The Internet and the development of Web 2.0 technologies have significantly changed the form of scientific activity. The new form is called Science 2.0. Its main features are: mainly a project form of organizing research activities, defined by the certain grant financing system; strengthening the role of computer technology in obtaining scientific results, expanding the functions of its use; open mode of research in the conditions of network interaction of project team members. The training of secondary school students for research and project activities should take into account these changes. The transfer of experience in research and project activities in new conditions requires the implementation of the idea/concept of network mentoring. This idea/concept involves students joining open scientific communities, their self-presentation and active work to create their own network of mentors who are ready to share their experience, provide all possible assistance to students in overcoming emerging difficulties. The article presents the experience of using network mentoring in the work of an international team of students to solve the Rupert problem.

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