Application of artificial intelligence technology in the process of improving the qualification and enhancement of self-educational activities of mathematics teachers

Statement of the problem. The innovative multi-vector process of digital transformation of the system of further pedagogical education poses questions to the scientific community related to the development, implementation, and methodological support of the use of web-oriented resources for advanced training and activation of self-educational activities of mathematics teachers. The article presents the authors' view on the solution of this problem. The purpose of the article is to determine the directions for resolving the discrepancy between the potentially effective didactic capabilities of modern web-oriented resources as a means of organizing advanced training and activation of self-educational activities of mathematics teachers and the lack of a theoretically sound, internally holistic and logically consistent didactic system for implementing these capabilities in the practice of further training of teachers. Methodology and research methods: study of philosophical, psychological, pedagogical and methodological literature, historical and genetic approach to identifying the genesis and determining the stages of development of the process of improving the qualifications of mathematics teachers, comparative analysis of educational mathematical applets, questionnaires. Research results. The article presents a description of the didactic system for improving the qualifications and activating the self-educational activities of mathematics teachers. Definitions are given for the concepts of ‘mobile educational mathematical applet' and ‘web-oriented learning resource'. The article shows the results of a comparative analysis of mobile applets containing reference information that allow processing mathematical data, solving mathematical problems, and help students to test their knowledge. A chronological line of development of Artificial Intelligence as a direction in science is constructed. The algorithm for working with GPT chat with text and graphic information and performing mathematical calculations is presented and analyzed. A substantive and functional description of the authors' web-oriented resource is given. It is intended to support the training of mathematics teachers during advanced training on the topic “Didactic design in teaching mathematics in general secondary education institutions” and to activate their self-educational activities. It includes a glossary, a feedback form (forum and telegram bot), educational materials (structured in a spiral structure of four turns), examples of fragments of didactic scenarios, a collection of ready-made educational mathematical applets and methodological instructions for their use, fragments of video lessons, materials for current and final certification (differentiated by three levels of complexity).