Purpose: to describe the results of a regional study of subject and methodological skills of teachers of mathematics in the Krasnoyarsk Territory; highlight the professional difficulties of teachers in the subject area "Mathematics"; determine a list of corrective measures to eliminate the identified problems. Methods: theoretical (analysis of scientific literature on the problem of research, systematization and generalization of the results of scientific research) and empirical (ascertaining pedagogical experiment, analysis and interpretation of the results). Results: a program for diagnosing the subject and methodological skills of the professional activity of a mathematics teacher was developed. A diagnostic toolkit has been developed, which is based on the following principles: orientation to current educational results and modern requirements for the labor actions of a teacher, a system-activity approach for determining deficiencies in the field of methods of teaching mathematics, the possibility of designing an individual trajectory of a teacher's professional development based on the results of diagnostics. The analysis of the research results and recommendations for eliminating the identified professional deficiencies are presented. Scientific novelty: developed and substantiated an approach to the formation of control and measuring materials for the diagnosis of professional deficiencies in mathematics teachers. Practical significance: the main results and conclusions of the article can be used to create a regional system for monitoring professional deficits of mathematics teachers, as well as to develop modular training programs for teachers that provide personalized assistance to teachers in eliminating professional difficulties.

Statement of the problem. The article analyzes the studies of foreign and Russian authors in the field of diagnostics of regulatory universal learning skills (RULS) of students. It is concluded that there is a shortage of adequate tools for assessing RULS in the process of teaching geometry. The present research is aimed at solving the following tasks: finding a connection between the process of formation of regulatory skills and the formation of subject skills in teaching geometry to schoolchildren; assessment of the educational results of students, taking into account the characteristics of the taught subject. The purpose of the article is to scientifically substantiate and describe the RULS diagnostic tools for students in the process of solving geometric construction problems. The methodology of the study is based on the use of system-activity and personality-oriented approaches to learning; analysis of modern research in the field of diagnostics of personal and meta-subject results of students. Research results. The operational detailing of the students’ RULS is determined and justified; the principles of development of the structural and content RULS map are highlighted. The article describes the relationship between the stages of solving construction problems and RULS, manifested by students in the process of their implementation. Priority regulatory actions are highlighted at each stage. The results of RULS diagnostics among 8-9 grade students, participants of the Regional Olympiad in Geometry named after Prof. S.A. Anishchenko. Conclusion. The structural and content map of students’ RULS proposed in the article corresponds to the principles of completeness of structural elements; takes into account the systemic nature of the formation of RULS, the adequacy of the list of structural elements for the purposes of diagnosis and the choice of diagnostic tools. This map determined the direction of the search for links between the stages of solving construction problems and the operations manifested in the process of their implementation. The article presents a methodology for assessing students’ RULS in the process of solving construction problems on the basis of expert assessment and self-assessment cards. The results obtained can be extended to other groups of students.

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The aim of the study is to substantiate that in order to implement efficient methodological practices of teaching mathematics to middle school students with academic failure risks, it is necessary to refer to certain indicators for the selection of appropriate pedagogical tools. The paper considers the parameters of assessing the efficiency of pedagogical tools for teaching mathematics offered in scientific-pedagogical literature. The scientific novelty of the study lies in the formulation of the notion of a “methodological practice of teaching mathematics” and the identification of the efficiency indicators for methodological practices of teaching mathematics to students with academic failure risks. As a result, the efficiency indicators for methodological practices of teaching mathematics to students with academic failure risks, which are proposed as guidelines for the selection of appropriate pedagogical tools, were identified and characterized.