408 



SCIENCE. 



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



tematic and formal sides of the instruc- 

 tion in mathematics. Undoiibtedly many 

 mathematicians will feel that this decrease 

 of emphasis will result in much, if not 

 irreparable, injury to the interests of 

 mathematics. But I am inclined to think 

 that the mathematician with the catholic 

 attitude of an adherent of science, in 

 general (and at any rate with respect to 

 the problems of the pedagogy of elemen- 

 ' tary mathematics there would seem to be 

 no other rational attitude) will see that 

 the boy will be learning to make practical 

 use in his scientific investigations— to be 

 sure, in a naive and elementary way — of 

 the finest mathematical tools which the 

 centuries have forged; that under skilful 

 guidance he will learn to be interested not 

 merely in the achievements of the tools, but 

 in the theory of the tools themselves, and 

 ihat thus he will ultimately have a feeling 

 towards his mathematics extremely differ- 

 ent from that which is now met with only 

 too frequently — a feeling that mathematics 

 is indeed itself a fundamental reality of 

 the domain of thought, and not merely a 

 matter of symbols and arbitrary rules and 

 conventions. 



The American Mathematical Society.— 

 The American Mathematical Society has, 

 naturally, interested itself chiefly in pro- 

 moting the interests of research in mathe- 

 matics. It has, however, recognized that 

 those interests are closely bound up with 

 the interests of education in mathematics. 

 I refer in particular to the valuable work 

 done by the committee appointed, with the 

 authorization of the Council, by the Chi- 

 cago section of the society, to represent 

 mathematics in connection with Dr. Night- 

 ingale's committee of 1899 of the National 

 Educational Association in the formulation 

 of standard curricula for high schools and 

 academies, and to the fact that two com- 

 mittees are now at work, one appointed 

 in December, 1901, by the Chicago Section, 

 to formulate the desirable conditions for 



the granting, by institutions of the Missis- 

 sippi valley, of the degree of Master of 

 Arts for work- in mathematics, and the 

 other appointed by the society at its last 

 summer meeting to cooperate with similar 

 committees of the National Educational 

 Association and of the Society for, the Pro- 

 motion of Engineering Education, in for- 

 mulating standard definitions of require- 

 ments in mathematical subjects for admis- 

 sion to colleges and technological schools; 

 and furthermore I refer to the fact that 

 (although not formally) the society has 

 made a valuable contribution to the inter- 

 ests of secondary education in that the 

 College Entrance Examination Board has 

 as its secretary the principal founder of 

 the society. I have accordingly felt at 

 liberty to bring to the attention of the 

 society these matters of the pedagogy of 

 elementary mathematics, and I do so with 

 the firm conviction that it would be possible 

 for the society, by giving still more atten- 

 tion to these matters, to further most effec- 

 tively the highest interests of mathematics 

 in this country. 



A VISION. 



An Invitation.— The pure mathemati- 

 cians are invited to determine how mathe- 

 matics is regarded by the world at large, 

 including their colleagues of other science 

 departments and the students of elementary 

 mathematics, and to ask themselves whether 

 by modification of method and attitude 

 they may not win for it the very high 

 position in general esteem and appreciative 

 interest which it assuredly deserves. 



This general invitation and the preceding 

 summary view invoke this vision of the 

 future of elementary mathematics in this 

 country. 



The Pedagogy of Elementary Mathe- 

 matics.— We survey the pedagogy of ele- 

 mentary mathematics in the primary 

 schools, in the secondary schools and in 

 the junior colleges (the lower collegiate 

 years). It is, however, understood that 



