Instructional scheme of organizing mental activity of future math's teachers while mastering basic concepts of functional analysis

The universality of mathematical knowledge, its a priori metasubject nature and fundamental role in forming the scientific style of thinking make high demands on the training of maths teachers within the framework of the higher professional education system. This training includes the formation of competencies related to the ability to understand and transmit knowledge formulated in the language of mathematics, the ability to embed it into the existing system of mathematical and general scientific training, as well as active, creative mastering of mathematical content. The article presents an instructional diagram of mental activity organization for solving educational mathematical problems. Being universal, the scheme meets the above requirements for training future maths teachers and it was developed specifically with an orientation towards this category of students. The article provides the specific example of the use of the scheme.