Development of a prototype system based on Markov representations to support the learning process in elementary school

<p><strong>Context and relevance.</strong> Individualization of the learning process is the most important task of modern pedagogy, especially in primary education, where basic mathematical skills are formed. The existing class-lesson system often does not allow to promptly identify and correct individual errors of students. The author's proposed development of an adaptive digital system based on Markov models is aimed at solving this problem. <strong>Objective.</strong> Development of a prototype of a digital educational system to support individualized learning process of mathematics in elementary school. <strong>Hypothesis.</strong> An adaptive system based on Markov processes with discrete states and continuous time can increase the efficiency of individualized learning and improve students' mathematical skills. <strong>Methods and materials.</strong> The study developed a web application that uses Markov processes to assess elementary school students' mathematical knowledge and skills. The system offers tasks with predefined answer choices, captures errors, generates error-appropriate prompts, and adapts task difficulty based on student progress. <strong>Results.</strong> A prototype of a digital system is presented, which allows effectively detecting and correcting typical errors of elementary school students in solving mathematical problems, providing an individualized approach to teaching and reducing the teacher's workload. <strong>Conclusions.</strong> The developed system provides opportunities for increasing individualization of learning and quality of mathematics education in elementary school. Further expansion of the system functionality is recommended, including integration of additional analytical modules and adaptation to other educational subjects and age groups.</p>