The following approaches to mathematics education, represented in German-speaking countries mainly, are analyzed: (1) the structuralist/formalistic approach; (2) the genetic approach; (3) the approach by elementarization; (4) the problem-solving approach; (5) the approach of Freudenthal; (6) the approach by project-orientation; (7) "anthroposophical" approaches; and (8) the approach by application. Similarities and differences are stressed, in the hopes of yielding some contribution to a theoretical foundation of mathematics education. It is felt that there is a current need for theoretical augmentation and guidelines and that this presentation highlights the norms and values of each analyzed approach. Suggestions are made for further study that could lead to a "meta-theory" of mathematics education. (MP)