This paper examines some of the key mechanisms for cultivating the skills of systems thinking using methodologies such as the theory of inventive problem solving (TRIZ) and algorithms for solving problem situations (ARPS) in media education. The author puts forward a suggestion that the realities and needs of the present-day economy and its transition to the fifth and sixth technological paradigms will transcend traditional methods of education, bringing about change in approaches, methodologies, and objectives associated with the educational process, with a focus on replacing extensive forms and ways of teaching and learning with methods related to the intensive development of skills and professional competencies associated with media literacy and media education. A key objective in this context is to cultivate and foster the skills of systems thinking, which implies a capacity for strategic planning and design and creative solving of non-routine problems and an ability to detect inconsistencies and interdependencies in media texts and media messages. In this context, the paper brings forward several tools for fostering the skills of systems thinking, which are as follows: case problems, systems thinking tests, and systems mapping. The paper examines some of the key theoretical and applied aspects of the theory of inventive problem solving and algorithms for solving problem situations in the media sphere. The author's conclusion is that the TRIZ-ARPS methodology can be employed quite efficiently in fostering the basic and professional competencies associated with media literacy and media education. © 2020 Academic Publishing House Researcher.