The Project Method (PM) is becoming more common in the teaching of mathematics. Most of the time, Project Method means solving open and relatively wide formulated problems for the application of particular mathematical topics and the solving of everyday life problems. At present many experts in the theory of teaching mathematics advocate teaching activities as the characteristic for most mathematical work in the classroom. Thus, there is a question: whether it is possible or eventual desirable to use the PM for solving genuine mathematical problems. This paper deals with this question and discusses the connection between the PM and investigation of new mathematical knowledge for students. Our experience has shown that the PM in connection with investigations can be a useful and effective approach to teaching mathematics.