Imatges de pàgina
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VALUE OF A LOVE AND A KNOWLEDGE OF NATURE.

10. If there is a more worthy aim for us than to be drudges—if there are other uses in the things around us than their power to bring money—if there are higher faculties to be exercised than acquisitive and sensual ones-if the pleasures which poetry and art and science and philosophy can bring are of any moment then is it desirable that the instinctive inclination which every child shows to observe natural beauties and investigate natural phenomena should be encouraged. But this gross utilitarianism which is content to come into the . world and quit it again without knowing what kind of a world it is or what it contains, may be met on its own ground. It will by and by be found that a knowledge of the laws of life is more important than any other knowledge whatever that the laws of life include not only all bodily and mental processes, but by implication all the transactions of the house and the street, all commerce, all politics, all morals-and that therefore without a due acquaintance with them neither personal nor social conduct can be rightly regulated. It will eventually be seen too, that the laws of life are essentially the same throughout the whole organic creation; and further, that they can not be properly understood in their complex manifestations until they have been studied in their simpler ones. And when this is seen, it will be also seen that in aiding the child to acquire the out-of-door information for which it shows so great an avidity, and in encouraging the acquisition of such information throughout youth, we are simply inducing it to store up the raw material for future organization-the facts that will one day bring home to it with due force those great generalizations of science by which actions may be rightly guided.

DRAWING-INCLUDING FORM AND COLOR.

11. The spreading recognition of drawing as an element of education, is one amongst many signs of the more rational views on mental culture now beginning to prevail. Once more it may be remarked that teachers are at length adopting the course which nature has for ages been pressing upon their notice. The spontaneous efforts made by children to represent the men, houses, trees, and animals around them-on a slate if they can get nothing better, or with lead-pencil on paper, if they can beg them-are familiar to all. To be shown through a picture-book is one of their highest gratifications; and as usual, their strong imitative tendency presently generates in them the ambition to make pictures themselves also. This attempt to depict the striking things they see is a further instinctive exercise of the perceptions-a means whereby still greater accuracy and completeness of observation is induced. And alike by seeking to interest us in their discoveries of the sensible properties of things, and by their endeavors to draw, they solicit from us just that kind of culture which they most need.

Had teachers been guided by nature's hints not only in the making of drawing a part of education, but in the choice of their modes of teaching it, they would have done still better than they have done. What is it that the child first tries to represent? Things that are large, things that are attractive in color, things round which its pleasurable associations most cluster-human beings from whom it has received so many emotions, cows and dogs which interest by the many phenomena they present, houses that are hourly visible and strike by their size and contrast of parts. And which of all the processes of

representation gives it most delight? Coloring. Paper and pencil are good in default of something better; but a box of paints and a brush-these are the treasures. The drawing of outlines immediately becomes secondary to coloring is gone through mainly with a view to the coloring; and if leave can be got to color a book of prints, how great is the favor! Now, ridiculous as such a position will seem to drawing-masters, who postpone coloring and who teach form by a dreary discipline of copying lines, we believe that the course of culture thus indicated is the right one. That priority of color to form, which, as already pointed out, has a psychological basis, and in virtue of which psychological basis arises this strong preference in the child, should be recognized from the very beginning; and from the very beginning also the things imitated should be real. That greater delight in color which is not only conspicuous in children but persists in most persons throughout life, should be continuously employed as the natural stimulus to the mastery of the comparatively difficult and unattractive form-should be the prospective reward for the achievement of form. And these instinctive attempts to represent interesting actualities should be all along encouraged; in the 'conviction that as, by a widening experience, smaller and more practicable objects become interesting, they too will be attempted; and that so a gradual approximation will be made towards imitations having some resemblance to the realities. No matter how grotesque the shapes produced: no matter how daubed and glaring the colors. The question is not whether the child is producing good drawings: the question is, whether it is developing its faculties. It has first to gain some command over its fingers, some crude notions of likeness; and this practice is better than any other for these ends; seeing that it is the spontaneous and the interesting one. During these early years, be it remembered, no formal drawing-lessons are possible: shall we therefore repress, or neglect to aid, these efforts at self-culture? or shall we encourage and guide them as normal exercises of the perceptions and the powers of manipulation? If by the supply of cheap wood-cuts to be colored, and simple contour-maps to have their boundary lines tinted, we can not only pleasurably draw out the faculty of color, but can incidentally produce some familiarity with the outlines of things and countries, and some ability to move the brush steadily; and if by the supply of temptingly-painted objects we can keep up the instinctive practice of making representations, however rough, it must happen that by the time drawing is commonly commenced there will exist a facility that would else have been absent. Time will have been gained; and trouble both to teacher and pupil, saved.

