Visualization and modeling techniques in teaching schoolchildren to solving probability theory problems

the article considers the current problem of teaching schoolchildren to solve problems in probability theory. The demand and relevance of this topic is due, on the one hand, to the introduction of a new school course in probability theory and mathematical statistics, and on the other hand, to the inclusion of problems from this section in control and measuring materials in mathematics. The article pays special attention to the technique of modeling as a means of visualizing a problem situation, which allows organizing students' activities to find a way to solve such problems. The author considers the most frequently used models in school practice, presented in textbooks and teaching aids for preparing for the Unified State Exam. The main stages of mathematical modeling when working on a problem are revealed. Specific examples are used to describe in detail the methodological features of organizing students' activities to create a model for the condition of the problem, which leads them to an independent discovery of a way to solve it and a theoretical justification for the solution found. The methodological approach to solving problems in probability theory using models proposed in the article provides a visual interpretation of the mathematical provisions of the theory itself and is an effective tool in finding a way to solve problems of this type.

modeling, probability of an event, solving problems in probability theory, independent events