The article is devoted to the challenge of bridging the knowledge gap on computer science in context of the Kazakhstani education. The authors discuss the main reasons of gap in knowledge on computer science at first-year students and suggest suitable teaching to solve the indicated challenge. The considered teaching is based on the principle of continuity to teaching which provide correlation between various levels of education and improving the effectiveness of teaching. The different levels of the students’ learning outcomes on computer science is considered as one of the most important cause of the investigated challenge. For this reason, the authors investigate the educational process design and the differentiated learning methodology using the Google Classroom technology aimed to the bridging knowledge gap in computer science.

Abstract— Learning the basics of financial computation to improve financial literacy of students in school mathematics is not enough to deepen modern eco-nomic knowledge and its correct application in life practice, which requires a more comprehensive view of the process of teaching mathematics. The purpose of the research – to prepare a teaching guide during the process of studying math-ematics in high school on the formation of financial literacy skills. Research methods - expertise and pedagogical experiment, theoretical, methodical and mathematical analysis of educational and methodical complexes and manuals, textbooks used in schools of the country, scientific and theoretical problems, philosophical, psychological and pedagogical, methodical and mathematical litera-ture aimed at teaching the basics of financial literacy in mathematics classes. Re-sults - methods of teaching the basics of financial statements in mathematics les-sons in high school will increase not only students' knowledge of mathematics, but also the level of knowledge about financial calculations and their interest in learning and their ability to read, the quality of knowledge acquisition and their ability to increase their financial literacy. The results of the study can be used to train future mathematics teachers in secondary schools and higher education institutions, to improve the teaching content and methodology of mathematics, and to improve the professional development of teachers.

In today's rapidly changing world of innovative technologies, it is necessary to search for means of modernization of educational process, where along with implementation and constant improvement of new technologies and software it is also important to update the content of education system as well. The modern and developing education institution requires experts in the various related fields. First, it is necessary to know the modern innovative technologies; second, to employ these technologies in various sectors and activities. With regard to the above, the content of education programs with respect to the development of the promising areas should be revised these days. The given article analyses the development of educational content in computer science of Kazakhstan, determines the theoretical basis, development and practical realization of introducing the content of computer science in secondary school. The authors of this article introduced information business in the course of computer science with an aim to develop the content of computer science discipline by introducing elements of information business. The content and structure of training in the fundamentals of information business was introduced in the educational process as a separate elective course and as a fragment of general education computer science course.

The article presents theoretical and empirical results of the study of the advantages of adaptive learning. The practice of creating and organizing adaptive learning for students using the «Moodle» platform is considered, and the results of the application of the adaptive learning model in the preparation of first and second-year students in secondary vocational education are presented. The article presents the results of the input, intermediate, and control measures that the control and experimental groups took. The results are presented both in tabular form, indicating the individual achievements of students in points, and in the form of bar charts. Based on the data obtained, it is possible to quantify the progress in the study of the discipline of mathematics and to compare the individual achievements of students. Thanks to a detailed assessment of various aspects of the results of experimental tasks, it is possible to identify with high accuracy the strengths and weaknesses in the preparation of each of the students, to give individual recommendations for further training. The verification of the validity of the coincidences and differences in the characteristics of the control and experimental groups was carried out by using the Kramer–Welch statistical criterion, which demonstrated, on the one hand, the equality of the training levels of the control and experimental groups at the beginning of the pedagogical experiment under consideration, and on the other hand, the significance of the difference in the level of training at the end of the training process through the application of the proposed methodology.

The article presents and describes a tool for the professional development of teachers. Special attention is paid to the subject-methodical section, the implementation of which since 2020 has been taking place in an online form with the use of distance educational technologies. The article describes and presents the concepts of «e-learning» and «distance learning technologies,» and briefly presents the history of the development of distance education in the world. The article contains a description of the advantages of distance learning, as well as an analysis of the difficulties experienced by students of training courses and seminars, and advanced training of distance courses. In the post-industrial world, one of the main qualification requirements is professional mobility, determined by readiness for continuous retraining and advanced training. The education system, designed to ensure the increase of human capital, and increase the efficiency and competitiveness of the economy, should, first of all, prepare people for life in rapidly changing conditions. Therefore, the system itself must keep up with the changes taking place. The main challenge of 2020 was the emergency transfer of the educational process to a remote form using e-learning technologies. The education system did not have time to «group up» and prepare. The implementation of educational programs in a remote format required careful coordination of pedagogical activities and thoughtful administration of the process. The crisis exposed serious substantive and organizational problems in the industry and identified professional-pedagogical difficulties in the field of ICT competence: both at the level of the general user and the level of the general pedagogical component. The pedagogical community has an objective need to master new competencies. We can assume that the current situation will inevitably entail changes in the standards of training and retraining, as well as the emergence of new training programs.