Degree courses related to the initial teacher education at pre-primary, primary, and secondary education levels are facing a situation of change. The so-called Bologna Agreement defines a new legal framework in which to develop instructional and professional activities in the training of mathematics teachers, with the assumption of the importance that this will have for improving the quality of mathematics education.

In the last few years, there has been an intensification of the number of specialized publications and professional meetings of the stakeholders involved (teachers, researchers, and government departments) to discuss the skills, content, methodology, etc. which should form the basis of these new degrees.

However, there have as yet been few specific proposals for the actual practice in undergraduate classes responsible for developing the different materials contained in the degree syllabi. This has been despite the considerable growth that research in mathematics teacher education has undergone in our country. It thus seems opportune in this new framework to describe the key variables to develop in mathematics teacher education that will enable prospective teachers to learn to teach mathematics at their corresponding levels.

The Symposia organized by the SEIEM (www.seiem.es), and the meetings of the Research Groups comprising our Society, have presented results of research projects on the professional development and different cognitive and affective aspects of prospective pre-primary, primary, and secondary teachers. One of the most frequently repeated conclusions is the need for the outstanding aspects of this research to be transferred to the centres of initial and continuing teacher education, so that the results of studies on teacher education can find their practical application.

Therefore, from the SEIEM we wish to propose a seminar with the following objective: To discuss and design the basics related to mathematics education that can be developed in the programs of the materials of the new degree courses of initial pre-primary and primary teacher education, and in the Master's courses of secondary teacher education.