work with the plea that he does not intend to follow the business any great length of time. Applicants for teachers' certificates do so constantly. Those preparing for other professions, and in need of a little ready money, complain when questioned sharply on theory and practice. They "do not intend to teach long;" they "have no time to study new methods;" they "are anxious to finish their professional studies as quickly as possible, and have no money to spend for educational works "-all prima facie evidences of incompetency, and very good reasons why they should be refused certificates. If they do not know anything about the professional part of our business, and do not want to, let them give way to such as do. If they really want to swindle the community, let them do it in some other manner than at the expense of the heads and hearts of the rising generation. The public good demands that they "clear the track." They never will do any good as missionaries to the many "Base-Lines" of our State.

ON THE PROPER PLACE OF ALGEBRA IN AN ELEMENTARY COURSE.

BY T. E. SULIOT.

Although I was not at liberty to attend the Teachers' Association last July, having to serve out the rest of my time on the Earlham tread-mill, I crave permission to make a few remarks on some of the points that were then discussed. I shall, to be sure, be compelled to repeat the substance of my former expressions of sentiments in this, perhaps, my last profession of faith. Still, seeing that these questions are yet unsettled, and have acquired a new freshness of interest from the light shed upon them by the various speakers, a calm review of the matter by an outsider may help some of our younger brethren and sisters to form an opinion of their own on the subject.

I. As to the propriety of substituting algebra for higher arithmetic in the upper classes of our graded schools. At the outset, I must once more protest against the supposed necessity of teaching any part of arithmetic, even the elementary processes, me

THE PLACE OF ALGEBRA IN AN ELEMENTARY COURSE. 399

chanically, instead of showing that they are all founded on common sense. Such opinions, when emitted at these anniversaries by men so deservedly looked up to by the younger teachers, may have an injurious tendency. We are, all of us, too prone already to teach mechanically, without such sanction from high places.

There seems to be no reason whatever why any young scholar should not be led to find for himself, by working on objects or their representatives, all the facts of addition and subtraction, on to the multiplication table, which he should not learn by rote, but construct for himself from the results of his experiments and discoveries in combining objects (beans, counters, etc.) in two's, three's, etc.

I will refrain from bringing forward, on the present occasion, what J. H. would probably call my "hobby," viz., that our elementary text-books should contain only well graduated groups of examples which the pupil should solve by an analytical or natural process, as in a course of mental arithmetic, and finally deduce. by inductive reasoning a rule as the expression of the process followed in the solutions.

May I be, at least, allowed to remark that our text-books do err in not confining themselves to the essentials of the subject. They contain much irrelevant matter, such as the extraction of roots, which can best be treated algebraically, and the application of which properly belongs to geometry. Least of all, should they be encumbered with mechanical rules or recipes for finding areas and volumes.

I would not go so far as to say, that as soon as the scholar understands the principles of fractions and their applications, he should be put to algebra. I would rather wait till he had mastered that elegant section of arithmetic, called percentage, of which the so-called rules of interest, insurance, profit and loss, partnership, etc., are only obvious applications. But in handling this portion of the subject, we should remember that the great object of an elementary course is not to teach the most compendious methods of working out sums: this may be left for future discovery by the learner himself when he is fitting himself for the counting-house or accountant's office. The important point now is to put him in the way of finding for himself the fundamental principle or law of percentage, viz., that since one per cent. is

one-hundredth of the number, the finding of that one per cent. should in every case be made the starting point, from which, by division or multiplication, the sub-multiple or multiples of one per cent. can be derived.

As there is not one question of proportion that can not be solved analytically, and as the laws of proportion are best demonstrated by using algebraic symbols, I would postpone the rule of three until the learner has gone as far as simple equations in elementary algebra.

