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with a dry analysis of elements, which, in the join these dots by lines; on doing which he teaching of language, has been exploded, is perceives that the lines he makes hide, or coto be re-instituted in the teaching of drawing. incide with, the outlines of the object. And The abstract is to be preliminary to the con- then on being asked to put a sheet of paper crete. Scientific conceptions are to precede on the other side of the glass, he discovers empirical experiences. That this is an inver- that the lines he has thus drawn represent sion of the normal order, we need scarcely the object as he saw it. They not only look repeat. It has been well said concerning the like it, but he perceives that they must be custom of prefacing the art of speaking any like it, because he made them agree with its tongue by a drilling in the parts of speech outlines; and by removing the paper he can and their functions, that it is about as reason- repeatedly convince himself that they do able as prefacing the art of walking by a agree with its outlines. The fact is new and course of lessons on the bones, muscles, and striking; and serves him as an experimental nerves of the legs; and much the same thing demonstration, that lines of certain lengths, may be said of the proposal to preface the art placed in certain directions on a plane, can of representing objects by a nomenclature represent lines of other lengths, and having and definitions of the lines which they yield other directions in space. Subsequently, by on analysis. These technicalities are alike gradually changing the position of the object repulsive and needless. They render the he may be led to observe how some lines study distasteful at the very outset; and all shorten and disappear, whilst others come with the view of teaching that, which, in the into sight and lengthen. The convergence of course of practice, will be learnt unconscious- parallel lines, and, indeed, all the leading facts ly. Just as the child incidentally gathers the of perspective may, from time to time, be simimeanings of ordinary words from the conver- larly illustrated to him. If he has been duly sations going on around it, without the help accustomed to self-help, he will gladly, when of dictionaries; so, from the remarks on ob- it is suggested, make the attempt to draw one jects, pictures, and its own drawings, will it of these outlines upon paper, by the eye only; presently acquire, not only without effort but and it may soon be made an exciting aim to even pleasurably, those same scientific terms produce, unassisted, a representation, as like which, if presented at first, are a mystery as he can, to one subsequently sketched on and a weariness.
the glass. Thus, without the unintelligent If any dependence is to be placed upon the mechanical practice of copying other drawgeneral principles of education that have ings, but by a method at once simple and atbeen laid down, the process of learning to tractive-rational, yet not abstract, a famildraw should be throughout continuous with iarity with the linear appearances of things, those efforts of early childhood described and a faculty of rendering them, may be, above, as so worthy of encouragement. By step by step, acquired. To which advantages the time that the voluntary practice thus ini- ald these :--that even thus early the pupil tiated has given some steadiness of hand, and learns, almost unconsciously, the true theory some tolerable ideas of proportion, there will of a picture-namely, that it is a delineation have arisen a vague notion of body as pre- of objects as they appear when projected on a senting its three dimensions in perspective. plane placed between them and the eye; and And when, after sundry abortive, Chinese- that when he reaches a fit age for commenclike attempts to render this appearance on ing scientific perspective he is already thorpaper there has grown up a pretty clear per-oughly acquainted with the facts which ception of the thing to be achieved, and a de-form its logical basis. sire to achieve it, a first lesson in empirical As exhibiting a rational mode of communiperspective may be given by means of the cating primary conceptions in geometry, we apparatus occasionally used in explaining cannot do better than quote the following perspective as a science. This sounds formid- passage from Mr. Wyse:able; but the experiment is both comprehensive and interesting to any boy or girl of or- "A child has been in the habit of using cubes for arithme
tic; let him use them also for the elements of geometry. I dinary intelligence. A plate of glass so
would begin with solids, the reverse of the usual plan. It framed as to stand vertically on the table, saves all the difficulty of absurd definitions, and bad explanabeing placed before the pupil, and a book, or tions on points, lines, and surfaces, which are nothing but ab
stractions.... A cube presents many of the principal like simple object, laid on the other side of it,
y elements of geometry; it at once exhibits points, straight lines, he is requested, whilst keeping the eye in one parallel lines, angles, parallelograms, etc., etc. These cubes position, to make ink dots upon the glass, so are divisible into various parts. The pupil has already been
familiarized with such divisions in numeration, and he now that they may coincide with, or hide the
10 proceeds to a comparison of their several parts, and of the corners of this object. He is then told to relation of these parts to each other. ... From thence de
advances to globes, which furnish him with elementary no- | propensity to cut out things in paper, to make, tions of the circle, of curves generally, etc., etc. "Being tolerably familiar with solids, he may now substi
to build-a propensity which, if duly encourtute planes. The transition may be made very easy. Let the aged and directed, will not only prepare the cube, for instance, be cut into thin divisions, and placed on way for scientific conceptions, but will develpaper: he will then see as many plane rectangles as he has divisions; so with all the others. Globes may be treated in
op those powers of manipulation in which
P the same manner; he will thus see how surfaces really are most people are so deficient. generated, and be enabled to abstract them with facility in When the observing and inventive faculties every solid.
