Each academic discipline has its place in the professional training of technical students. However, mathematical training of future specialists occupies a special place. But we will not talk about the place of mathematics in learning. In this article, we share views related to the creation of mathematics education content and the competence of technical specialists in the context of STEAM education. We will consider the methodological system for developing professional competencies of future specialists in the technical field of STEAM education using the example of teaching mathematics. In the article we cannot show the weight of the complex, but we can consider the main ones with an example. In addition, we will also talk about the transition of the role of the teacher in STEAM education situations to a completely different quality. In the article, the considered tasks of creating an educational complex in higher mathematics for technical specialties are divided into three main types. These are: problems in mathematics that study various phenomena of the world around us; tasks that are performed using ICT tools; tasks that determine the professional competence of specialists. This set of problems was prepared based on the method of disciplinary integration of STEAM education. Of course, within the framework of these tasks the content of STEAM education is revealed. Evaluation criteria have been created for each block of tasks. In the final part of the article, we examined several tasks using examples and criteria for their evaluation in the table.