This paper discusses how elitism and anti-intellectualism have affected the teaching of intellectually gifted students. It examines methods of identifying the intellectually gifted child. It traces trends in education of the gifted through history and discusses the issues of equity, elitism, and anti-intellectualism which have resulted in discrimination against gifted children. The purpose of education is addressed, concluding that an anti-intellectual approach to education has been developed which sees children as a form of capital to be developed rather than allowing them the luxury of developing their minds without a specific or practical purpose. Methods of educating gifted students are outlined, including acceleration, pull-out programs, and homogeneous and heterogeneous grouping. The role of teachers and administrators in educating the intellectually gifted is analyzed. Three proposals to benefit public education are presented: (1) look carefully at the successes of the private schools and incorporate ideas that have worked; (2) have preservice teachers follow a rigorous course of study in liberal arts or math and science before studying for a graduate degree in education; and (3) encourage the growth of private schools. The paper also advocates small schools in which students work with a relatively small number of teachers, with some heterogeneous grouping and some homogeneous grouping in accelerated programs that are relevant to the curriculum. (Contains 55 references.) (JDD)