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In modern conditions, the main task of the student is not only to obtain knowledge about the existing dependencies in the surrounding world, but also to master the skills of creative and independent learning. In materials of modernization of education the competent approach is proclaimed. And how to implement a competent approach at school today? We have made an assumption that the activity of pupils in the construction of tasks can contribute to the formation of their mathematical competence. The work consists of two chapters, a conclusion, a bibliographic list of used literature and 3 annexes. The first chapter analyzes the essence of the concepts of "competence approach", "competence", "problem construction". The second chapter presents: methods of teaching students to design mathematical problems, stages of formation of skills to design mathematical problems, description of the experiment. The results of the research can be useful for teachers of general educational institutions and used in courses of professional development of mathematics teachers.