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The role of mathematical education constantly increases in actual world. Educators play the main role in developing the mathematical competence and preserving the traditions of Russian mathematical school. One of the crucial problems in contemporary mathematical education is the low level of graduates assigning to schools. The article reveals the period of adapting beginning teachers of math. Highly qualified and systematic methodological support for young teachers allows identifying the main difficulties and mistakes within their pedagogical performance, and designing the recommendations to overcome it. Observations enable to reveal the ways improving future math teachers training that turns out to be the purpose of current research work. We used the observation as the leading research method to monitor the performance of beginning teachers within the first three years after university. As a result, we designed recommendations for adjusting the special, psychological, pedagogical and methodological training of future teachers contributing the competitiveness of graduates and ensuring the success in chosen profession. The study is of practical importance. It includes the designing of methodological recommendations for beginning teachers and the approximate program for individual self-development. [ABSTRACT FROM AUTHOR]