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SCIENCE 



[N. S. Vol. XXVIII. No. 709 



and common-sense conclusions, who have 

 an equipment of technical knowledge and 

 who can produce results. 



In discussing the teaching of mathe- 

 matics to engineers, we should emphasize 

 not the mathematics nor the engineers, but 

 the teaching. Aside from the imparting 

 of knowledge and technical ability, the 

 teaching of mathematics gives opportunity 

 for training in the use of logical methods 

 and in the drawing of intelligent conclu- 

 sions from unorganized data which will 

 make efficient men, whether they follow 

 pure engineering, or semi-technical, or 

 business pursuits. Such teaching does not 

 come from the text-book; it must be per- 

 sonal — it comes from the teacher. He 

 must be in sympathy with engineering 

 work and have a just appreciation of its 

 problems and its methods. He must be 

 imbued with the spirit and the ideals of 

 the engineer. 



Chas. F. Scott 



THE POINT OF VIEW IN TEACHING 

 ENGINEERING MATHEMATICS ^ 



I HARDLY know why I should have been 

 asked to address you at this conference. 

 Possibly, however, the fact that I am a 

 civil engineer by profession, without hav- 

 ing been pex-mitted ever to practise this 

 profession, and the additional fact that I 

 have been a professional teacher of mathe- 

 matical physics, without having been per- 

 mitted to continue in this work, have led 

 your committee to think that I might 

 furnish a conspicuous illustration of the 

 failures to which colleges and universities 

 may lead in these lines of endeavor. 



Having listened attentively to the three 

 formal papers just read, I find it essential 



* Extempore remarks before Sections A and D 

 of the American Association for the Advancement 

 of Science and the Chicago Section of the Amer- 

 ican Mathematical Society, at the Chicago meet- 

 ing, December 30, 1907. 



to revise my program and instead of fol- 

 lowing similar lines to those of the preced- 

 ing speakers, it seems essential to take 

 direct issue with them. This I am dis- 

 posed to do, not so much because I differ 

 wholly from the views they have set forth, 

 as because it seems necessary to have other 

 sides of the questions they have discussed 

 represented. The preceding speakers ap- 

 pear to me to have taken themselves some- 

 what too seriously. This is a general 

 fault of both theoretical and practical edu- 

 cationalists. My own experience leads me 

 to conclude that in educational affairs the 

 teacher, the school, the college and the 

 university play a much less important role 

 than we commonly suppose. In fact, I 

 have reached the provisional conclusion 

 that the majority of our students turn out 

 fairly well in the world not so much by 

 reason of the academic instruction they 

 receive as in spite of it. 



My impression also is that in taking our- 

 selves too seriously as teachers of one sub- 

 ject or another, we have, as a rule, quite 

 underestimated the magnitude and the dif- 

 ficulty of the psychological problems with 

 which we have to deal. We have, as a 

 rule, quite overestimated the capacity of 

 our average student, and have thus 

 usually expected too much from him. It 

 is, of course, desirable to set our ideal 

 high and try to rise to an elevated in- 

 tellectual level; but in doing so we have 

 commonly neglected the influence of 

 heredity as well as of environment. I am 

 inclined to think Dr. Holmes was right 

 when he said that it is essential in the 

 generation of a gentleman to begin four 

 hundred years before he is born. So also 

 is it necessary, if we wish to develop a 

 student into a first-class scholar, to begin 

 back some generations before we take up 

 the formal work of training in our col- 

 leges or schools of engineering. It is an 

 important fact, also too commonly over- 



