Revolutionary ideas about the teaching of high school “math” have been fermenting in the United States since the 1950s. Several major experimental courses have been pioneered and in addition unpublished courses on similar lines are being used in some of the 20,000 high schools and junior schools throughout the nation. In examining these ideas the Englishman needs to consider them in the context of American mathematical education, and this in turn needs to be viewed against the background of American education, which is different in detail, method and philosophy from the English system.