is, to bring it up in the report. The remedy in such a case is a very simple one. Suppose, however, that instead of the _simple_ remedy, our committee should propose that the classes reciting in the said corner should be dissolved and the studies abolished? We should know the proposal was an absurd one, but then it would do no hurt; we should have only to reject it.

"Again, besides our faults, let our committee notice the respects in which we are doing particularly well, that we may be encouraged to go on doing well, or even to do better. If they think, for example, that we are deserving of credit for the neatness with which books are kept--for their freedom from blots, or scribblings, or dog's-ears, by which school-books are so commonly defaced, let them tell us so. And the same of any other excellence."

With the plan as thus presented, the scholars were very much pleased. It was proposed by one individual that such a committee should be appointed immediately, and a report prepared for the ensuing week. This was done. The committee were chosen by ballot. The following may be taken as a specimen of their reports:

WEEKLY REPORT.

"The Committee appointed to write the weekly report have noticed several things which they think wrong. In the first place, there have been a greater number of tardy scholars during the past week than usual. Much of this tardiness, we suppose, is owing to the interest felt in building the bower; but we think this business ought to be attended to only in play-hours. If only one or two come in late when we are reading in the morning, or after we have composed ourselves to study at the close of the recess, every scholar must look up from her book--we do not say they ought to do so, but only that they will do so. However, we anticipate an improvement in this respect, as we know 'a word to the wise is sufficient.'

"In the two back rows we are sorry to say that we have noticed whispering. We know that this fact will very much distress our teacher, as she expects assistance, and not trouble, from our older scholars. It is not our business to reprove any one's misconduct, but it is our duty to mention it, however disagreeable it may be. We think the younger scholars, during the past week, have much improved in this respect. Only three cases of whispering among them have occurred to our knowledge.

"We remember some remarks made a few weeks ago by our teacher on the practice of prompting each other in the classes. We wish she would repeat them, for we fear that, by some, they are forgotten. In the class in Geography, particularly in the questions on the map, we have noticed sly whispers, which, we suppose, were the hints of some kind friend designed to refresh the memory of her less attentive companion. We propose that the following question be now put to vote. Shall the practice of prompting in the classes be any longer continued?

"We would propose that we have a composition exercise _this_ week similar to the one on Thursday last. It was very interesting, and we think all would be willing to try their thinking powers once more. We would propose, also, that the readers of the compositions should sit near the centre of the room, as last week many fine sentences escaped the ears of those seated in the remote corners.

"We were requested by a very public-spirited individual to mention once more the want of three nails, for bonnets, in the entry. Also, to say that the air from the broken pane of glass on the east side of the room is very unpleasant to those who sit near.

"Proposed that the girls who exhibited so much taste and ingenuity in the arrangement of the festoons of evergreen, and tumblers of flowers around the teacher's desk, be now requested to remove the faded roses and drooping violets. We have gazed on these sad emblems long enough.

"Finally, proposed that greater care be taken by those who stay at noon to place their dinner-baskets in proper places. The contents of more than one were partly strewed upon the entry floor this morning."

If such a measure as this is adopted, it should not be continued uninterrupted for a very long time. Every thing of this sort should be occasionally changed, or it sooner or later becomes only a form.

14. THE SHOPPING EXERCISE.--I have often, when going a shopping, found difficulty and trouble in making change. I could never calculate very readily, and in the hurry and perplexity of the moment I was always making mistakes. I have heard others often make the same complaint, and I resolved to try the experiment of regularly teaching children to make change. I had a bright little class in Arithmetic, the members of which were always ready to engage with interest in any thing new, and to them I proposed my plan. It was to be called the Shopping Exercise. I first requested each individual to write something upon her slate which she would like to buy, if she was going a shopping, stating the quantity she wished and the price of it. To make the first lesson as simple as possible, I requested no one to go above ten, either in the quantity or price. When all were ready, I called upon some to read what she had written. Her next neighbor was then requested to tell us how much the purchase would amount to. Then the first one named a bill, which she supposed to be offered in payment, and the second showed what change was needed. A short specimen of the exercise will probably make it clearer than mere description.

