The role of Training Colleges and University Departments of Education in the training of mathematics teachers makes their attitude towards modern mathematics of more than parochial interest. The working conditions of these two types of institution, however, are so very different that it is impossible to discuss them as a single unit. This article has therefore been prepared by collaboration, with two main sections. In spite of these differences of structure, however, the general attitudes of mathematics staff in the two types of institution have so much in common that it has been possible to write a concluding section expressing these views. It may be that this final section will be the most characteristic part of this contribution to the symposium.