This publication identifies some of the underlying ideas relevant to improved mathematics programs of the elementary school. This publication does not prescribe a course of study. It does, however, provide ideas to assist school personnel in their analysis of mathematics programs and textbooks. It presents an orderly outline of topics and concepts of the improved mathematics programs of the elementary school. Included are (1) some of the major mathematical content that presently constitutes elementary mathematics textbooks, and (2) a set of criteria to be considered in the selection of textbooks. (RP)