Modern mathematical education is focused on the formation of a competent and creative personality of pupil in grades 5-6. The article discusses the renewal of the education system on a competence basis, considering the transition from the traditional education system to the humanistic one. The article is devoted to the state and prospects for the implementation of competence-oriented problems in mathematical education. The importance of using new components of educational goals, using innovative technologies and non-standard forms of conducting mathematics lessons in grades 5-6. Three blocks for the development of a creative and competent personality of the student base, incentives and work are analyzed. Block base covers the knowledge and skills of the student to the beginning of the lesson. At the heart of the incentive block is the creation of a problem situation or the use of another motivational technique to attract the pupil to work. Block work - the work of the student and getting new knowledge for him through some kind of discovery. Examples are offered for conducting research lessons when studying the topic “Triangle and its types” in the 5th grade and when studying the 6th grade of the circumference. The tasks for the development of a competent and creative personality of the pupil are given, which provide a link between knowledge and practical skills: “Find Differences”, “Find Superfluous”, “Labyrinth”, “Chain”, work with cards, compose and recognize diagrams, etc.