Note V, p. 320.—Arithmetic, and numerical calculations of every kind, are wrought by what have been termed "the four simple Rules," viz. Addition, Subtraction, Multiplication, and Division. They who are expert and accurate in working these, have only to learn the several rules by which they are applied to all the varied purposes of life, to be perfect arithmeticians.

But when the working of these four rules is analysed, we find that, with the exception of the multiplication table, the whole four are merely different applications of the rule of addition. Subtraction is wrought by adding a supposed sum to the figure to be subtracted;—multiplication (with the exception mentioned above,) it wrought simply by adding the carryings and the aggregate of the several lines;—and division, with the same exception, is also in practice wrought by a series of additions. If then we shall suppose the multiplication table fully mastered, it follows, that the person who has attained greatest expertness in addition, will be the most expert in the working of any and every arithmetical exercise to which he may be called.

But expertness in arithmetical calculations, is by no means so valuable as accuracy;—and upon the above principle, it also follows, that the person who acquires the greatest degree of accuracy and confidence in working addition, must, of course, be most accurate in all his calculations. The importance of this principle will be much more prized by and bye than it can be at present;—we shall however shew here how it may be taken advantage of.

Upon the principle of Individuation, we have seen, that a child will learn one thing much better and sooner by itself, than when it is mixed up with several others; and therefore we come to the conclusion, that a child, when taught the practice of addition by itself, till he is fully master of it, both as respects rapidity and accuracy, has afterwards little more to do than to get a knowledge of rules. One month's systematic exercise in this way, will do more in forming a desirable accountant for a desk, than a whole year's exercise otherwise. In the one case, the pupil starts to the race without preparation, and with all his natural impediments clinging to him, which he has to disentangle and throw off one by one during the fatigues and turmoil of the contest; while the other, on the contrary, delays his start till he has deliberately searched them out and cast them aside, and thus prepared himself for the course. He then starts vigorous and light, to outstrip his labouring and lumbering competitors, not only in this, but in every after trial of strength and skill of a similar kind.

To follow out this plan with success, the "Arithmetic Rod," containing three sides, has been provided. On one side there is a single line of figures, on the second two, and on the third three. These lines of figures for a school, ought to be painted on three boards sufficiently large for all to see them distinctly. The first line is to be mastered perfectly, before the second or the third is to be taught.

The way to begin with the first line, is to make the pupil mentally add a certain sum to each figure on the board, say two, or seven, or fourteen, or any other sum, beginning always with a small one. He is besides to add the carryings also to each figure, and to write down the sum as he goes on. The beginner may be exercised with the sum of two, or even one, and have the sum increased, as he acquires a knowledge of the method. These sums, as the pupils advance, may be extended to any amount. The Key will shew, in every case, whether the exercise has been accurately performed; and by marking the time in any particular case, the teacher can measure exactly, every week or month, the advance of each pupil.

The mental advantages of this exercise are numerous. Among other things it trains to a great command of the mind; and brings into exercise an important principle formerly illustrated, (Part III. ch. xi. p. 288,) by which the pupil acquires the ability to think one thing, and to do another.

When the pupil is sufficiently expert at one line of figures, he should be exercised upon the B side of the rod, containing the double line. He is to practise adding each pair of the figures at a glance,—till he can run them over without difficulty, as if they were single figures. He is then to add a sum to them, as he did on the single line, till he can add the sum and the double figure as readily as he did one. The C side of the rod is to be treated in the same way;—first by adding all the three figures at a glance, and naming the sum of each, till he can do it as readily as if there was but one; and then he is to add any special sum to them as before.

Note W, p. 321.—Children generally delight in music, and seldom weary in its exercise. It forms therefore, when judiciously managed, a most useful exercise in a school for the purposes of relaxation and variety, and for invigorating their minds after a lengthened engagement in drier studies. It thus not only becomes desirable to teach music in the seminary as a branch of education for after life, but for the purposes of present expediency.

That music may be taught to the young in a manner much more simple than it has yet generally been done, is now matter of experience. The notes are only seven, and these are each as precise and definite in proportion to the key note as any letter in the alphabet. There is obviously no difficulty in teaching a child seven figures,—and there is in reality as little difficulty in teaching him seven notes; so that, having the key note, he will, in reading a tune, sound each in its order when presented to him, as readily and accurately as he would read so many figures.

To render this exercise more simple to children, and more convenient in a school, the notes have been represented by figures, 1 being the key note. The other notes rise in the common gradation from 1 to 8, which is the key note in alt. By this means, the teacher by writing on the common black board a few figures, gives the children the tune, which a very little practice enables them to read as readily as they would the words to which they adapt it.

For particulars as to time, &c. see "Shorter Catechism Hymn Book," p. 23 and 24.

