The article presents the experience of developing skills in future teachers of mathematics related to the use of open tasks in the professional activities of a teacher. The article notes the importance of developing the ability of students to solve open tasks, emphasizes the developing potential of open tasks. The authors reveal the didactic possibilities of different academic disciplines in the formation of the very concept of "open task" among students. The article describes the main directions of preparing students for the use of open tasks in teaching mathematics to schoolchildren: involving students in research activities in the field of mathematics; enrichment of students' personal experience in solving open mathematical tasks, the formation of students' skills to design open tasks, the formation of students' skills to design situations for the use of open tasks in the lessons, the formation of skills to use open tasks in classroom and extracurricular activities in mathematics. The article describes methods of construction of open tasks, including: various options for reformulating the original tasks, introducing uncertainty into the task situation, the use of life, everyday situations, the use of fragments from fiction and popular science literature, films, the use of facts from the history of mathematics. Keywords: open tasks, methods of compiling open tasks, training of future teachers of mathematics. Качественное образование сегодня делает ставку на подготовку выпускника, способного самостоятельно приобретать знания и умения, проявлять творческую активность и инициативность, готового к решению проблем, демонстрирующего широкую эрудицию. Это касается и среднего, и высшего образования. Многие педагоги учат решать в основном закрытые задачи, т.е. задачи, в которых предложено полное условие, сформулировано конкретное требование и, чаще всего, возможен единственный правильный ответ. А в жизни
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