“We remember when the sciences were taught wholly from the text. Later, the principles of Pestalozzi entered the class room, and we stood open-eyed and open-minded, as the truths of science were demonstrated with the proper apparatus in the hands of the teacher. But to-day Froebel’s idea has taken possession, and the pupil performs the experiment. It is his hand that creates the conditions; it is his eye that watches the changes, his hand that notes them. Science teaching has thus adopted the manual training idea; and such are the results that Latin, Greek, and mathematics are no longer considered as the only intellective subjects for college training. “What the manual training idea has done for science teaching, it will do for mathematics and other kindred subjects. The dissatisfaction among professional and business men regarding the teaching of practical things in our schools is wide-spread. This is especially true regarding arithmetic, penmanship, spelling, and language. Anyone who doubts this needs but to enter the business places of his own city and make inquiry. There is a well-grounded feeling that in the mastery of arithmetic is a discipline closely allied to that needed in the activities of life; and when a father discovers that his child of sixteen or seventeen years has no idea of practical business questions and little skill in analytical processes, he justly charges the school with inefficiency. The difficulty, however, is that the pupil has had no opportunity to sense arithmetic. To him measurements and values are indefinite ideas. He commits facts to memory, and blindly tries to work out problems. If his memory and imagination are good, he stands well, and receives a high mark. But still the work is vague; it does not touch his life or experience; it has no meaning. Put that pupil into a manual-training school,—the boy in the shop, the girl in the kitchen [practical experience has demonstrated that the girl has a place in the shop also],—and at once mathematical facts become distinct ideas. “Step into the shop of a manual-training school [or step into the well-ordered kitchen], and observe the boy with a project before him. What are the steps through which his mind must bring him to the final perfection of the work. “First, he must give the project careful study. “Second, he must design it and make a drawing of it. This at once puts mathematics into his hand as well as his head. He must use square, compass, try-square, and pencil. Exact measurements must be made, divisions and subdivisions calculated, lines carefully drawn. “Third, he must select material of proper dimensions and fiber, and then must reflect how to apply it to the draught made so that there is no waste.