SOMETHING ENTIRELY A Book for Every Teacher in Arithmetic. QUESTIONS ON THE PRINCIPLES OF ARITHMETIC, Designed to indicate an Outline of Study, to incite among pupils a spirit of Independent Inquiry, and especially fitted to facilitate a Thorough System of Reviews. Adapted to any Text-Book, and to all grades of learners. Paper Covers. BY JAMES S. EATON, M. A., Some of the Advantages of using these Questions. 1. They are separate from any text-book, and equally well adapted to all text-books. On this account they present all the benefits of the Question Method, and none of its defects. 2. They indicate a definite outline of study, and afford a substantial guide to the pupil in the preparation of his lesson. 3. They incite the pupil to inquiry, awakening that thirst for knowledge which is the best motive for its acquirement. 4. They open up the several subjects by such short and suggestive steps, one question following upon another in the chain, that the pupil is thus led to follow out and develop the subject for himself. 5. By inciting the pupil to inquiry, and guiding him in developing the subject for himself, they subserve the highest and only true style of teaching, namely, to draw out and develop the faculties and thus lead the pupil, instead of dictating to him and driving him. 6. They afford the best means for frequent reviews and examinations, since it is the Principles of Arithmetic that should be reviewed, and not the mechanical operations. 7. The use of these Questions will not fail to ground the principles of Arithmetic in the mind of the pupil, and thus give him the KEY which will command all practical operations. These Questions are published in the form of a pamphlet, and sold at a very low price, in order to render it easy for all schools to supply themselves with them. As they are not in the form of, nor designed for, an exclusive text-book, they do not require to be adopted by Boards of Education, but the use of them, like cards or other illustrations, will be at the option of teachers. Price 12 cents. Teachers supplied at $9.00 per hundred. FOR SALE BY ALL BOOKSELLERS. Specimen copies mailed to teachers on receipt of ten cents. Address Dec., '65. TAGGARD & THOMPSON, Publishers, 29 CORNHILL, BOSTON. This is a subject which has justly received considerable attention from the thinking men and women who are interested in the advancement of education in our country and in others; and I hold that, of all the branches taught in our common schools, there is no one better adapted to wake up the mind of a child, and put in action his intellectual machinery, no one in which he can be so enthusiastically interested, and led to meet the teacher with such eagerness; no one, indeed, which admits of so much exercise of real teaching skill. And yet it is the one of all others, on which the most time and patience have to be expended by the instructor, and over which most tears are shed and heart-aches endured by unfortunate little urchins, racking their brains to remember the long, dry definitions, devised by some learned, doubtless, but most injudicious grammarian. To most children at the age when grammar is usually commenced - at least, in the Public Schools of Boston- these definitions are only meaningless strings of words, conveying to the mind no more idea than so much Greek or Hebrew. Nor is this necessarily the result of poor teaching. I have heard teachers of deservedly good repute say that they considered the time devoted to grammar in the third class of our Grammar Schools, where the average age of the children is about ten years, as so much time wasted. And they are right. As they teach it, it is time wasted, and worse than wasted; for the child, whenever he is unfortunate enough to prepare the lesson assigned in such a manner as to make a creditable recitation, not only does not gain an intelligent idea of a single principle, but is forming a bad, a most pernicious habit of mind; a habit of taking on trust, of learning by rote, before grasping the ideas contained in the words he repeats. As grammar lessons are generally, or, at least frequently, conducted, it seems to me, that the child who takes his seat in disgrace, with a reproof for idleness, carelessness, or whatever the teacher may consider the cause of his failure, is far better off than his neighbor, who has the whole lesson at his tongue's end, and can discharge his polysyllabic volleys without apparent effort. The former, in disgrace though he be, has lost nothing, even if he has gained nothing; but the latter has not only gained nothing, but has lost much: for the step which he has taken towards the formation of a bad habit of mind has retarded the free development of his mental powers more, much more, than any information he may have contrived to glean can atone for. Better that a child should have a thorough understanding of some one thing, an understanding acquired by the exercise of his own reason, an understanding in which there is no weak joint, than that he should have a vague, general impression — it cannot be called an idea of five hundred. It is really surprising that, in the present advanced state of civilization, any children should be so imposed upon, as are our precious, much-talked-of