Elena V. Pozdnyakova

In the modern world, the role of mathematics as the universal language of science and communication is increasing. These trends are reflected in the system of school mathematical education: the priority goals of teaching mathematics lie in the field of the subject knowledge formation, meta-subject skills and creativity of students. This actualizes the problem of designing an appropriate educational environment as a set of conditions for student's self-development and self-learning. The openness of the educational environment presupposes the involvement of students in the process of its design; however, the methodological aspects of such joint activities have not been sufficiently studied. The aim of the article is to present the characteristics of the subject educational environment (SEE) as a factor in achieving the priority goals of teaching mathematics in secondary schools using the example of joint design of visual technology with students. To achieve this goal, theoretical methods of scientific research were applied: analysis and generalization of scientific, pedagogical and methodological literature; systematization of the information received; modeling. The following empirical methods were chosen: questionnaires; analysis of diagnostic work of students; presentation of data in graphical form. As a result, the basic principles of SEE design were formulated, its model was constructed, and the author's original approach was tested. The theoretical significance of the research is represented by the formulated principles of designing a subject-based educational environment: student-centered approach; openness of the educational environment; integration of the digital environment, where artificial intelligence is its important component; three-part structure of the educational environment; dosed gamification of the educational environment. The practical significance of the research lies in the development and testing of a model for the joint design of a visual novel game based on probability theory for ninth grade students. The experience of implementing the model is shown by describing each of its stages: identifying emotional triggers for studying mathematics; defining the subject content of a novel; creating a storyline based on storytelling; developing character images using neural networks; choosing a platform and creating a novel; testing the novel and analyzing its results. Checking the effectiveness of the author's approach allowed us to conclude that the novel game has a positive effect on overcoming mathematical anxiety and developing students' subject and meta-subject skills.

The global changes taking place in modern society are orienting the school education system towards the development of meta-subject skills or "soft skills" among students. In this regard, the priority goals of teaching mathematics lie in the formation of not only central mathematical concepts, but also the creative abilities of students, as well as functional mathematical literacy, which is based on universal learning activities. This actualizes the problem of choosing educational technologies that make it possible to achieve the stated goals in their unity, while taking into account the phenomenon of the digital generation. Domestic and foreign studies indicate the high potential of TRIZ technologies for achieving subject and meta-subject educational results, developing students' creativity, and the specifics of blended learning technology correspond to the psychological and pedagogical characteristics of the Alpha generation. However, the issue of the use of TRIZ in the context of blended learning of mathematics has not been studied properly. The aim of the article is to study the experience of implementing TRIZ technology in the model of blended learning of mathematics for primary school students. To achieve this goal, a set of theoretical and empirical methods of scientific knowledge was applied. Theoretical methods included analysis and generalization of scientific, pedagogical and methodological literature, normative documentation; systematization of information; modeling. Empirical methods included the analysis and evaluation of students' diagnostic works, statistical data processing, and graphical representation of data. The theoretical significance of the study is represented by a model of the process of organizing the cognitive activity of schoolchildren using TRIZ technologies and digital tools, based on student-centered and problem-based approaches. The practical significance of the research lies in the development and testing of educational activities based on the integration of TRIZ technologies and blended learning in mathematics. As an illustration of the author's approach, the content of a geometry lesson based on the "Station Rotation" model is given. To test the effectiveness of the methodology, the diagnosis of students' meta-subject skills was carried out using dyadic educational research. The analysis of the results using the statistical criterion of uniformity allowed the author to conclude that the level of development of meta-subject skills in the experimental group increased.

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.