Elements of stochastic in Mendel's Laws

The article is devoted to the questions of formation of a scientific understanding of the statistical nature of the laws of heredity by Gregor Mendel at pupils of the institutions of general secondary education. The article notes that pupils will understand the essence of the statistical nature of Mendel's laws only if they are familiar with the basics of combinatorics, probability theory and statistics, which is the subject of stochastics. It is noted that the familiarization of pupils with elements of stochastics is provided for by the content of the discipline “Mathematics. Grade 9”, and the formation of pupils ideas about the statistical nature of Mendel's laws is provided by the content of the subject “Biology and Ecology. Profile level. Grade 10". It is noted that in the relevant textbook recommended by the Ministry of Education and Science of Ukraine, this issue is not addressed. Attention is drawn to the lack of domestic scientific research on the formation of pupils knowledge about the statistical nature of the laws of heredity, it is noted that the development of methodological support for teachers on this issue is relevant. 

An example is given of explaining to pupils the content of the statistical nature of Mendel's laws: why the results of real crosses and their quantitative relationships often do not coincide with the theoretically expected ones. The examples show that mendelian splittings obey the law of large numbers, and to determine the fit of the experimentally obtained data to the theoretically expected ones, you can use the criterion χ². An example is given of solving a typical problem of determining the character of inheritance of a trait during monohybrid crossing using the χ² method. It is noted that the introduction of a probabilistic statistical line in the content of the school course of genetics will allow students to understand Mendel’s laws qualitatively. This is necessary for the formation of basic competencies in the application of mathematical methods for solving problems of heredity and variability, as well as the ability to explain genetic phenomena with the help of scientific thinking. In addition, pupils will better understand that most of the processes in nature are not strictly deterministic, that the deterministic approach to their study is the first approximation to reality; the next step in the path of knowledge is a stochastic approach.