The high-school subjects in mathematics are algebra and plane geometry. Changes in content or in method, if any, should be made for purposes that may be enumerated as follows: first, to secure more perfect continuity with the elementary school work; second, to prepare more perfectly for comprehension of mathematical science in general; third, to secure the pupil’s spontaneous interest by giving him as wide command as possible of such utilitarian problems as are likely to enlist his ambition.