Authors present a brief overview of the main results of the international comparative study TEDS-M. Russian final year university students which were going to become qualified primary school teachers and math teachers demonstrated the results in mathematics and methods of teaching mathematics which were above average international rates. Authors show strengths and weaknesses of Russian training programs and reveal differences between graduates results in teacher training colleges and state universities. It was found out that there is a relationship between the quality of education of potential teachers and their attitudes to teaching mathematics — orientation on conceptual models and cognitive-constructivist approach to teaching mathematics or computational model and an approach to teaching which is based on the direct transfer of knowledge.