610 



SCIENCE 



[N. S. Vol. XXXIX. No. 1008 



December 5, 1913, entitled " The Human 

 Worth of Eigorous Thinking." Professor 

 Keyser is the head of the department of mathe- 

 matics at Columbia University, Professor 

 Thorndike's own institution, and is a writer 

 of international repute on mathematical sub- 

 jects and particularly on the educational value 

 of mathematics. I leave it to any one to judge 

 as to who is better qualified to speak with 

 authority on the subject of mathematics and 

 the pedagogy of mathematics, Professor 

 Thorndike or Professor Keyser. 



Professor Keyser says in the course of his 

 paper : 



We are beginning to see that to challenge the 

 human worth of mathematics, to challenge the 

 worth of rigorous thinking, is to challenge the 

 worth of all thinking, for now we see that mathe- 

 matics is but the ideal to which all thinking, by 

 an inevitable process and law of the human spirit, 

 constantly aspires. We see that to challenge the 

 worth of that ideal is to arraign before the bar 

 of values what seems the deepest process and in- 

 most law of the universe of thought. Indeed we 

 see that in defending mathematics we are really 

 defending a cause yet more momentous, the whole 

 cause, namely, of the conceptual procedure of sci- 

 ence and the conceptual procedure and activity of 

 the human mind, for mathematics is nothing but 

 such conceptual procedure and activity come to its 

 maturity, purity and perfection. 



If Professor Thorndike had read Professor 

 Keyser's paper, of which I have only quoted 

 a brief extract, I doubt if he would have 

 characterized as " superstition " ideas which 

 are so vigorously maintained by one of the 

 men best qualified to speak with authority on 

 the subject in question. 



Another statement by Professor Thorn- 

 dike is that 



Mathematics improves mathematical reasoning 

 but not the power to reason in general. 



I am yet to be convinced that there is more 

 than one kind of reasoning; whether one rea- 

 sons in mathematics or in some other subject, 

 he is going through the same process. Mathe- 

 matics furnishes the best training in reason- 

 ing because the student is required to reason 

 more frequently than in any other subject, and 



because he is always in a position to test the 

 validity of his reasoning by means of exact 

 concepts. 



However, I am not writing this letter be- 

 cause the opinion of some of the educational 

 faddists of the day with regard to the educa- 

 tional value of mathematics is a matter of 

 much significance to a mathematician, in it- 

 self. I am writing it in defense of a rational 

 curriculum in the high schools and the ele- 

 mentary schools. Having received my own 

 preliminary education in the Cincinnati 

 schools, and having had considerable oppor- 

 tunity of late to observe the preparation 

 of students entering college from this com- 

 munity as compared with that preparation 

 some fifteen years ago, I can only deplore the 

 modern tendency to give at most a superficial 

 attention to fundamental subjects, and to 

 divide the student's energy and attention 

 among a multitude of subjects in such a 

 manner as to create in his mind hopeless con- 

 fusion and to prevent his having really def- 

 inite ideas about anything in particular. 



The teachers in the high schools and the ele- 

 mentary schools are working just as hard as 

 ever, are just as efiicient as ever, but they can 

 not obtain as good results under the handicap 

 of present-day curricula. The student can not 

 be trained to think in as effective a manner 

 as he was fifteen or twenty years ago, under 

 present circumstances. And I believe any 

 reasonable person will agree that the primary 

 object of education is to teach the student to 

 think, whether he is going to enter college or 

 is going out into the world at the end of his 

 high-school course. 



But those who have been most responsible 

 for this unfortunate state of affairs in the 

 high schools and the elementary schools, far 

 from realizing the work of destruction that 

 they have already done, are now endeavoring 

 to complete it by attacking what is left of 

 valuable educational training in the curricula 

 of to-day. It is high time that those who see 

 the danger of this movement, and I know there 

 are many, make a resolute stand against it. If 

 such statements as those of Professor Thorn- 

 dike are allowed to go unchallenged, and thus 