_Mary_. Eight ounces of candy at seven cents.

_Susan_. Fifty-six cents.

_Mary_. One dollar.

_Susan_. Forty-four cents.

* * * * *

_Susan_. Nine yards of lace at eight cents.

_Anna_. Seventy-two cents.

_Susan_. Two dollars.

_Anna_. One dollar and twenty-eight cents.

* * * * *

_Anna_. Three pieces of tape at five cents.

_Jane_. Fifteen cents.

_Anna_. Three dollars.

_Jane_. Eighty-five cents.

_Several voices_. Wrong.

_Jane_. Two dollars and eighty-five cents.

* * * * *

_Jane_. Six pictures at eight cents.

_Sarah_. Forty-two cents.

_Several voices_. Wrong.

_Sarah_. Forty-eight cents.

_Jane_. One dollar.

_Sarah_. Sixty-two cents.

_Several voices_. Wrong.

_Sarah_. Fifty-two cents.

* * * * *

It will be perceived that the same individual who names the article and the price names also the bill which she would give in payment; and the one who sits next her, who calculated the amount, calculated also the change to be returned. She then proposed _her_ example to the one next in the line, with whom the same course was pursued, and thus it passed down the class.

The exercise went on for some time in this way, till the pupils had become so familiar with it that I thought it best to allow them to take higher numbers. They were always interested in it, and made great improvement in a short time, and I myself derived great advantage from listening to them.

There is one more circumstance I will add which may contribute to the interest of this account. While the class were confined, in what they purchased, to the number ten, they were sometimes inclined to turn the exercise into a frolic. The variety of articles which they could find costing less than ten cents was so small, that, for the sake of getting something new, they would propose examples really ludicrous, such as these: three meeting-houses at two cents; four pianos at nine cents. But I soon found that if I allowed this at all, their attention was diverted from the main object, and occupied in seeking the most diverting and curious examples.

15. ARTIFICES IN RECITATIONS.--The teacher of a small newly-established school had all of his scholars classed together in some of their studies. At recitations he usually sat in the middle of the room, while the scholars occupied the usual places at their desks, which were arranged around the sides. In the recitation in Rhetoric, the teacher, after a time, observed that one or two of the class seldom answered appropriately the questions which came to them, but yet were always ready with some kind of answer--generally an exact quotation of the words of the book. Upon noticing these individuals more particularly, he was convinced that their books were open before them in some concealed situation. Another practice not uncommon in the class was that of _prompting_ each other, either by whispers or writing. The teacher took no notice publicly of these practices for some time, until, at the close of an uncommonly good recitation, he remarked, "I think we have had a fine recitation to-day. It is one of the most agreeable things that I ever do to hear a lesson that is learned as well as this. Do you think it would be possible for us to have as good an exercise every day?" "Yes, sir," answered several, faintly. "Do you think it would be reasonable for me to expect of every member of the class that she should always be able to recite all her lessons without ever missing a single question?" "No, sir," answered all. "I do not expect it," said the teacher. "All I wish is that each of you should be faithful in your efforts to prepare your lessons. I wish you to study from a sense of duty, and for the sake of your own improvement. You know I do not punish you for failures. I have no going up or down, no system of marking. Your only reward, when you have made faithful preparation for a recitation, is the feeling of satisfaction which you will always experience; and when you have been negligent, your only punishment is a sort of uneasy feeling of self-reproach. I do not expect you all to be invariably prepared with every question of your lessons. Sometimes you will be unavoidably prevented from studying them, and at other times, when you have studied them very carefully, you may have forgotten, or you may fail from some misapprehension of the meaning in some cases. Do not, in such a case, feel troubled because you may not have appeared as well as some individual who has not been half as faithful as yourself. If you have done your duty, that is enough. On the other hand, you ought to feel no better satisfied with yourselves when your lesson has not been studied well, because you may have happened to know the parts which came to you. Have I _done_ well? should always be the question, not, Have I managed to _appear_ well?

