38 



SCIENCE 



[N. S. Vol. XXX. No. 758 



omitted would be compensated for by an 

 increase in youthful enthusiasm and the 

 development of individuality and invent- 

 iveness. 



It is well recognized that the study of 

 natural science is essential to all courses of 

 study. Such study, however, is impossible 

 without a practical, working knowledge of 

 mathematics, and facility in its application 

 to problems in engineering and general 

 science. The elementary study of nature 

 requires skill in computing with logarithms ; 

 knowledge of, and power to manipulate, 

 algebraic formulas; the use of squared 

 paper, and the methods of the calculus. 

 Professor Perry believes that boys may not 

 only become skilful in the use of these 

 instruments, but will learn them with pleas- 

 ure. He also asserts that the men who are 

 teaching orthodox mathematics are not only 

 destroying what power to think exists, but 

 are also producing a dislike and hatred for 

 all kinds of computations, and, therefore, 

 for all scientific studies of nature. 



As the basis of his belief that instruction 

 in elementary mathematics should be made 

 more practical, Professor Perry states that 



In the whole history of the world there was 

 never a race with less liking for abstract reason- 

 ing than the Anglo-Saxon. Every other race has 

 perfected abstract schemes of government. Here 

 common-sense and compromise are believed in; 

 logical deductions from philosophical principles 

 are looked upon with suspicion not only by legis- 

 lators but by all our most learned professional 

 men. 



All of this indicates that philosophy is 

 certainly not intended for children. This 

 was also the view of the ancient Greeks, 

 who held that only a few men were capable 

 of philosophic insight. Eeading, writing 

 and ciphering were at one time regarded as 

 learned studies. However, when they be- 

 came essential to the correct doing of one 's 

 daily work, they were taught quite readily 



to children without unnecessary philos- 

 ophy. So the child should learn mathe- 

 matics without unnecessary philosophy. 

 Omitting this philosophic insight, the av- 

 erage boy may learn much useful mathe- 

 matics which wiU serve him all through 

 his life. 



Professor Perry's plan lays emphasis 

 upon the following propositions: (1) Ex- 

 perimental methods in mensuration and 

 geometry ought to precede demonstrative 

 geometry, although even in the earliest 

 stages some demonstrative reasoning may 

 be introduced. (2) The experimental 

 methods adopted may be left largely to the 

 teacher. (3) Decimals ought to be used 

 in arithmetic from the beginning. (4) 

 The numerical solution of complex mathe- 

 matical expressions may be taken up almost 

 as a part of arithmetic, or the beginning of 

 algebra, as it is useful in familiarizing 

 pupils with the meaning of mathematical 

 symbols. (5) Logarithms should imme- 

 diately follow the theory of exponents. 

 ( 6 ) The study of the calculus may precede 

 advanced algebra, advanced trigonometry, 

 or analytical geometry, and may be illus- 

 trated by any quantitative study in which 

 the pupil may be engaged. 



The course in elementary mathematics 

 suggested by Professor Perry includes the 

 following : 



In arithmetic, the use of decimals from 

 the outset; contracted and approximate 

 methods, and rough checks on mimerical 

 calculation; the meaning and use of loga- 

 rithms, including the construction and use 

 of the slide rule; calculation of numerical 

 value from algebraic formulas; extraction 

 of square roots ; simplification of fractions ; 

 calculation of percentage, interest, dis- 

 count, etc. 



In algebra, the translation of verbal 

 statements into algebraic language ; numer- 

 ical application of formulas; rule of in- 



