Improving the efficiency of the students' learning process, finding ways to activate their independence, the teacher and the student entering into a productive dialogue are topical issues of modern education. In the conditions of the credit system of teaching students, the main tasks are to unify the amount of knowledge, create conditions for maximum individualization of training, strengthen the role and effectiveness of independent work of students. We believe that students' mastery of self-control and mutual control skills through the use of criteria-based assessment technology is extremely necessary, and the use of criteria allows us to assess the advantages and disadvantages of specific assessment procedures. The article describes the results of a pedagogical study conducted by the authors among students of the 1-2 courses of the Innovative Eurasian University, where the method of  L.V. Baiborodova was chosen as a tool to identify problems of interaction between a teacher and students. In the course of the study, the problems encountered by students in the learning process were analyzed, algorithms for organizing and conducting lectures and practical classes were proposed, allowing the teacher and the student to build an effective interaction process, the results of testing the proposed algorithms were described. The conducted experiment showed that the use of criteria-based assessment allows  to effectively organize pedagogical interaction at the university.

The need to understand the concept of critical thinking grows out of the requirements for a modern person, in addition, critical thinking is an important component of the state strategy for the development of education and science of the Republic of Kazakhstan. We are convinced that this topic will develop together with the educational system of our country. The monitoring study presented in the article is the first in Kazakhstan, its purpose is to find out how successfully the concept of critical thinking as a way of thinking has been conveyed to students over the years since the adoption and implementation of the updated content of secondary education program. The study compared two groups of students: those who studied and those who did not study according to the updated content of secondary education, in order to find out how effectively the concept of critical thinking was learned by students. According to the monitoring results, there was no significant difference between the two groups of students, but the respondents' answers showed that there is a persistent non-distinction between such concepts as decision-making in emergency and critical situations, analysis, conclusions, self-regulation, speed of decision-making and success in the exact sciences in the perception of the concept of "critical thinking". At the end of the article, recommendations are given for further use of the obtained data for other studies.

Only with logically correct thinking and understanding, we distinguish between cause-and-effect relationships, dependence on each other, the origin and path of development of things around us. The process of logically correct thinking expands the student's ability to treat his assumptions skeptically and critically, thereby deepening and expanding his understanding of the world, existence and being. The logical process is the result of scientific knowledge of the world, memorization of objects and phenomena of the external world in the human brain, consideration of the correct forms and laws, rules of this image. Logical methods of thinking cannot be formed independently from the day children come to school, for this the teacher must lay the foundations of logical knowledge and skills. It is necessary to work out the material, describing each action taking into account the age capabilities of children, hence the use of a large number of logical tasks in teaching is an important factor in quality learning. And the assimilation of logical techniques, forms of thinking, concepts, judgments to primary school students by conclusions is provided by the primary school program. This article discusses the pedagogical prerequisites for performing a system of tasks in the main subjects of primary school as a way of forming logical thinking skills of younger schoolchildren, skills and means of practical study of logical concepts.

There is a significant increase in the number of children who do not have developed writing and reading skills among primary school students. "Specific" violation of written speech, that is, dysgraphy, is a serious obstacle to the development of the school curriculum by primary school students, which does not allow at a certain point in time to fully master the educational program in a number of academic subjects, so the identification and correction of dysgraphy is one of the urgent problems. The article examines the writing process from a neuropsychological point of view and highlights the special stages of the writing process. The definitions given by the authors in connection with the violation of the writing process are analyzed, the classification of dysgraphy is briefly described, the importance of timely detection of violations of written speech and the development of appropriate correctional work taking into account the neuropsychological approach is emphasized, modern manifestations and promising areas of the study of dysgraphy are considered based on the analysis of theoretical sources. Defining the concept of "innovation", the significance of one of the innovative approaches to the correction of dysgraphy – the use of cerebellar stimulation-is described, that is, the models of performing exercises in the" balametrics " complex are shown. The article describes the methodology and results of the ascertaining and formative experience conducted on the basis of the analysis of errors that occur in the writing of primary school students studying in the Kazakh language.

Currently, the problem of teaching genetics through students’ independent work is one of the most important areas of higher education. In this article, we offer several methods and techniques for organizing students’ independent work  on the subject of genetics in a multilingual education. The methodological improvement course of the biology subject  is comprehensively studied from year to year and the results are being published. From this point of view, analyses were conducted on the biology teaching at the university and the independent work of foreign and domestic scientific works in recent years. The article presents the experience of teaching genetics based on the independent work organization of future biology teachers in the conditions of multilingual education at Abai University. The results of experimental studies aimed at testing the effectiveness of independent work have been presented. The analysis of the studies made it possible to conclude that the methodological training of biology students as an object of pedagogical research should include various professional training system aspects. The teaching genetics process in English through independent work encourages students to further in-depth subject and language study.