Massachusetts children; more surprising still, that no teachers, or at least so few, have broken through the hedge of custom, and declared against this imposition upon the brain of childhood. All, or nearly all, content themselves with declaring against the introduction of the study into our public schools, I speak more particularly of Boston public schools, at the age at which it is now commenced. Look at one of the grammars whose use by children just entering on the new and untried fields of grammatical lore has been sanctioned by high authority: what is the first statement we find? "Language is the medium by which we express our thoughts." The beauty of the adaptation of this information to the mind of a child will be at once perceived. Before the poor child has recovered from the effects of it, behold, another shock! "Language consists of a great variety of sounds which are used as the signs of our ideas, and are called words." After that, what child could have any difficulty in defining a word? Of course it is of immense importance that he should be able to do so, promptly and fluently. But now comes number three, capping the climax! "All these sounds may be reduced to a small number of simple sounds, which are made intelligible to the eye, as well as to the ear, by means of certain marks called letters!" Now, how can a child ever feel any interest in, or attraction towards a study which is presented to him in this appalling, and awe-inspiring manner? What possible benefit can it be to him, to have these learned and incomprehensible definitions thus hurled at him, at the very outset of his long and toilsome journey? It may be said the teacher can make it intelligible; but I think not. If she puts the book into the child's hands, he will learn those definitions, without attaching the least idea to them, however much they may be explained. And yet each teacher in our city schools is required to carry her class to a certain limit in this book, and almost all teachers, understanding this regulation, literally do carry their classes to the required limit, at the same time feeling its uselessness, even if they do not feel its hurtfulness. All through the grammar from which I have already quoted, and the preface of which states that it it is designed for beginners, the same glaring defects present themselves; for instance: "A vowel denotes pure sound only; a consonant, a contact of the organs of speech." Or again: "Case is the sense or form in which nouns and pronouns are construed with other words, to express thought." Or still again: "A participle is a form of the verb, that merely assumes the act, or state, and is construed like an adjective." Perhaps it may be urged: "But the author of this book explains all these difficult terms in notes at the bottom of the page." Very true; take for example his term "reflexive": "Reflexive,- turning back upon itself, that the act or relation reverts to the subject." What child could possibly have a false idea of the term "reflexive" after that! I was present at a recitation not long since, in a school that shall be nameless, when the following incident occurred. A child was asked to give the definition of a primitive, a derivative, and a compound word. Without a moment's hesitation, he rattled it glibly off. "Very well," said the teacher with an approving smile, "now, will you give an example of a compound word?" That was something of a poser; he hesitated and began to look somewhat alarmed at the near prospect of a lost credit, when all at once his face brightened, he had it! "Well," said the teacher, encouragingly; "Breeze-build!" exclaimed the boy in a triumphant tone. Recovering from my first amused surprise, I glanced down the page to see if I could discover any clew to the idea in his mind, which might have led to such an absurd reply, and discovered that the examples of primitive, derivative, and compound words were contained in the same paragraph, and the poor child, probably thinking that any two words coming together, constituted a compound word, had given the two examples of a primitive word. But I suppose readers will say by this time: "We know all this. If you have any suggestions to offer, as to how these difficulties may be obviated, let us have them." Here, then, are my suggestions. New ideas I will not call them, for I doubt not some dissatisfied and determined teacher may have devised something similar, before now. To go back, then, to my first statement, I hold that grammar, from being the special object of school-boy hatred, may be made his delight; that from being the drudgery of the teacher's life, it may be made a recreation. How? By taking a firm stand on these principles of Pestalozzi, the great educational law-giver:- 1. "Develop the idea, then give the term. 2. "Proceed from the known to the unknown; from the particular to the general; from the concrete to the abstract; from the simple to the more difficult." 3. First synthesis, then analysis not the order of the subject, but the order of nature." The truth of these principles, I believe, will be admitted by every teacher; and no one can fail to see the glaring violations of them, furnished by all the examples I have quoted. But how, in |
