Febkuaky 26, 1904.] 



SCIENCE. 



323 



ing. If the reformation whieli has been 

 planned and begun shall go on to comple- 

 tion, the mathematical teaching in the sec- 

 ondary schools of the middle west will have 

 little resemblance ten years hence to the 

 work of to-day. 



Arithmetic, algebra, geometry and trigon- 

 ometry will no longer be set off in 'water- 

 tight compartments,' but will all be de- 

 manded in various combinations for the 

 solution of single elementary problems. 

 Squared and polar coordinate paper will 

 represent the facts to the eye in geometrical 

 sjonbolism and at the same time will give 

 a practical introduction to the fundamental 

 ideas of analytics and the calculus. By 

 pursuing through the four years of second- 

 ary school life a carefully selected and 

 properly graded problem course the pupil 

 will review the whole range of elementary 

 mathematical truth and become familiar 

 with it, not only in theory, but also in prac- 

 tice. He will never be asking, 'what use?' 

 But with the enthusiasm which original in- 

 vestigation only can arouse he will find 

 his educational material in the simpler 

 problems of the shop, the store, the farm, 

 the bank, the railroad, the steam-boat, the 

 steam-engine, the electric motor, political 

 economy, geodesy, astronomy, time, space, 

 force and so on through the range of the 

 elementary aspects of the things of daily 

 thought and experience in this complex and 

 highly developed life of ours. Such a 

 change can not be perfected in a day. No 

 inferior or untrained teacher can succeed 

 with it. Elementary work must be in the 

 hands of those who have come into living 

 contact with some of the deep, broad prob- 

 lems of chemistry, of physics and of engi- 

 neering, demanding for their solution a 

 large acquaintance with^the higher ranges 

 of mathematics. In turn colleges and uni- 

 versities which strive to train such teachers 

 must revise their mathematical courses and 

 adjust themselves to these new ideas. 



In many of our leading institutions ex- 

 actly that thing is occurring, stimulated 

 perhaps in the first place by the great de- 

 mand of technical colleges for mathema- 

 ticians in sympathy with engineering ideas. 



Those who are dealing with freshmen 

 in colleges are asking the question, 'What 

 is the matter with our preparatory schools ? ' 

 If you wish to see this question strongly 

 formulated and illustrated, read the com- 

 mencement address of 1903 by President 

 Ira Remsen at Mount Holyoke College. 



This is the indictment of the schools, that 

 they use, largely to the exclusion of the 

 thought element, a mass of formal and 

 conventional educational material and thus 

 paralyze thought and make abortive any 

 natural mental growth. 



In the grades the clear, keen, accurate 

 thinking of childhood soon disappears and 

 does not usually show itself again until the 

 laboratory or the practical problems of life 

 make it once more dominant. We refer to 

 President Remsen 's question only so far as 

 it relates to mathematical training. The 

 technical schools long ago recognized the 

 barren results of primary and secondary 

 mathematical instruction and have been 

 deeply interested in its improvement. Most 

 keenly this loss has come to the engineer 

 who must subject himself to the long, hard 

 discipline necessary in his profession for 

 the successful solution of his original and 

 independent problems. Yet certain people 

 seem to look askance upon the engineer and 

 discover no advancement of science in the 

 design of an entirely new machine to carry 

 out an entirely novel idea. According to 

 their notion, Whitney was not a scientist 

 when he invented the cotton gin, nor Fulton 

 when he constructed the first steam-boat, 

 nor Morse when he perfected the telegraph. 



This was all pure commercialism. Even 

 if these worthies cared nothing for the 

 financial side of their work and only sought 

 to serve and benefit their fellow men, they 



