frequently say to our pupils that their education is but begun at school; that all that can be done there is to lay the foundation for an education; the erecting of a superstructure must be the work of a life. We would teach them that the education acquired while at school is by no means complete. If they would be highly useful, they must continue, at home, the studies which have been commenced at school. They must choose for their literary companions, not the novelist, and the miserable scribblers of the light literature of the day, which are taken as the only companions of so many of our youth on leaving the schoolroom; but they must select the works of men and women who have thought much, whose minds have been disciplined by study; whose writings can be appreciated only by minds disciplined by study; which indeed will be read by few whose minds have not been accustomed to study. But will the youth who have been taught by long years of training that schoolbooks, books that require study, are for the schoolroom only, whose fireside associates and home companions have been confined to the light literature just referred to, will such a youth, after leaving school, undertake a course of reading which will require vigorous, independent, manly thought, and hard labor? It should never be forgotten by the teacher or the parent, that "man is a bundle of habits ;" that the habits he forms during his school-days, are more important than any amount of knowledge he may there acquire. Let then the youth early learn to study his book at home; and, during his whole pupilage, let him not, for a single day, be excused from the labor of preparing some exercise at the fireside. We may then hope that when he leaves school, he will not utterly forsake his studies; that, in his future intercourse with books, he will not be confined to those of a light and frivolous character; but that from choice, as well as from a sense of duty, he will cultivate the acquaintance of authors, whose works are adapted to perfect the mental and moral training already so happily commenced. The healthful moral influence of such evening exercises deserves a passing notice. The mind of youth is ever active. If not employed upon one thing it will be upon some other. If suitable employment be not provided for it, it will almost certainly seek employments which are unsuitable and degrading. How are our youth exposed to temptation, in consequence of having nothing at home to occupy and interest them! Whatever, therefore, we can do to furnish them with such occupation, especially, whatever we do to form in them habits of home-study, and a love for substantial literature, is so much done to save them from the snare of him who "finds some mischief still, For idle hands to do." How many a victim to vicious habits might have been saved to his family and friends, and to society, if suitable employment had, in his youthful days, been provided for him by his parents and teachers. Again: The influence of such home preparation for school upon the family. Not only is the individual benefited by such a course, but other members of the family partake with him in its benefits. Parents are usually interested in what interests their children; and if the son or daughter spends an hour or two daily at home in preparing some school exercise, the father and mother, and not unfrequently the brothers and sisters, become interested in the school and its exercises, as they otherwise would not do. The lesson will sometimes suggest topics for conversation and inquiry; questions will often be raised which cannot be settled without some research. Other authors will be consulted if they can be obtained. Older members are invited to hear the lesson recited, and are led in this way, to review the studies of their earlier years; the younger are encouraged to persevere in their studies, and thus, by such secret and unseen influences, the whole family is affected. A love for books of standard excellence is begotten, and home influence becomes something superior to the fireside gossip which characterizes so many family circles. And while the school is thus made to act upon the family, the family reacts favorably upon the school; the whole district is benefited; and, as the community is made up of families and school districts, society at large is benefited. We do not say that this is the only means of benefiting society, but we do say it is a means of doing extensive good, which no teacher should omit to use. Is it asked how early such home preparation should be commenced? We answer as soon as the child begins to go to school. To the Abecedarian's apron we would daily, at least, pin a letter, either from the printed book, or from nature's alphabet, though it were but the letter A, or an oak leaf, that he might tell the folks at home its name, and be led to search for other A's and oak leaves, in other books, or by the wayside, to show to his mother and schoolmistress. Yes, from the tenderest to the most mature age, I would bring the schoolroom and the fireside as close together as possible; and make each, as it ever should be, an auxiliary of the other. Our free schools are, under God, the hope of the country. On them, more than upon any other instrumentality, depend the prosperity and perpetuity of our free institutions. But not till parents and teachers unite their efforts more than they have been wont to do, will either our schools or our families become what they ought to be, and what they might become, if parents and teachers were more careful to co-operate with each other, in their efforts for the welfare of those committed to their charge. "ALGEBRAIC PARADOX." "1. Let ax, then, 2. multiplying by x, ax = x2, 3. adding a2, ax a2 = x2 — a2, 4. resolving into factors, a (x-a) = (x + a) (x − a), 6. substituting a for