Abstract
Introduction of Concept of the New Ukrainian School and transition from the knowledge to competence paradigm lead to reconsidering of the content and structure of mathematical competence and factors of its development. The purpose of the article is to clarify the content and structure of the problem-based system of competence-oriented teaching of mathematics to primary school students. For this reason, such research methods as theoretical and structured system analysis, theoretical modeling as well as content and theoretical generalization are used. The constructed problem-based system of teaching of mathematics implements the principle of developmental continuity. On the one hand, it serves as a program of educational and mathematical activities, and on the other hand, it actualizes the three-dimensional structures of external and internal demonstration of mathematical competence. The specific character of this system is in the variety and different types of the problems, integration of deductive essence of mathematics, personality and activity-based as well as competence theory of its teaching. There is justification of an opinion that the competence mathematical problem is a type of reflexive problems in the process of solving and as a result of which zones of current and nearest mathematical development of personality are formed, there are qualitative changes of the subject of mathematical (educational and mathematical) activity which are reflected in internal and external dimensions of his mathematical competence. Such problems are solved by the subjects of mathematical (educational and mathematical) activity in order to diagnose their mathematical competence and at the same time they are used as a means of such competence development. It was found that there are four levels of content and theoretical generalization which are considered as classification basis for competence mathematical problems and which enable to distinguish basic, educational, educational and theoretical as well as educational and research competence mathematical problems. The article establishes a generalized method of action in the process of solving competence mathematical problems. It provides diagnosis and development of both the external demonstration of mathematical competence and its internal demonstration. Keywords: problem-based system of teaching, competence problem, competence mathematical problem, mathematical competence, primary school students.
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