66 day of doom, so that we shall be witnesses against ourselves? And does he not teach us that the only way to escape his judgment is to judge ourselves; to have a lively remembrance of our own faults; to acknowledge our transgressions," and "keep our sins ever before us;" and so to confess them all with our own lips to him. If the method which I have related were adopted, would it not be training children to the practice of remembering and confessing their faults to their Heavenly Father? Would it not bring them under the eye of their minister in a manner which would mark distinctly the line between a mere breach of discipline punishable by the master, and a deep moral stain which requires the rebuke and the intercession of the appointed guide of their souls. The opinion of any who have laboured longer and more faithfully for the younger ones of Christ's flock than I have, will greatly oblige Yours obediently, Jan. 8, 1845. VICAR. NEW METHOD OF TEACHING THE ALPHABET, REV. SIR, I shall be glad, with your permission, to lay before your readers the following description of a method of teaching the alphabet, which I have used with great success. Cut up a convenient quantity of cartridge paper to the same size as the separate sums I formerly described, and place them, fifty-two pieces in each, in cases similar to those which contain the sums. In the left hand upper corner of one of the sets, make the characters R. L. 1 (Reading Lessons, Case First), and in the right hand corner write the number; in the middle of each fix, with paste or gum, three of the first thirteen capitals. The following specimen may help to explain my meaning: R. L. 1 AM G In making the lessons, care must be taken that no two be alike, and that each letter be repeated the same number of times, and in as many different situations. As there are fifty-two papers in a case, and three letters on each, and but thirteen different letters, it follows that each letter will be found on twelve different papers; it will be first on four papers, it will be second on four others, and it will be last on another four. Thus prepared, take two children, the younger the better,* provided they be able to do what is required of them; seat them six or eight feet apart, and call one the "hearer," and the other the "teacher :' give the hearer the lessons I have been describing; now bring two * I choose the smaller children for various reasons:-first, because they are exceedingly happy to be employed; next, because I believe that such employments sharpen their intellects; thirdly, because I like to make the children useful, and take an interest in what is going on in the school, as soon as possible; and, fourthly, because I would never employ a large boy, where a smaller would do equally well. learners to the hearer, and let him give each of them a lesson; as soon as a learner has received it, let him run to the teacher and read it, if he be able, if not, the teacher will read it to him; then let the learner return to the hearer and repeat it to him, the hearer carefully looking on to see if he reads correctly; if he does so, the hearer will give him another paper, with which he will proceed in the same manner, laying by the first in a convenient place. Should the child not read it correctly to the hearer, he must send him back to the teacher to hear it read again. When the papers are all read, let each learner count how many he has read, the hearer and teacher standing by to render assistance should it be required, but they should not be allowed to interfere unnecessarily ; first, because the learners like to do it themselves; and, secondly, because the practice teaches them by degrees to count correctly. The number read by each must then be marked on the proper list; this done, send the learners to their place, and call two others whose names stand next on the list, and proceed with them in the same manner. When a hearer and teacher have been appointed, they should remain an hour; in this time they will hear four or five sets of learners. I have sometimes found it expedient to allow beginners to read only the first letter on each paper, during a lesson or two. When a child goes to school for the first time, he has generally a very exaggerated idea of the difficulties he will have to encounter; hence, when called upon to commence his lessons, he very naturally says, "I can't do it," and appears very unwilling to try. Now, as it is one of a master's principal objects to make their children love the school and himself, he will be very desirous to overcome this diffidence, without recourse to harshness in word or deed. When a child makes such a reply to a judicious instructor who taught the alphabet on this system, he would probably reply in some such way as this: " Well, I'll show you the way." He would then take him to the hearer for a paper, then to the teacher to hear it read; when the latter has told the child the name of the first letter on the paper, the master would take him back to the hearer, and tell the child to point to the first letter on the paper and tell the hearer the name of it; when the master has gone with him a few times, he will be able and desirous of going on alone, and will cost the master no more trouble till he has learned the alphabets. When a child can read the first case without assistance or hesitation, he must be advanced to case second," which contains the remaining thirteen capitals, arranged on