The researches presented in the article continue the experimental approach of obtaining and analyzing empirical data and solving practical problems of forming natural neural networks of the human brain. Such socio-psychological approach made it possible to consider neurodidactics as a methodological source of ideas for the formation of certain skills and competencies in a person. The main research question is how to ensure the purposeful formation of the necessary competencies in a person, which are sustainably preserved and reproduced over a given period. The development of the ideas of neurodidactics expands the range of application of research in the field of engineering education, in particular the formation of modern engineering thinking, which forms the basis of the professional competencies of university graduates and is in demand on the labor market. An attempt was made to solve this research problem in the conditions of Russian university education on the basis of teaching mathematical disciplines at the Ural Federal University. The neurobiological basis of the study was a computational structure that combines the theoretical concepts obtained as a result of the study of two neurosystems: the choice of multiple possibilities and the system of mirror neurons. The main empirical results presented in the article demonstrate the significant effectiveness of the applied neurodidactic modeling approaches. From the results presented, there are significant differences between the results of work in the conditions of neuromethods and traditional forms. A statistically significant improvement in the average results for the entire sample of students was revealed.