THE KNOWLEDGE OF THE UNIVERSE
THE question of Arithmetic and of Mathematics generally is one of great import to us as educators. So long as the idea of ‘faculties’ obtained no doubt we were right to put all possible weight on a subject so well adapted to train the reasoning powers, but now we are assured that these powers do not wait upon our training. They are there in any case; and if we keep a chief place in our curriculum for Arithmetic we must justify ourselves upon other grounds. We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law. It is a
great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence,—that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda [Latin-lift up your hearts, Catholic church opening to liturgy or prayer]which we should hear in all natural law.
Again, integrity in our dealings depends largely upon ‘Mr. Micawber’s’ golden rule, while ‘Harold Skim- pole’s’ disregard of these things is a moral offence against society. Once again, though we do not live on gymnastics, the mind like the body, is invigorated by regular spells of hard exercise.
But education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child’s mind should deal with. Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.
What is better, it will be said, than a training in exactness and ingenuity? But in saying so we assume that this exactness and ingenuity brought out in Arithmetic serve us in every department of life. Were this the case we should indeed have a royal road to learning; but it would seem that no such road is open to us. The habits and powers brought to bear upon any one educational subject are exercised upon that subject simply. The familiar story of how Sir Isaac Newton teased by his cat’s cries to be let in caused a large hole in the door to be made for the cat and a small one for the kitten, illustrates not a mere amusing lapse in a great mind but the fact that work upon special lines qualifies for work
upon those lines only. One hears of more or less deficient boys to whom the study of Bradshaw is a delight, of an admirable accountant who was otherwise a little ‘deficient.’
The boy who gets ‘full marks’ in Arithmetic makes a poor show in history because the accuracy and ingenuity brought out by his sums apply to his sums only: and as for the value of Arithmetic in practical life, most of us have private reasons for agreeing with the eminent staff officer who tells us that,—
“I have never found any Mathematics except simple addition of the slightest use in a work-a-day life except in the Staff College examinations and as for mental gymnastics and accuracy of statement, I dispute the contention that Mathematics supply either any better than any other study.”
We have most of us believed that a knowledge of the theory and practice of war depended a good deal upon Mathematics, so this statement by a distinguished soldier is worth considering. In a word our point is that Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind. But then how profoundly worthy are these subjects of study for their own sake, to say nothing of other great branches of knowledge to which they are ancillary! Lack of proportion should be our bête noire [strongly detested or avoided] in drawing up a curriculum, remembering that the mathematician who knows little of the history of his own country or that of any other, is sparsely educated at the best.
At the same time Genius has her own rights. The born mathematician must be allowed full scope even to the omission of much else that he should know. He soon asserts himself, sees into the intricacies of a problem with half an eye, and should have scope. He would perfer not to have much teaching. But why should the tortoise keep pace with the hare and why should a boy’s success in life depend upon drudgery in Mathematics?
That is the tendency at the present moment—to close the Universities and consequently the Professions to boys and girls who, because they have little natural aptitude for mathematics, must acquire a mechanical knowledge by such heavy all-engrossing labour as must needs shut out such knowledge of the ‘humanities’ say, as is implied in the phrase ‘a liberal education.’
The claims of the London Matriculation examination, for example, are acknowledged by many teachers to be incompatible with the wide knowledge proper to an educated person.
Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the ‘Captain’ ideas, which should quicken imagination.
How living would Geometry become in the light of the discoveries of Euclid as he made them!
To sum up, Mathematics are a necessary part of every man’s education; they must be taught by those who know; but they may not engross the time and attention of the scholar in such wise as to shut out any of the score of ‘subjects,’ a knowledge of which is his natural right.
It is unnecessary to exhibit mathematical work done in the P.U.S. as it is on the same lines and reaches the same standard as in other schools. No doubt his habit of entire attention favours the P.U.S. scholar.