have attained the requisite power, the pupil “ He has thus acquired the alphabet and reading of geometry. He now proceeds to write it.
may be introduced to empirical geometry; "The simplest operation, and therefore the first, is merely that is-geometry dealing with methodical to place these planes on a piece of paper, and pass the pencil soluti round them. When this has been frequently done, the plane
solutions, but not with the demonstrations of may be put at a little distance, and the child required to copy them. Like all other transitions in education, it, and so on."
this should be made not formally but incidentA stock of geometrical conceptions having ally; and the relationship to constructive art been obtained, in some such manner as this should still be maintained. To make a tetrarecommended by Mr. Wyse, a further step hedron in cardboard, like one given to him, is may, in course of time, be taken, by introduc- a problem which will alike interest the pupil, ing the practice of testing the correctness of and serve as a convenient starting-point. In all figures drawn by the eye; thus alike excit- attempting this, he finds it needful to draw ing an ambition to make them exact, and con- four equilateral triangles arranged in special tinually illustrating the difficulty of fulfilling positions. Being unable in the absence of an that ambition. There can be little doubt that exact method to do this accurately he discovgeometry had its origin (as, indeed, the word ers on putting the triangles into their respecimplies) in the methods discovered by artisans tive positions, that he cannot make their and others, of making accurate measurement sides fit, and that their angles do not properly for the foundations of buildings, areas of in- meet at the apex. He may now be shown how closures, and the like; and that its truths came by describing a couple of circles, each of these to be treasured up, merely with a view to their triangles may be drawn with perfect correctimmediate utility. They should be introduced ness and without guessing; and after his failto the pupil under analogous relationships. ure he will duly value the information. HavIn the cutting out of pieces for his card-houses, ing thus helped him to the solution of his first in the drawing of ornamental diagrams for problem, with the view of illustrating the coloring, and in those various instructive oc- nature of geometrical methods, he is in future cupations which an inventive teacher will to be left altogether to his own ingenuity in lead him into, he may be for a length of time solving the questions put to him. To bisect & advantageously left, like the primitive builder, line, to erect a perpendicular, to describe a to tentative processes; and will so gain an square, to bisect an angle, to draw a line parabundant experience of the difficulty of achiev-allel to a given line, to describe a hexagon, ing his aims by the unaided senses. When, are problems which a little patience will enahaving meanwhile undergone a valuable dis- ble him to find out. And from these he may cipline of the perceptions, he has reached a fit be led on step by step to questions of a more age for using a pair of compasses, he will, complex kind; all of which, under judicious whilst duly appreciating these as enabling management, he will puzzle through unhelped. him to verify his ocular guesses, be still hin- Doubtless, many of those brought up under dered by the difficulties of the approximative the old regime, will look upon this assertion method. In this stage he may be left for a sceptically. We speak from facts, however, further period: partly as being yet too young and those neither few nor special. We have for anything higher; partly because it is de- seen a class of boys become so interested in sirable that he should be made to feel still making out solutions to these problems, as to more strongly the want of systematic contri- look forward to their geometry lesson as a vances. If the acquisition of knowledge is to chief event of the week. Within the last be made continuously interesting; and if, in month, we have been told of one girls' school, the early civilization of the child, as in the in which some of the young ladies voluntarily early civilization of the race, science becomes occupy themselves with geometrical questions attractive only as ministering to art; it is out of school-hours; and of another, in which manifest that the proper preliminary to geom | they not only do this, but in which one of them etry is a long practice in those constructive is begging for problems to find out during the processes which geometry will facilitate. Ob- holidays—both which facts we state on the serve that here, too, nature points the way. authority of the teacher. There could indeed Almost invariably, children show a strong be no stronger proofs than are thus afforded
