Abstract

This article presents the origins of the design and research activities of students. A system of means that form the design and research activities of students has been developed. Four types of design and research activities of students (imitative, reproductive, partially exploratory and creative) and the mechanisms of their formation are described. The main ways of activating the project activity of students are revealed: the formation of learning motives, the use of problematic elements, the system of various types of project work, the connection of the studied material with the life and personal experience of the student. Work built on active cognitive activity brings students feelings of deep satisfaction, develops their imagination , develops a creative initiative, forms a worldview and moral character. We have made an attempt to analyze the theoretical foundations, methods and techniques of activating the project activity of students in the lessons of the course of mathematical analysis.

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