Read Ebook: Practical Education Volume II by Edgeworth Maria Edgeworth Richard Lovell

Font size: 10 px 15 px 20 px 25 px 30 px 35 px

Background color: BlackWhiteGrayLight GrayDark GrayDim Gray

Text color: BlackWhiteGrayLight GrayDark GrayDim Gray

Apply/Save settings

Ebook has 487 lines and 101845 words, and 10 pages

We should like to see the book which helped Mr. Ludwig to conquer his difficulties. Introductions to Arithmetic are, often, calculated rather for adepts in science, than for the ignorant. We do not pretend to have discovered any shorter method than what is common, of teaching these sciences; but, in conformity with the principles which are laid down in the former part of this work, we have endeavoured to teach their rudiments without disgusting our pupils, and without habituating them to be contented with merely technical operations.

In arithmetic, as in every other branch of education, the principal object should be, to preserve the understanding from implicit belief; to invigorate its powers; to associate pleasure with literature, and to induce the laudable ambition of progressive improvement.

As soon as a child can read, he should be accustomed to count, and to have the names of numbers early connected in his mind with the combinations which they represent. For this purpose, he should be taught to add first by things, and afterwards by signs or figures. He should be taught to form combinations of things by adding them together one after another. At the same time that he acquires the names that have been given to these combinations, he should be taught the figures or symbols that represent them. For example, when it is familiar to the child, that one almond, and one almond, are called two almonds; that one almond, and two almonds, are called three almonds, and so on, he should be taught to distinguish the figures that represent these assemblages; that 3 means one and two, &c. Each operation of arithmetic should proceed in this manner, from individuals to the abstract notation of signs.

One of the earliest operations of the reasoning faculty, is abstraction; that is to say, the power of classing a number of individuals under one name. Young children call strangers either men or women; even the most ignorant savages have a propensity to generalize.

We may err either by accustoming our pupils too much to the consideration of tangible substances when we teach them arithmetic, or by turning their attention too much to signs. The art of forming a sound and active understanding, consists in the due mixture of facts and reflection. Dr. Reid has, in his "Essay on the Intellectual Powers of Man," page 297, pointed out, with great ingenuity, the admirable economy of nature in limiting the powers of reasoning during the first years of infancy. This is the season for cultivating the senses, and whoever, at this early age, endeavours to force the tender shoots of reason, will repent his rashness.

One cube and one other, are called two.

Two what?

Two cubes.

One and three are four.

Two and two are four.

Three and one are four.

There is an enumeration in the note of the different combinations which compose the rest of the Arabic notation, which consists only of nine characters.

Before we proceed to the number ten, or to the new series of numeration which succeeds to it, we should make our pupils perfectly masters of the combinations which we have mentioned, both in the direct order in which they are arranged, and in various modes of succession; by these means, not only the addition, but the subtraction, of numbers as far as nine, will be perfectly familiar to them.

It has been observed before, that counting by realities, and by signs, should be taught at the same time, so that the ear, the eye, and the mind, should keep pace with one another; and that technical habits should be acquired without injury to the understanding. If a child begins between four and five years of age, he may be allowed half a year for this essential, preliminary step in arithmetic; four or five minutes application every day, will be sufficient to teach him not only the relations of the first decade in numeration, but also how to write figures with accuracy and expedition.

Our pupil may next be taught what is called numeration, which he cannot fail to understand, and in which he should be frequently exercised. Common addition will be easily understood by a child who distinctly perceives that the perpendicular columns, or places in which figures are written, may distinguish their value under various different denominations, as gallons, furlongs, shillings, &c. We should not tease children with long sums in avoirdupois weight, or load their frail memories with tables of long-measure, and dry-measure, and ale-measure in the country, and ale-measure in London; only let them cast up a few sums in different denominations, with the tables before them, and let the practice of addition be preserved in their minds by short sums every day, and when they are between six and seven years old, they will be sufficiently masters of the first and most useful rule of arithmetic.

From 94 Subtract 46

And then, "One that I borrowed and four are five, five from nine, and four remains."

"If one number is to be deducted from another, the remainder will be the same, whether we add any given number to the smaller number, or take away the same given number from the larger." For instance:

Let the larger number be 9 And the smaller 4 If you deduct 3 from the larger it will be 6 From this subtract the smaller 4 -- The remainder will be 2 --

Or if you add 3 to the smaller number, it will be 7 -- Subtract this from the larger number 9 7 -- The remainder will be 2

In division, what is called the Italian method of arranging the divisor and quotient, appears to be preferable to the common one, as it places them in such a manner as to be easily multiplied by each other, and as it agrees with algebraic notation.

The usual method is this:

Divisor 71)83467 into a tub of water; in drawing it backwards and forwards, he will perceive that the clack, which should now be called the valve, opens and shuts as the piston is drawn backwards and forwards. It will be better not to inform the child how this mechanism is employed in the pump. If the names sucker and piston, clack and valve, are fixed in his memory, it will be sufficient for his first lesson. At another opportunity, he should be present when the fixed or lower valve of the pump is drawn up; he will examine it, and find that it is similar to the valve of the piston; if he sees it put down into the pump, and sees the piston put into its place, and set to work, the names that he has learned will be fixed more deeply in his mind, and he will have some general notion of the whole apparatus. From time to time these names should be recalled to his memory on suitable occasions, but he should not be asked to repeat them by rote. What has been said, is not intended as a lesson for a child in mechanics, but as a sketch of a method of teaching which has been employed with success.

