This chapter focuses on means to identify and facilitate the education of gifted children, especially those who reason extremely well mathematically. It emphasizes programs developed at Johns Hopkins by the Study of Mathematically Precocious Youth (SMPY) and the Office of Talent Identification and Development (OTID), now called the Center for the Advancement of Academically Talented Youth (CTY). These programs cover the Middle Atlantic region. The chapter illustrates that SMPY's educational facilitation of the ablest students it identifies relies heavily on acceleration. Much concern continues to be expressed about the presumed dangers of acceleration, especially with respect to social and emotional development. Because of the many sex differences in ability and achievement in mathematics among its participants, SMPY has attempted to devise suitable ameliorative strategies. It was also of interest to see what effects the sex difference in mathematical reasoning ability might have had for achievement in high school science.