Development of methodical support of hybrid intellectual system with cognitive modeling of design and research activity of schoolchildren in mathematics. Construction of this system is carried out on the basis of integration of thinking profiles, modified with the development of learning technologies in the context of digitalization of education, and typology of levels of project-research activities of schoolchildren in intellectual knowledge environment (search and reproductive, empirical, theoretical). When forming the content of the system were taken into account the personalized profiles such as: symbolic, geometric, specific, computational, historical and genetic. The filling of the system was determined by research tasks on the main sections of the topic «Complex numbers». Tasks were selected in the context of cognitive characteristics and principles of personalized profiles, their accuracy and ability to reflect the student’s preferences and needs.