Excerpt from The Teaching of Mathematics in Secondary Schools

Since 1906 the author has delivered a yearly course of lectures at New York University on the Teaching of Mathematics in Secondary Schools. These lectures consisted largely of a concrete discussion of the problems that arise in actual teaching. This book was planned on similar lines, but the pressure of professional duties, coupled with ill health, made it impossible to carry out this concrete treatment of the subject through the entire extent of secondary school work. The author hopes, however, that all important and fundamental topics have been treated in such detail as to be of real assistance to the inexperienced teacher, to whom the generalities of abstract pedagogy are not only useless, but often meaningless.

The chief object of this book is to contribute towards making mathematical teaching less informational and more disciplinary. Most teachers admit that mathematical instruction derives its importance from the mental training that it affords, and not from the information that it imparts. But in spite of these theoretical views, a great deal of mathematical teaching is still informational. Students still learn demonstrations instead of learning how to demonstrate.

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