DIMENSIONS IN PERSPECTIVE.

12. If any dependence is to be placed upon the general principles of education that have been laid down, the process of learning to draw should be throughout continuous with those efforts of early childhood described above, as so worthy of encouragement. By the time that the voluntary practice thus initiated has given some steadiness of hand, and some tolerable ideas of proportion, there will have arisen a vague notion of body as presenting its three dimensions in perspective. And when, after sundry abortive, Chinese-like attempts to render this appearance on paper, there has grown up a pretty clear perception of the thing to be achieved, and a desire to achieve it, a first lesson in empirical perspective may be given by means of the apparatus occasionally used in explaining perspective as a science. This sounds formidable; but the

experiment is both comprehensive and interesting to any boy or girl of ordinary intelligence. A plate of glass so framed as to stand vertically on the table, being placed before the pupil, and a book, or like simple object laid on the other side of it, he is requested, whilst keeping the eye in one position, to make ink dots upon the glass, so that they may coincide with, or hide the corners of this object. He is then told to join these dots by lines; on doing which he perceives that the lines he makes hide, or coincide with the outlines of the object. And then on being asked to put a sheet of paper on the other side of the glass, he discovers that the lines he has thus drawn represent the object as he saw it. They not only look like it, but he perceives that they must be like it, because he made them agree with its outlines; and by removing the paper he can repeatedly convince himself that they do agree with its outlines. The fact is new and striking; and serves him as an experimental demonstration, that lines of certain lengths, placed in certain directions on a plane, can represent lines of other lengths, and having other directions in space. Subsequently, by gradually changing the position of the object, he may be led to observe how some lines shorten and disappear, whilst others come into sight and lengthen. The convergence of parallel lines, and, indeed, all the leading facts of perspective may, from time to time, be similarly illustrated to him. If he has been duly accustomed to self-help, he will gladly, when it is suggested, make the attempt to draw one of these outlines upon paper, by the eye only; and it may soon be made an exciting aim to produce, unassisted, a representation, as like as he can, to one subsequently sketched on the glass. Thus, without the unintelligent, mechanical practice of copying other drawings, but by a method at once simple and attractive-rational, yet not abstract, a familiarity with the linear appearances of things, and a faculty of rendering them, may be, step by step, acquired. To which advantages add these:-that even thus early the pupil learns, almost unconsciously, the true theory of a picture—namely, that it is a delineation of objects as they appear when projected on a plane placed between them and the eye; and that when he reaches a fit age for commencing scientific perspective he is already thoroughly acquainted with the facts which form its logical basis.

GEOMETRY-PRIMARY.

13. As exhibiting a rational mode of communicating primary conceptions in geometry, we can not do better than quote the following passage from Mr. Wyse:-*

"A child has been in the habit of using cubes for arithmetic; let him use them also for the elements of geometry. I would begin with solids, the reverse of the usual plan. It saves all the difficulty of absurd definitions, and bad explanations on points, lines, and surfaces, which are nothing but abstractions.

. . A cube presents many of the principal elements of geometry; it at once exhibits points, straight lines, parallel lines, angles, parallelograms, &c., &c. These cubes are divisible into various parts. The pupil has already been familiarized with such divisions in numeration, and he now proceeds to a comparison of their several parts, and of the relation of these parts to each other. . . From thence he advances to globes, which furnish him with elementary notions of the circle, of curves generally, &c., &c.

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"Being tolerably familiar with solids, he may now substitute planes. The

*Education Reform." By Thomas Wyse.

transition may be made very easy. Let the cube, for instance, be cut into thin divisions, and placed on paper; he will then see as many plane rectangles as he has divisions; so with all the others. Globes may be treated in the same manner; he will thus see how surfaces really are generated, and be enabled to abstract them with facility in every solid.

"He has thus acquired the alphabet and reading of geometry. He now proceeds to write it.

"The simplest operation, and therefore the first, is merely to place these planes on a piece of paper, and pass the pencil round them. When this has been frequently done, the plane may be put at a little distance, and the child required to copy it, and so on."

