Foundations of the Methodology for Continuity of Teaching Mathematics at School and University in the Context of Digital Renewal of the Educational Environment

This article examines the issue of teaching elements of mathematical analysis based on continuity in high schools and higher education institutions in the context of digital education. The meaning of the concept of "continuity", methods of continuous teaching of elements of mathematical analysis in high schools and higher educational institutions, as well as the reasons for the lack of academic hours for studying mathematical subjects in higher educational institutions and the deterioration of mathematical training of school graduates entering higher educational institutions are determined. At the same time, in the context of digital education, this is due to the creation of a methodological system for the consistent teaching of elements of mathematical analysis in the course of teaching the course "Algebra and the beginning of analysis". External factors are identified when developing a methodological system. In order to clarify the content components and simplify the explanation of complex tasks to students, in the procedural component we used the capabilities of computer technologies, which are the basis for the development of pedagogical science in the context of digital education. The effectiveness of the proposed methodological system has been introduced into the educational process in secondary schools of the Turkestan region and the city of Turkestan and has been proven experimentally. Received: 11 March 2024 / Accepted: 19 June 2024 / Published: 05 September 2024