The following topics are discussed in this state handbook: (1) characteristics of a modern math program (structure, vocabulary, correctness); (2) teacher preparation (program descriptions and source material lists for inservice education and the CUPM recommendations for training math teachers); (3) initiating a modern program in mathematics in a particular school system (programs for different types of students, resources for administrators, guidelines for improving programs); (4) mathematics for the underachiever (content suggestions, objectives, teachers of low achievers, experimental programs, high school general mathematics); and (5) mathematics for the talented student (resources, club activities, content topics, suggestions for the disinterested student). (JG)