Formation of a model of an inquisitive, intelligent, thoughtful, sociable, consistent, fair, caring, risky, harmonious, reflective student through the organization of research work in mathematics lessons. To show students the importance of organizing research work in mathematics lessons in educating a person with comprehensively developed high moral values, who is ready to apply the acquired knowledge in the process of continuing education in unfamiliar situations.
The article discusses how students can develop their research skills through small research activities. The work of various scientists is analyzed, the results of jointly planned classes on the development of students ' motivation for learning and research skills are analyzed. In the course of organizing research work in action, effective points of joint planning of teachers were identified and outlined. As a result of the study, it was found that the compilation of problems related to real life in a practical direction develops the ability of thinking to synthesize, analyze.

Conducting meaningful research work in mathematics lessons is the basis for developing students ' deeper understanding of the subject and the ability to apply it in real life. The fact that students learn, Act and reflect in a repeated cycle can lead them from academic knowledge to practical insight and the development of its positive attitude to learning, as well as personal and social responsibility.

The purpose of the study: to study the logical abilities of students through a problematic learning approach

to increase interest in their work, to teach students to work consciously on themselves, as well as to achieve solid knowledge, high learning outcomes through this method of teaching.
Research objectives:
Definition of the theoretical, basis of problem-based learning in the scientific and methodological literature;
- Consider ways to solve problems in the development of students ' thinking;
- Pedagogical and psychological description of the level of development of students;
Scientific forecast of the study: if the organized work is organized systematically, purposefully, it will be possible to develop students ' thinking through problem-based learning approaches.

A mathematical study is a long-term, open-ended study consisting of a set of questions, the answers of which are interconnected and mutually contribute to obtaining a solution. The problems are open-ended, unfinished, because students always come up with new questions based on their observations. Additional characteristics of student research include the following:
Students use the same methods used in mathematical research. They work through data acquisition, visualization, abstractions, and proof cycles.
Students communicate with each other through mathematical language: they describe their thoughts, write their judgments and predictions, use symbols, prove their conclusions, and study mathematics.
If the study consists of class or group work, then students become a community of mathematicians, exchanging experience and complementing each other with questions, assumptions, theorems.

Influence of mathematical research work on the subject
The student has a high memory and ability to concentrate, develops the ability to quickly complete a task in unfamiliar situations, and develops the skills of logical thinking, effective use of information.
It is clearly seen that the student is more motivated in the learning process, the ability to identify and find an effective solution to the problem is improved, and he gets pleasure in solving it.
The student has a high ability to think creatively, is able to identify complex patterns using mathematical approaches, such as mathematical language, developed creative thinking, and the ability to visualize tasks in space.
Every research work shows that students can think critically, analyze and present something new, new ideas with energy, whether on their own or in a group. When we find mathematical patterns, we feel that real pleasure is experienced through emotion.

According to the statement of Artemenkova in the article "the role of a differentiated approach in the development of personality", "learning must somehow coincide with the level of development of the child – this is a well-established and repeatedly verified fact that cannot be empirically disputed." on the basis of this opinion, when analyzing with colleagues, we realized that the need to create conditions for learning and development depends on how students perceive information (audial, visual, kinesthetic). According to the work of Lebedeva, in addition to education, it is the acquisition by students of the skills of conducting research activities as a universal way of mastering the world around them. The General task is to find an answer to the question through interaction, cultural information between students, the result of which should be the formation of the worldview of students and the formation of a research position. Based on the foregoing, we aimed to improve the skills of critical thinking, interpretation, research, choosing methods of active teaching and learning that cover the entire class. We organized the work by dividing it into small groups to increase the motivation of students to learn, taking into account the needs of all students. As a result of the Gardner test obtained from students, we were convinced of the need to divide them into groups according to the level of perception of information. In accordance with the evaluation criteria, practical research work and tasks related to real life based on the jigsaw method not only develop students ' research skills, critical thinking skills, but are important for achieving the purpose of the lesson and evaluation criteria. When summarizing the practical work, students were able to compare the data obtained with reference values. To explain to them the reasons for the difference between these data from each other, they compiled a list of evidence, and also analyzed what changes in the technique and equipment of the experiment allowed to obtain a more accurate result. The use of assessment strategies developed students ' skills of preparation for work, skills of working with information, skills of induction (generalization), skills of deduction (transfer), skills of substantiating their point of view, skills of decision-making, the ability to see the benefits of communication in accordance with educational achievements.

In summarised, mathematical research the student engages in more mathematics, he improves his confidence in the form of mathematical contemplation and enthusiasm. Creativity, risk, decision-making, surprises, and achievements that are part of the study help students answer questions about the meaning of learning mathematics. They learn new techniques to be able to answer their questions. Scientific practice requires the repeated use of technical skills in the process of searching for templates and testing assumptions. In the context of incentives and important issues, it is this repetition trend that leads to a deeper understanding and maintenance of mathematical skills. In the course of the research work, students create a close relationship between the retention of further acquired knowledge and the ideas that increase it. The student will determine which side of the problem he will study and develop his mathematical vision through the skill of making a choice. In the study of students, written mathematics and problem solving occupy a leading place. It fosters the student's unwavering perseverance in achieving the goal and tolerance for perfection, as it is strengthened that they reach their goal by encouraging, encouraging and giving them the opportunity to think again in a few days or weeks. In conclusion, the implementation of research work related to real life in a practical direction develops the ability of students to synthesize, analyze their thinking. This section led to an increase in the research abilities of students with a high concentration of attention. We hope that the organization of research work will be very effective not only for the student, but also for the teacher to master the discipline and find a great application in the future. We are ready to bring up the modern generation and realize the coming changes in education.

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