This document is concerned with problems in the education of mathematics teachers. Part 1 gives an overall introduction to the papers included in this volume. Part 2 is concerned with problems of educational reform and provides a survey of the literature on innovation research, discusses some contradictions in the innovation process, and describes prerequisites for a reform of the teaching of mathematics. Part 3 deals with new forms for relating theory to practice in teacher education, describing special instructional methods and competency-based teacher education and discussing a few problems that arise from these approaches. Part 4 looks at general problems of the relationship between theory and practice in teacher training. Part 5 is concerned with mathematics knowledge and the training of teachers of mathematics, and discusses some of the different conceptions of the subject matter and of learning theories. Part 6 offers preliminary conclusions for research and development as well as for content and organization of the training of mathematics teachers. A list of references from European and American sources is included. (Author/DT)