Bosovskyy M. Succession in Studying the Theory of Limits in General and Higher Educational Institutions.

The methodology of teaching the theory of limits in the course of mathematical analysis in higher educational institutions, which is directed to provide the succession of studying in general and higher educational institutions, is developed and scientifically proved. The main stages of studying the theory of limits (propaedeutical, selective and immediate) are figured out; their peculiarities and time frames are determined. The levels of studying the theory of limits (intuitive, infinitesimal, and definite) are formulated; their specificity and correlation with the stages of studying is distinguished. The levels of understanding the theory of limits are specified. The types of succession (evolutionary, revolutionary, regressive) in studying the theory of limits at transition from general educational institutions to higher educational ones are determined; the conceptual fundamentals of continuity in studying the theory of limits in general educational and higher educational institutions are established; the components of the succession system (personal, content-semiotic, and organizational) in studying the theory of limits in general educational and higher educational institutions are outlined and analyzed. The methodological complex, which includes diagnostic instruments and means of studying the theory of limits, a dual-purpose study guide, an interactive textbook, a system of methodological recommendations concerning the organization of studying the theory of limits during the lectures and seminars, and in students' independent work is worked out. The efficiency of the offered methodology is proved through experiment.