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persistent perversity, are easily pigeon-holed when their occurrences are grasped as items of a period of development, i. e., as details of a historical system. Likewise the peculiar usages of Latin, perplexing in translation and baffling in composition, are rendered much more familiar if learned in relation to certain broad principles of the language. Furthermore, it often happens that our subsequent use of a fact regards just this systematic relationship. Economic statistics, for most of us, are a burden which should be reduced to a minimum; but the outlines of economic structure and development are of great importance for our thinking. Hence for at least two good reasons it is desirable to cultivate the habit of learning things systematically.
That the study of algebra and geometry confirm this habit is certain. An algebraic exercise or problem, or a geometrical demonstration, is in itself a small system, an essential feature of which is orderliness; proper arrangement of parts is necessary to success. In the problem the central thought to be reached by analysis is the equation ; secondarily, if there are several unknown quantities, their relations must also be analytically determined. Construction of the equation by synthesis of known and unknown quantities is, in point of difficulty, nine tenths of the performance; it remains only to complete the solution by following definite rules of simplification. In elementary algebra the solution of problems is by far the best illustration of what I have called systematization, although factoring, simultaneous equations, and other minor subjects may be turned to account in developing the same mental habit. A bit of analysis discovers that 4.46 — 9(y + 2)i is the difference between the squares of 223 and 3(y + 2)}; this is the fundamental thought. Synthesis, by rule, of these latter quantities gives the desired factors, viz., 238 + 3(y + 2)} and 2x3 — 3(y+z)t. Likewise a pair of simultaneous equations stand in some relation, to be ascertained by analysis, such that a certain process, let us say division, will eliminate an unknown quantity, or otherwise simplify the solution.
A geometrical theorem is a fertile field for systematic procedure. The analytic question is, What previous theorems or
relationships that may be turned to account are suggested by what is here 'given ? Synthesis, in logical form, of elements thus obtained constitutes the demonstration. For example, analysis of the proposition “ The sum of the angles of any triangle is equal to two right angles” reminds us that the “ sum” of angles implies arrangement side by side around a common vertex. Once this idea is grasped, the further insight that such an arrangement corresponds to certain theorems about parallel lines cut by a transversal follows by simple association of geometrical ideas. These elements are then easily arranged in a logical system which proves the proposition. It is indeed unfortunately true that most text-books of geometry minimize the necessity for analysis both by offering synthetic demonstrations without explaining or even mentioning their important analytic foundations, and also by accompanying “original” exercises with appropriate “hints " which discourage and frustrate originality. Nevertheless the teacher can inculcate the habit of systematization in at least some members of a class by discussing theorems in the way suggested.
Such a habit, I repeat, becomes useful in all further study. So also with the habit of precision. Let me guard, however, against certain possible objections. It does not follow that good students must possess mathematical proficiency, or have had extraordinary mathematical training. Neither is a mathematical habit of mind in itself a reliable mental equipment for dealing with practical problems. Nor, indeed, are the beneficial results of such habit always distinctly obvious. Our mental life is vastly complex; our theoretical beliefs and practical decisions are due to all sorts of conflicting causes, many of them emotional and irrational. Mathematical habit can be at best but a strictly limited function of life. Yet the importance in education of elementary mathematical study is none the less ; indeed, its very abstractness seems to give it a superior general utility. The fact that good students of mathematics are usually good students of other subjects also lends authority to this opinion. Algebra and geometry are therefore valuable features of school training.
J. H. ATKINSON, BLAIR ACADEMY, BLAIRSTOWN, N. J.
BAN a recent communication to the New York
y Times, President Thwing says: “ The primary U function of the preparatory school is twofold,-it
is to fit boys for college ; it is also to fit boys, to use the phrase which is used in one of the earliest documents of the Phillips Academy at Andover,
for the great business of living.'” The preparaSSE
tory schools are to turn out not only the most but the best freshmen, if they are not sorely tempted to slight “the great business of living" until their walls picture forth but feebly the splendid and hopeful idea. The temptation is strong, owing to the intense energy that is applied to the training for examinations. There is a premium on that for which marks and credits are given and an inclination to slur what, worthy as it may be, in the immediate test makes no “ points." This is reflected in the bearing of many students, college and preparatory, a bearing which depreciates their heritage of the rich and sacred things of life. They seem in a manner to have naturalized themselves in a realm apart from that in which human nature unfolds itself in a natural and characteristic way. Immunity from ties and responsibilities through a series of years, and exclusive attention to the processes that refine and sharpen the intellect, tend somewhat to desiccate the emotional nature, and to this extent to unfit them for life's higher contentments. It has been said that women sometimes seem to have let pale the rose-hue of their domestic affections through a prolonged season of ambitious intellectual gymnastics. The inference is that some of the nurture of youth seems of a kind to attenuate the affections for the remedial and wholesome influences of home life.
