But how shall better methods of mathematical and scientific education be combined with the decrease of the subject-matter of instruction? I think, by abandoning systematic instruction altogether, at least in so far as that is required of all young pupils. I see no necessity whatever that the graduates of our high schools and preparatory schools should be little philologists, and at the same time little mathematicians, physicists, and botanists; in fact, I do not see the possibility of such a result. I see in the endeavor to attain this result, in which every instructor seeks for his own branch a place apart from the others, the main mistake of our whole system. I should be satisfied if every young student could come into living contact with and pursue to their ultimate logical consequences merely a few mathematical or scientific discoveries. Such instruction would be mainly and naturally associated with selections from the great scientific classics. A few powerful and lucid ideas could thus be made to take root in the mind and receive thorough elaboration. This accomplished, our youth would make a different showing from what they do to-day.[128]
What need is there, for example, of burdening the head of a young student with all the details of botany? The student who has botanised under the guidance of a teacher finds on all hands, not indifferent things, but known or unknown things, by which he is stimulated, and his gain made permanent. I express here, not my own, but the opinion of a friend, a practical teacher. Again, it is not at all necessary that all the matter that is offered in the schools should be learned. The best that we have learned, that which has remained with us for life, outlived the test of examination. How can the mind thrive when matter is heaped on matter, and new materials piled constantly on old, undigested materials? The question here is not so much that of the accumulation of positive knowledge as of intellectual discipline. It seems also unnecessary that all branches should be treated at school, and that exactly the same studies should be pursued in all schools. A single philological, a single historical, a single mathematical, a single scientific branch, pursued as common subjects of instruction for all pupils, are sufficient to accomplish all that is necessary for the intellectual development. On the other hand, a wholesome mutual stimulus would be produced by this greater variety in the positive culture of men. Uniforms are excellent for soldiers, but they will not fit heads. Charles V. learned this, and it should never be forgotten. On the contrary, teachers and pupils both need considerable latitude, if they are to yield good results.
With John Karl Becker I am of the opinion that the utility and amount for individuals of every study should be precisely determined. All that exceeds this amount should be unconditionally banished from the lower classes. With respect to mathematics, Becker,[129] in my judgment, has admirably solved this question.
With respect to the upper classes the demand assumes a different form. Here also the amount of matter obligatory on all pupils ought not to exceed a certain limit. But in the great mass of knowledge that a young man must acquire to-day for his profession it is no longer just that ten years of his youth should be wasted with mere preludes. The upper classes should supply a truly useful preparation for the professions, and should not be modelled upon the wants merely of future lawyers, ministers, and philologists. Again, it would be both foolish and impossible to attempt to prepare the same person properly for all the different professions. In such case the function of the schools would be, as Lichtenberg feared, simply to select the persons best fitted for being drilled, whilst precisely the finest special talents, which do not submit to indiscriminate discipline, would be excluded from the contest. Hence, a certain amount of liberty in the choice of studies must be introduced in the upper classes, by means of which it will be free for every one who is clear about the choice of his profession to devote his chief attention either to the study of the philologico-historical or to that of the mathematico-scientific branches. Then the matter now treated could be retained, and in some branches, perhaps, judiciously extended,[130] without burdening the scholar with many branches or increasing the number of the hours of study. With more homogeneous work the student's capacity for work increases, one part of his labor supporting the other instead of obstructing it. If, however, a young man should subsequently choose a different profession, then it is his business to make up what he has lost. No harm certainly will come to society from this change, nor could it be regarded as a misfortune if philologists and lawyers with mathematical educations or physical scientists with classical educations should now and then appear.
The view is now wide-spread that a Latin and Greek education no longer meets the general wants of the times, that a more opportune, a more "liberal" education exists. The phrase, "a liberal education," has been greatly misused. A truly liberal education is unquestionably very rare. The schools can hardly offer such; at best they can only bring home to the student the necessity of it. It is, then, his business to acquire, as best he can, a more or less liberal education. It would be very difficult, too, at any one time to give a definition of a "liberal" education which would satisfy every one, still more difficult to give one which would hold good for a hundred years. The educational ideal, in fact, varies much. To one, a knowledge of classical antiquity appears not too dearly bought "with early death." We have no objection to this person, or to those who think like him, pursuing their ideal after their own fashion. But we may certainly protest strongly against the realisation of such ideals on our own children. Another,—Plato, for example,—puts men ignorant of geometry on a level with animals.[131] If such narrow views had the magical powers of the sorceress Circe, many a man who perhaps justly thought himself well educated would become conscious of a not very flattering transformation of himself. Let us seek, therefore, in our educational system to meet the wants of the present, and not establish prejudices for the future.
But how does it come, we must ask, that institutions so antiquated as the German gymnasiums could subsist so long in opposition to public opinion? The answer is simple. The schools were first organised by the Church; since the Reformation they have been in the hands of the State. On so large a scale, the plan presents many advantages. Means can be placed at the disposal of education such as no private source, at least in Europe, could furnish. Work can be conducted upon the same plan in many schools, and so experiments made of extensive scope which would be otherwise impossible. A single man with influence and ideas can under such circumstances do great things for the promotion of education.