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Abstract: In the context of the problem of improving the quality of mass mathematical education, the article discusses the problems of the initial period of building a professional career by a graduate mathematician of a pedagogical university. So, one of the tasks that today’s graduate will face on the eve of the international study PISA-2021 will be the task of forming functional subject mathematical literacy of students of the basic school. It’s emphasized that in modern educational realities, when the main educational learning outcomes are, rather, formed stable personal and meta-subject “soft” skills, the mathematics teacher can and should build the pedagogical process, in accordance with both the psycho-pedagogical characteristics of the students and with their own psycho-pedagogical characteristics. A suitable tool that allows the teacher to obtain sufficiently objective quantitative data for the conscious building of pedagogical interaction with a specific group of students, according to the author, is to measure the severity of various types of intelligence. The theoretical basis of this approach is the theory of multiple intelligences by Professor Howard Gardner (USA); a measuring tool is a specially prepared self-assessment questionnaire. Another task that a graduate of a pedagogical university will have to find a solution to will be the task of setting his own effective and effective teaching style that allows him to optimally achieve educational goals. It seems to the author that the theory of pedagogical resonance is a suitable theoretical basis for this. This article presents and discusses the results of a psycho-pedagogical study of the structure of intelligence by Gardner of pedagogical mathematicians (graduation of 2020), who were trained in the direction of preparation 44.03.01 – Pedagogical education, Mathematics. The results of the study allowed us to make predictions about the success of future independent professional activities and formulate specific group and individual recommendations for the optimal construction of a pedagogical career by our graduates.