The publication states that the modern labor market, professional conditions in the new Ukrainian school, the requirements of inclusive education, STEM-education make serious demands not only on the professional training of future educators, but also on the level of their personal development. extracurricular work ", which was previously associated only with independent preparation of applicants for practical laboratory classes, with the educational work of the curator (tutor), and today it has many significant aspects. In this regard, the article considers the essence of extracurricular work of higher education students at the Pedagogical University, which in our own research we understand as a special form of organization of life of future teachers, which takes place in extracurricular time to ensure meaningful, active and useful recreation. various interests of applicants, deepening and expanding their knowledge, skills and abilities, development of intellectual, creative abilities, self-organization, self-learning, etc. The purposes of extracurricular activities, varieties (individual, group, frontal (mass)), forms of organization and holding (self-governing bodies of applicants, clubs, clubs, studios of interest, agency of social projects, scientific society of applicants, sports clubs, sections, master class are presented , volunteering, creative laboratory), as well as the principles that we consider necessary to follow in extracurricular work with applicants (cooperation, humanization, voluntariness, expediency, interest, practical orientation). In addition, the article presents methods of extracurricular activities of future mathematics teachers used in the implementation of the author's model of the system of development of their creativity (problem-searching methods, project method, methods of collective mental activity, methods of applying the latest information and communication technologies). Therefore, organized in the general system of creativity of future teachers of mathematics extracurricular activities promote the development of intellectual, creative abilities of higher education, has a significant impact on the development of their creative potential, critical, logical and creative thinking, cognitive and creative abilities.