Research projects and Moscow Mathematical Conference for high school students

This paper shares some experience in advanced mathematical education. We show how a high school student can be naturally and gradually introduced to basic steps of scientific research: developing intuition by finding and correcting mistakes through discussions and writing a paper, (transparent) anonymous peer review, recognition and award. We show that most of this can be done in research projects not aiming at scientific novelty. We share the experience (both principles and examples) of the Moscow Mathematical Conference of High School Students.