Teaching Learners of Specialized Classes the Method of Mathematical Modeling based on Solving Problems with Practical Content

The state of the art for research focused on the formation of mathematical thinking and analytical skills in learners revolves around several key developments and approaches in modern education, cognitive science, and instructional technology. It should also be noted that this topic is not sufficiently studied by other researchers, educators, and mathematicians. The research aims to understand how using mathematical modeling in specialized classes can make learning more effective. By focusing on real-world, practical tasks, the study seeks to show how applying math to everyday problems can deepen students' understanding and make the subject more engaging and relevant to their lives. Analysis, induction, deduction, and synthesis are the main methods of the research, allowing the description and highlighting of the most important aspects of the mathematical modeling methods application in profile classes. The article presents the following information: the study of the impact of learners' use of mathematical modeling on their understanding of the material presented; the definition of the concepts of "model" and "mathematical modeling" is given, the stages of this process are described; the application of tasks with practical content is studied; the concept of "system of tasks" and the main methods of its construction are considered; an elective course "Mathematical modeling" for learners of profile classes is proposed. The materials of the article are of practical and theoretical value for teachers, mathematicians, other representatives of the scientific community, and researchers of the topic of implementation of methods of mathematical modeling in the course of mathematics for specialized classes, interested in features and aspects of the application of tasks with practical content in the learning process, explore the role of mathematical modeling in the process of formation of mathematical thinking.