Until a book of arithmetic is compiled according to my peculiar notion or "hobby," without rules, but with a variety of model solutions at the heads of each group of questions, I would be well satisfied with Felter's Analysis, which, as an instrument for developing the analytical and reasoning powers of the learner, is far ahead of our common text-books. I only wish we had an elementary algebra on the same principle. If I were trying to make up such a book, I would not run the risk of repelling the pupil, at the very outset, by a formidable array of dry definitions, for most of which he will have, at first, no manner of use. I would introduce them just as they are needed and can be understood, therefore appreciated and therefore remembered. In the first course, I would eschew all complicated questions in the elementary processes-all isolated negative quantities which must be perfectly unintelligible. I would certainly omit the "theorems," those stumbling-blocks and bug-bears of the young algebraist: I mean those that treat of the nature of negative exponents and of the exponent 0. The only theorems I would retain, because he can easily test their truth by a simple operation, are those relating to the product of a + b by a + b and of a b by a―b. Also, as a matter of fact, not of general reasoning, I would show them by a number of examples, that am- bm is always divisible by a b. I would hasten on to the subject of simple equations, so as to enable the learner, as soon as possible, to solve real questions, and thus to test by his own experience the power of this new instrument of computation.

The laws of proportion and their natural deduction, the rule of three, would bring us back to arithmetic; next would follow involution and evolution, equations of the second degree, etc.

In the second ccurse of algebra, more complicated questions

may be given by way of review, and when equations are again reached, generalization or algebra proper should be made perfectly familiar, by each problem being solved in a general form as soon as a particular or numerical solution has been obtained.

At this stage of the course, when, by patient drilling, the scholar feels at home in true algebraical notation by general symbols, and can readily handle general formulas, the various processes of arithmetic should be illustrated algebraically, and the common rules of interest, discount, annuities, etc., should be represented by formulas.

From this time to the end of the course, algebra and higher arithmetic should go hand in hand, and whenever it is practicable, should illustrate each other. The scholar should be trained to give arithmetical and algebraical solutions of such questions as are susceptible of both.

For that combination of algebra and arithmetic, I know no better book than Palmer's Elements of Algebra and Higher Arithmetic.

ABOUT TEACHING YOUNG PUPILS TO READ.

BY B. E.

There is what may be called the mechanical execution of reading. It consists in pronouncing the words of a printed page in succession as they pass under the eye. It is needful that the pupil be able to do this readily and correctly. To secure such ability, his eye and his vocal organs must be trained, especially his eye. Not that the eye is more important to the reader than the vocal organs, but in general it needs more special attention from the primary teacher. The pupil needs to be able to see a whole word at once, without being compelled to analyze it, or resolve it into its letters. Any person may learn the advantage of this by a short experiment in reading with light enough to discern the general forms of words, but not enough to see letters distinctly. The pupil never reads well until he can call words at first sight; and yet this mechanical operation is but a small part of true reading. Many a teacher, indeed, seems satisfied if his

pupil merely calls off the words of his reading-lesson correctly. Such a teacher is unworthy of his calling.

It must not be forgotten that the child learns by imitating others. Before he makes his appearance in the school-room, he has learned the language, the tones, the inflections of anger, delight, pain, pleasure, surprise, demand, entreaty, yes, of human passions in general; and he has learned them from imitationfrom the lips of other people. He has done as they did. This process does not stop when he becomes a pupil in the school. Hence it is plain that the teacher must himself be a good reader. He must be able to do the thing that the child is to do; yet this is a point in which many teachers do not understand their duty. Indeed, we may go farther back, and impeach the judgment of examiners often. A candidate for a certificate may answer correctly any number of questions in rhetoric and about reading, and yet be a poor reader. If his qualifications in this department are to be tested, let him read audibly before the examiners. There can be no substitute for this.

To proceed: The pupil must be taught to throw his own thought and feeling into his reading lesson. This can be done in most cases with little trouble. Let the teacher say to him: "John, I want you to read this sentence just as if you were telling James or me what it says. I want you to read this question just as if you expected me to answer it. I want you to read the whole lesson just as if you made it up, and were in earnest, and meant it all." Accompany this with exemplification, showing the pupil just what is meant, and he will understand and profit by the instruction. No mere instruction without the example to imitate can be expected to produce a good result, for it does not awaken his imitative powers. The example without the instruction is not enough, for the pupil needs to know why he is desired to read as he is told. Or, it were better to say, he must be furnished with a criterion which he can carry in his own bosom, and which will teach him how to read. When he learns that he is to

read every thing just as if he himself were speaking it in earnest, he has the rule within him. For want of this rule, men often read the most earnest things, and even speak the most earnest. things to others, without effect. By the aid of this rule, other men often move their auditors with the utterances of bald fiction.