410 



SCIENCE. 



[N.S. Vol. XVII. No. 428 



The Secondary Sc/iools.— Pending the 

 reform of the primary schools, the second- 

 ary schools must advance^ independently. 

 In these schools at present, according to 

 one type of arrangement, we find algebra 

 in the first year, plane geometry in the 

 second, physics in the third, and the more 

 difficult parts of algebra and solid geom- 

 etry, with review of all the mathematics, 

 in the fourth. 



Engineers* tell us that in the schools 

 algebra is taught in one water-tight com- 

 partment, geometry in another, and physics 

 in another, and that the student learns to 

 appreciate (if ever) only very late the 

 absolutely close connection between these 

 different subjects, and then, if he credits 

 the fraternity of teachers with knowing 

 the closeness of this relation, he blames 

 them most heartily for their unaccountably 

 stupid way of teaching him. If we con- 

 trast this state of affairs with the state of 

 affairs in the solid four years' course in 

 Latin, I think we are forced to the conclu- 

 sion that the organization of instruction in 



* Why is it that one of the sanest and best-in- 

 formed scientific men living, a man not himself an 

 engineer, can charge mathematicians with killing 

 off every engineering school on which they can lay 

 hands? Wliy do engineers so strongly urge that 

 the mathematical courses in engineering schools 

 be given by practical engineers? 



And why can a reviewer of ' Some Recent Books 

 of Mechanics ' write with truth : " The students' 

 previous training in algebra, geometry, trigonom- 

 etry, analytic geometry and calculus as it is 

 generally taught has been necessarily quite formal. 

 These mighty algorithms of formal mathematics 

 must be learned so that they can be applied with 

 readiness and precision. But with mechanics 

 comes the application of these algorithms, and 

 formal, do-by-rote methods, though often possible, 

 yield no results of permanent value. How to 

 elicit and cultivate thought is now of primary im- 

 portance"? (E. B. Wilson, Bulletin Amer. Math. 

 Soc, October, 1902.) But is it conceivable that 

 in any part of the education of the student the 

 problem of eliciting and cultivating thought 

 should not be of primary importance? 



Latin is much more perfect than that of 

 the instruction in mathematics. 



The following question arises: Would it 

 not be possible to organize the algebra, 

 geometry and physics of the secondary 

 school into a thoroughly coherent four 

 years' course, comparable in strength and 

 closeness of structure with the four years' 

 course in Latin? (Here under physics I 

 include astronomy and the more mathe- 

 matical and physical parts of physiog- 

 raphy.) It would seem desirable that, 

 just as the systematic development of theo- 

 retical mathematics is deferred to a later 

 period, likewise much of theoretical physics 

 might well be deferred. Let the physics 

 also be made thoroughly practical. At any 

 rate, so far as the instruction of boys is 

 concerned, the course shotild certainly have 

 its character largely determined by the 

 conditions which would be imposed by en- 

 gineers. What kind of two or three years' 

 course in mathematics and physics would 

 a thoroughly trained engineer give to 

 boys in the secondary school? Let this 

 body of material postulated by the engineer 

 serve as the basis of the four years ' course. 

 Let the instruction in the course, however, 

 be given by men who have received expert 

 training in mathematics and physics as 

 well as in engineering, and let the instruc- 

 tion be so organized that with the develop- 

 ment of the boy, in appreciation of the 

 practical relations, shall come simultane- 

 ously his development in the direction of 

 theoretical physics and theoretical mathe- 

 matics. 



Perry is quite right in insisting that it 

 is scientifically legitimate in the pedagogy 

 of elementary mathematics to take a large 

 body of basal principles instead of a small 

 body, and to build the edifice upon the 

 larger body for the earlier years, reserving 

 for the later years the philosophic criticism 

 of the basis itself and the reduction of the 

 basal system. 



