Research objectives in teaching mathematics to students of pedagogical universities
The development of society requires modern graduates to be ready for continuous self-education, updating their knowledge and skills, the ability to solve research problems and to scientific research. One of the most important goals of the implemented educational programs that meet the requirements of the federal state educational standards of higher education is the formation of research competencies. This is especially relevant for future teachers, as they will be able to apply the acquired skills in their future professional activities. The article actualizes the issue of using research problems in the study of mathematics as a forming means of research competencies, since in the process of solving them, all components of research activity are mastered. The content features of various mathematical disciplines make it possible to do this especially effectively. The article describes the method of using research problems in the study of the discipline «Algebra and number theory», which is one of the components of mathematical and professional pedagogical education. The listing of the material is presented by a detailed description of the study of indefinite equations solved by the method of searching the remainders of dividing an algebraic expression which is containing a variable by a certain number. It is presented how a change in some parameters of the problem leads to a change in the result. The solution of such an equation is already a full-fledged research task. In addition, experience has shown that a positive cognitive result is obtained by a method that allows, based on the analysis of ready-made solutions, learning how to construct new equations with predefined properties, which brings students to a new level of creative work. In conclusion, it is noted that, despite a number of objective difficulties associated with the low level of training of some students, the need for additional time expenditures, this is significant, not only from the point of view of forming the necessary research competencies, but also contributes to the activation of educational and cognitive activities, the motivation growth to study the discipline.