The article presents the issues of school environment expertise and discusses the possibilities and prospects of using digital tooling for its assessment in mass educational practice and scientific research. The proposed method of vector modeling of the environment of personality development allows determining the activity of the individual in mastering educational resources in various types of environments. This digital tooling allows school management teams and organizational consultants to conduct management and pedagogical analysis of the current status and complementarity of various system components of school environments with each other, as well as with the school’s mission, and implement their managerial and vocational design; to develop programs for the progression of school organizations based on environment methodology using expert project management technology; to carry out organizational and pedagogical consulting of schools taking into account the “built-in” nature of environments of various levels (the environment of the lesson, class, club, school, and educational complex).

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We present the experience of reflexive activity approach to the preparation of future teachers to work on the management of project and research activities of younger schoolchildren. The theoretical basis of the research conducted at the university school of the Moscow City University is revealed. The description of an empirical stage of research of process of acquisition by bachelor degree students of the important labor functions focused on development of cognitive interests and cognitive abilities of younger schoolchildren is stated. The described program includes several interrelated blocks: theoretical block of the course “Research and Project Activities of Schoolchildren”, training research abilities, independent research practice of students and monitoring research activities of students. The experiment showed a high level of readiness for the management of research and project activities of younger schoolchildren. In addition, the generalized reflective data obtained during the training of students of different courses. As a result, we discovered that the training of students in the framework of reflexive activity approach creates conditions for the formation of future teacher’s competencies, the most popular in the modern labor market, the so-called “future skills”: general research skills; critical thinking; communication skills; teamwork skills; creative approach; skills in situations of uncertainty and risk.

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The article presents a description of the study of the effectiveness of methodological tools aimed at developing metacognitive competence in future elementary school teachers in the classroom on the methodology of teaching mathematics to younger students.The aim of the study is to empirically test the effectiveness of a set of methodological techniques used in the classroom on the methodology of teaching mathematics to future elementary school teachers as a means of developing their metacognitive competencies. The hypothesis of the study is the assumption that one of the effective means of developing metacognitive competencies in future elementary school teachers is special classes for compiling original scenarios of verbal mathematical problems for younger students. A professionally developed verbal composition of a mathematical problem sets the vector of mental activity for the younger student. It requires the developer to build a forecast of the child’s mental actions, determine algorithms and levels of difficulty in obtaining the right solution. The study used methods for testing students’ cognitive characteristics (intelligence) and peer review of their “metacognitive knowledge”, “metacognitive skills”, “metacognitive experience” and “metacognitive strategies”. The methodological solutions implemented in the classroom have shown their effectiveness. For the practice of preparing future primary school teachers, it is important that the well-organized development of compositions of textual mathematical problems for younger students is an effective means of developing their metacognitive competencies.