The problem is much simpler in the case of mathematical teaching than in the case of English, because the educational theory and method have been more thoroughly discussed. There is no need for the ten years of experiment and trial I have suggested for the organization of English teaching. The mathematical reformer may begin now at a point the English language reformer will not reach for some years. Suppose now a suitably authenticated committee were to work out—on the basis of Professor Perry's syllabus perhaps—a syllabus of school mathematics, and then make a thorough review of all the mathematical textbooks on sale throughout the English-speaking world, admitting some perhaps as of real permanent value for teaching of the new type, provisionally recognizing others as endurable, but with clear recommendations for their revision and improvement, and condemning the others specifically by name. Let them make it clear that this syllabus and report will be respected by all public examining bodies; let them spend a hundred pounds or so in the intelligent distribution of their report, and the scholastic profession will not be long before it is equipped with the recommended books. Meanwhile, the English and American scholastic publishers will become extremely active, the warned books will be revised, and new books will be written in competition for the enormous prize of the committee's final approval, an activity that a second review, after an interval of five or six years, will recognize and reward.
Such measures as these will be worth reams of essays in educational papers and Parents' Reviews, worth thousands of inspiring and suggestive lectures at pedagogic conferences. If, indeed, such essays and such lectures do any good at all. The more one looks into scholastic affairs the more one is struck not only by the futility but the positive mischievousness of much of what passes for educational liberalism. The schoolmaster is criticised vehemently for teaching the one or two poor useless subjects he can in a sort of way teach, and practically nothing is done to help or equip him to teach anything else. By reason of this uproar, the world is full now of anxious muddled parents, their poor brains buzzing with echoes of Froebel, Tolstoy, Herbert Spencer, Ruskin, Herbart, Colonel Parker, Mr. Harris, Matthew Arnold, and the Morning Post, trying to find something better. They know nothing of what is right, they only know very, very clearly that the ordinary school is extremely wrong. They are quite clear they don't want "cram" (though they haven't the remotest idea what cram is), and they have a pretty general persuasion that failure at examination is a good test of a sound education. And in response to their bleating demand there grows a fine crop of Quack Schools; schools organized on lines of fantastic extravagance, in which bee-keeping takes the place of Latin, and gardening supersedes mathematics, in which boys play tennis naked to be cured of False Shame, and the numerical exercises called bookkeeping and commercial correspondence are taught to the sons of parents (who can pay a hundred guineas a year), as Commercial Science. The subjects of study in these schools come and go like the ravings of a disordered mind; "Greek History" (in an hour or so a week for a term) is followed by "Italian Literature," and this gives place to the production of a Shakesperian play that ultimately overpowers and disorganizes the whole curriculum. Ethical lessons and the school pulpit flourish, of course. A triennial walk to a chalk-pit is Field Geology, and vague half-holiday wanderings are Botany Rambles. "Art" of the copper punching variety replaces any decent attempt to draw, and an extreme expressiveness in music compensates for an almost deliberate slovenliness of technique. Even the ladies' seminaries of the Georgian days could scarcely have produced a parallel to the miscellaneous incapacity of the victim of these "modern" schools, and it becomes daily more necessary for those who have the interests of education at heart to disavow with the most unmistakable emphasis these catch-parent impostures.
With the other subjects under the headings of A and B, it is not necessary to deal at any length here. Drawing begins at home, and a child should have begun to sketch freely before the formal schooling commences. It is the business of the school to teach drawing and not to teach "art," which, indeed, is always an individual and spontaneous thing, and it need only concern itself directly with those aspects of drawing that require direction. Of course, an hour set aside from the school time in which boys or girls may do whatever they please with paper, ink, pens, pencils, compasses, and water-colour would be a most excellent and profitable thing, but that scarcely counts (except in the Quack Schools) as teaching. As a matter of fact, teaching absolutely spoils all that sort of thing. A course in model drawing and in perspective, however, is really a training in seeing things, it demands rigorous instruction and it must be the backbone of school drawing, and, in addition, studies may be made from flowers that would not be made without direction: topography (and much else) may be learnt by copying good explicit maps; chronology (to supplement the child's private reading of history) by the construction of time charts; and much history also by drawing and colouring historical maps. With geometrical drawing one passes insensibly into mathematics. And so much has been done not only to revolutionize the teaching of modern languages, but also to popularize the results, that I may content myself with a mere mention of the names of Rippmann, S. Alge, Hölzel, and Gouin as typical of the new ways.
There remains the question of C, the amount of Information that is to take a place in schooling. Now there is one "subject" that it would be convenient to include, were it only for the sake of the mass of exercise and illustration it supplies to the mathematical course, and that is the science of Physics. In addition, the science of physics, since it culminates in a clear understanding and use of the terminology of the aspects of energy and a clear sense of adequate causation, is fundamentally necessary to modern thought. Practical work is, no doubt, required for the proper understanding of physical science, and so far it must enter into schooling, but it may be pointed out here that in many cases the educational faddist is overdoing the manual side of science study to a ridiculous extent. Things have altered very much at the Royal College of Science, no doubt, since my student days, but fifteen years ago the courses in elementary physics and in elementary geology were quite childishly silly in this respect. Both these courses seemed to have been inspired by that eminent educationist, Mr. Squeers, and the sequel to spelling "window" was always to "go and clean one." The science in each course in those days could have been acquired just as well in a fortnight as in half a year. One muddled away three or four days etching a millimetre scale with hydrofluoric acid on glass—to no earthly end that I could discover— and a week or so in making a needless barometer. In the course in geology, days and days were spent in drawing ideal crystalline forms and colouring them in water-colours, apparently in order to get a totally false idea of a crystal, and weeks in the patient copying of microscopic rock sections in water-colours. Effectual measures of police were taken to prevent the flight of the intelligent student from these tiresome duties. The mischief done in this way is very great. It deadens the average students and exasperates and maddens the eager ones. I am inclined to think that a very considerable proportion of what passes as "practical" science work, for which costly laboratories are built and expensive benches fitted, consists of very similar solemnities, and it cannot be too strongly urged that "practical" work that does not illuminate is mere waste of the student's time.