Reform in Mathematical Teaching

Abstract

THERE are two places in Prof. Perry's letter appearing in your issue of March 27 in which he mentions schoolmasters in terms of, in the one case praise, in the other blame. The first passage is where he congratulates the “reformers” “on having with them the good wishes of every thoughtful teacher of the whole country,” but in the last passage he expresses the conviction that we shall “not very long remain in the foremost files of our time if we depend upon the schoolmasters.” I hope that teachers are good for more than mere good wishes, and I think Prof. Perry will find that the reform he laments as scarcely within sight has not only begun, but is actually bearing fruit in the place in which, though the subject of controversy, the noise of the conflict is heard least—the schoolroom. Schoolmasters, like others, move with the times, and the “conventional schoolmaster” is a much rarer bird than the conventional examiner or the conventional inspector. I suppose syllabuses and textbooks are a necessity still, but the competent teacher of mathematics needs not to be bound by anything of the kind. Personally, I see no necessity for this ideal text-book one hears about which is to replace Euclid, and those who caricature him; we are better without a text-book at all. Let a master be engaged capable of making his own syllabus for his own pupils, and give him a free hand to introduce modern geometry, differential calculus, &c., as he sees fit; such a man will welcome the appreciation of a competent inspector, himself a mathematician and, beyond that, a successful teacher of mathematics. As I have already hinted, reform in the schoolroom proceeds as rapidly as examiners will allow, rather more so in fact, for I know that many boys learn much that no examination they have been in for, or are likely to take, tests. My own work is in such a small way that I do not care much to bring it forward, but I must confess to periods of guilty satisfaction when I have robbed time from examination teaching and introduced boys, much to their interest, and I feel sure profit, to such things as coaxal circles, theory of inversion, cross ratios, and fundamentals of the integral calculus. Let the mouse help the lion!