July 3, 1908] 



SCIENCE 



these students take up their major subject 

 without preparation in calculus, with the 

 result that some of the most important 

 phases of their subject, depending upon 

 higher mathematics, always remain ob- 

 scure to them. This is true with lawyers, 

 for instance, as regards questions of sta- 

 tistics, insurance, etc. With physicians the 

 lack is felt at the very beginning of experi- 

 mental physics, by reason of which instruc- 

 tion in the subject is necessarily placed on 

 a much lower plane and the most im- 

 portant principles are only understood in 

 a hazy way. It is still worse in chemistry, 

 where quantitative determinations require 

 the use of comparatively complicated 

 formulas. 



The text-books in these various subjects 

 try to meet this situation with short pref- 

 aces on calculus, which the students are 

 supposed to acquire in this condensed form. 

 How then can the statement that calculus 

 is too difficult for the higher schools be 

 reconciled with the fact that students just 

 released from the higher schools are ex- 

 pected to acquire this important subject 

 from such condensed materials. Evidently 

 conditions in the university emphasize the 

 haziness of the aims of higher school 

 mathematics. 



Klein seems especially anxious to have 

 it thoroughly understood that his plan is 

 perfectly feasible, and comes well within 

 the pedagogical possibilities of the case. 

 In the first place, no more time is required 

 than at present given to the mathematical 

 curriculum. Moreover, he is not demand- 

 ing a change in the course of study, but 

 rather is urging that advantage be taken 

 of the present leaning toward calculus, and 

 carried out to its logical sequence. This, 

 of course, can not be the work of a univer- 

 sity professor, but must be that of the 

 practical schoolmaster. The chief difficulty 

 at present is that there are no text-books 

 which fully meet the situation. Again, 



it is necessary to proceed with care and 

 circumspection so as not to arouse the an- 

 tagonism of the gymnasial leaders, but 

 rather secure their friendly cooperation. 

 There can be little opposition from the 

 physicist if he is assured that there is no 

 intention of invading his province, and it 

 is pointed out to him that the pupils are 

 being given tools for a far more complete 

 mastery of his specialty. Neither should 

 opposition be encountered from the repre- 

 sentatives of the language and history de- 

 partments if it is fully impressed upon 

 their minds that the guiding principle of 

 instruction should be the study of special 

 subjects not as isolated from the rest of the 

 curriculum, but with reference to the gen- 

 eral culture which his particular type of 

 school aims to produce. 



The two main objections which are 

 always urged when a university professor 

 discusses educational problems of a general 

 nature are that too little heed is given to 

 pedagogical possibilities, and that univer- 

 sity professors are only concerned about 

 those pupils who will later come under their 

 instruction. Concerning these objections, 

 Klein answers the first by stating that he 

 is keenly alive to the difficulty of the task 

 of raising a large number of pupils, not 

 especially gifted with mathematical ability, 

 to a certain established level, and that his 

 aim is not to raise this level, but rather to 

 move it in what might be termed a hori- 

 zontal direction. 



As regards the second objection, he says 

 that those pupils who take mathematics at 

 the university are precisely the ones about 

 whom he is not concerned, but that it is 

 the future chemist, physician or lawyer 

 whose mathematical training needs to be 

 improved in order to bring about the best 

 results., 



Charles Otteemann 



WooDWABD High School, 

 Cincinnati 



