This paper appraises recent developments in the curriculum and teaching of mathematics in the secondary schools and analyzes mathematics education in the United States with particular emphasis on Nebraska. The first section focuses upon characteristics that distinguish the modern secondary school mathematics curriculum from the traditional. The following sections emphasize the understanding and the structure of mathematics. Ability groupings and the various types of programs which have resulted from it are also discussed. Further analyses deal with a college preparatory sequence for Grades 9-12, new mathematics programs to attract and to motivate students, and new techniques in mathematics at the secondary level. Suggestions for implementing new developments are also provided. (RP)