Аңдатпа
Today, modern Internet technologies allow you to access the necessary information at any time from anywhere. In such a situation, the ability to find what is needed from different sources and critically revise it becomes of particular importance, which, in turn, leads to the formation of basic knowledge. Consequently, when preparing young people for real life, the need to develop their critical attitude and thinking is urgent. As a rule, in real life, the initial data is not always clear, the goal is not set clearly, and there may be cases when the way out of this situation is also not the only one. Therefore, a person often faces open-type problems. Such cases can be taken as an interpretation of mathematical open problems. Indeed, open tasks are understood as tasks in which the initial data or the final goal are not clearly formulated. At the same time, students are given the freedom to set tasks to a certain extent, choose a way of thinking and enter additional parameters necessary for its solution. The article discusses plausible reasoning in the process of solving open problems and its role in the formation of students' competencies on plausible reasoning. In addition, various examples of how plausible reasoning arises when solving open problems are given, and an algorithm of actions for composing and solving open problems is given. Here the algorithm is only as an orienting basis, since there are no algorithms for solving open problems. It can be seen from the algorithm that when forming the competence of plausible reasoning, students should be able to solve closed and open problems and combine them in a certain effective sequence. Thus, it is concluded that the analysis of the compilation and solution of open mathematical problems plays an important role in the formation of the competence of plausible reasoning of future mathematics teachers and has a great influence on the preparation of young people for changing real life.