"I will say a word here," continued the teacher, "upon a practice which I have known to be very common in some schools, and which I have been sorry to notice occasionally in this. I mean that of prompting, or helping each other along in some way at recitations. Now where a severe punishment is the consequence of a failure, there might seem to be some reasonableness in helping your companions out of difficulty, though even then such tricks are departures from honorable dealing. But, especially where there is no purpose to be served but that of appearing to know more than you do, it certainly must be considered a very mean kind of artifice. I think I have sometimes observed an individual to be prompted where evidently the assistance was not desired, and even where it was not needed. To whisper to an individual the answer to a question is sometimes to pay her rather a poor compliment at least, for it is the same as saying 'I am a better scholar than you are; let me help you along a little.'

"Let us then, hereafter, have only fair, open, honest dealings with each other; no attempts to appear to advantage by little artful manoeuvring; no prompting; no peeping into books. Be faithful and conscientious, and then banish anxiety for your success. Do you not think you will find this the best course?" "Yes, sir," answered every scholar. "Are you willing to pledge yourselves to adopt it?" "Yes, sir." "Those who are may raise their hands," said the teacher. Every hand was raised; and the pledge, there was evidence to believe, was honorably sustained.

16. KEEPING RESOLUTIONS.--The following are notes of a familiar lecture on this subject, given by a teacher at some general exercise in the school. The practice of thus reducing to writing what the teacher may say on such subjects will be attended with excellent effects.

This is a subject upon which young persons find much difficulty. The question is asked a thousand times, "How shall I ever learn to keep my resolutions?" Perhaps the great cause of your failures is this. You are not sufficiently _definite_ in forming your purposes. You will resolve to do a thing without knowing with certainty whether it is even possible to do it. Again, you make resolutions which are to run on indefinitely, so that, of course, they can never be fully kept. For instance, one of you will resolve to _rise earlier in the morning._ You fix upon no definite hour, on any definite number of mornings, only you are going to "_rise earlier_." Morning comes, and finds you sleepy and disinclined to rise. You remember your resolution of rising earlier. "But then it is _very_ early," you say. You resolved to rise earlier, but you didn't resolve to rise just then. And this, it may be, is the last of your resolution. Or perhaps you are, for a few mornings, a little earlier; but then, at the end of a week or fortnight, you do not know exactly whether your resolution has been broken or kept, for you had not decided whether to rise earlier for ten days or for ten years.

In the same vague and general manner, a person will resolve to be _more studious_ or more diligent. In the case of an individual of a mature and well-disciplined mind, of acquired firmness of character, such a resolution might have effect. The individual will really devote more time and attention to his pursuits. But for one of you to make such a resolution would do no sort of good. It would only be a source of trouble and disquiet. You perceive there is nothing definite--nothing fixed about it. You have not decided what amount of additional time or attention to give to your studies, or when you will begin, or when you will end. There is no one time when you will feel that you are breaking your resolution, because there were no particular times when you were to study more. You waste one opportunity and another, and then, with a feeling of discouragement and self-reproach, conclude to abandon your resolution. "Oh! It does no good to make resolutions," you say; "I never shall keep them."

Now, if you would have the business of making resolutions a pleasant and interesting instead of a discouraging, disquieting one, you must proceed in a different manner. Be definite and distinct in your plan; decide exactly what you will do, and how you will do it--when you will begin, and when you will end. Instead of resolving to "rise earlier," resolve to rise at the ringing of the sunrise bells, or at some other definite time. Resolve to try this, as an experiment, for one morning, or for one week, or fortnight. Decide positively, if you decide at all, and then rise when the time comes, sleepy or not sleepy. Do not stop to repent of your resolution, or to consider the wisdom or folly of it, when the time for acting under it has once arrived.

In all cases, little and great, make this a principle--to consider well before you begin to act, but after you have begun to act, never stop to consider. Resolve as deliberately as you please, but be sure to keep your resolution, whether a wise one or an unwise one, after it is once made. Never allow yourself to reconsider the question of getting up, after the morning has come, except it be for some unforeseen circumstance. Get up for that time, and be more careful how you make resolutions again.

