In the article the essence and peculiarities of the research teaching method usage in the training of future primary school teachers to the mathematics teaching is revealed. It is emphasized that the present reforms of the primary education system have influence on the future primary school teachers training so far as they should be ready to the new conditions of junior schoolchildren teaching. In is found out that one of the high school educational process modernization directions is the application of the problem of teaching technology, especially the research method, to the future primary school teachers' training. The functions of the research method such as the creative activity features forming; the creative knowledge learning organization; mastering of the scientific perception methods in the process of these methods search ensuring; interest and need in the creative activity forming, are ascertained. According to the functions the purpose of the research method is in the organization of the students' searching and creative activity connected with the problems and problem tasks solution organization. It is stated that by means of the research method of teaching the instructor systematically advances a research task problem as the students through their independent learning fulfil the creative search. It is stressed that the research method realization is the result of the research tasks fulfilling organised not only as a simple complex but as a system answering number of the didactical and methodological indexes. The research tasks are observed as partial searching tasks which need all or most of all stages of the research process passing as far as their solution integrity ensures the research method functions accomplishment. These stages mean: 1) facts and phenomena observation and study; 2) incomprehensible phenomena, which need investigation, clarification (the problem stating); 3) hypothesising; 4) the plan of the research composition; 5) this plan accomplishment; 6) the practical conclusions about the gained knowledge applying possibility and necessity. The peculiarity of the article is in the demonstration of the research method realization on the specific subject material during the course «Mathematics teaching technique» learning.