While educationists appear willing to consider what can be learnt from comparing Eastern and Western perceptions of teaching and learning, few have explored the effect that different cultural and structural traditions have on teaching in Europe. In order to fill this gap, twelve mathematics teachers, four in each country, were studied, in order to develop an understanding of their beliefs concerning teaching and their classroom practices. The work was carried out within the framework of an ethnographic approach, in combination with stimulated recall, in order to explore how these twelve teachers conceived of and carried out their tasks. The proposed paper is concerned with answering the original question of the study, the question of mobility, which involves considering the likely problems for mathematics teachers at secondary level in England, France and Germany to teach in one of the other countries, and why there are these 'obstacles'. This is done by distinguishing between teachers of particular countries going to teach in another. Having studied teachers from three countries, there are six possibilities (English teacher going to teach in France; English teacher going to teach in Germany; French teacher going to teach in England; etc) which are discussed in turn.