July 9, 1909] 



SCIENCE 



37 



solid geometry, and the elements of de- 

 scriptive geometry; plane and spherical 

 trigonometry; introduction to the theory 

 of maxima and minima; plane analytic 

 geometry. 



In addition to this the Oberreakehule 

 requires the most important parts of alge- 

 braic analysis. Equations of the fourth 

 degree, and the approximate numerical 

 solution of algebraic and transcendental 

 equations may be taken up at the option of 

 the instructor. In all these topics the aim 

 is to give practise in the application of the 

 theorems, as well as to lead to a mastery 

 of the proofs. Considerable stress is also 

 laid upon the oral solution of easy exercises. 



The German higher school system speaks 

 with no uncertain tone of the practical ad- 

 vantage of beginning both algebra and 

 geometry early ; and continuing their study 

 simultaneously through a niunber of years. 



The method of instruction in Prussia 

 may be styled the genetic method in that 

 it does not require any previous prepara- 

 tion of the pupil for the work of the hour. 

 The quantity of home work is kept as small 

 as possible, and material that has not been 

 thoroughly explained in the class is never 

 assigned to be studied privately by the 

 pupil. A text-book is officially required 

 but is seldom used, and at most the pupil 

 is only referred to it after class treatment, 

 and not before. The genetic method has 

 been but little used in America, but there 

 is a strong trend toward the use of the 

 heuristic method, which is somewhat sim- 

 ilar. It resembles the genetic method in 

 its marked effort to keep the pupil thinking 

 for himself, but differs from it in that the 

 class is the working unit in the genetic 

 method, whereas the pupil is the unit in the 

 heuristic method. This difference may be 

 said to be characteristic of the German and 

 American methods of mathematical in- 

 struction. In Germany the class works 



as a whole under the guidance of an in- 

 structor. In America the individual pupil 

 demonstrates, explains and asks and an- 

 swers questions, while the others listen to 

 him. 



While the results of the genetic system 

 as applied to the Prussian schools amply 

 justify its use with German pupils, it by 

 no means follows that the method is of 

 universal application, and could be used to 

 advantage in this or other countries. The 

 other features of the German school sys- 

 tem, however, relating to the high standard 

 of technical excellence in the teaching pro- 

 fession, and the correlation and continuity 

 of instruction, are of the deepest and most 

 general pedagogical significance. 



ENGLISH REFORMS: THE PERRY MOVEMENT 



The English reforms are largely based 

 on the so-called ' ' Perry movement, ' ' which 

 originated from a paper on the teaching of 

 mathematics read by Professor John Perry 

 at a meeting of the British Association in 

 Glasgow in 1901.° In this paper Professor 

 Perry maintained that usefuUiess should be 

 the criterion for determining what subjects 

 should be taught to children, and in what 

 way they should be taught. 



The present methods of teaching mathe- 

 matics keep students so long upon the 

 knowledge already organized that there is 

 neither time nor enthusiasm for undiscov- 

 ered fields. Absolute correctness and philo- 

 sophical insight receive too much attention 

 in the teaching of elementary subjects. 

 For example : the first four books of Euclid 

 might be assumed, or accepted partly by 

 faith and partly by trial, and the sixth 

 book regarded as axiomatic. In this way 

 the student might begin his work earlier 

 and much more be accomplished. What is 



° " Diacussion on the Teaching of Mathematics," 

 edited by Professor Perry. British Association 

 Meeting, Glasgow, 1901. Maemillan, 1902. 



