The development of students' analytical and synthetic activities in studying mathematical analysis

Introduction. The article addresses the problem of developing undergraduate students' analytical and synthetic activities. The purpose of the article is to identify the characteristics for the development of students' analytical and synthetic activities in the process of studying Mathematical analysis. Materials and Methods. Characteristic features of developing students' analytical and synthetic activities are considered in the unity of systemic, activity-based, cultural, anthropological and environmental approaches. The main research methods are analysis of scientific literature, analysis of university practice and personal teaching experience, experimental methods, and methods of statistical processing of empirical data. Results. The factors contributing to the development of students' analytical and synthetic activities within the improvement of educational process are established. The study reveals the features of teaching Mathematical analysis focused on improving the development of analytical and synthetic activities. The authors have designed the model of solving a mathematical problems within the framework of analytical and synthetic activities. Conclusions. The recommendations provided in the article can be used to increase the effectiveness of teaching a range of scientific disciplines to undergraduate and high school students.