x, a=a+a=2a, and In the January number of the Teacher, the above paradox occurs, with this query: "Where is the fallacy?" I have hoped some one would answer the question; but, being disappointed in this, I will, without claiming any originality, suggest that there is fallacy in passing from the fourth to the fifth equation. The division there required being indicated, gives us a ( (x+a) (x-a) x-a x-a ", an equation in which the numerator and the denominator of each member is equal to 0, that is, the equation may be reduced to the form, 8%. But Professor Chase, on the one hundredth page of his Algebra, says: "In regard to the result 8, it is obvious that any finite quantity whatever, multiplied by the divisor 0, will produce the dividend 0, and is therefore a proper value of the expression. This expression may therefore represent any quantity whatever." Professor Whitlock, on the one hundred and twenty-fourth page of his Geometry, says of the symbol 8, "This, in itself, abstractly considered, has no meaning at all, for to it we cannot attach any idea independent of its origin." Professor Davies, in his translation of Bourdon, pages 102104, gives various examples showing that 8, may express a determinate, an infinite, or an indeterminate quantity. It is sufficient for my present purpose to copy a single example giving a determinate value. (a-b) (a+b) Suppose, in which let ab, then, by resolving, we have x = (a-b) (a2+ab+be) or by suppressing the common factor and substituting a for b, we have x = ata a determinate and definite quantity. 3a2 20 Sa 29 x-a9 If we take the first member of the equation in question, (a), (=},) and reduce it, we find its determinate value is a; in the same manner we find the value of the second member, (x − a) (x + (= 8,) to be x + a, or 2a, since x = a. Now although there is no impropriety in the equation, a (x − a) = (x + a) (x− a), that is, 0=0, yet there is an absurdity in saying that the determinate values of the two fractions, a (x-a) and (x+a) (x−a) are equal, for each of those determinate values depends upon the forms of these fractions respectively. x-a Sherwin, Perkins, and others, discuss the signification of this symbol, 8, which, in its relations to the higher mathematics, is very important and quite intricate. Feeling that my remarks may be erroneous or deficient, I shall be content if my effort shall call forth, from any source, a more correct, more full and lucid solution of this question, which has so long troubled many teachers and pupils. In view of the apparently correct process by which we arrive at the absurd conclusion that 1=2, many have been ready to declare that implicit reliance could not be placed in mathematical calculations, but nothing is farther from the truth. In no science is the beautiful consistency and harmony of truth more admirably exhibited than in the multifarious, the wonderful, and always perfectly accurate results of mathematical analyses, when a right interpretation is given to the conditions of problems and to each successive step in their solution. J. S. E. HEALTH.-We had designed to write a short homily on this topic. But the editor of the August number, in his own effective manner, has done the thing so happily, that we can only recommend to every one who has not read it, to do so; and to those who have read it, to read it again, and to all, to put in practice the recommendations of the writer. TEACHERS' INSTITUTES. Six Teachers' Institutes have been arranged for the present autumn. Each is to continue for one week only. The first will be held at Lenox, commencing September 30; the second at Fitchburg, commencing October 7; the third at Milford, commencing October 21; the fourth at Hadley, commencing October 28; the fifth at Falmouth, commencing November 11; the sixth at Monson, commencing November 18. Each Institute will be opened on Monday, at 10 o'clock, A. M., and will be closed on Saturday, at noon. Every teacher, who intends to become a member, should be present at the opening. THE 371 MASSACHUSETTS TEACHER. Vol. III. No. 11.] WILLIAM D. SWAN, EDITOR OF THIS NUMBER. [November, 1850. AGRICULTURAL EDUCATION. KNOWLEDGE is the basis of freedom; therefore, how to gain knowledge and how to impart it, are important considerations to those who, being themselves freemen, desire to transmit the priceless boon of freedom unimpaired and untarnished, to their posterity. Wealth is the basis of knowledge; not wealth in the common acceptation of the term, which enables its possessor to live without labor; but that degree of it which should ever be the reward of well directed, patient industry; a sufficiency for all reasonable wants as the result of parental labor, without the necessity of so employing children as to deprive them of ample opportunities for the acquisition of knowledge. If these propositions are true, then the importance of such a social system as will give to each industrious member of the State this necessary share of wealth, is equally plain. The first settlers of Massachusetts were educated men; they acquired knowledge, and they longed for freedom. When they sought these shores it was not only that they might escape from religious persecution, but that they might also become freemen. They scorned the dogma of "the divine right of kings;" and if they did not proclaim, they felt and acted upon the great truth, that "all men are born free and equal." That freedom for which they became voluntary exiles from their native land, they found on these shores, and the means by which they transmitted it to their children were, INDUSTRY and EDUCATION. These means were sufficient in their hands, and it is for us to see to it that they lose none of their efficiency in ours, for we shall not stand excused unless we fully pay to our children the great debt we owe to our fathers. |