Mat 18, 1906.] 



SCIENCE. 



Ill 



riculum laying more stress on mathematics 

 and the natural sciences than any now in 

 force, but no one seems to have suggested 

 that it might be best to turn over to each 

 boy the task of making his own curriculum. 

 The attitude of mind on which elective 

 systems are fundamentally based is quite 

 foreign to the German temperament. 



Passing to the detailed reports, the com- 

 mission does not ask for an increase in the 

 time devoted to mathematics, but recom- 

 mends that still further changes be made in 

 the same spirit as those introduced in the 

 official curricula of 1901. While recog- 

 nizing the formal value of mathematics, the 

 commission believes that some of its more 

 remote and technical phases may be dis- 

 pensed with and the time thus gained util- 

 ized in awakening and developing the 

 ability to regard and interpret mathemat- 

 ically the processes of nature and the oc- 

 currences of human relationships. The 

 most important office of the instruction in 

 mathematics is to strengthen the power of 

 space 'intuition and to train to the habit of 

 functional thinking. Logical training will 

 not suffer if mathematical instruction be 

 given this trend, but will even gain. 



A detailed curriculum is proposed em- 

 bodying the ideas held by the commission. 

 As compared with the curriculum of 1901 

 now in force, the proposed curriculum cuts 

 down somewhat the more complex calcula- 

 tions and defers to later periods the more 

 abstract topics and methods; on the other 

 hand, it introduces concrete geometry a 

 year earlier (at the age of ten instead of 

 eleven), demands constant use of drawing 

 and measuring, utilizes graphic methods 

 throughout, brings the idea of functionality 

 and of functional variation into the fore- 

 ground early (at the age of twelve), and 

 utilizes it freely thereafter, introduces the 

 idea of coordinates, of plotting linear ex- 

 pressions and the graphic solution of linear 

 equations at the age of thirteen (four years 



earlier than in the curriculum of 1901), 

 permits the introduction of the idea of the 

 derivative and of the integral in the next 

 to last year of the course (age seventeen), 

 and lays marked stress on the application 

 of mathematics as widely as possible. A 

 threefold final goal for the mathematical 

 work as brought to a close in the last year 

 is set up: 



1. A scientific survey of the organization 

 of the mathematical material treated in the 

 school. 



2. A certain power of mathematical per- 

 ception and its use in the treatment of 

 problems. 



3. Finally and above all, insight into the 

 importance of mathematics for the exact 

 cognition of nature. 



The reports on the natural sciences call 

 for more time in these subjects even in the 

 classical schools, at least while, as at pres- 

 ent, these schools far outnumber the others, 

 and consequently their graduates in all 

 influential walks of life furnish the great 

 majority of those taking the lead. The 

 commission calls for three hours weekly 

 throughout five years in physics, two hours 

 weekly for four years in chemistry and two 

 hours weekly for nine years in the biologic 

 sciences (and geology). 



The report on physics sets up three fun- 

 damental principles: 



1. Physics is not to be taught as a mathe- 

 matical science but as a natural science. 



2. Physics is to be taught so that it may 

 serve as a type of the manner in which 

 knowledge is attained throughout the do- 

 main of the experimental sciences. 



3. Suitably planned exercises in observa- 

 tion and experimentation by the pupil 

 himself are necessary. 



Specimen courses in physics, in chem- 

 istry with mineralogy, in zoology with an- 

 thropology, in botany and in geology are 

 given. Detailed discussion of these courses 

 and the recommendations that accompany 



