Elena V. Pozdnyakova

In the modern paradigm of school education, the formation of universal learning actions (ULA) among students becomes significant because they ensure a broad orientation of schoolchildren both in various subject areas and in various types of cognitive activity. The Federal State Educational Standard of Basic General Education, defining the meta-subject results of learning the basic educational program, actualizes the task of their formation by means of subject disciplines (including mathematics). Despite the great number of research that touch upon the structural, substantive, procedural, technological and diagnostic aspects of universal learning actions formation among schoolchildren in the process of mathematical training, the systematic organization of mathematical education for the integrated formation of meta-subject and subject skills, self-determination and creative development of all categories of secondary school students has not been sufficiently studied. New educational opportunities for the development of ULA, which are opened on the basis of modern digital technologies, have not been fully realized. The purpose of the article is to present the main ideas of the concept of key ULA formation among students in grades 5 – 9 in the process of mathematical training in the context of digital transformation of education. To achieve this goal, a set of theoretical methods was used, as well as such methods of empirical research as pedagogical observation, generalization of pedagogical experience, and the use of specialized computer programs. The leading methodological approaches in the construction of the author's original concept were chosen systemic (the basis of scientific knowledge), systemic activity-oriented (ensures the development of the student's personality based on the acquisition of universal methods of activity by means of the academic subject "Mathematics"), environmental (ensures the availability of a subject-based active digital educational environment), informational (provides the option of creating individual learning trajectories, application of synchronous and asynchronous technologies and the implementation of models of blended teaching mathematics). The core of the pedagogical concept is represented by the patterns and principles of the formation of key universal learning actions. On the basis of the selected methodological approaches, patterns and principles, the leading provisions of the concept are formulated, which form the ground for designing a model of the corresponding methodological system.

Currently, the basic education system is undergoing transformations related to the establishment of guidelines for the personal development of students and relevant competences, the so-called «soft skills». At the same time, one of the complex tasks of school mathematical education is the integrated formation of meta-subject skills and creativity in school students. The analysis of research on this problem in domestic and foreign literature and educational practice allows us to reveal diverse techniques and methods for developing students' creativity. However, the issue of using the potential of the digital educational environment remains relevant, which allows us to enhance the effectiveness of this process, taking into account the characteristics of the modern generation of adolescents. The purpose of the article is to present a methodology for developing and evaluating students' creativity based on themed web quests in the process of mathematical training in grades 7-9. A set of scientific methods was used to achieve this goal. The theoretical basis of the study consisted of: analysis and generalization of scientific, pedagogical and methodological literature in order to determine the main provisions of the studied problem; systematization of the information received; modeling. Empirical methods included questioning of students for self-assessment of meta-subject and creative skills; analysis and evaluation of students' creative products; primary static data processing, their graphical representation (in the form of diagrams) and comparative analysis. Personality-oriented and problem-based approaches were chosen as the leading methodological approaches in the design of themed web quests, and gamification technology was chosen as the leading educational technology. Based on the selected approaches, the characteristics of the original author's web quests were identified: integration of personal and game context; priority of creative development; maximum visualization; thematic focus; problem-based part of the tasks; digitalization of content; creation of quest plots based on the children's film and game industry. To illustrate the characteristic features of the content of the designed web quests, the author gives examples of geometry quest tasks for 7th grade students created using the Google Sites website builder. A methodology for evaluating the creative component of the quest results (creative product) is presented; criteria and indicators for determining the level of «small» creativity of a student («Follower", «Initiator", «Strategist") are defined. To illustrate the author's methodology, the results of testing a web quest for 8th grade students on the topic «Square» are presented, and a primary statistical analysis is shown to assess the creativity of students.

