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| 1 | Effective forms of educational activity are design and research activity of students. In the article the general and distinctive characteristics of these concepts are allocated; the expediency of inclusion of such forms of activity into process of mathematics studying of teenagers is proved; the experience of the organization of the project “Creation of the training table on the subject “Divisibility Signs” with pupils of the sixth grade is described; the bilateral analysis of efficiency of each stage of design activity of students is provided: from the teacher and from students (on the basis of their questionnaires). Keywords: system and activity approach, design activity of students, research activity of students, competences | 1433 | ||||