Fields, factories and workshops

by kniaz Petr Alekseevich Kropotkin

There is, however, the other method which permits the pupil to progress, as a whole, at a much speedier rate, and under which he who once has learned geometry will know it all his life long. Under this system, each theorem is put as a problem; its solution is never given beforehand, and the pupil is induced to find it by himself. Thus, if some preliminary exercises with the rule and the compass have been made, there is not one boy or girl, out of twenty or more, who will not be able to find the means of drawing an angle which is equal to a given angle, and to prove their equality, after a few suggestions from the teacher; and if the subsequent problems are given in a systematic succession (there are excellent text-books for the purpose), and the teacher does not press his pupils to go faster than they can go at the beginning, they advance from one problem to the next with an astonishing facility, the only difficulty being to bring the pupil to solve the first problem, and thus to acquire confidence in his own reasoning.

Moreover, each abstract geometrical truth must be impressed on the mind in its concrete form as well. As soon as the pupils have solved a few problems on paper, they must solve them in the playing-ground with a few sticks and a string, and they must apply their knowledge in the workshop. Only then will the geometrical lines acquire a concrete meaning in the children’s minds; only then will they see that the teacher is playing no tricks when he asks them to solve problems with the rule and the compass without resorting to the protractor; only then will they know geometry.

“Through the eyes and the hand to the brain”—this is the true principle of economy of time in teaching. I remember, as if it were yesterday, how geometry suddenly acquired for me a new meaning, and how this new meaning facilitated all ulterior studies. It was as we were mastering at school a Montgolfier balloon, and I remarked that the angles at the summits of each of the twenty strips of paper out of which we were going to make the balloon must cover less than the fifth part of a right angle each. I remember, next, how the sinuses and the tangents ceased to be mere cabalistic signs when they permitted us to calculate the length of a stick in a working profile of a fortification; and how geometry in space became plain when we began to make on a small scale a bastion with embrasures and barbettes—an occupation which obviously was soon prohibited on account of the state into which we brought our clothes. “You look like navvies,” was the reproach addressed to us by our intelligent educators, while we were proud precisely of being navvies, and of discovering the use of geometry.

By compelling our children to study real things from mere graphical representations, instead of making those things themselves, we compel them to waste the most precious time; we uselessly worry their minds; we accustom them to the worst methods of learning; we kill independent thought in the bud; and very seldom we succeed in conveying a real knowledge of what we are teaching. Superficiality, parrot-like repetition, slavishness and inertia of mind are the results of our method of education. We do not teach our children how to learn.

The very beginnings of science are taught on the same pernicious system. In most schools even arithmetic is taught in the abstract way, and mere rules are stuffed into the poor little heads. The idea of a unit, which is arbitrary and can be changed at will in our measurement (the match, the box of matches, the dozen of boxes, or the gross; the metre, the centimetre, the kilometre, and so on), is not impressed on the mind, and therefore when the children come to the decimal fractions they are at a loss to understand them. In this country, the United States and Russia, instead of accepting the decimal system, which is the system of our numeration, they still torture the children by making them learn a system of weights and measures which ought to have been abandoned long since. The pupils lose at that full two years, and when they come later on to problems in mechanics and physics, schoolboys and schoolgirls spend most of their time in endless calculations which only fatigue them and inspire in them a dislike of exact science. But even there, where the decimal measures have been introduced, much time is lost in school simply because the teachers are not accustomed to the idea that every measure is only approximate, and that it is absurd to calculate with the exactitude of one gramme, or of one metre, when the measuring itself does not give the elements of such an exactitude. Whereas in France, where the decimal system of measures and money is a matter of daily life, even those workers who have received the plainest elementary education are quite familiar with decimals. To represent twenty-five centimes, or twenty-five centimetres, they write “zero twenty-five,” while most of my readers surely remember how this same zero at the head of a row of figures puzzled them in their boyhood. We do all that is possible to render algebra unintelligible, and our children spend one year before they have learned what is not algebra at all, but a mere system of abbreviations, which can be learned by the way, if it is taught together with arithmetic.[190]

The waste of time in physics is simply revolting. While young people very easily understand the principles of chemistry and its formulæ, as soon as they themselves make the first experiments with a few glasses and tubes, they mostly find the greatest difficulties in grasping the mechanical introduction into physics, partly because they do not know geometry, and especially because they are merely shown costly machines instead of being induced to make themselves plain apparatus for illustrating the phenomena they study.

Instead of learning the laws of force with plain instruments which a boy of fifteen can easily make, they learn them from mere drawings, in a purely abstract fashion. Instead of making themselves an Atwood’s machine with a broomstick and the wheel of an old clock, or verifying the laws of falling bodies with a key gliding on an inclined string, they are shown a complicated apparatus, and in most cases the teacher himself does not know how to explain to them the principle of the apparatus, and indulges in irrelevant details. And so it goes on from the beginning to the end, with but a few honourable exceptions.[191]

If waste of time is characteristic of our methods of teaching science, it is characteristic as well of the methods used for teaching handicraft. We know how years are wasted when a boy serves his apprenticeship in a workshop; but the same reproach can be addressed, to a great extent, to those technical schools which endeavour at once to teach some special handicraft, instead of resorting to the broader and surer methods of systematical teaching. Just as there are in science some notions and methods which are preparatory to the study of all sciences, so there are also some fundamental notions and methods preparatory to the special study of any handicraft.

Reuleaux has shown in that delightful book, the Theoretische Kinematik, that there is, so to say, a philosophy of all possible machinery. Each machine, however complicated, can be reduced to a few elements—plates, cylinders, discs, cones, and so on—as well as to a few tools—chisels, saws, rollers, hammers, etc.; and, however complicated its movements, they can be decomposed into a few modifications of motion, such as the transformation of circular motion into a rectilinear, and the like, with a number of intermediate links. So also each handicraft can be decomposed into a number of elements. In each trade one must know how to make a plate with parallel surfaces, a cylinder, a disc, a square, and a round hole; how to manage a limited number of tools, all tools being mere modifications of less than a dozen types; and how to transform one kind of motion into another. This is the foundation of all mechanical handicrafts; so that the knowledge of how to make in wood those primary elements, how to manage the chief tools in wood-work, and how to transform various kinds of motion ought to be considered as the very basis for the subsequent teaching of all possible kinds of mechanical handicraft. The pupil who has acquired that skill already knows one good half of all possible trades.

Besides, none can be a good worker in science unless he is in possession of good methods of scientific research; unless he has learned to observe, to describe with exactitude, to discover mutual relations between facts seemingly disconnected, to make inductive hypotheses and to verify them, to reason upon cause and effect, and so on. And none can be a good manual worker unless he has been accustomed to the good methods of handicraft altogether. He must grow accustomed to conceive the subject of his thoughts in a concrete form, to draw it, or to model, to hate badly kept tools and bad methods of work, to give to everything a fine touch of finish, to derive artistic enjoyment from the contemplation of gracious forms and combinations of colours, and dissatisfaction from what is ugly. Be it handicraft, science, or art, the chief aim of the school is not to make a specialist from a beginner, but to teach him the elements of knowledge and the good methods of work, and, above all, to give him that general inspiration which will induce him, later on, to put in whatever he does a sincere longing for truth, to like what is beautiful, both as to form and contents, to feel the necessity of being a useful unit amidst other human units, and thus to feel his heart at unison with the rest of humanity.