September 13, 1907] 



SCIENCE 



335 



called educative in which esoteric develop- 

 ment does not result in exoteric manifesta- 

 tion. This is especially important in the 

 case of mathematical instruction which ex- 

 hibits an unfortunate tendency to run to 

 the extremes of either pure logic or em- 

 piricism. 



Having defined the aim of education, the 

 most efficient means of attaining it becomes 

 the great problem of pedagogy. The first 

 step towards the solution of this problem 

 may be said to have been taken by biology 

 in the establishment of the law of physical 

 evolution. Following out the analogy thus 

 suggested, modern psychology has practi- 

 cally solved the problem by studying the 

 content of the child mind at different ages, 

 thus determining the natural course of 

 mental evolution. In this way it has been 

 conclusively shown that mental processes 

 follow the historical order of development, 

 or, as Herbert Spencer expressed it, that 

 "the genesis of knowledge in the individual 

 follows the same course as the genesis of 

 knowledge in the race." More recently 

 modern psychologists have found even in 

 the most minute activities of the child 

 psychic atavisms as remarkable as con- 

 vincing, proving conclusively that the nat- 

 ural course of mental evolution is but a 

 repetition of civilization in miniature. 



Since pedagogy, like engineering, is 

 chiefly concerned with the utilization of 

 natural forces and their direction in the 

 proper channels, it follows that the funda- 

 mental principle underlying general peda- 

 gogy must necessarily be the historical 

 method of presentation. In, the case of 

 mathematics this is the logical as well as 

 the psychological sequence of development, 

 which obviates many of the difficulties en- 

 countered in applying the historical method 

 to other branches of instruction. The his- 

 torical method thus fulfills the prime requi- 

 sites for a practical working theory in being 



simple in application as weU as powerful 

 in results. 



A notable instance of the application of 

 the historical method to general pedagogy 

 has already been made, and is embodied in 

 the well-known "culture epoch" theory, 

 originated by Pestalozzi and Herbart and 

 elaborated by their disciples.^ This theory 

 consists, in brief, in applying the evolution- 

 ary idea with the utmost detail to the ele- 

 mentary school curriculum, with the pur- 

 pose of leading the child successively 

 through each stage of culture occupied by 

 the race in the evolution of modern civiliza- 

 tion. As a typical instance of the applica- 

 tion of this method, Ziller's interpretation 

 of the culture-epoch theory may be cited, 

 as it is now well established in Germany 

 on a practical footing. 



In outline Ziller's method consists in ar- 

 bitrarily selecting eight great historical 

 culture epochs, corresponding as nearly as 

 possible to the first eight years of school 

 life. Material is then selected to embody 

 the culture of each epoch, that chosen by 

 Ziller being as follows : (1) epic fairy tales; 

 (2) Robinson Crusoe; (3) history of the 

 patriarchs; (4) history of the judges in 

 Israel; (5) history of the kings in Israel; 

 (6) life of Christ; (7) acts of the Apostles; 

 (8) history of the Reformation. The sub- 

 jects thus selected are known as "concen- 

 tration centers" for the reason that each is 

 used as a nucleus around which to group 

 supplementary courses in language, science, 

 etc. These supplementary courses are then 

 so chosen that each group shall form a unit, 

 representing, so far as possible, a complete 

 stage of civilization in miniature. 



The results of Ziller's method are in the 

 main satisfactory, and at least afford a sug- 



^ See any of the numerous treatises on Herbart's 

 educational theories, e. g., " Ufer's Pedagogy of 

 Herbart," by De Garmo; or "Introduction to 

 Herbart's Science and Practise of Education," by 

 Felkin. 