The article describes the problem of low availability and inaccessibility of new information technologies in the Kazakh language in universities, analyzes the pros and cons of electronic textbooks based on theoretical data. The textbooks used by teachers show the effectiveness and usefulness of multimedia, in order to make them more valuable, it is necessary to add digital resources, such as academic games and interactive websites. The questions of the popularity of textbooks compiled using a computer are touched upon, the analysis and testing of programs for compiling electronic textbooks is carried out. The importance of methodological support of the textbook in the creation of electronic information tools is analyzed. Automation of all the main stages of training with electronic textbooks is provided before monitoring the content of the educational material and making recommendations for final grades, thanks to which all mandatory educational materials are replaced by bright, interesting, with a share of intelligence game moves, i.e. widely used multimedia, including interactive and voice. For students and teachers of chemistry, the authors have compiled an electronic textbook in the Kazakh language, the effectiveness of the textbook has been analyzed and studied in accordance with theoretical data and surveys, according to the results of the study, positive indicators of the assimilation of educational material have been demonstrated.

The paper substantiates the need for the formation of a logical and algorithmic culture of students, which contributes to the conscious perception of educational material, which is adequate to modern school and university education in order to instill information and computer literacy in the younger generation. Teaching students to generalize, systematize, apply logical knowledge in a new situation, transfer the acquired knowledge from one subject to another is one of the main tasks of a modern school. At the same time, the logical and algorithmic level of their assimilation provides such a quality of knowledge as completeness and effectiveness, i.e. the student can list all the leading elements of knowledge, define each of them, characterize their main features, and also perform tasks on the topic using the acquired knowledge and skills. The generalization of the practical experience of the organization of the educational process allowed us to offer methodological recommendations for the organization of the formation of the logical and algorithmic culture of students on the basis of interdisciplinary connections in the process of teaching natural science disciplines. In the article, this technique is implemented with the help of one of the new forms of organization of classroom work at the university – complex seminars. The plans of conducting complex seminars on the topics "Harmonic oscillations" and "Integral and its application in physics" are given.

The study presented in the article analyzes and summarizes world experience on the problem of implementing criteria-based assessment in education; the system of risks of using criteria-based assessment in educational practice is revealed; the analysis of methodological recommendations and teaching aids used by teachers of Kazakhstan in organizing the assessment of educational results of schoolchildren was carried out; a focus group survey was conducted to identify problematic aspects of educational assessment in teaching mathematics to schoolchildren. On the basis of the study, we have to state that despite the broad potential benefits of assessment based on criteria, problematic aspects of the ill-considered use of such assessment in educational practice inevitably arise, the study of which is not given sufficient attention by Kazakhstani scientists and teachers. The effectiveness of the use of criteria-based assessment in educational practice depends on many factors: the unambiguity and clarity of the assessment criteria, their unified interpretation by evaluators; the conformity of methods, tools and evaluation materials to the subject area; the level of competence of teachers as evaluators. The introduction of a new assessment system should be associated with constant work on the creation and improvement of assessment tools and procedures, with the study of the most effective practices of criteria-based assessment, their adaptation to the realities of the Kazakhstani education system.

In the article, adapted to the school course, the second order linear differential equations with constant coefficients and trigonometric free terms are investigated. The basic elementary methodological approaches to solving the equation are given. The solutions of the second order linear differential equation with constant coefficients and trigonometric free terms are investigated, which is a model of many phenomena. In addition, the applied values of the equation and its solutions were noted. The results obtained are presented in the form of theorems. The main novelty of the study is that these results are proved and generalized by elementary methods. These conclusions are proved in the framework of the methods of high school mathematics. This theory, known in general mathematics, is fully adapted to the implementation in secondary school mathematics and developed with the help of new elementary techniques that are understandable to the student. The main purpose of the research is to develop methods for solving a non-uniform linear differential equation of the second order with a constant coefficient at a level that a schoolboy can master. The result will be the creation of a special course program on the basics of ordinary differential equations in secondary schools of the natural-mathematical direction, the preparation of appropriate content material and providing them with a simple teaching method.

The article considers the essence of the concept of mental activity, analyzes the problem of human thinking, shows the role of building tasks in the formation of mental activity of secondary school students. The main feature of the construction tasks is that they develop search skills for solving problems, introduce them to feasible independent research, contribute to the development of geometric representations and the processing of knowledge, skills, thereby strengthening not only the applied orientation of geometry teaching, but also the polytechnic one. Construction tasks do not allow a formal approach to them, they create a problematic situation that needs to be solved, as a result of which the level of mental activity increases. Pedagogical experience shows that due to lack of time, teachers do not see the need to return to the construction tasks, and school textbooks pay little attention to the construction tasks, so elective classes and elective seminars on this topic are necessary. The optimal number of classes should be 10 hours, especially for grades 7-9. The authors tested their own methodology (ascertaining, forming and control stages) among students of the 7th grade of one of the schools in Uralsk.

