A Practical Enquiry into the Philosophy of Education

by James Gall

At every new lesson he must learn to read the words which precede it, and to read them well before beginning. The great design of his reading being to collect the ideas conveyed by the words, his doing so is greatly facilitated by his learning to read the words before beginning to the lesson. It is only necessary to remark, that the homely nature of the lessons tends greatly to produce the effect here designed, and which would not perhaps be so successfully accomplished at this stage in any other way.

Children may be taught to write almost as soon as they can read a few of their lessons. Care being taken that they hold the pen properly, they will soon learn to form the letters as an amusement;—and when these are known, they will soon be able to combine them into words. When they begin to write sentences, it ought to be from their own minds, or memories, but not from copies. Writing is merely an imitation of Nature in her operation of conveying ideas by speech; and the nearer the imitation can be made to correspond with the original, the more perfect will it be. Speech is intended solely for the communication of our ideas;—and so should writing. We teach children words and the names of things, but we never teach them to express their own thoughts, by rehearsing after us either long or short speeches of our own. Neither can we so readily teach children to express their own thoughts by writing, if we attempt to do it by making them copy words which others have thought for them, and the ideas of which they themselves perhaps do not perceive. Copy-lines are a great hinderance to the young; and even for teaching the correct and elegant formation of the letters they do not appear to be always necessary.

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.