The purpose of this work is to develop a model for the construction of STEAM-education, which is based on project training in the so-called "creative spaces". "Creative spaces" are integration areas of schoolchildren, students and graduate students working in the format of joint work on projects initiated by various structures of a society and business. The authors of the article analyzed the experience of different countries in the implementation of STEM and STEAM-education and identified the effective ways of structuring technical disciplines, art and creative activity into a single integration program. During 2017-2018 years within the framework of informal and nonformal education, an experimental work was carried out with 32 schoolchildren and 34 students, aimed at determining the level of the development of such competences as: the ability to manage projects and processes, system thinking, the ability to art creativity, the ability to work within the teams, groups and individuals, the ability to work in a regime of high uncertainty and a rapid change in the conditions of tasks. Analysis of the results of experimental work has shown that the use of "creative spaces" for the implementation of project activities of schoolchildren and students, the inclusion of the category "art" in its content allows students to form skills and competencies necessary for the Industry 4.0.