288 THE POPULAR SCIENCE MONTHLY 



metic, say, has upon the mind of the one who assimilates it. The 

 majority of the responses he receives will be based upon an argument 

 something like this: Arithmetic is an exact science; everything in it 

 can be definitely proved; accuracy is absolutely essential in resolving 

 arithmetical problems; therefore, the pupil who learns arithmetic will 

 be trained in accuracy of thinking more thoroughly than he could be in 

 assimilating history or geography or music. And since accurate think- 

 ing is the first requirement for success in life, it follows that this sub- 

 ject constitutes the most valuable study in the curriculum. People 

 who reason about education in this manner will assign to algebra, 

 geometry, trigonometry and other branches of mathematics the first 

 place in the high-school curriculum, because they are all concerned with 

 principles which are apparently exact; and the learner takes on the 

 quality of the material which he learns. Those who proceed in this 

 manner in determining values do not think it needful to observe 

 whether, even if a pupil in assimilating algebra is trained to be accurate 

 in his thinking, this kind of accuracy is of service to him in the prac- 

 tical situations of every-day life. 



If one will examine the opinions of lay writers on teaching since 

 Plato's day, he will find that many of them have regarded the materials 

 and the methods of education in a purely a priori manner. They have 

 analyzed the matter of any subject of study, as mathematics, and they 

 have naively inferred that the properties of any special material, viewed 

 objectively, will be grafted on to the mind and character of the indi- 

 vidual who masters it. Take, for instance, the view held by some older 

 writers, that it is debasing to study what is to-day called natural science, 

 because of the baseness of physical objects; one who studies these 

 things will take on their qualities. On the other hand, if the indi- 

 vidual in his education is made to learn things that relate to the spirit, 

 he will become more highly spiritualized. Persons who gain their 

 notions in this manner do not think it necessary actually to observe 

 what effect the study of any subject has upon an individual, whether as 

 a fact it exalts him spiritually or debases him; whether it makes him 

 more of a friend to his fellows or cultivates unsocial and selfish atti- 

 tudes. He infers that a certain result must follow from the study of 

 any branch, because of the nature of the material learned. 



This logical, analytic method is the popular one in use among lay- 

 men and among some teachers to-day, as it has been in all times. It is 

 in principle like the method which has been followed heretofore in the 

 study of values in nutrition. The older nutritionists worked out tables 

 of food values based entirely on chemical analyses of different articles. 

 They said, to cite a typical instance, " Cheese contains 70 per cent, of 

 albumen; albumen is an essential element in nutrition; therefore 

 cheese constitutes a valuable food." These analysts went through with 

 all the articles of food in order to determine their chemical constituents ; 



