Introduction. In recent years the development of student’s creativity and self-organization has been the basic trend of mathematical education in schools and universities due to the need of large amounts of information process, the variability and uncertainty of external factors impact, the increasing role of competencies importance in practice-oriented tasks solving. The works of philosophers, psychologists, and teachers show that the main means of these problems solving in modern world can be overcoming difficulties in complex systems and knowledge study by students based on a symbiosis of mathematical and computer modeling (including modern achievements in mathematics, robotics, information and intelligent systems). Pedagogical experience, theory and practice, requests and challenges of real life show that the teacher's readiness to manage the process of mastering complex systems and knowledge in mathematical education plays a central role in determining the various levels of intellectual and personal development success (including the formation of mathematical literacy) of students. The purpose of the study is to identify of teacher’s personal, subject and professional deficits and their meters in readiness for the management and interpretation of student’s complex systems and knowledge as a factor of personality development, using original competence meters in the form of case tests. Materials and methods. Personality-activity, competence-based, integrative and synergetic approaches are implemented, diagnostic materials of case tests for measuring teachers' professional deficits, methods of content analysis, founding of personal experience and visual modeling of determining criteria, features, content and structure of teacher’s readiness to manage the processes of student’s complex systems mastering based on the interpretation of mathematical and computer modeling methods. The results of the study. Revealed that the criteria, content and structure of teacher's readiness to manage of student’s complex systems and knowledge development are identified; teacher’s professional deficits in the readiness to manage of student’s complex systems and knowledge development are identified; approaches, directions and methods for creating a rich information and educational environment for complex systems and knowledge development (including robotic systems, virtual and augmented reality technologies, elements of fractal geometry, fuzzy sets and fuzzy logic, etc.) are developed based on a symbiosis of mathematical and computer modeling. Conclusions. The state of personal, subject and professional competencies expression should determine the teacher’s value-motivational, personal-adaptive, cognitive, procedural and generalizing-transforming readiness to manage the mastering processes and ways of complex systems and knowledge adapting (modern achievements in science) to student’s current state of experience, the presenting variability of generalized constructs forms and means, the possession of methods mathematical and computer modeling, samples and standards of popular applications of complex knowledge to real life, technologies and productions. The experiment was conducted on representative sample of mathematics teachers of Perm Region in Russia with the identification of teacher’s patterns and professional deficits in the context of complex systems and knowledge teaching possibility.