Note X, p. 264.—There is perhaps no department in the family economy which ought to be so cautiously filled up as the nursery maid; and yet we generally find, that the duties of this office are frequently handed over to any thoughtless giddy girl, whose appearance is "shewy," although she be without education, without experience, and often without principle. Why there has been as yet no regular seminary for the training of young persons of good principles, for the responsible duties of the nursery, is not a little remarkable. Not one of the many valuable institutions for particular classes is so much wanted, and which, if properly conducted, would be a greater blessing to families and to society generally. One of the most beautiful features in our infant schools is the circumstance, that they have tended greatly to lessen this evil, and in some measure to supply the desideratum.

Note Y, p. 268.—The question of rewards and punishments in a public school is a difficult one; and although there has of late been an obvious improvement in this respect, we are afraid that the principles which ought to regulate them are not yet very clearly understood. Hence the contrariety of sentiments on the subject, with little more than mere opinions offered to support them. The following few crude thoughts on the subject, may perhaps lead others better qualified to consider it more extensively.

We can all readily enough distinguish the difference between physical efforts, intellectual efforts, and moral efforts; but we are very ready to confound the rewards which, we think, Nature has pointed out as most appropriate to each. For physical exertions, such as the race, or the wrestling match, physical returns appear natural and appropriate enough; and therefore, money, decorations, or other physical honours, are the ordinary rewards for excelling in any of them. But to desire money as a return for intellectual excellence, appears to every well constituted mind as sordid and unseemly. The reward for the exertion of intellect must partake of intellectual dignity; and hence it is, that esteem, applause, or admiration,—the incense of the mind,—appears to be the natural return for such exertions. In proof of this, we may instance the sensible degradation which is felt, when the reward proffered for mental efforts, even in children, takes the form of food, or clothing, or money;—and the kind of estimation in which students hold their medals, books, and other prizes, acquired at their several seminaries. These are never valued for their intrinsic worth, but only as permanent signs of approbation, or admiration,—feelings which are purely intellectual in their character, and perfectly distinct from the grossness of physical rewards on the one hand, and the affections—the moral incense of the heart,—on the other.

All this appears pretty evident; and it obviously leads us to the next and concluding step, which is, that the natural and proper reward for moral actions, ought to partake of the moral character. It is the love and affection of those we serve, or who are called on to estimate, or to decide on the character of our actions,—that is the proper, the natural, the desirable return. A little consideration, we think, will shew us, that this, as a general principle, is really correct; and that applause, admiration, or wonder, when they are afforded without affection, do not satisfy the heart, that in the exercise of love, seeks love in return.—It is the friendship, the fellowship, the affections of those whom we aim at pleasing, that alone can approve itself to our minds as the appropriate returns for moral actions.

Note Z, p. 299.—The following are a few specimens of the paraphrastic exercise, as employed upon different subjects:—

"But Martha was [cumbered] [about much serving,] and came to [him,] and said, Lord, [dost thou not care] that my sister hath left me to [serve] alone? [bid] her, therefore, that she [help] me."

This verse is paraphrased in the Help to Luke by substituting the explanation of the words printed in Italics, and within brackets, for the words themselves, in the following manner:

"But Martha was [much incommoded and harassed] [to get every thing in order for the temporal accommodation of Jesus and his disciples,] and came to [Jesus,] and said, Lord, [art thou indifferent or careless about the circumstance] that my sister hath left me to [prepare the victuals, and do all the work of the house] alone? [Command] her, therefore, that she [leave her seat at thy feet, and come to assist] me."

"Every thing [in nature] [shews forth] God's [wisdom,] [power,] and [goodness;] but the Bible, which is the [word of God,] and which was [written] by [holy] men at [different times,] under [his direction,] has most [clearly] [revealed] what [God is,] what he has done and what [we should do."]

This is paraphrased in the Key to the Second Initiatory Catechism thus:

"Every thing [that has been made in the world and sky] [gives clear and constant proof of] God's [chusing the best ends, and accomplishing these by the best means,] [his being able to do any thing, and every thing,] and [never ceasing to care for, and to promote the happiness of all his creatures;]—but the Bible,—which is the [only declaration of God's mind and will to man,] and which was [composed, and put, with pen and ink, upon parchment or paper,] by [good and pious] men, at [dates long distant from each other,] under [the care of God, who told them what they were to write,]—has most [distinctly and plainly,] [brought into view, and let us know,] what [God's character and perfections are,] what he has done, and what [is our duty, both to God and man."]

"The [word of God,] which is contained in the [Scriptures] of the Old and New Testament, is the only [rule] to [direct us] how we may glorify and enjoy him."

