Apbil 16, 1909] 



SCIENCE 



605 



First, the institutions must know what is 

 needed and the knowledge can be acquired 

 only by close relations with the industries. 

 Teachers should have ready access to the 

 industries and their work for themselves 

 and their students. Problems should be 

 submitted for the research laboratories and 

 needed means and materials provided. 

 Such cooperation must certainly lead to 

 important progress, not only in the indus- 

 tries, but in the related sciences, and 

 progress under such circumstances is in- 

 evitable. May the influences which con- 

 trol have free course, and be not only justi- 

 fied but glorified. 



"Wm. McMxxbteie 



TEE PROGRAM OF THE INTERNATIONAL 



COMMISSION ON THE TEAOHING OF 



MATHEMATICS ' 



"If we could first know where we are and 

 whither we are tending, we could better judge 

 what to do and how to do it." These words of 

 Lineola, like the words of many another 

 genius, adapt themselves to divers situations. 

 This statement epitomizes what the Interna- 

 tional Commission on the Teaching of Mathe- 

 matics is to do. The first purpose of this body- 

 is to investigate the actual state of the teach- 

 ing of mathematics in the various countries, 

 and the second purpose is to discover the tend- 

 encies of the changes effected during the last 

 two decades. Both of these investigations are 

 to be made with a view to determining " what to 

 do and how to do it." In the language of the 

 central committee the aim of the commission is 

 to suggest those general principles which should 

 guide the teacher rather than to provide pro- 

 grams which should be adapted at the same 

 time to the schools of all countries. 



To Professor David Eugene Smith, of Co- 

 lumbia University, belongs the credit of hav- 

 ing first suggested the formation of such a 

 commission in the French mathematical 

 iournal, L'Enseignement Mathematique, in 



^ The complete Preliminary Report appeared in 

 L'Enseignement Mathematique, and a translation 

 by the author (of this article) in School Science 

 ami Mathematics, February, 1909. 



1905 and again at the International Congress 

 of Mathematicians at Eome in April, 1908. 

 This congress authorized a committee consist- 

 ing of Professor Felix Klein, Gottingen, Ger- 

 many; Professor Sir George Greenhill, 

 London, and Profesor H. Pehr, Geneva, 

 Switzerland, to form an international com- 

 mission. Those countries which have been 

 represented at certainly two of the interna- 

 tional congresses of mathematicians, with an 

 average of at least two members, are entitled 

 to representation on the active membership of 

 the commission, while other countries are in- 

 vited to be represented by associate members. 

 The national delegations are urged to affiliate 

 with themselves national subcommissions, 

 comprising representatives of the various 

 stages of the teaching of mathematics in the 

 general schools and in the technical and pro- 

 fessional schools. 



General direction is lodged in the original 

 committee of three, Klein, GreenhiU and 

 Fehr. The official organ is L'Enseignement 

 Mathematique^ and the official languages are 

 English, French, German and Italian. 



The whole field of mathematical instruc- 

 tion, from the earliest primary work to the 

 higher mathematics of the universities, is to 

 be included in the investigation. A large 

 place will be given to applied mathematics for 

 technical and professional schools. 



The work of the commission will be based 

 upon the reports of the delegations, which are 

 to be made out with the aid of the national 

 subcommissions in conformity with the gen- 

 eral plan fixed by the central committee of 

 three. In the first part of these reports will 

 be given a view of the actual scheme of 

 studies, the corresponding examinations, the 

 methods of teaching and the preparation of 

 the teaching body. In the second part will be 

 presented the actual tendencies of the instruc- 

 tion. 



The aim of the mathematical instruction in 

 the different types of schools — ^primary, secon- 

 dary, trade schools, normal schools and teach- 

 ers' colleges, and colleges and universities — 

 wiU be discussed. Should the aim of the in- 

 struction be the development of the mathe- 

 matical faculties, or logical reasoning, or 