Whatever repairs are carried on in a house, children should be permitted to see: whilst every body about them seems interested, they become attentive from sympathy; and whenever action accompanies instruction, it is sure to make an impression. If a lock is out of order, when it is taken off, show it to your pupil; point out some of its principal parts, and name them; then put it into the hands of a child, and let him manage it as he pleases. Locks are full of oil, and black with dust and iron; but if children have been taught habits of neatness, they may be clock-makers and white-smiths, without spoiling their clothes, or the furniture of a house. Upon every occasion of this sort, technical terms should be made familiar; they are of great use in the every-day business of life, and are peculiarly serviceable in giving orders to workmen, who, when they are spoken to in a language that they are used to, comprehend what is said to them, and work with alacrity.

To understand prints of machines, a previous knowledge of what is meant by an elevation, a profile, a section, a perspective view, and a bird's eye view, is necessary. To obtain distinct ideas of sections, a few models of common furniture, as chests of drawers, bellows, grates, &c. may be provided, and may be cut asunder in different directions. Children easily comprehend this part of drawing, and its uses, which may be pointed out in books of architecture; its application to the common business of life, is so various and immediate, as to fix it for ever in the memory; besides, the habit of abstraction, which is acquired by drawing the sections of complicated architecture or machinery, is highly advantageous to the mind. The parts which we wish to express, are concealed, and are suggested partly by the elevation or profile of the figure, and partly by the connection between the end proposed in the construction of the building, machine, &c. and the means which are adapted to effect it.

A knowledge of perspective, is to be acquired by an operation of the mind directly opposite to what is necessary in delineating the sections of bodies; the mind must here be intent only upon the objects that are delineated upon the retina, exactly what we see; it must forget or suspend the knowledge which it has acquired from experience, and must see with the eye of childhood, no further than the surface. Every person, who is accustomed to drawing in perspective, sees external nature, when he pleases, merely as a picture: this habit contributes much to form a taste for the fine arts; it may, however, be carried to excess. There are improvers who prefer the most dreary ruin to an elegant and convenient mansion, and who prefer a blasted stump to the glorious foliage of the oak.

PLATE 1. FIG. 1.

A B C, three mahogany boards, two, four, and six inches long, and of the same breadth respectively, so as to double in the manner represented.

PLATE 1. FIG. 2.

The index P is to be set with it sharp point to any part of an object which the eye sees through E, the eye-piece.

The machine is now to be doubled as in Fig. 2, taking care that the index be not disturbed; the point, which was before perpendicular, will then approach the paper horizontally, and the place to which it points on the paper, must be marked with a pencil. The machine must be again unfolded, and another point of the object is to be ascertained in the same manner as before; the space between these points may be then connected with a line; fresh points should then be taken, marked with a pencil, and connected with a line; and so on successively, until the whole object is delineated.

"Did the horses in the mill we saw yesterday, go as fast as the horses which are drawing the chaise?" "No, not as fast as the horses go at present on level ground; but they went as fast as the chaise-horses do when they go up hill, or as fast as horses draw a waggon."

"No, not near so fast."

"But that part goes as often round in a minute as the rest of the sail."

"Yes, but it does not go as fast."

"How so?"

Momentum, a less common word, the meaning of which is not quite so easy to convey to a child, may, by degrees, be explained to him: at every instant he feels the effect of momentum in his own motions, and in the motions of every thing that strikes against him; his feelings and experience require only proper terms to become the subject of his conversation. When he begins to inquire, it is the proper time to instruct him. For instance, a boy of ten years old, who had acquired the meaning of some other terms in science, this morning asked the meaning of the word momentum; he was desired to explain what he thought it meant.

He answered, "Force."

"What do you mean by force?"

"Effort."

"Of what?"

"Of gravity."

"Do you mean that force by which a body is drawn down to the earth?"

"No."

"Would a feather, if it were moving with the greatest conceivable swiftness or velocity, throw down a castle?"

"No."

"Would a mountain torn up by the roots, as fabled in Milton, if it moved with the least conceivable velocity, throw down a castle?"

"Yes, I think it would."

The rest of the machine is intelligible from the drawing.

When both balls were let fall together, they drove the ball that was at rest diagonally, so as to reach the opposite corner. If the same board were placed as an inclined plane, at an angle of five or six degrees, a ball placed at one of its uppermost corners, would fall with an accelerated motion in a direct line; but if another ball were made to strike the first ball at right angles to the line of its former descent, at the moment when it began to descend, it would not, as in the former experiment, move diagonally, but would describe a curve.

The reason why it describes a curve, and why that curve is not circular, was easily understood. Children who are thus induced to invent machines or apparatus for explaining and demonstrating the laws of mechanism, not only fix indelibly those laws in their own minds, but enlarge their powers of invention, and preserve a certain originality of thought, which leads to new discoveries.

Share on: WhatsApp @Hash Facebook Tweet