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SCIENCE 



[N. S. Vol. XXVIII. No. 714 



never do anything in it. He would have 

 gone through, life with that notion, if some 

 one had not offered him an appointment 

 to West Point. He doubted his ability to 

 pass the entrance examination in arith- 

 metic; but his friends advised him to get 

 an arithmetic and study. He bought a 

 book and sat down and read the book 

 through, and to his astonishment he found 

 it easy. He passed his examination with 

 flying colors. He entered "West Point and 

 graduated at the head of his class in 

 mathematics, and is now at the head of a 

 high grade technical school. If it had not 

 been for the opportunity of going again 

 over his whole course of mathematics, he 

 would have gone to his grave thinking he 

 had no capacity for mathematical analysis. 

 That comes from poor or premature teach- 

 ing. 



I am opposed to putting college mathe- 

 matics in high schools. Those young 

 people may get a glimmer of it, but they 

 get false impressions from it which are 

 hard to remove. I have been teaching 

 mathematics for forty years or more, and 

 have been teaching applied mechanics for 

 the same time. I taught Rankine for 

 twenty-five years. It has always been my 

 duty and my privilege to make my stu- 

 dents see what mathematics was good for. 

 And I want to defend the teachers of high 

 school and freshman mathematics from 

 what I think is unjust criticism. It is 

 charged they do not make their students 

 understand what mathematics is good for. 

 It is simply impossible for them to do so, 

 as I can do in mechanics. A man is very 

 fortunate who can teach mathematics and 

 then show what it is good for. I am old 

 enough to quote a little of my early experi- 

 ence. I am led to it by something Pro- 

 fessor Swain said in regard to mental 

 processes. There is nothing so valuable to 

 mathematical success as a clear grasp of 

 fundamental principles. When I was pre- 



paring for college I gave all my time to 

 Latin and Greek. I had done all my 

 freshman mathematics and was reputed to 

 be strong on that branch, when a new 

 teacher came into the school who said, 

 "Here's a new book in intellectual arith- 

 metic, and I would like to have every stu- 

 dent in the school go through it." It was 

 fun for me, of course, but I went through 

 the book from A to Z; no other mathe- 

 matics that I ever studied did me so much 

 good. The teacher's maxim was, "Take 

 hold of the thread at the right end." 

 That was the secret of his splendid teach- 

 ing. I have applied that maxim to every 

 branch of mathematics I have ever studied 

 or taught. I have learned to take hold of 

 mathematics at the right end, and in a 

 measure I have taught my students to do 

 so. 



By B. F. Groat, Professor of Mechanics 

 and Mathematics, School of Mines, Uni- 

 versity of Minnesota. 

 Most of the speakers have stated that 

 what they were about to say had already 

 been said by preceding speakers. I am 

 going to try to state a general principle I 

 have not heard clearly put since I came 

 here. During the lunch hour Professor 

 Slaught said that he had not heard a 

 single general pedagogical principle 

 brought out. I am going to take the 

 honor to myself, to give expression to what 

 seems to me to be a general educational 

 principle. 



Mathematics is mathematics and engi- 

 neering is engineering. There is just as 

 much art, science or principle in the teach- 

 ing of mathematics as there is in the teach- 

 ing of engineering and these two subjects 

 should be distinguished, separated and 

 kept separate. If you are going to teach 

 engineering you must teach the pure prin- 

 ciples. If you are going to teach mathe- 

 matics you have got to teach pure mathe- 



