Visual modeling of mathematics unity in tasks

The article presents the development of the innovative training course of united mathematics based on mathematical knowledge consolidation in the course of research activities of future mathematics teachers. The academic discipline bases on the study of integrative connections in mathematics and their transfer to the didactic field of scientific cognition and sustainable learning motivation of students in the context of research of so-called integrative tasks (genesis, content, analysis, application, estimation, presentation), the selection of which is implemented by exposure of the proved criteria. The presentation of the studied material is supported by research and creative activities of the future mathematics teachers in the direction of professionalization, enrichment and consolidation of experience and development of personal qualities on the basis of actualization of personal learning values.