ІНТЕГРАЦІЯ ЦИФРОВОГО ЧАТ-БОТА У ПРОФЕСІЙНУ ДІЯЛЬНІСТЬ: ПЕДАГОГІЧНИЙ ПОТЕНЦІАЛ, ДИЗАЙН ТА ТЕНДЕНЦІЇ РОЗВИТКУ

This article explores the pedagogical potential of integrating a digital chatbot into an educational environment using adaptive and cognitively oriented approaches. The proposed model combines mathematical modeling techniques, reinforcement learning algorithms (Q-learning), and principles of instructional design to create a digital tutor capable of dynamic interaction with the learner. The system architecture is based on four key modules: a user state analyzer, a task generator, a reinforcement module, and a dialogue manager. Particular attention is paid to modeling the user's knowledge growth function EXP(t) using stochastic differential equations that take into account learning efficiency, response time, number of errors, and random disturbances. The use of a stochastic task selection mechanism enhances pedagogical variability and supports learner motivation. The model is implemented as a simulation-based educational game that allows for real-time tracking of cognitive dynamics. Simulation results confirm that the system can adapt to different learner profiles, ensuring a personalized learning trajectory and stable knowledge acquisition even under conditions of fluctuating learning effectiveness. By combining formal mathematical representations with well-designed functional and pedagogical architecture, the proposed model can be viewed as a promising tool for the digital transformation of education.