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1 | Introduction. The question of the development of students’ creative abilities through the new phenomenon of facilitation has aroused increased interest on the part of the scientific and practical communities. Facilitation imposes certain requirements on the learning process. Purpose – the requirements provision theoretical analysis of the pedagogical facilitation technology to the teaching mathematics process for the students’ creative abilities development. Material and methods. The research draws on the work of domestic and foreign researchers in the field of general psychology, pedagogical facilitation and the development of creative abilities. The main research methods are study and analysis of psychological and pedagogical literature on the problem, questioning of students. Results and discussion. Pedagogical facilitation imposes such requirements on the learning process as ensuring the importance of learning, psychological security and psychological freedom, as well as the personality of the teacher and his ability to build relationships with students. A meaningful learning involves changing the personality, changing the behavior of the student due to his or her inner sensory-cognitive experience. To fulfill this requirement in teaching mathematics, you can use various facilitation tools in integration with entertaining tasks, non-traditional forms of organizing classes, and demonstrating the teacher’s respect for students. In the process of facilitation, psychological security is achieved by creating an environment that ensures the presence of trust on the part of the student, as well as the absence of fear, anxiety and other negative feelings arising from external evaluation. It is important to organize work with low-performing students, use modern pedagogical technologies to create a situation of success, and increase the level of comfort in the classroom. Psychological freedom presupposes the formation of students’ creativity, their self-expression, in the formation of which it is important to provide an opportunity to show activity, independence, responsibility. Conclusion. The results of the study make it possible to speak about the features of the organization of the educational process with ensuring the importance of learning, psychological safety and psychological freedom of students on the part of the teacher, as well as about the qualities, competence, personality of the teacher-facilitator, which increases the effectiveness of the development of creative abilities through special trusting relationships, recognition and acceptance of the students’ values, optimization of the process of joint work in the mathematics training. Keywords: creative ability, pedagogical facilitation, significance of teaching, teacher’s personality, psychological safety, psychological freedom | 730 |