The author describes the process of pupils’ own active independent work and evaluates the research into it, which was carried out in the course of nearly four months in two classes of fourteen-year olds (eighth formers) at the Elementary Nine-Year School in Bratislava, Košická Street. Both classes where the research was being used the same experimental textbooks, whose content corresponds to the contemporary trend in modern school mathematics. A statistical evaluation of the didactic tests showed that in the experimental class where pupils’ own active work strongly predominated over the traditional teaching forms the pupils were achieving at least as good results in acquiring new knowledge and skills as the pupils in the control class where, in turn, emphasis was laid on teamwork and also on such traditional teaching methods that stimulated the activity of pupils in their work. During the lessons the pupils in the experimental class acquired a certain habit and technique of approaching on their own the study of the text and the solution of the problems and the corresponding problem assignments. At the end of the article there are three appendices: the text of the pre-test of the A-group, summarized content of one teaching period together with the marking of the problems solved by pupils on their own, and the text of didactic test 3 A.