The loudest note sounded in all recent educational discussions is the call for more practical methods in presenting the fundamental subjects of study. It is claimed that language, science, and mathematics have been taught with too little reference to their utility in the vocations and in the ordinary affairs of life. The methods commonly employed in presenting mathematical subjects have been especially open to criticism. This is true even in some schools designed to give vocational training. Mathematical books of the kind traditional in the older schools have been continued in use in the newer and more practical schools. These books were written almost entirely from the point of view of the teacher of pure mathematics with little reference to concrete problems of life and' having no reference whatever to the actual problems of the drafting-room and the shop. As a natural consequence the class room work in mathematics, in many of our most practical schools, has failed to utilize the material afforded by the shops and science laboratories to fix the knowledge of mathematical principles by concrete illustration and by practice.