17. TOPICS.--The plan of the Topic Exercise, as we called it, is this. Six or seven topics are given out, information upon which is to be obtained from any source, and communicated verbally before the whole school, or sometimes before a class formed for this purpose the next day. The subjects are proposed both by teacher and scholars, and if approved, adopted. The exercise is intended to be voluntary, but ought to be managed in a way sufficiently interesting to induce all to join.

At the commencement of the exercise the teacher calls upon all who have any information in regard to the topic assigned--suppose, for example, it is _Alabaster_--to rise. Perhaps twenty individuals out of forty rise. The teacher may perhaps say to those in their seats,

"Do you not know any thing of this subject? Have you neither seen nor heard of alabaster, and had no means of ascertaining any thing in regard to it? If you have, you ought to rise. It is not necessary that you should state a fact altogether new and unheard-of, but if you tell me its color, or some of the uses to which it is applied, you will be complying with my request."

After these remarks, perhaps a few more rise, and possibly the whole school. Individuals are then called upon at random, each to state only one particular in regard to the topic in question. This arrangement is made so as to give all an opportunity to speak. If any scholar, after having mentioned one fact, has something still farther to communicate, she remains standing till called upon again. As soon as an individual has exhausted her stock of information, or if the facts that she intended to mention are stated by another, she takes her seat.

The topics at first most usually selected are the common objects by which we are surrounded--for example, glass, iron, mahogany, and the like. The list will gradually extend itself, until it will embrace a large number of subjects.

The object of this exercise is to induce pupils to seek for general information in an easy and pleasant manner, as by the perusal of books, newspapers, periodicals, and conversation with friends. It induces care and attention in reading, and discrimination in selecting the most useful and important facts from the mass of information. As individuals are called upon, also, to express their ideas _verbally_, they soon acquire by practice the power of expressing them with clearness and force, and communicating with ease and confidence the knowledge they possess.

18. Music.--The girls of our school often amused themselves in recess by collecting into little groups for singing. As there seemed to be a sufficient power of voice, and a respectable number who were willing to join in the performance, it was proposed one day that singing should be introduced as a part of the devotional exercises of the school.

The first attempt nearly resulted in a failure; only a few trembling voices succeeded in singing Old Hundred to the words "Be thou," etc. On the second day Peterborough was sung with much greater confidence on the part of the increased number of singers. The experiment was tried with greater and greater success for several days, when the teacher proposed that a systematic plan should be formed, by which there might be singing regularly at the close of school. It was then proposed that a number of singing-books be obtained, and one of the scholars, who was well acquainted with common tunes, be appointed as chorister. Her duty should be to decide what particular tune may be sung each day, inform the teacher of the metre of the hymn, and take the lead in the exercise. This plan, being approved of by the scholars, was adopted, and put into immediate execution. Several brought copies of the Sabbath School Hymn-Book, which they had in their possession, and the plan succeeded beyond all expectation. The greatest difficulty in the way was to get some one to lead. The chorister, however, was somewhat relieved from the embarrassment which she would naturally feel in making a beginning by the appointment of one or two individuals with herself, who were to act as her assistants. These constituted the _leading_ committee, or, as it was afterward termed, _Singing Committee_.

Singing now became a regular and interesting exercise of the school, and the committee succeeded in managing the business themselves.

19. TABU.--An article was one day read in a school relating to the "Tabu" of the Sandwich Islanders. Tabu is a term with them which signifies consecrated--not to be touched--to be let alone--not to be violated. Thus, according to their religious observances, a certain day will be proclaimed _Tabu_; that is, one upon which there is to be no work or no going out.

