У роботі запропоновано теоретично обґрунтовану та експериментально перевірену методику інтерактивного навчання старшокласників початків математичного аналізу, визначено дидактичні умови інтерактивного навчання старшокласників початків математичного аналізу. У дисертації проаналізовано стан вивченості проблеми інтерактивного навчання у психолого-педагогічній та методичній літературі, досліджено психолого-педагогічні основи інтерактивного навчання старшокласників математики, побудовано модель інтерактивного навчання старшокласників алгебри і початків аналізу.У дисертації запропоновано: структуру інтерактивного уроку алгебри і початків аналізу, доцільні методи інтерактивного навчання старшокласників початків математичного аналізу. У науковій роботі досліджено інформаційно-комунікаційні технології інтерактивного навчання старшокласників початків математичного аналізу, запропоновано методику оцінювання навчальних досягнень та діяльності старшокласників під час інтерактивного навчання математики, наведені результати педагогічного експерименту.^UTheoretically justified and experimentally tested methodology of senior pupils interactive teaching of mathematical analysis principles is offered in this thesis. Scientific novelty of the research is that: 1) didactic terms of senior pupils interactive teaching of mathematical analysis principles have been determined, theoretically justified and experimentally verified according to communicative-dialogue and computer-multimedia approaches; 2) conceptual model of senior pupils interactive teaching of algebra and analysis principles has been established; 3) method of realization of defined didactic terms in the process of teaching of mathematical analysis principles in senior school has been developed; 4) approaches to evaluation of the educational and cognitive achievements of senior pupils during interactive mathematics studying have been improved; 5) approaches to the organization of teaching based on the platform Moodle and the conducting of webinars, consideringthe specific of the interactive teaching of mathematical analysis principles have been offered; 6) interactive form application method and methods of senior pupils interactive teaching of mathematical analysis have been further developed; 7) the role and place of the teacher in the interactive teaching of mathematics have been specified.The research is based on the scientific developments in the field of pedagogy, psychology, innovation, philosophy of education, theory and methodology of teaching mathematics, concerned with the problems of fundamental basis of innovative pedagogical activity and with the method of teaching mathematics (papers on the problems of teaching methods and organization of education activities; papers on the problems of methods improving of teaching of components of school mathematical education; research on informatization of education; papers thathighlight the communicative- dialogue aspect of interactive teaching; the theory of symbolic interactionism; ideas of pedagogical interaction and other).In this research interactive teaching of mathematics to senior pupils – is a type of teaching in which interaction of senior pupils with their own educational and cognitive experience appears as well as with the experience of other pupils (experience is realized, accumulated, systematized). Its core is to organize a mutual process of teaching, when the realization of the natural need of senior pupils to have a dialogue, a polylogue with a teaching environment appears, the structure and content of which effect the achievement of the main goal of studying mathematics in seniorschool.The model of interactive teaching of mathematical analysis principles is considered from the communicative-dialogue and computer-multimedia approaches and consists of the following structural components: a goal; subjects of teaching process (senior pupils, a teacher-facilitator); the academic subject "Algebra and principles of analysis", the final result of which is formed key competencies; interactive forms, methods and teaching tools.The effectiveness of senior pupils interactive teaching of mathematical analysis principles has been tested during the forming stage of the experiment. The set of the results achieved during the research allows affirm that the developed method of senior pupils interactive teaching of mathematical analysis principles contributes to increasing of motivation, cognitive interest, the level of students' progress in algebraand analysis principles.Materials presented in this thesis can be used in the process of teaching mathematics by senior school teachers, at the training courses for teachers of mathematics and subjects of the natural and mathematical cycle, during the preparation of students of pedagogical specialties in higher educational establishments as well as when writing manuals on mathematics.