fifty-two papers, similarly to the first thirteen. From this he is successively promoted into "case third," which contains the first seven and last six small roman letters; case fourth," which contains the remaining thirteen small letters; and "case fifth," which contains all the letters, capital and small. The first letter on each paper in this case should be a capital, the second a roman small, and the third an italic small. The advantages of this method are various and important: first, it is healthy, from the exercise it affords; next it is agreeable, indeed, I may say, it is extremely amusing to the children; hence it induces a love of school at their first entrance into it, when it is so desirable that such a feeling should be implanted in their minds. That they are fond of learning by this method I have often proved, by sending the little ones into the yard to play, and after the lapse of a few minutes desiring the boy, whose duty it was to call the boys in their turn to read, to go to the door and call the two whose turn it happened to be; at such times I have been almost always gratified to see the children leave their play, however interesting, and run into the school without a moment's hesitation, their little countenances beaming with pleasure. It has been often asserted that children naturally dislike learning; my experience teaches me a different lesson. But if we wish to teach children, we must use childish methods; we must descend to their capacity, and, as far as possible, suit their inclinations. Another important advantage of the system is, that the children learn the alphabets much faster than by any other method I have seen employed; this may seem strange, when the number of cases they have to go through is considered, but it is no less true. To make the different cases of which I have spoken, I employed a boy to cut out the alphabets from some school books, where they were of no service, and fix them, one by one, on the prepared paper, according to a form which I laid before him. In a very short time after the commencement of this method of teaching, there was not a child to be found in the school unacquainted with the alphabet. Finding the plan successful thus far, I attempted to extend it by making other cases; first, for teaching words of two letters; next, short lessons, containing words of two letters only; then, single words, containing three letters, &c.; but I soon found it necessary to give up all except the alphabets, from the confusion it occasioned in the school; yet I did not relinquish the attempt, until I saw enough to convince me that children would learn much faster by this than by the ordinary methods. In conclusion, I would respectfully urge such of your readers as have had any trouble in teaching the alphabets, and especially teachers of infant schools, to give this system a trial, and, I have no doubt, that they will soon consider themselves amply repaid for the trouble of making the lessons. Clerkenwell, Jan. 1845. Your obedient servant, AN EXPLANATION OF THE SQUARE AND CUBE ROOTS. SQUARE ROOT. THE product of a number multiplied by itself is called a square number, because, if we take a line, of any number of yards, feet, or inches, and construct a square on it, the contents of such a square will equal the product of the number multiplied by itself. The original number is Here we may observe that the square of any one digit is less than 100, i.e., never exceeds two digits; but that the square of 10 amounts to three places of figures. So, again, the square of 99 (9,801) does not exceed four places; but the square of 100 (10,000) occupies five places. Again, the square of 999 (998,001) does not exceed six places. And we may observe, that every two places of figures in the square has one place in the root, e.g.— Again, we may observe that the square of which the side is divided into two parts, is in reality made up of the squares of each of the parts, and the product of the two parts taken twice. + G F Fig. 2. If A B be 12, i.e., 10+ 2, then the whole square of A B (10 × 10) + (2 × 2) + 100 or + D E In order that we may see this clearly, we will take another example. Let A B be 35, i.e., 30 + 5. MEM. For the convenience of notation it may be observed, that a × a is expressed thus a2. Therefore 30 × 30 will be written 302; 5 x 5 = 52. So also 7 x 7 x 7 will be written 73, 7 cubed or cube 343; and the steps alrea y gone through, will be expressed algebraically thus: = square, when In all these cases, it is obviously an easy task to find the the root is given; but the point which we now wish to investigate is, how to find the root when the square is given; let us for example try to find the root of 1,225. First, I see that there are four places of figures; therefore the root must consist of two: it is greater than 9, and less than 100. I mark off two places in the figures of the square, for each figure in the root,1,225, and regarding the 12, at first, without reference to the rest, I seek the largest square contained in it, which is 9, of which the root is 3, and I proceed as follows: 1,225 (3 9 325 Here then the 3 put down is 30 in reality, for it is to be in the place of tens in the root, and it represents A C in Fig. 2, and the 900 represents A D. The remaining part CEG 325, and I want to find C B. BD 30 × C B 30 X CB} = = CB 60 × CB СВ × СВ Or CE G = 64 × 4 = 256 If we take it at 5, we have 65 × 5 325, and the true root will be 35. |