In accordance with the requirements of the Federal State Educational Standards of Higher Education, educational organizations face the task of introducing effective tools for systemic cognition of the world and critical analysis of objective reality, solving complex problematic tasks by future specialists. Research in the field of the formation of processes and the development of information and mathematical competence can help in solving the task. The aim of the study is a model representation of information and mathematical competence and the process of its formation among undergraduate students, as well as an illustration of some elements of the methodology for the formation and evaluation of such competence with the involvement of a regional component. The processes of both mathematical and information competence formation in the system of basic, secondary general and higher education in the context of integration with other competences of university students are clarified by the method of theoretical analysis. The need to adjust the structure, content and model for the formation of information and mathematical competence in the context of the digital transformation of society as a whole is determined. The information and mathematical competence of a bachelor is evaluated through a set of competences, its structural components are considered from the point of view of an activity-based approach. Thus, the data obtained will be the basis for the design of the model. Building methodology for the formation of information and mathematical competence on the ground of competence-based, practice-oriented and personal approaches integration, a regional component is introduced into the content of competence-oriented tasks, when the problem situation presented in the task is not only characteristic of the student's daily academic and extracurricular life, but also reflects the peculiarities of the region (cultural, historical, socio-economic, environmental, natural, etc.). An assessment of the effectiveness of group work with the author's case task including a regional component was carried out by means of a pedagogical experiment for a comprehensive and differentiated assessment of the level of formation of the IMC. Illustrating the elements of the experimental methodology, we conclude that further research in the field of information and mathematical competence formation is promising.

Modern school education actualizes the issue of functional literacy formation, the system component of which is mathematical literacy. Despite the numerous and diverse studies of this problem in domestic and foreign literature and educational practice, the issue of workig out a methodology for teaching students practical applications of mathematics based on the development of meta-subject skills implemented in the unity of the classroom and extracurricular activities of students remains relevant. The purpose of the article is to design a model of an extracurricular activity course in a digital educational environment aimed at the development of meta-subject skills and mathematical literacy, and its demonstration on the example of the author's digital resource of the training course for the ninth grade. To achieve this goal, a number of scientific methods was used. The theoretical basis of the research are: analysis and generalization of scientific, pedagogical and methodological literature in order to determine the principal tenets of the studied issue; systematization of the information obtained; modeling. A survey (in the form of a conversation) of Kuzbass mathematics teachers was used as an empirical method. The principles of designing the training course were based on practice-oriented, personality-oriented and problem-based approaches. The formulated principles determine the specifics of the design model of the training course, which includes target, content, technological and effective components. Based on this model, a training course for ninth grade students “Formation of mathematical literacy: Mathematics in the city of N” was worked out. The practice-oriented meta-subject tasks are the core of this course’s resource component. To implement the course in an online format (the “blended learning” model), it is proposed to use a digital resource created and functioning with the help of online services (Google Sites, Yandex, CORE, GeoGebra, Learningapps, GoogleForms). The analysis of the users’ survey allows the authors to conclude that the use of the designed digital resource will contribute to improving the didactic potential of the extracurricular training course for the development of meta-subject skills and mathematical literacy.

In accordance with the requirements of the Federal State Educational Standards of Higher Education, the training of specialists with universal competences in the field of systemic and critical thinking is of particular importance. At the same time, mathematics, as a tool for systemic cognition of the world and critical analysis of objective reality, plays a particularly important role in education. The purpose of the study is to present a model of information and mathematical competence formation (on the example of student teachers) and to evaluate its effectiveness by methods of statistical analysis. A hypothesis about the predictive role of information and mathematical competence (IMC) in the development of students' critical thinking is suggested. The concept of information and mathematical competence was clarified with the method of theoretical analysis, its characteristic features and structural components were defined. It is proposed to design a model for the formation of an IMC based on the principles of compliance with the key competences of the future, the requirements of the federal state educational standard and the corresponding professional standards. Thus, this model includes target, content, technological and effective components. The target component actualizes the formation of the IMC as willingness to apply mathematical knowledge, skills and abilities, as well as ICT tools for searching, critical analysis and synthesis of information, solving complex problems in professional and subject areas; the tasks of forming a creative educational environment and designing a program and diagnostic tools for monitoring the dynamics of the considered competence development among student teachers are concretized. The content component reflects the invariant and variable components of the curriculum, which are revealed in the disciplines of the compulsory part and the part formed by the participants in educational relations. The technological component reveals methods and technologies, as well as forms and means of teaching. The effective component is presented in three aspects: motivational-value, emotional-voluntary and reflexive ones. The effectiveness of the designed model in the point-rating system was assessed by means of the pedagogical experiment. The correlation analysis methods reveal the relationship between the levels of IMC development and critical thinking of student teachers. The conclusion is made about the prospects of further research in the field of designing a model for the formation of information and mathematical competence as a predictor of critical thinking in the system of higher education.