A few days after this article was read, the scholars observed one morning a flower stuck up in a conspicuous place against the wall, with the word TABU in large characters above it. This excited considerable curiosity. The teacher informed them, in explanation, that the flower was a very rare and beautiful specimen, brought by one of the scholars, which he wished all to examine. "You would naturally feel a disposition to examine it by the touch," said he, "but you will all see that, by the time it was touched by sixty individuals, it would be likely to be injured, if not destroyed. So I concluded to label it _Tabu_. And it has occurred to me that this will be a convenient mode of apprising you generally that any article must not be handled. You know we sometimes have some apparatus exposed, which would be liable to injury from disturbance, where there are so many persons to touch it. I shall, in such a case, just mention that an article is Tabu, and you will understand that it is not only not to be _injured_, but not even _touched_."

A little delicate management of this sort will often have more influence over young persons than the most vehement scolding, or the most watchful and jealous precautions. The Tabu was always most scrupulously regarded, after this, whenever employed.

20. MENTAL ANALYSIS.--Scene, a class in Arithmetic at recitation. The teacher gives them an example in addition, requesting them, when they have performed it, to rise. Some finish it very soon, others are very slow in accomplishing the work.

"I should like to ascertain," says the teacher, "how great is the difference of rapidity with which different members of the class work in addition. I will give you another example, and then notice by my watch the shortest and longest time required to do it."

The result of the experiment was that some members of the class were two or three times as long in doing it as others.

"Perhaps you think," said the teacher, "that this difference is altogether owing to difference of skill; but it is not. It is mainly owing to the different methods adopted by various individuals. I am going to describe some of these, and, as I describe them, I wish you would notice them carefully, and tell me which you practice."

There are, then, three modes of adding up a column of figures, which I shall describe.

1. I shall call the first _counting_. You take the first figure, and then add the next to it by counting up regularly. There are three distinct ways of doing this.

(a.) "Counting by your fingers." ("Yes, sir.") "You take the first figure--suppose it is seven--and the one above it, eight. Now you recollect that to add eight, you must count all the fingers of one hand, and all but two again. So you say 'seven--eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen.'"

"Yes, sir, yes, sir," said the scholars.

(b.) The next mode of counting is to do it mentally, without using your fingers at all; but, as it is necessary for you to have some plan to secure your adding the right number, you divide the units into sets of two each. Thus you remember that eight consists of four twos, and you accordingly say, when adding eight to seven, 'Seven; eight, nine; ten, eleven; twelve, thirteen,' &c.

(c.) "The third mode is to add by threes in the same way. You recollect that eight consists of two threes and a two; so you say, 'Seven; eight, nine, ten; eleven, twelve, thirteen; fourteen, fifteen.'"

The teacher here stops to ascertain how many of the class are accustomed to add in either of these modes. It is a majority.

2. The next general method is _calculating_; that is, you do not unite one number to another by the dull and tedious method of applying the units, one by one, as in the ways described under the preceding head, but you come to a result more rapidly by some mode of calculating. These modes are several.

(a.) "Doubling a number, and then adding or subtracting, as the case may require. For instance, in the example already specified, in order to add seven and eight, you say, 'Twice seven are fourteen, and one are fifteen'" ("Yes, sir, yes, sir"); "or, 'Twice eight are sixteen, and taking one off leaves fifteen." ("Yes, sir.")

(b.) Another way of calculating is to skip about the column, adding those numbers which you can combine most easily, and then bringing in the rest as you best can. Thus, if you see three eights in one column, you say, 'Three times eight are twenty-four,' and then you try to bring in the other numbers. Often, in such cases, you forget what you have added and what you have not, and get confused ("Yes, sir"), or you omit something in your work, and consequently it is incorrect.

(c.) If nines occur, you sometimes add ten, and then take off one, for it is very easy to add ten.

(d.) Another method of calculating, which is, however, not very common, is this: to take our old case, adding eight to seven, you take as much from the eight to add to the seven as will be sufficient to make ten, and then it will be easy to add the rest. Thus you think in a minute that three from the eight will make the seven a ten, and then there will be five more to add, which will make fifteen. If the next number was seven, you would say five of it will make twenty, and then there will be two left, which will make twenty-two.' This mode, though it may seem more intricate than any of the others, is, in fact, more rapid than any of them, when one is a little accustomed to it.

