In many countries, research on the problems of personality is actively carried out. Due to the mathematization of science and, as a consequence, an increase in the significance of work-in mathematics, teachers are more attracted to teaching mathematics in school. However the teacher-centered reproductive learning style dominates and students lack the facilities for independent problem-based learning activities and the development of scientific thinking skills. Today the world is developing a new paradigm of international education, the essence of which is mainly determined by the ideas of integrity, fundamentality and the interests of the individual. The development of a pupil's personality and the learning of mathematics are linked closely and so, for this purpose, it is necessary to introduce developmental learning.

What is the role played by mathematics courses in the education and development of a pupil's personality? The answer to this question depends on the aims for teaching mathematics.

General pedagogical learning objectives are within the requirements of the general system of society and the problems of the educational system. It is important to specify these common goals, splitting them through the prism of the subject content of science studies. The "content of learning contributes to the development of personal human structure. It fills in the spiritual world and identifies the world of the growing personality "[1, p. 35].

Mathematics as a subject develops qualities that can be attributed to general learning (thinking, memory, attention, language, moral ideals), and special qualities that can be imparted only through the process of mathematics teaching; namely, the mind-set to build mathematical real phenomena models and processes for the mastery of the apparatus for certain types of mathematical models.

The primary means of building a thinking culture in the context of mathematical education is learning and adequate creative mathematical activities. A necessary condition for the development of the learner is an active position in teaching and learning, which is, moreover, an inner activity, making it a subject of activity.

In the learning process organization proposed by Galperin, there should be a control over the pupils work in order to help them avoid possible errors. But such control must be only short-term with a gradual transition to self -control. As you know, any work is carried out in two ways: the external, ie.visible, and internal, which is not accessed by an unauthorized observer, and which is not recognized by the person himself. The internal way is the most important here because the work is directed by the human brain and consciousness. Due to this, the assimilation of knowledge depends on the ability to carry out relevant work.

Monitoring the progress of "inner thoughts" allows the teacher to establish strengths and weaknesses of the pupil's thinking ability, thereby being able to draw concrete conclusions about how to direct student thinking on the right path. That is why, in order to teach pupils to solve mathematics problems, it is important to establish in what way the pupil thinks while solving these problems and in what way the pupil grasps the statement of the problem? What will he do? What are the subsequent stages of his thinking to find the solution to the problem? etc. To find these answers the teacher asks, "Why?", "On what basis?" etc.

The cognitive interest of the individual is an important characteristic and is a sustainable condition of the person. It is expressed in its targeted active-cognitive activity in relation to an object important for him.

Knowledge is a non-personal component of educational content, as it covers only intelligence but not man's consciousness as a whole. In other words it points to the mind, but not to the whole person. Even images of a person's thoughts are not always adequate for knowledge. Therefore, the process in which teaching prevails, answers the question. "What is to be done?", while a pupil, studying at school, must be given an answer to the question, "How do I live?" that is determined by up-bringing. In our opinion, how to "teach to live and learn to live together" is becoming more and more important in modern society. This is one of the main goals of education, which can be attained by pupils to a certain extent from mathematical tasks and the history of mathematics.

2. P. Galperin. Psychology of thinking and learning about staged formation of mental skills. Research of thinking ability in soviet psychology. - М: Pedagogy, 1969. – p. 347.