Page:Popular Science Monthly Volume 68.djvu/168

164 As might be expected these agitations have led to the most severe attacks on the present state of mathematical instruction. Professor Perry seems to have especial gifts along this line, as may be inferred from the following quotation: "I would rather be utterly ignorant of all the wonderful literature and science of the last twenty-four centuries, even of the wonderful achievements of the last fifty years, than not to have the sense that our whole system of so-called education is as degrading to literature and philosophy as it is to English boys and men." This is the view of a man who, as chairman of the Board of Examiners of the Board of Education of London in engineering, applied mechanics and practical mathematics, has charge of about a hundred thousand apprentices in English night schools.

One of the main contentions of the agitators is that our mathematical instruction should be more concrete and inductive. This is frequently expressed by the term 'the laboratory method of teaching mathematics' and several of our leading universities have announced courses to be taught by this method. This gives evidence of a profound movement in methods of mathematical instruction, which will doubtless effect many reforms even if it can not be expected that the extreme views will find general adoption.

The teaching of elementary geometry has perhaps been most severely attacked. This attack has been supported, if not directed, by some of the very foremost mathematicians. Klein has recently said that the methods adopted in Euclid's geometry are unsuited for boys. It has become the fashion of text-book writers to call especial attention to the rigor of their presentation. Fortunately these claims are generally unsubstantiated. There are few things that would give more definite proof of the perfect unsuitableness of an elementary text-book than the fact that every step in the presentation was rigorous. The history of mathematics shows that periods of discovery are followed rather than preceded by examination into the rigor of methods, and the same general principle holds in reference to the training of students.

In France C. Méray has perhaps done the most effective work towards reform in elementary instruction in geometry. At the last meeting of the French Association the section of mathematical sciences passed a resolution to request the association to address the minister