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The article is devoted to the problem of increasing the cognitive activity of students in the current environment of preparing future specialists in accordance with the Federal State Educational Standard of the Secondary Education and the Federal State Educational Standard of Higher Education in teaching mathematical disciplines. The article shows that in the psychological-pedagogical literature cognitive activity is considered both as a personality trait and as a student's activity. The author's definitions of students' cognitive activity¿ and educational-cognitive activity of students¿ are formulated, their correlation is shown. The levels of formation of cognitive activity are highlighted: reproducing, interpreting, searching, and creative. A set of indicators of these levels has been formulated in accordance with the motivational, content-operational, value-volitional and evaluative components for didactic monitoring. The pedagogical conditions for the activation of students' cognitive activities in mathematical subjects have been established, which are the implementation of a differentiated approach and the application of pedagogical technologies, methods and techniques (the use of educational and technological maps, the technology of a portfolio of achievements, the propaedeutics of the professional competencies formation by means of mathematical problems, historical excursions, independent work of students), as well as didactic monitoring of cognitive activity. Experimental testing of pedagogical conditions has demonstrated a positive dynamics of changes in complex indicators of motivational, content-operational, value-volitional and evaluative components. The research results can be used in teaching mathematical subjects in higher educational establishments and specialized secondary-education institutions.students'