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 thinking is the first requirement for success in life, it follows that this subject 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 practical 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 naïvely inferred that the properties of any special material, viewed objectively, will be grafted on to the mind and character of the individual 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 individual 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 attitudes. 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 laymen 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;
