COMPOUND SENTENCES. How does it read, then, with the word always in it? 275 To what part of the sentence, and to what word in it does the word always belong? What difference is there between the meaning of the second sentence, as it stood before, and as it now stands with the always in it? Is this difference an alteration of the meaning, or an addition to it? Could you insert the word always in the first sentence? To what word does the always here belong? In what part of the sentence is that word? What difference is there between the meaning of the first sentence as it stood before, and as it stands now, with always in it? What do you call this difference? And so on, till the children have a perfectly clear view of the meaning of these two sentences, both when taken separately, and when compared to each other. Other sets of questions would bear upon the difference between before, and after, the preservation of the natural order of facts with the former, and the inversion of it with the latter, the change of I mended, into I had mended, and so on. But enough has been said, to shew in what manner the subject ought to be handled, in order to impress upon the mind with all the power of a living interest, that which the grammar gives in unintelligible definitions and unpalatable rules. The cultivation of language would then become, as it ought to be, subservient to the cultivation of self-knowledge, self-command, and self-improvement; and to a teacher, not quite asleep to his task, a wide field would be opened for intellectual and moral influence. Before concluding this Chapter we should add, that there ought to be another course, running parallel throughout, as regards the structure of the sentences, to that above described, the only difference being, that while the one is concentrated upon the pupil himself as the object of his thought 276 NATIONAL LITERATURE. and language, the other course would suggest subjects from the whole range of creation, a selection being made for that purpose of the most suitable verbs, adjectives, and substantives, which might be arranged under different heads, according to the nature of the actions, properties, and things, which they represent. Finally, to make the instruction in the mother-tongue complete, there should be put into the pupil's hands a selection of national literature, from the time, at least, when the language had accomplished its transition from the Norman to the English idiom. Such a selection, made on a sufficiently extensive scale, and accompanied by a history of literature, and short biographical notices of the different writers from whose works it contained extracts, would be of immense service to the cause of education. It might contribute powerfully to emancipate the rising generation from the Liliputian fetters of a nerveless age, and reinstil into national life some of that genuine patriotism, and that manly frankness, which, in our polite days, is hardly tolerated, except on the pages of an historical novel. CHAPTER XXV. Method of teaching Number-Arithmetic. In this calculating world shall we be understood, if we say that Pestalozzi's arithmetic had no reference to the shop or the counting-house; that it dealt not in monies, weights, nor measures; that its interest consisted entirely in the mental exercise which it involved, and its benefit in the increase of strength and acuteness which the mind derived from that exercise? Again, in this mechanical, sign-loving age, shall we be understood, if we say that his arithmetic was not the art of handling and pronouncing ciphers, but the power of comprehending and comparing numbers? And, lastly, with a public whose faith is exclusively devoted to what is immediately and palpably "practical and useful," shall we be believed if we add that, notwithstanding the apparently unpractical tendency of Pestalozzi's arithmetical instruction, he numbered among his pupils the most acute and rapid "practical arithmeticians?" Such, however, was the case; his course of arithmetic excluded ciphers until numbers were perfectly understood, and the rules of reduction, exchange, and others, in which arithmetic is applied to the common business of life, were superadded at the close of his arithmetical course, as the 278 THE FUNDAMENTAL FORMULA. pupil's future calling might require it. The main object of his instruction in this branch of knowledge was the development of the mental powers; and this he accomplished with so much success, that the ability which his pupils displayed, especially in mental arithmetic, was the chief means of attracting the public notice to his experiments. In his letters to Gessner, he gives the following account of his views and proceedings on this subject: "This science arises altogether out of the simple composition and separation of units. Its fundamental formula is this: 'One and one are two;' 'One from two remains one.' Any number, whatever be its name, is nothing else but an abridgment of this elementary process of counting. Now it is a matter of great importance, that this ultimate basis of all number should not be obscured in the mind by arithmetical abbreviatures. The science of numbers must be taught so as to have their primitive constitution deeply impressed on the mind, and to give an intuitive knowledge of their real properties and proportions, on which, as the groundwork of all arithmetic, every farther proficiency is to be founded. If that be neglected, this first means of acquiring clear notions will be degraded into a plaything of the child's memory and imagination, and its object, of course, entirely defeated. "It cannot be otherwise. If, for instance, we learn merely by rote: 'three and four make seven,' and then we build upon this 'seven,' as if we actually knew that three and four make seven; we deceive ourselves; we have not a real apprehension of seven, because we are not conscious of the physical fact, the actual sight of which can alone give truth and reality to the hollow sound. It is the same in all departments of human knowledge. In drawing, for instance, if there be no reference to the art of measuring, from which it arises, the internal reality of the operation is lost, and it ceases to be a means of leading our mind to clear ideas. "The first impressions of numerical proportions should be given to the child by exhibiting the variations of more and less in real objects placed before his view. My first arithmetical exercises are, therefore, derived from 'the Mother's Manual.'* The first tables of that book contain a series of objects, in which the ideas of one, two, three, &c. up to ten, are distinctly and intuitively presented to his eyes. I then call upon him • For an account of the Mother's Manual, see Ch. xxii. from page 224-226; and, for the details of the exercises, which serve as introduction to the arithmetical course, see the Christian Monitor and Family Friend, pp. 40 and 41. NUMBER IN VISIBLE OBJECTS. 279 which occur in the number one, After this I make him to go over to pick out in those tables the objects then those which are double, triple, &c. the same numbers again on his fingers, or with beans, pebbles, or any other objects which are at hand. He is still more deeply impressed by repeating them a hundred times a day on the spelling-tablet,* first dividing each word into its syllables, and then asking: 'how many syllables has this word?' 'what is the first, the second, the third?' 'how many letters in the first, second, third syllable?' &c. In this manner children are made perfectly familiar with the elements of number; the intuitive knowledge of them remains present to their minds while learning the use of their abridgments, the ciphers, in which they must not be exercised before that point be fully secured. The most important advantage gained by this proceeding is, that arithmetic is made a foundation of clear ideas; but, independently of this, it is almost incredible how great a facility in the art of calculating the child derives from this intuitive knowledge. Experience has proved, that if the beginnings seemed involved in difficulties, it has only been because full effect was not given to this method; and it will, therefore, be necessary for me to enter farther into the details of the means which I have adopted. "I have already mentioned, that the spelling-tablet is made use of for teaching arithmetic, each letter-square representing an unit. At the same time at which the children are introduced to the knowledge of the letters, they are led to observe their numerical proportions. A square is put up, and the teacher asks: 'Are there many squares here? Answer: No, there is but one. The teacher adds one, and asks again: "One and one, how many are they? Answer: 'One and one are two;' and so on, adding at first by ones, afterwards by twos, threes, &c. "After the child has in this manner come to a full understanding of the composition of units up to ten, and has learned to express himself with perfect ease concerning each particular case, the squares are again put on the tablet in the same manner, but the question is changed: 'If there are two squares, how many times have we one square?' The child looks, counts, and answers correctly: 'If there are two squares, we have two times one square.' "The child having thus distinctly and repeatedly counted over the parts of each number up to ten, and come to a clear view of the number of units contained in each, the question is changed again, the squares being still put up as before. Two, how many times one is it? Three, how many times one?' &c.; and again: 'How many times is one contained in two, three,' &c. After the child has in this manner been introduced to the simple This spelling-tablet is an apparatus, on which the letters, fixed on separate little squares of pasteboard, can be made to slide in and out; and thus words and sentences are composed by children, before their hand has acquired sufficient ability for writing. |