This textbook is a teaching manual for arithmetic, algebra, and geometry. Historical sketches on the subjects are included. Each topic is discussed in detail, and the teacher is advised along what lines to work, and how the work may be successfully accomplished.

The usual Euclidean metric definition is modified; new figures and measures are defined and analyzed using this different distance function. (DT)

A geometric construction for a line parallel to a given line through a given point is explained and analyzed. (DT)

The content of geometry in new mathematics books and in secondary school mathematics courses is discussed, and the suggestion is made that appropriate doses'' of formal reasoning be included at appropriate levels. (DT)

Discusses ways in which geometry can become the perfect answer for preholiday mathematics lessons. (Author)

The author presents research implications in the areas of geometric capabilities of elementary school students, instructional variables related to geometry achievement, transfer effects, and some findings concerning teachers and geometry. (JG)