, theory of functioning and development of systems of pedagogical interactions, diagnostic levels, stages, modules Abstract:It is shown that the selection of a controlled single circuit of the criterion-correctness in training in the content of education of Bachelors in physical and mathematical areas and its methodological implementation through a six-level mechanism of the theory of functioning and development of systems of pedagogical interactions has innovative characteristics with the potential of widespread adoption. The integration of the educational system solves in its plane the problem of object separation in mathematics education, contributes to the formation of a holistic picture of the world, the realization of the idea of incomplete knowledge. Didactic characteristics of a system: practical and methodological relevance, meaningful value, didactic logic of construction, clarity of installations and diagnostics, performance, optimality, the possibility of creative reproduction, and the possibility of technologizing system monitoring.
:In the modern theory and methodology of teaching mathematics, the theoretical basis for the application of problems in the learning process is developing. In particular, the traditional view on the species composition of tasks is also changing. Their new species are proposed. A few years ago, elements of the theory of probability and mathematical statistics were strongly included in the school course of mathematics, a significant part in the study of which consists of stochastic problems. These tasks should be not only an integral part of the stochastic educational material, but also get a full description in the general theory of school math problems. In particular, this article shows that stochastic problems fully satisfy the species diversity of problems in a school mathematics course.
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