ISSUES OF TEACHING PROBABILITY THEORY AND MATHEMATICAL STATISTICS IN SECONDARY SCHOOL

Abstract

Probability theory and mathematical statistics represent a distinct branch of mathematical science. The axiomatization of probability theory in the early 20th century marked its emergence as an independent and fundamental field of mathematics. At the same time, probability theory serves as the foundation for mathematical statistics. The development of these disciplines has contributed to the emergence of new areas of knowledge such as risk theory, actuarial mathematics, stochastic analysis, biostatistics, and others, and has led to the formation of several specialized fields. Given the growing importance of probabilistic and statistical methods in various areas of science and practice, their inclusion in school mathematics curricula is both timely and justified. Therefore, the theoretical and practical teaching of probability theory and mathematical statistics is highly relevant.

One of the key issues is the methodology for teaching fundamental concepts, which are often overlooked during instruction and reduced to mere formula substitution and calculations. Furthermore, since elements of probability theory and mathematical statistics have been introduced into the school curriculum in recent years, determining the age-related capabilities of pupils—namely, in which grades and to what extent each topic should be taught—is a crucial component of the teaching methodology for this subject. The purpose of this article is to discuss and propose mathematically accurate definitions of certain fundamental concepts in probability theory and mathematical statistics, as well as teaching methods for these concepts, taking into account the age-related characteristics of students.

In this regard, the article examines key aspects of the methodology for teaching elements of probability theory and mathematical statistics in school mathematics that require particular attention. Specifically, it addresses the importance of distinguishing between the concepts of an experiment, an experiment's realization, and its outcome, as well as an event and its realization, statistical population, and proposes an instructional approach for teaching these concepts. Based on empirical experience that helps determine the appropriate grade levels at which to introduce these and other topics in probability theory and mathematical statistics, the article draws conclusions about the age-related characteristics of students in relation to a number of fundamental concepts. The results of this study can serve as a foundation for the development of school curricula and corresponding textbooks.