of the practicability and the immense advan-| finding some of his own methods proved to be iage of self-development. A branch of knowl- true. Thus he enjoys what is to the unpreedge which as commonly taught is dry and pared a dreary task. It only remains to add, even repulsive, may, by following the method that his mind will presently arrive at a fit of nature, be made extremely interesting and condition for that most valuable of all exerprofoundly beneficial. We say profoundly cises for the reflective faculties—the making beneficial, because the effects are not confined of original demonstrations. Such theorems to the gaining of geometrical facts, but often as those appended to the successive books of revolutionize the whole state of mind. It has the Messrs. Chambers' Euclid, will soon berepeatedly occurred, that those who have been come practicable to him; and in proving them stupefied by the ordinary school-drill—by its the process of self-development will be not abstract formulas, by its wearisome tasks, by intellectual only, but moral. its cramming-have suddenly had their intel- To continue much further these suggestions lects roused, by thus ceasing to make them would be to write a detailed treatise on educapassive recipients, and inducing them to be- tion, which we do not purpose. The foregocome active discoverers. The discouragement ing outlines of plans for exercising the percepbrought about by bad teaching having been tions in early childhood for conducting objectdiminished by a little sympathy, and sufficient lessons for teaching drawing and geometry, perseverance induced to achieve a first success, must be considered as roughly-sketched illusthere arises a revulsion of feeling affecting the trations of the method dictated by the genwhole nature. They no longer find them- eral principles previously specified. We beselves incompetent; they too can do some- lieve that on examination they will be found thing. And gradually as success follows suc- not only to progress from the simple to the cess, the incubus of despair disappears, and complex, from the concrete to the abstract, they attack the difficulties of their other from the empirical to the rational; but to satstudies with a courage that insures conquest. isfy the further requirements that education
This empirical geometry which presents an- shall be a repetition of civilization in little, endless series of problems, and should be con- that it shall be as much as possible a process tinued along with other studies for years, may of self-evolution, and that it shall be pleasurathroughout be advantageously accompanied ble. That there should be one type of method by those concrete applications of its principles capable of satisfying all these conditions, tends which serve as its preliminary. After the alike to verify the conditions, and to prove cube, the octahedron, and the various forms that type of method the right one. And when of pyramid and prism have been mastered, we add that this method is the logical outmay come the more complex regular bodies-come of the tendency, characterizing all modthe dodecahedron, and the icosahedron-to ern systems of instruction that it is but an construct which out of single pieces of card- adoption in full of the method of nature which board requires considerable ingenuity. From they adopt partially—that it displays this these, the transition may naturally be made complete adoption of the method of nature, to such modified forms of the regular bodies not only by conforming to the above princias are met with in crystals—the truncated ples, but by following the suggestions which cube, the cube with its dihedral as well as its the unfolding mind itself gives, facilitating its solid angles truncated, the octahedron and the spontaneous activities, and so aiding the devarious prisms as similarly modified; in imi- velopments which nature is busy with-when tating which numerous forms assumed by we add this, there seems abundant reason to different metals and salts, an acquaintance conclude, that the mode of procedure above with the leading facts of mineralogy will be exemplified, closely approximates to the true incidentally gained. After long continuance one. in exercises of this kind, rational geometry, as may be supposed, presents no obstacles. A few paragraphs must be appended in furConstantly habituated to contemplate rela- ther inculcation of the two general principles, tionships of form and quantity, and vaguely alike the most important and the least atperceiving from time to time the necessity of tended to: we mean the principle that throughcertain results as reached by certain means, out youth, as in early childhood and in matuthe pupil comes to regard the demonstrations rity, the process shall be one of self-instrucof Euclid as the missing supplements to his tion; and the obverse principle, that the menfamiliar problems. His well-disciplined facul- tal action induced by this process shall be ties enable him easily to master its successive throughout intrinsically grateful. If progrespropositions, and to appreciate their value;sion from simple to complex, and from conand he has the occasional gratification of crete to abstract, be considered the essential requirements as dictated by abstract psychol- duces. That it is thoroughly practicable to ogy, then do these