The preparatory school separates the boy from home at a time when the home influence ought to be in effect. From fourteen onwards a few years the boy acquires an attitude likely to be afterwards a distinguishing characteristic. Away from parental restraints he is inclined to exult in his personal liberty, to become forward and self-confident, blasé, in imitation of conduct that goes with riper years. All imitation is usually of the worse and not the better. He is of an age to profit ill by independent association with large numbers. The prospect of a long career of independence in school and college looms large, offers privileges that tend to make him an autocrat, sets him forward, in his own imagination, with a bound, to that maturity which entitles him to keep his own counsel and tempts him to assume license to a season of impudence and tyranny. This is manifest in the endeavor of boys in preparatory schools to copy the ways of college men, and especially to organize secret societies and through them arrogate to themselves a power in the school to influence the administration. They bound over the dew and the bud of life, which if possible ought to be prolonged fresh and innocent and susceptible, miss the inspiration and the fervor of adolescence, which ought to approach gradually the larger expectations. This practice is to be sentenced as not in good form. The lengthened period of youth still is brief and rightly extends through the preparatory school, an institution that supplants the home life of its pupils. The restraints and exactions of the home which refine away conceit, suppress irregularities, check wrong tendencies, are in force in the preparatory school by implication of President Thwing and the Andover document.
As the boy is transplanted into the preparatory school he loses much of the personal attention that is due him. In the repair of this loss the school looks towards the great business of living.” One of the obvious reasons the boy needs special attention is that he is likely to be gifted with a certain amount of ambiguity. Allowance is to be made for it as the astronomer makes allowance for the “ personal equation.” If the boy lacks it, as he commonly does, he has in him the making of a Togo. He needs no brace or strait-jacket to keep him upright, but ought to be appointed monitor, or given some other responsible position in the school, for the good he can do. If he registers the equation he is the last to acknowledge it. If induced to acknowledge it, he does not yet see the harm of it. To him it is like the
image on the retina, which, though top side down, he naturally regards as right side up. For instance, he does not see the essential unmanliness of magnifying into an illness a disinclination to attend class, or of construing a permission to see his tailor into a privilege to lounge about the railway station. He has not yet learned to distinguish between his own will and necessity, between the ostensible and the real. The school endeavors to point out this distinction, to eliminate the equation. · The school is supposed to impress him with a definite notion of what is becoming, of honesty, fair play, manly conduct. A moral pressure equal to a tonic atmosphere is supposed to emanate from the authorities, sufficient to blight any tendency to double dealing or underhand methods—the methods of the mask and the stiletto. Shams and cant and snobbery are supposed to be exotic, unreality and veneer to find no salubriety, personal purity and openness of character to be indigenous.
As the school looks towards “ the great business of living,” it endeavors to encourage a chivalrous spirit, which manifests itself in kindly service and in generosity of word and action ; it helps the student to realize the higher benefits of school life and the substantial pleasures of later life which he ought to enjoy. This spirit identifies itself with a wholesome outlook, represents the preservative quality which takes its tincture from goodness of heart-represents the spirituality of a regenerate nature.
Right feeling is desired, as the ivy-growth that is native and becoming, that adorns and gives grace to the thing it touches. But it cannot be imparted as a matter of policy, is not taught in a formal or even in a conscious way. Its rise partakes in no wise of the nature of hothouse growth, but rather of the nature of a mood, which communicates itself unwittingly as a contagion. It is not induced, as it seems, by studied words of instruction, but as if by the unconscious reflection of personality. Its impartation is the method of educating the heart, is resident and dominant in the source of influence, a life-giving motive traceable in every feature of the school's activity.
In the interest of the great business of living,” the openhearted manifesto exemplifying the principle of the “square