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The article is devoted to the formalization of a gamified educational environment as a managed organizational system in the context of digital transformation of education. In contrast to the prevailing psychological and pedagogical interpretations of gamification, the work considers it as a controlling influence that regulates the parameters of students' behavior. Based on system analysis, structural and functional modeling methods, and logical and analytical construction of control contours, a model of a gamified EdTech environment has been developed that includes a managed object, a control subsystem, a digital infrastructure, and external disruptive factors. The functional decomposition was performed using the IDEF0 notation, and the process dynamics was described using BPMN tools, which made it possible to formalize inputs, outputs, control actions, and feedback mechanisms. The concept of the stability of the educational process is introduced as a property of the system to maintain the trajectory of learning activity under the influence of external and internal factors. The levels of stability are highlighted: local, structural and trajectory. It is shown that gamified mechanisms can be interpreted as regulatory signals that ensure adaptability and controllability of educational activity. The results obtained expand the tools of organizational systems management theory in relation to digital educational ecosystems and create the basis for the development of adaptive algorithmic management models in EdTech.
Keywords:gamification, digital educational environment, EdTech, educational system management, organizational system, system analysis, IDEF0, BPMN.
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