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Having finished his alphabet in sand after this manner, he writes the whole at once, when those letters in which he fails, are given him for his daily tasks, till he can write all of them well. He next goes through exactly the same process with slates and pencils. And when he can exhibit a perfect alphabet, and write well on his slate; he is advanced to write with paper, pen, and ink, on a copy-book, the reward of his proficiency. Here the same process is followed as before. The scholar learns to write the letters one by one. But for the economy of paper, when he comes to write them together, he writes, all those letters, in the first instance, which are confined within his ruled lines, and then all those, which fall below, lastly all which rise above them, till he is perfect in these respective lessons. The paper is ruled accordingly, so that there may be no waste. When he can write every letter well, he is advanced to joining band. All along the scholar's progress is marked by his rank on the writing bench, a constant spirit of emulation is thereby kept in action, and his proficiency receives its due reward (which is not a little prized) of precedence and honour.
My correspondents will read with peculiar interest the instruction on this head, of one, who is himself so distinguished a proficient in the art, which he would communicate to the pupils of his English school.
The learning to count as far as 100, and to repeat the arithmetical tables from the mouth of the teacher, begins (like the religious exercises) as soon as the child enters the school, although he may not have learnt his alphabet. It is a relief from his daily tasks, to get by heart, in a short lesson every afternoon, a small portion of these preliminary exercises, which pave the way for his entering on this art, and render its future operations easy and pleasant.
Begin by teaching the scholar to read and write any digit by itself as 7, then any number of two places, as, 70 and 58, then of three places, or a half period, as, 400, and 506, and 320, and 637. These seven cases embrace all the variety, which can occur. For every number, however long, is composed of a successive repetition of half periods. In these elements, therefore, viz. in reading and writing, units, tens, and hundreds, or a single half period, the scholar is made perfect. No more is necessary to enable him to read the longest number, which is only a succession of half periods. The usual practice, and waste of time in counting thousands, tens of thousands, hundreds of thousands, millions, &c. is entirely superseded by a mechanical contrivance, which renders all the operations of numeration and notation, facile and expeditious. This contrivance consists in dividing every long number, into half periods of 3 places each, and periods of 6 places each, by alternate commas and semicolons, placing 1, 2, 3, 4, &c. dots respectively over the figures, in the left of each successive semicolon. Thus to read:
7 3 8 079 0 0 0 4 8 0 0 5 6 7 0 0 0 0 5 9 8 4 2 0070801 inark as follows:
73; 807,900; 048,005; 670,000; 598,420; 070,801.
And read the divisions, one by one, each by itself, as if it was a single half period for previous instruction, thus-Seventy-three; eight hundred and seven, nine hundred forty-eight, five; six hundred and seventy;
ive hundred and ninety-eight, four hundred and twenty; seventy, eight hundred and one: and, then, precisely, in the very same manner, only pronouncing thousands for each comma, and millions for every dot; thus-Seventy-three millions of M. of M. of M. of M (or quintillions); eight hundred and seven thousand, uinehundred M. of M. of M. of M. (or quartillions); fortyeight thousand, and five M. of M. of M. (or trillions);
six hundred and seventy thousand M. of M. (or billions); five hundred and ninety-eight thousand, four hundred and twenty millions; seventy thousand, eight hundred and one.
Numeration thus taught, notation may be said to be already learnt. The distinguishing marks enable the scholar, to begin to write down the number, at the left hand. An example will suffice. Note down seventy septillions, eighty thousand quadrillions, five hundred billious, and four thousand and ten.
70; 000,000; 000,000; 080,000; 000,000; 000,500; 000,000; 004,010.
In proceeding to the four cardinal rules of arithmetic, which indeed constitute the whole, let the same principle be still pursued. Let the elementary parts be perfectly learnt in classes, by short, easy, and frequent lessons, repeated as often as necessary. Particularly, before you begin to add, subtract, multiply, or divide, let every member of the class be able to say the addition, subtraction, multiplication, and division tables respectively, in any and every way, without the smallest hesitation or mistake. Examine thus, 6+9 and 9+6= 15; 15-69 and 15—9—6; 8 x 12 or 12 x 8 = 96; 96128, and 968 12. In this specimen, will be seen, by those who are versed in arithmetic, the construction of the addition table, which serves for a subtraction table, and is of the same form, with the wellknown multiplication table, which also serves for a division table. These thoroughly and perfectly learnt, every operation is comparatively easy. The farthing, pence, shilling, and pound tables are in effect included in them, at least in the operations of dividing and substracting.
For the rest, as well as for the explication of the preceding hints, I must refer to the practice of the Madras
school, as my limits do not admit of entering into details, or writing a treatise on arithmetic, which, an illustration of all the peculiar processes of that school, would require. I observe only, that the mode of the teacher's instructing by classes, detailed above, in teaching writing on sand, and on slate, and tables in arithmetic, &c. applies equally to subtraction, multiplication, and division, &c. and it need not here be repeated.
The teacher dictates extempore a sum by word of mouth, as in the sand, and the whole class set it down without any copy before their eyes, and then read it. After which, the boys begin to perform the operation, each doing a single step by turns. When the whole is performed, the teacher inspects the slates, assigns his due rank to each performer, and sets the scholar who does not write down his sum correctly and properly, to copy it, till it is well done.
The advantage of this process is, not only that the most numerous class are instructed with a facility and effect, far greater than a single scholar can be taught in the usual mode of proceeding; but that every sc lar must necessarily be master of every operation, which he has performed, of every rule, in which he has been instructed. How seldom this is the case, when scholars perform individual sums, and copy from books, and from one another; or are individually directed by the masters, or helped by their school-fellows, may be ascertained by any one who will make the trial, with the common run of arithmeticians.
It is important to conduct the scholar through the simple rules of addition, subtraction, multiplication, and division; and then to proceed to compound addition, subtraction, &c.
Rewards and Punishments.
"Cædi, vero discentes, quanquam & receptum sit, & chrysippus non improbet, minime velim; Postremo quod ne opus quidem erit hac castigatione
si assiduus studiorum exactor adstiterit. Nunc fere negligentia pædagogorum sic emendari videntur, ut pueri non facere quæ recta sunt, cogantur, sed, cum non fecerint, puniantur." QUIN.
The author has had so many applications made to him, relative to the rewards and punishments of the new school, that he deems it expedient to give a general answer to these interrogatories under a distinct head.
On the introduction of the system into England, many of those who undertook the management and the visiting, as well as the teaching of schools, and who had imperfectly learnt to wield the mighty machine, did not perceive its powers of discipline, as well as of tuition. They did not perceive that the system comprehends within itself, and distributes with an impartial and unerring hand, rewards and punishments of the most appropriate kind. Now, however, that it begins to be generally understood, and carried into effect, under the direction of the ablest heads, it is safe to dismiss the rod as a powerless and mischievous weapon, from the hands, by which it has been so long wielded.
Hitherto details on this subject were not thought necessary, because the system, being a system of prevention, did not require the contrivance of new modes of punishment, but aimed at the superseding of those which were established: and that such was its effects, see the report of the Madras Asylum, Exp. p. 27, 28, El. p. 43, 44, and the corresponding extracts of the Barrington school, p. 28, &c. &c.
Not to punish but to prevent idleness or misbehaviour of any kind in school, a tutor is assigned to every. boy, who is inattentive, or disorderly. The master does not (as often happens in other schools) allow idleness, for example, to take place, and judge of it by a false criterion and after test-the scholar's knowledge of his lesson. This he may be ignorant of, not through idleness, but inability; not from any fault of his own, but that of those who assigned to him a task above his