A stock of geometrical conceptions having been obtained, in some such man. ner as this recommended by Mr. Wyse, a further step may, in course of time, be taken, by introducing the practice of testing the correctness of all figures drawn by the eye; thus alike exciting an ambition to make them exact, and continually illustrating the difficulty of fulfilling that ambition. In the cutting out of pieces for his card-houses, in the drawing of ornamental diagrams for coloring, and in those various instructive occupations which an inventive teacher will lead him into, he may be for a length of time advantageously left, like the primitive builder, to tentative processes; and will so gain an abundant experience of the difficulty of achieving his aims by the unaided senses. When, having meanwhile undergone a valuable discipline of the perceptions, he has reached a fit age for using a pair of compasses, he will, whilst duly appreciating these as enabling him to verify his ocular guesses, be still hindered by the difficulties of the approximative method. In this stage he may be left for a further period: partly as being yet too young for any thing higher; partly because it is desirable that he should be made to feel still more strongly the want of systematic contrivances. If the acquisition of knowledge is to be made continuously interesting; and if, in the early civilization of the child, as in the early civilization of the race, science becomes attractive only as ministering to art; it is manifest that the proper preliminary to geometry is a long practice in those constructive processes which geometry will facilitate. Observe that here, too, nature points the way. Almost invariably, children, show a strong propensity to cut out things in paper, to make, to build—a propensity which, if duly encouraged and directed, will not only prepare the way for scientific conceptions, but will develop those powers of manipulation in which most people are so deficient.

GEOMETRY-EMPIRICAL.

14. When the observing and inventive faculties have attained the requisite power, the pupil may be introduced to empirical geometry; that is-geometry dealing with methodical solutions, but not with the demonstrations of them. Like all other transitions in education, this should be made not formally but incidentally; and the relationship to constructive art should still be maintained. To make a tetrahedron in cardboard, like one given to him, is a problem which will alike interest the pupil, and serve as a convenient starting-point. In attempting this, he finds it needful to draw four equilateral triangles arranged in special positions. Being unable in the absence of an exact method to do this accurately he discovers on putting the triangles into their respective positions, that he can not make their sides fit, and that their angles do not properly meet

at the apex. He may now be shown how by describing a couple of circles, each of these triangles may be drawn with perfect correctness and without guessing; and after his failure he will duly value the information. Having thus helped him to the solution of his first problem, with the view of illustrating the nature of geometrical methods, he is in future to be left altogether to his own ingenuity in solving the questions put to him. To bisect a line, to erect a perpendicular, to describe a square, to bisect an angle, to draw a line parallel to a given line, to describe a hexagon, are problems which a little patience will enable him to find out. And from these he may be led on step by step to questions of a more complex kind; all of which, under judicious management, he will puzzle through unhelped. Doubtless, many of those brought up under the old regime, will look upon this assertion skeptically. We speak from facts, however, and those neither few nor special. We have seen a class of boys become so interested in making out solutions to these problems, as to look forward to their geometry-lesson as a chief event of the week. Within the last month, we have been told of one girls' school, in which some of the young ladies voluntarily occupy themselves with geometrical questions out of school-hours; and of another, in which they not only do this, but in which one of them is begging for problems to find out during the holidays-both which facts we state on the authority of the teacher. There could indeed be no stronger proofs than are thus afforded of the practicability and the immense advantage of selfdevelopment. A branch of knowledge which as commonly taught is dry and even repulsive, may, by following the method of nature, be made extremely interesting and profoundly beneficial. We say profoundly beneficial, because the effects are not confined to the gaining of geometrical facts, but often revolutionize the whole state of mind. It has repeatedly occurred, that those who have been stupefied by the ordinary school-drill-by its abstract formulas, by its wearisome tasks, by its cramming-have suddenly had their intellects roused, by thus ceasing to make them passive recipients, and inducing them to become active discoverers.

This empirical geometry which presents an endless series of problems, and should be continued along with other studies for years, may throughout be advantageously accompanied by those concrete applications of its principles which serve as its preliminary. After the cube, the octahedron, and the various forms of pyramid and prism have been mastered, may come the more complex regular bodies the dodecahedron, and the icosahedron-to construct which out of single pieces of cardboard requires considerable ingenuity. From these, the transition may naturally be made to such modified forms of the regular bodies as are met with in crystals-the truncated cube, the cube with its dihedral as well as its solid angles truncated, the octahedron and the various prisms as similarly modified; in imitating which numerous forms assumed by different metals and salts, an acquaintance with the leading facts of mineralogy will be incidentally gained. After long continuance in exercises of this kind, rational geometry, as may be supposed, presents no obstacles. Constantly habituated to contemplate relationships of form and quantity, and vaguely perceiving from time to time the necessity of certain results as reached by certain means, the pupil comes to regard the demonstrations of Euclid as the missing supplements to his familiar problems. His well-disciplined faculties enable him easily to master its successive propositions, and to appreciate their value; and he has the occasional gratification of finding some of his own methods proved to be true.

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