"These are the four principal modes of calculating which occur to me. Pupils do not generally practice any of them exclusively, but occasionally resort to each, according to the circumstances of the particular case."

The teacher here stopped to inquire how many of the class were accustomed to add by calculating in either of these ways or in any simpler ways.

3. "There is one more mode which I shall describe: it is by _memory_. Before I explain this mode, I wish to ask you some questions, which I should like to have you answer as quick as you can.

"How much is four times five? Four _and_ five?

"How much is seven times nine? Seven _and_ nine?

"Eight times six? Eight _and_ six?

"Nine times seven? Nine _and_ seven?"

After asking a few questions of this kind, it was perceived that the pupils could tell much more readily what was the result when the numbers were to be multiplied than when they were to be added.

"The reason is," said the teacher, "because you committed the multiplication table to memory, and have not committed the addition table. Now many persons have committed the addition table, so that it is perfectly familiar to them, and when they see any two numbers, the amount which is produced when they are added together comes to mind in an instant. Adding in this way is the last of the three modes I was to describe.

"Now of these three methods the last is undoubtedly the best. If you once commit the addition table thoroughly, you have it fixed for life; whereas if you do not, you have to make the calculation over again every time, and thus lose a vast amount of labor. I have no doubt that there are some in this class who are in the habit of _counting_, who have ascertained that seven and eight, for instance, make fifteen, by counting up from seven to fifteen _hundreds of times_. Now how much better it would be to spend a little time in fixing the fact in the mind once for all, and then, when you come to the case, seven and eight are--say at once 'Fifteen,' instead of mumbling over and over again, hundreds of times, 'Seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen.'

"The reason, then, that some of the class add so slowly, is not, probably, because they want skill and rapidity of execution, but because they work to a great disadvantage by working in the wrong way. I have often been surprised at the dexterity and speed with which some scholars can count with their fingers when adding, and yet they could not get through the sum very quick--at least they would have done it in half the time if the same effort had been made in traveling on a shorter road. We will therefore study the addition table now, in the class, before we go any farther."

21. TARDINESS.--When only a few scholars in a school are tardy, it may be their fault; but if a great many are so, it is the fault of the teacher or of the school. If a school is prosperous, and the children are going on well and happily in their studies, they will like their work in it; but we all come reluctantly to work which we are conscious we are not successfully performing.

There may be two boys in a school, both good boys; one, may be going on well in his classes, while the other, from the concurrence of some accidental train of circumstances, may be behindhand in his work, or wrongly classed, or so situated in other respects that his school duties perplex and harass him day by day. Now how different will be the feelings of these two boys in respect to coming to school. The one will be eager and prompt to reach his place and commence his duties, while the other will love much better to loiter in idleness and liberty in the open air. Nor is he, under the circumstances of the case, to blame for this preference. There is no one, old or young, who likes or can like to do what he himself and all around him think that he does not do well. It is true the teacher can not rely wholly on the interest which his scholars take in their studies to make them punctual at school; but if he finds among them any very general disposition to be tardy, he ought to seek for the fault mainly in himself and not in them.

The foregoing narratives and examples, it is hoped, may induce some of the readers of this book to keep journals of their own experiments, and of the incidents which may, from time to time, come under their notice, illustrating the principles of education, or simply the characteristics and tendencies of the youthful mind. The business of teaching will excite interest and afford pleasure just in proportion to the degree in which it is conducted by operations of mind upon mind, and the means of making it most fully so are careful practice, based upon and regulated by the results of careful observation. Every teacher, then, should make observations and experiments upon mind a part of his daily duty, and nothing will more facilitate this than keeping a record of results. There can be no opportunity for studying human nature more favorable than the teacher enjoys. The materials are all before him; his very business, from day to day, brings him to act directly upon them; and the study of the powers and tendencies of the human mind is not only the most interesting and the noblest that can engage human attention, but every step of progress he makes in it imparts an interest and charm to what would otherwise be a weary toil. It at once relieves his labors, while it doubles their efficiency and success.