1 64 POPULAR SCIENCE MONTHLY 



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 : 6 " 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 mathe- 

 matical 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 pro- 

 found 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. 7 

 It has become the fashion of text-book writers to call especial attention 

 to the rigor of their presentation. Fortunately these claims are gen- 

 erally 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. Meray 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 



Central Association of Science and Mathematics Teachers, Association of 

 Teachers of Mathematics in the Middle States and Maryland, Association of 

 Ohio Teachers of Mathematics and Science, Mathematical Section of the Cali- 

 fornia Teachers' Association, Missouri Society of Teachers of Mathematics, 

 Mathematical Association of Washington, Association of Mathematical Teachers 

 in New England, Kansas Association of Mathematics Teachers. 



6 Nature, Vol. 65 (1902), p. 484. 



7 Jahresbericht der Deutscken Hathematiker-Vereinigung, Vol. 14 (1904), 

 p. 41. 