This is paraphrased in the Key to the Shorter Catechism in the following manner:

"The [revelation of God's will,] which is contained in the [writings] of the Old and New Testament, is the only [guide] to [give us information] how we may glorify and enjoy him."

Note A a, p. 321.—Nature has obviously intended that all men should be both physically and mentally employed; and that, for the proper maintenance of health, the time occupied by physical exercise, ought in general to exceed that which is employed exclusively in study. The combination of both in ordinary cases, however, is still more plainly indicated. In the circumstances of the young, physical exercise is peculiarly necessary. The writer looks forward with confidence to a time, when to every seminary of eminence will be attached a sufficient plot of ground for gardening and agricultural purposes, that the physical energies of the pupils may not be allowed irregularly to run to waste, as at present; but when they shall be systematically directed to interesting, and at the same time to useful purposes. The hand-swing, although an excellent substitute, will never cope in interest, even to a child, with the moderate use of the hoe, the rake, or the spade. Such a system will produce many and valuable advantages to the young. Gardening, by postponing the results of labour, exciting hope, and by its daily advances, encouraging to perseverance, will tend to produce a most beneficial moral effect; and will greatly assist the teacher in establishing and strengthening some of those valuable checks upon the volatility of the young mind, which are exceedingly necessary for the proper conduct of life, but which there is usually but small opportunity of cultivating in youth.

But even then, for the proper conducting of a school, there will, for in-door exercise, be something more required than has yet been provided, both as to kind and degree. When we examine a number of children at play, we seldom find them sitting, or even standing for any length of time, when they have space and opportunity to exercise their limbs. The hand-motions of the infant schools, therefore, although excellent so far as they go, do not go far enough; and even the marching of the children is obviously too monotonous, and not sufficiently lively, for throwing off the accumulated mass of animal spirits, which is so speedily formed in young persons while engaged at their lessons. It was to supply this defect that the writer, a number of years ago, made some experiments with a large class of children, and with complete success. The exercise was founded on the singing and marching of the infant schools, and consisted in what is known in certain seminaries, as "Rights and Lefts." The children were taught to meet each other in bands of equal number, and by giving the right and left hand alternately to those who came in the opposite direction, they undulated, as it were, through each others ranks, and passed on to their own music, till they met again on the other side of the room, and proceeded as before. The exercise thus afforded to the upper and lower extremities of each child, the expansion caused to the chest, and the play given to the muscles of the back and body, are exceedingly beneficial; and the whole being regulated by their own song, gives healthy, and not excessive exercise to the lungs and the whole circulation.

It was also found, that this amusing employment for the young, was capable of great variety. Instead of two bands meeting each other in lines in opposite directions, and parting, to meet again at the other side of the room, they were formed into a circle, one-half moving in one direction, and one-half moving in the opposite, by which means the circle was never broken. It was also found, that one of these circles, containing six or eight children only, could move within the other when it contained a larger number, without those in the one interfering in the least with those of the other; and the effect became still more imposing when between these, and without them, two other bands of children joined hands, united in the song, and moved round in opposite directions.

These details may appear trifling to some; but experience will soon convince practical men, that in education, as in Nature, the most simple means often produce the most powerful and the most beneficial results.

THE END.



- Transcriber's Note: Footnotes listed as a Note followed by a letter are gathered together at the end of the book. Inconsistent hyphenation and spelling in the original document has been preserved. Typographical errors corrected in the text: Page 20 he changed to be Page 28 vallies changed to valleys Page 36 pullies changed to pulleys Page 38 bye changed to by Page 45 recal changed to recall Page 57 inconsistences changed to inconsistencies Page 59 recal changed to recall Page 61 he changed to be Page 67 oppreseive changed to oppressive Page 68 word "is" added Page 73 recals changed to recalls Page 77 harrassed changed to harassed Page 103 missle changed to missile Page 113 decrepid changed to decrepit Page 120 pronouned changed to pronounced Page 142 slighest changed to slightest Page 144 intance changed to instance Page 150 educa- changed to education Page 152 Jessus changed to Jesus Page 166 fourteeen changed to fourteen Page 168 Pestalozzie's changed to Pestalozzi's Page 169 unnaccountable changed to unaccountable Page 183 recal changed to recall Page 192 missing word "be" supplied Page 195 indispensible changed to indispensable Page 197 exceeedingly changed to exceedingly Page 197 recal changed to recall Page 210 comtemplation changed to contemplation Page 211 soffa changed to sofa Page 234 than changed to then Page 245 Terrestial changed to Terrestrial Page 277 forwarned changed to forewarned Page 280 aplication changed to application Page 283 speciment changed to specimen Page 302 faultering changed to faltering Page 326 Princiciples changed to Principles Page 333 desireable changed to desirable Page 339 faultering changed to faltering Page 340 ungodily changed to ungodly -

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