Chapter X
Section III
THE KNOWLEDGE OF THE UNIVERSE
(b) MATHEMATICS
The question of Arithmetic and of Mathematics generally is one of great import to us as educators.
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.
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 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.”
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.
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.
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’…
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…
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.
