The thesis is devoted to the development of an experimental methodology for teaching mathematics in elementary school, focused on the development of pupils' critical thinking. The study analyzes the achievements and problems of dissertations, scientific and methodological literature on the methodology of teaching mathematics in elementary school, the development of critical thinking of pupils in secondary schools. The dissertation is a theoretical and experimental study of the psychological, pedagogical, scientific and methodological foundations of the development of critical thinking of elementary school students in the process of teaching mathematics. The dissertation examines critical thinking as a philosophical and psychological category, covers the concept of “critical thinking” in pedagogical and methodological literature, analyzes the importance of the technology for the development of critical thinking in the modern educational space, in particular in the context of the New Ukrainian School, interprets the content of the concepts of “critical thinking”, “the technology for the development of critical thinking in the process of teaching mathematics”. The author has developed a model for the organization of teaching mathematics in elementary school, focused on the development of students’ critical thinking, consisting of 4 blocks, each of which has a specific meaning. In the first − a theoretical and descriptive block − pedagogical approaches and general didactic principles are described, in the second − procedural − pedagogical conditions and stages of education are defined; in the third − functional-activity – educational, methodological and technological support are characterized; in the fourth − diagnostic-evaluative − the components and levels of development of pupils’ critical thinking in the process of teaching mathematics are disclosed. In the thesis, the author proposed a methodology for the development of critical thinking of younger students in the process of teaching mathematics that is reasoned and tested in schools in different regions of Ukraine. The essence of the methodology is the systematic involvement of primary schoolchildren in critical thinking through the application of methods and techniques for the development of critical thinking and the system of tasks for the development of critical thinking of primary schoolchildren in the process of teaching mathematics. The dissertation defines the pedagogical conditions for the development of critical thinking of elementary school students in the process of teaching mathematics: a) providing a stable motivational-activity environment as the basis for the development of critical thinking of elementary school students; b) the systematic use of special methods and techniques for the development of critical thinking of students in mathematics; c) the psychological and methodological readiness of primary school teachers to master and introduce technology for the development of critical thinking of students in the process of teaching mathematics. In experimental research training, the author describes the methodology for developing critical thinking of younger schoolchildren in the process of teaching mathematics, traces the influence of methods, techniques and learning tools on the activation of students' mental activity, on the development of critical thinking signs and the level of critical thinking development of primary school students in the process of teaching mathematics. The essence of the methodology for the development of critical thinking of primary schoolchildren in the process of teaching mathematics consists in using tasks to study and determine a mathematical problem; tasks for modeling strategies to solve a mathematical problem; tasks for critical evaluation of data, process and result of the outcome (analytical tasks, analytical and synthetic problems, control and correction tasks); tasks on the application of the experience of mathematical activity. The results of the experiment confirmed the effectiveness of the proposed methodology for the development of critical thinking of younger students in the process of teaching mathematics. The dissertation materials can be used in the process of improving standard educational programs, school textbooks and study guides for mathematics in elementary school and teaching methods of mathematics in higher education.