818 



SCIENCE 



[N. S. Vol. XXXVI. No. 937 



nearer to our understanding the complicated 

 phenomena of retarded and accelerated growth. 



It seems very likely that the abnormally 

 large amount of energy expended upon rapid 

 growth during a short period is an unfavor- 

 able element in the individual development. 

 A study of the phenomena of growth of vari- 

 ous groups of the same population has shown 

 that early development is a concomitant of 

 economic well-being, and that a characteristic 

 of the poor is the general retardation in early 

 childhood, and the later rapid grovyth. It 

 follows from this that there is a correspond- 

 ing, although not equal, retardation in early 

 mental development, and a crowding of devel- 

 opmental processes later on, that probably 

 place a considerable burden on the body and 

 mind of the poor, which the well fed and cared 

 for do not bear. The general laws of growth 

 show also that a retardation kept up for an 

 unduly long period can not be made up in the 

 short period of rapid grovrth; so that it would 

 seem that, on the whole, excessive retardation 

 is an unfavorable element in the groveth and 

 development of the individual. Whether there 

 are similar disadvantages in a considerable 

 amount of early acceleration is not so clear. 

 Teanz Boas 



Columbia University 



TSE WOSK BONE BY THE GEBMAN SUB- 

 COMMITTEE On the teaching 

 OF MATHEMATICS^ 



1 REGRET very much, that Mr. F. Klein, Got- 

 tingen, the president of the German subcom- 

 mittee of the International Commission on 

 the teaching of mathematics, is not able to 

 come to Cambridge. It thus happens that I 

 have the honor, in his place, of presenting to 

 you the following short report of the present 

 state of the work done in Germany. 



When we consider the historical develop- 

 ment of the German empire, it is very evident 

 that we should not expect to find a homogene- 

 ous system of schools, controlled by a central 

 board of education, as is usually the case in 



'■ Eeport presented at the meeting of the Fifth 

 International Congress of Mathematicians, at 

 Cambridge (England), August 23, 1912. 



other countries. The various sections of the 

 German people may be looked upon as different 

 sources of the stream of German culture. 

 Furthermore, the religious reformation tended 

 to increase the variety of the German schools ; 

 for while in some parts of Germany the 

 schools of to-day can be traced directly to the 

 ancient cloister-schools, in other sections of 

 the country there is not such a connection ap- 

 parent. And finally the modern development 

 of Germany from an agricultural state to an 

 industrial one has also had a large influence 

 on the formation of schools, so that a great 

 difference in types must be expected and actu- 

 ally does exist. 



A recognition of all these influences, the po- 

 litical, the religious and the economical, is es- 

 sential to a complete understanding of Ger- 

 man education, and they are therefore in evi- 

 dence in the general plan of the German re- 

 port as well as in the individual essays of which 

 it consists. 



The German report' is composed of 5 vol- 

 umes, treating: 



I. The secondary schools of northern Ger- 

 many. 



II. The secondary schools of southern and 

 middle Germany. 



m. Special problems of the secondary 

 mathematical instruction. 



IV. The mathematics at the technical 

 schools. 



V. The teaching of mathematics in elemen- 

 tary schools, and in the seminaries or train- 

 ing schools for elementary teachers. 



These five volumes will comprise 36 indi- 

 vidual reports and I have the honor to present 

 2Y of them to the congress. 



The German subcommittee has succeeded 

 in engaging a staff of specialists in the vari- 

 ous fields of mathematical instruction, and it 

 has taken care to harmonize all the single re- 

 ports with the general plan. The president, 

 Mr. Klein, had the general supervision of aU 



' ' ' Abhandlungen tiber den mathematischen 

 Unterricht in Deutsehland, veranlasst durch die 

 Internationale Mathematische Unterrichtskommis- 

 sion, ' ' Herausgegeben von F. Klein, Leipzig, B. 

 G. Teubner. 



