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.

Teaching mathematics based on the development of generalized constructs of complex knowledge (for example, modern achievements in science) becomes an effective direction for the formation of student’s mathematical literacy with a significant applied and mathematical-informational potential of personal development. At the same time, the task is to create a rich information and educational environment for teaching mathematics by changing the content of educational programs in the direction of the possibility for students to master of complex knowledge generalized constructs in the context of information support (including remote environments), the implementation of mathematical and computer modeling symbiosis with the effects of universal educational actions formation and student’s mathematical literacy. Such a technology of mathematics teaching organizing is actualized during the stage-by-stage research and adaptation of complex knowledge generalized constructs to school mathematics based on the criteria for selecting modern achievements in science with the included effect of practice-oriented subtasks solving and the ability to interpret the situations from real life: that is, to solve a wide range of tasks in various spheres of human activity, communication and social relations. The visual modeling concept of mathematical objects and processes of educational paradigms integration for complex knowledge development and student’s mathematical literacy formation is the foundation of personal experience and the core actualization of universal educational actions manifested in the corresponding student’s cognitive activity. The authors have developed a technology for student’s mathematical literacy formation (including in primary school) based on the development of complex knowledge mathematics. The features of complex knowledge phenomenon in teaching mathematics and universal educational actions underlying the development of generalized constructs and student’s mathematical literacy formation are revealed. The founding clusters of research and adaptation of complex multi-level knowledge, methods and tools hierarchies in student’s cognitive activity based on didactic rules and patterns of mastering mathematical activity concern with synergetic approach are constructed. Educational practices have shown the high efficiency of this method of student’s mathematical literacy forming in mastering process of modern achievements in science adaptation. Such didactic solutions and practices are characterized by the ability to fully meet the needs of each student in self-education and self-actualization. So we master the essence of complex knowledge constructs adaptation to school mathematics and set the value of personal imperative development, including mathematical literacy.

Introduction. Mathematics teaching based on the development of complex knowledge generalized constructs (for example, modern achievements in science) becomes an effective direction for the formation of school student’s mathematical literacy with a significant applied and mathematical-informational potential of personal development. The purpose of the study: to develop a technology for student’s mathematical literacy formation during the development of complex mathematical knowledge and in the context of universal educational actions actualization by means of mathematical and computer modeling. Materials and methods. The research materials are based on the historiogenesis and actualization of mastering processes of complex mathematical knowledge by students as an effective mechanism for personal development. A synergetic approach, digitalization tools and visual modeling methods are being implemented to adapt the mastering processes of complex knowledge to school mathematics with the effect of student’s mathematical literacy forming. The choice and justification of methods for personal experience founding create the effect of core actualization of universal educational actions, manifest themselves in the processes of students ' activities individualization. The results of the study. For the first time, a technology for student’s mathematical literacy formation based on the symbiosis of mathematical and computer modeling in mathematics development of complex knowledge has been developed. The founding clusters and research and adaptation technology of hierarchies of complex multi-level knowledge (including modern achievements in science) to school mathematics are constructed. The stages and means of visual modeling and personal experience founding with the effect of student’s mathematical literacy forming in a rich information and educational environment are clarified. Conclusion. Educational practices have shown the high efficiency of this method to school student’s mathematical literacy forming in the process of modern achievements mastering in science. Such didactic solutions and practices are characterized by the ability to fully meet the needs of each school student in self-education and self-actualization when complex knowledge constructs mastering and set the value imperative of personal development, including mathematical literacy.

La búsqueda de los medios efectivos para mejorar la formación de un profesor de matemáticas condujo a la idea de crear proyectos por parte de los estudiantes demostrando la metodología del trabajo del profesor con el alumno en la tarea, el teorema o el texto del libro de texto. El artículo resume los resultados del estudio experimental. Los métodos de experiencia subjetiva colectiva y modelado visual se consideraron básicos. El formulario de presentación del proyecto fue una presentación en computadora, cuyos efectos de animación permiten la creación consistente de imágenes gráficas, así como la organización de una pausa en el diálogo del docente con los estudiantes. Las condiciones para asegurar el éxito de los estudiantes en el desarrollo del proyecto son las siguientes: 1) Observancia de las etapas del método de experiencia colectiva del sujeto; 2) Formulación de la tarea al proyecto metódico, que refleje los requisitos para los resultados de su creación; 3) Razonabilidad de las decisiones metódicas según los requisitos del enfoque de la actividad y la capacitación orientada personalmente. Los requisitos del enfoque de actividad son los siguientes: 1. La existencia del objetivo como un resultado de actividad planificado; 2. Uso de bases indicativas de actividad, formuladas en forma generalizada; 3. Desarrollo de pasos individuales de actividad. Los requisitos de la capacitación orientada a la persona son los siguientes: 1) Orientación de capacitación para enriquecer la experiencia de los estudiantes en el tema (Yakimanskaya, 2014). 2) Garantizar la posición de liderazgo de los estudiantes en la actividad cognitiva y reflexiva; 3) Cumplimiento de los requisitos para la organización del diálogo de formación (motivación de las preguntas, su naturaleza general, conectividad, enfoque y naturaleza del diálogo etapa por etapa, registro de la experiencia personal de los estudiantes, iniciativa de los estudiantes) y posibilidades del polílogo).