This article discusses the results of the study, which determine the theoretical foundations and pedagogical features of the development of research activities of students in the lesson «Algebra» of the 9th grade. One of the most pressing issues is the identification and development of research activities of students in the course of teaching mathematics in general secondary schools. In the course of conducting research activities, methods of special pedagogical analysis, control, survey of the subject of Algebra, the method of pedagogical experiment of research activities were used. Based on the results of the research, a set of special tasks for the development of research activities of students was compiled. Through specially compiled tasks, the research activity of students increased from 8% to 25%. First of all, in the course of research activities, students were surveyed. 72 students took part in the survey, as a result of which it was found that 36 (50%) of the students were motivated to self-study and engage in research work, but only 18 (25%) of them completed research tasks. Based on the results of the survey, it was found that students who can work with additional sources of literature, actively participate in self-search, research work, were able to perform these exercises. The definition of «research activity» in teaching mathematics has been clarified. The concept of «research task» was considered and examples of some types of research problems were given. A pedagogical analysis of the textbook «Algebra» of the 9th grade was carried out and the advantages in it were shown. As a result of research activities, teachers who teach algebra in schools use a set of tasks designed specifically for the development of students' research activities in the form of a methodological manual.