Elena V. Pozdnyakova

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.