Methods of teaching of using computer experiments in solving mathematical problems

Problem statement. One of the current trends in mathematical science is the strengthening of the role of the experimental component of mathematical activity under the influence of the development of digital technologies. A manifestation of this trend in the education system is the introduction of requirements for the formation of experimental skills of students in the process of teaching mathematics and the use of digital tools in solving problems. Solving a new educational problem requires not only the inclusion in the system of mathematics teaching tools that require the formulation and conduct of computer experiments, but also the development of teaching methods for their formulation, conduct, analysis of experimental data, obtaining adequate conclusions based on these data and their appropriate use. Methodology. Due to the fact that the knowledge and skills associated with involving computer experiments in solving mathematical problems are methodological in nature, the authors of the article propose to base the methodology on the technology of methodologically oriented mathematics education. This technology was developed by one of the authors of the article and provides for the creation of conditions in the educational process for the objectification and rationalization of the methodological foundations of mathematical activity, as well as the cultivation of the subjective experience of this activity. The substantive basis of the methodology is the archive of experimental and theoretical problems of the Experimental Mathematics Tournament, conducted by the authors of the article among students in grades 5-9 of secondary schools for more than 10 years. The methodology is intended for the preparation of tournament participants in extracurricular activities and in the system of additional mathematical education. The study of the effectiveness of the methodology was conducted in the classes of the Experimental Mathematics circle. Results. It has been established that there is a positive trend in the development of the computer experiment method among those regular participants of the tournament who study according to the described methodology. However, due to the willingness to use a computer experiment in combination with theoretical methods of solving problems, it presents a certain difficulty for a number of participants. Conclusion. The identified difficulties indicate the direction of further refinement of the methodology, taking into account the level of mathematical training of students.