requirements that knowl-carry out instruction after this fashion we edge shall be self-mastered, and pleasurably can ourselves testify; having been in youth mastered, become the tests by which we may thus led to successively solve the comparajudge whether the dictates of abstract psy- tively complex problems of Perspective. And chology are being fulfilled. If the first em- that leading teachers have been gradually Body the leading generalizations of the science tending in this direction is indicated alike in of mental growth, the last are the chief can- the saying of Fellenberg, that “the individons of the art of fostering mental growth. ual, independent activity of the pupil is of For manifestly if the steps in our curriculum much greater importance than the ordinary are so arranged that they can be successively busy officiousness of many who assume the ascended by the pupil himself with little or no office of educators; " in the opinion of Horace help, they must correspond with the stages of Mann, that“unfortunately education amongst evolution in his faculties; and manifestly if us at present consists too much in telling, not the successive achievements of these steps are in training;” and in the remark of M. Marcel intrinsically gratifying to him, it follows that that “what the learner discovers by mental they require no more than a normal exercise exertion is better known than what is told to of his powers.
him." But the making education a process of self- Similarly with the correlative requirement, evolution has other advantages than this of that the method of culture pursued shall be keeping our lessons in the right order. In the one productive of an intrinsically happy ac first place, it guarantees a vividness and per-tivity,-an activity not happy in virtue of ex manency of impression which the usual meth- trinsic rewards to be obtained, but in virtue ods can never produce. Any piece of knowl- of its own healthfulness. Conformity to this edge which the pupil has himself acquired, requirement not only guards us against any problem which he has himself solved, be- thwarting the normal process of evolution, but comes by virtue of the conquest much more incidentally secures positive benefits of im thoroughly his than it could else be. The portance. Unless we are to return to an as preliminary activity of mind which his suc-cetic morality, the maintenance of youthful cess implies, the concentration of thought nec- happiness must be considered as in itself a essary to it, and the excitement consequent worthy aim. Not to dwell upon this, how on his triumph, conspire to register all the ever, we go on to remark that a pleasurable facts in his memory in a way that no mere state of feeling is far more favorable to intel information heard from a teacher, or read in lectual action than one of indifference or dis a school-book, can be registered. Even if he gust. Everyone knows that things read fails, the tension to which his faculties have heard, or seen with interest, are better remem been wound up insures his remembrance of bered than those read, heard, or seen with the solution when given to him, better than apathy. In the one case the faculties ap half a dozen repetitions would. Observe again, pealed to are actively occupied with the sub that this discipline necessitates a continuous ject presented; in the other they are inac organization of the knowledge he acquires. I tively occupied with it; and the attention i It is in the very nature of facts and infer- continually drawn away after more attractiv ences, assimilated in this normal manner, I thoughts. Hence the impressions are respec that they successively become the premises tively strong and weak. Moreover, the intel of further conclusions,—the means of solving lectual listlessness which a pupil's lack of in still further questions. The solution of yes- terest in any study involves, is further com terday's problem helps the pupil in mastering plicated by his anxiety, by his fear of conse to-day's. Thus the knowledge is turned into quences, which distract his attention, and in faculty as soon as it is taken in, and forth-crease the difficulty he finds in bringing hi with aids in the general function of thinking faculties to bear upon these facts that are re
-does not lie merely written in the pages of pugnant to them. Clearly, therefore, the el an internal library, as when rote-learnt. ficiency of any intellectual action will, othe Mark further, the importance of the moral things equal, be proportionate to the gratif culture which this constant self-help involves.cation with which it is performed. Courage in attacking difficulties, patient con- It should be considered also, that importan centration of the attention, perseverance moral consequences depend upon the habitud through failures—these are characteristics pleasure or pain which daily lessons produce which after-life specially requires; and these No one can compare the faces and manners are characteristics which this system of mak- two boys—the one made happy by masterin ing the mind work for its food specially pro- interesting