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The research is relevant as educational computer games are included in students' mathematical activity and form additional opportunities to improve the quality of teaching mathematics in a digital school, to support the formation of the demanded professional competence - computational thinking. To form the appropriate skills that determine the essence of special computational thinking, the authors propose to include game educational spaces based on digital gamification resources into students' mathematical activities. The research aims to resolve the contradiction between requirements of the modern economy for specialists' high level of computational thinking and an insufficiently developed methodological base for training graduates that meets these requirements. The purpose of this research is to study the features of using gamification technologies in teaching mathematics to form the skills and abilities that make up the essence of computational thinking. The article describes directions of educational and cognitive mathematical activity based on the principles of gamification. The authors clarify the concept of "computational thinking", which includes a system of actions for activating patterns, connections between them from human memory, and compile an effective algorithm for solving them: to obtain relevant information on advanced technological developments; to state the problem and model; to use a software product with mathematical content.

The problem that the given paper aims to solve is associated with the need to resolve the contradiction between the requirements of the digital economy for a high level of computational thinking of specialists of the future and an insufficiently developed methodological base for training graduates that meets these requirements. The purpose of the research is to theoretically prove and experimentally verify the need for the use of gamification technology in training of specialists of the future to form computational thinking skills which are most in demand in the digital society. The research methodology includes the analysis and generalization of scientific works on the problem of determining the phenomenon of computational thinking, the use of digital gamification resources in training, and clarifying the requirements for training of highly qualified specialists of the future. The HTML 5 language was used as a software tool. The pedagogical experiment is presented on the example of the assessment of changes in the levels of skills that make up the essence of computational thinking. Results: The paper clarifies the concept of computational thinking and describes the directions of educational and cognitive activity based on the gamification principles which most effectively form computational thinking. The authors formulate didactic principles for the inclusion of computer games to foster students' cognitive activity, support professional self-determination, and develop systematic and critical thinking. Specific materials are proposed to improve the methods, tools, and organizational forms of the training focused on the formation of computational thinking as the basis for the supra-professional skills of specialists of the future. In the end, conclusions are made which confirm that the included educational and cognitive activities on game designing in the training of highly qualified specialists of the future fosters the formation of computational thinking skills.

The study is aimed at solving a problem generated by the necessity to change the organizational forms of digital learning to prepare graduates who meet the requirements of today's labor market; who are equipped with teamwork skills and skills of project-management under uncertainty which are especially relevant nowadays. The purpose of the study is to provide a theoretical foundation for and experimentally verify the effectiveness of involving students in project teamwork on designing smart applications by means of modern digital technologies; project teamwork activities allow developing the skills and abilities characteristic of a strong research culture necessary for making future discoveries in science and technology. The research methods are the analysis and generalization of psychological and pedagogical literature, of development strategies and education theories; mathematical methods of statistics, psychodiagnostics and survey methods. The pedagogical experiment is illustrated by the example of assessing the development of teamwork skills, project management skills, and programming skills which form the basis for professional self-realization of graduates. The study results. The study specifies the concepts of the ability to work in a team and smart application in the context of training professionals for digital economy. The didactic potential of project team work in the sphere of self-realization of graduates is described. The authors reveal the characteristics, principles, and stages of team work on the project aimed at designing a smart application. They offer their recommendations regarding the process of planning and organizing team activities, specifying the skills and abilities necessary to help a person succeed in today's digital society and to get a profession which is in demand on the labor market. The authors draw a conclusion that project teamwork meets the requirements of digital education and contributes to successful professional self-realization of university graduates if it is well designed, accurately planned, and monitored by the educator to the extent necessary.

The relevance of the research is due to additional opportunities to improve the quality of teaching mathematics in a digital school, support professional orientation and self-determination of young people through the inclusion of mobile services and platforms in mathematical activities. The research problem is determined by the following contradictions: 1) between the capabilities of modern digital technologies in terms of improving the quality of mathematical training, the formation of universal skills required by the economy of the future, and the model implemented by educational institutions; 2) between the need to provide resources for solving problems of a socio-economic nature in the conditions of the fourth industrial revolution and the insufficient level of mathematical literacy of graduates. The purpose of this research is to study the didactic potential of mobile technologies to support mathematical education in a digital school while preparing specialists of the future. Moreover, the research offers a methodological approach to organize project activities of developing applications in terms of increasing the effectiveness of teaching mathematics and vocational guidance. The article clarifies the concepts "mathematical thinking", "mathematical literacy" for a digital school and describes the didactic principles of incorporating mobile resources into the educational space which increase the efficiency of training engineers of the future, support vocational guidance and self-determination. The author offers methodological methods and recommendations for organizing creative interdisciplinary project activities in order to develop mobile applications that contribute to the formation of qualities and skills forming the basis of mathematical thinking. The materials of the article can be used: firstly, to ensure the personalization of mathematical training in the course of creative, interdisciplinary, cognitive research activities of students while developing mobile applications, social integration and vocational guidance; secondly, to change the concept of mathematical education at school; thirdly, to improve the implemented model of education based on the traditional trajectory "preschool education-school-university-additional education" in the context of the new requirements of business, society, and the state for the training of highly qualified professionals in the professions of the future.