Pavel Gorev

The paper offers an option of filling the content of the discipline "Fundamentals of design" for 10 grade students of higher school. The program is an obligatory component of the regional curriculum of edu-cational institutions of the Kirov region. Organization of students activities is performed in the active form in three complementary and interdependent lines: technology of creation and description of a project; improving students’ personal qualities for successful mastering project activity; methods of scientific creativity and development of creative personality by means of project activities. The result of the discipline are socially relevant research projects, designed by students.

The paper describes the experience of the regional innovation project “Connection of matter, forms and methods of basic and supplementary mathematical education of schoolchildren”, which was carried out at Lyceum #21 in Kirov, Russia. The paper outlines the key points of scientific advisor’s activities, which help to improve school teacher’s professional skills; the possible ways of conducting innovative activities with schoolchildren and students – future teachers of mathematics.

The paper discusses one of the solutions to the problem of increasing interest of younger students for studying the subject through the organization of their work on humanitarian-oriented projects in mathematics. There are the examples of projects, their phases and the possibilities of program realization.

The authors emphasize the possibilities of the use of open problems in the teaching of mathematics, de-scribe a number of requirements for such tasks. Provides examples of the use of open and partially open tasks at different stages of math lesson to enhance the creative potential of high school students.

The authors examine the evaluation of education quality through the evaluation of metasubject results of mastering the general educational programs. Open type tasks in three directions (mathematical, humanities and natural problems) are proposed as he main mean of evaluation. The authors designed and tested the integrated assessment of the relative character – intelligence quotient – reflecting the degree of mastering the general educational programs at the level of metasubject results. The intelligence quotient is based on the analysis of more than 200,000 works of pupils.