subjects, and the other made mi erable by disgust with his studies, by conse- tion of knowledge has been rendered habituquent failure, by cold looks, by threats, by ally gratifying, then will there be as prevail-. punishment-without seeing that the disposi- ing a tendency to continue, without superintion of the one is being benefited, and that of tendence, that same self-culture previously the other greatly injured. Whoever has carried on under superintendence. These remarked the effect of intellectual success upon sults are inevitable. While the laws of menthe mind, and the power of the mind over the tal association remain true-while men disbody, will see that in the one case both tem- like the things and places that suggest painper and health are favorably affected; whilst ful recollections, and delight in those which in the other there is danger of permanent call to mind bygone pleasures-painful lesmoroseness, of permanent timidity, and even sons will make knowledge repulsive, and of permanent constitutional depression. To pleasurable lessons will make it attractive. all which considerations we must add the fur. The men to whom in boyhood information ther one, that the relationship between teach- came in dreary tasks along with threats of ers and their pupils is, other things equal, punishment, and who were never led into rendered friendly and influential, or antago- habits of independent inquiry, are unlikely nistic and powerless, according as the system to be students in after years; while those to of culture produces happiness or misery. Hu- whom it came in the natural forms, at the man beings are at the mercy of their associ- proper times, and who remember its facts as ated ideas. A daily minister of pain cannot not only interesting in themselves, but as the fail to be regarded with a secret dislike, and occasions of a long series of gratifying sucif he causes no emotions but painful ones, will cesses, are likely to continue through life that inevitably be hated. Conversely, he who con- self-instruction commenced in youth. stantly aids children to their ends, hourly provides them with the satisfactions of conquest, hourly encourages them through their difficul. ties and sympathizes in their successes, can
CHAPTER III. not fail to be liked; nay, if his behavior is
MORAL EDUCATION. consistent throughout, must be loved. And when we remember how efficient and benign STRANGELY enough, the most glaring defect is the control of a master who is felt to be a in our programmes of education is entirely friend, when compared with the control of one overlooked. While much is being done in who is looked upon with aversion, or at best the detailed improvement of our systems in mdifference, we may infer that the indirect ad- respect both of matter and manner, the most vantages of conducting education on the hap- pressing desideratum has not yet been even piness principle do not fall far short of the di- recognized as a desideratum. To prepare the rect ones. To all who question the possibility young for the duties of life is tacitly admitted of acting out the system here advocated, we by all to be the end which parents and schoolreply as before, that not only does theory point masters should have in view; and happily to it, but experience commends it. To the the value of the things taught, and the goodmany verdicts of distinguished teachers who ness of the method followed in teaching them, since Pestalozzi's time have testified this, may are now ostensibly jugded by their fitness to be here added that of Professor Pillans, who this end. The propriety of substituting for asserts that “where young people are taught an exclusively classical training a training in as they ought to be, they are quite as happy which the modern languages shall have a in school as at play, seldom less delighted, share, is argued on this ground. The necesmaş, often more, with the well-directed exer- sity of increasing the amount of science is tise of their mental energies, than with that urged for like reasons. But though some of their muscular powers.”
care is taken to fit youth of both sexes for soAs suggesting a final reason for making ed- ciety and citizenship, no care whatever is ucation a process of self-instruction, and by taken to fit them for the still more important consequence a process of pleasurable instruc-position they will ultimately have to fill-the tion, we may advert to the fact that, in pro- position of parents. While it is seen that for portion as it is made so, is there a probability the purpose of gaining a livelihood, an elabothat education will not cease when school- rate preparation is needed, it appears to be days end. As long as the acquisition of thought that for the bringing up of children, knowledge is rendered habitually repugnant, no preparation whatever is needed. While so long will there be a prevailing tendency to many years are spent by a boy in gaining discontinue it when free from the coercion of knowledge, of which the chief value is that it parents and masters. And when the acquisi- constitutes “the education of a gentleman;"