In this article, we will consider the parallel implementation of the Yanenko algorithm for the two-dimensional heat equation, and the sweep method was used to numerically solve  the heat equation. The implementation of the sequential  program is carried out simply in two-part steps by the longitudinal-transverse run, however, parallelization of two fractional  steps with an indefinite scheme is difficult due to the creation of inter-process communication of data. In the course of the study, a parallel data distribution with one-dimensional decompositions is shown in the application of the Yanenko method for calculating heat conductivity. The results of parallelization of this task using the 1D decomposition were obtained and acceleration and efficiency images were analyzed in order to evaluate the parallel program. Currently, modeling of processes by numerical solution of differential equations is widely used in every field of Science, the most common methods bring the differential problem to a system of linear algebraic equations, methods that solve such systems include various startup options. The emergence and development of computing systems using Multi-Core processors and graphics accelerators make the problem of startup parallelization relevant; the results of the study are used for teaching in research institutes and universities.

This study aims to create a classifier using machine learning methods that determine the psychological type of people based on the text published on social networks according to the Myers-Briggs Type Index classification. The article is based on the implementation of automation of the task of determining the personality type using machine learning, with an explanation for determining the characteristics of a person using the MBTI personality indicator. The methods of logistic regression, random forest and support vector machines were used, and a literary analysis of similar works was carried out. The article presents the progress of research work and the results of each classifier, as well as an analysis of the approaches used. In the context of the current quarantine restrictions, such studies can be of great help in the selection of personnel in companies due to the transition of people to an online format of work, since the study involves determining the personal qualities of people based on their posts in social networks. In this paper, the most effective machine learning algorithms for the Kazakh language, which are simple to use and do not require a lot of computing power, were used and, accordingly, the results of the work for each method were presented, among these methods, the accuracy and reliability of the classifier for the Kazakh language by the method of support vectors were at a good level.

The article emphasizes the importance of conceptual study of terms that have linguistic meaning. In particular, one of the concepts reflecting the worldview of the Kazakh people was the concept of "amanat". For the cognitive disclosure of the concept of amanat, it is necessary to give a binary oppositional pair formed by the concept of "kiyanat" (abuse, violence), through which it is possible to determine the meaning of the concept of amanat for the people. To determine the application of the concept of amanat in the XIX-XX centuries, work was carried out with sources of that period, for example, the concept of amanat, found in the works of the traveler F. A. Fielstrup, the historian E. Bekmakhanov, describing that time, reflects the worldview of the people, as well as the analysis of proverbs and sayings that are firmly entrenched in the minds of the people, is widely reflected in this article. Kiyanat is widely discussed as a concept denoting violence, injustice, imperiousness and arbitrariness committed by a person when it is believed that the moral qualities of the offended person are destroyed. The concept of kiyanat forms a binary oppositional pair to the concept of amanat, hence we have grouped the types of abuse against a person, violence against oneself - an insult to the senses, lies, rude speech as an insult to the language. To determine how deeply modern society understands the concepts of amanat and kiyanat, a sociological survey was conducted, the results of which are presented in this work.

Even the groundswell of interest in mobile applications has not so far contributed to their integration into educational programs as an EFL learning tool. The purpose of the present review is to identify the current state and prospects for the use of mobile technologies in EFL teaching. The methodological basis of this research is a theoretical analysis of the literature data on the research topic. The evaluation of contemporary empirical studies conducted in Australia, China, Iran, Turkey, Saudi Arabia, Cyprus, Japan, Malaysia, Spain, Taiwan and other countries, has led to a conclusion that the implementation of mobile technology in EFL teaching gives predominantly positive results due to several merits of mobile devices relative to standard pedagogical tools. It was however underlined that researchers have yet to learn how to conduct methodologically sound, statistically relevant studies that would cover aspects of learning activities beyond the use of mobile technology. The authors conclude that when studying applications, researchers should not try to find a mobile application that can teach students everything they need, but should study the ways in which individual applications help to master a foreign language.

Ecodesign is a direction in design and architecture aimed at protecting the environment, creating a comfortable human environment in harmony with nature. The article deals with the issues of introducing the ecodesign of modern national art into the scientific and pedagogical sphere, the pedagogical foundations of ecodesign, its scientific, theoretical and practical content in various aspects. The purpose of this study is to show the aesthetic and ecological nature of ecodesign in traditional and modern national art, as well as their application and importance in the education system. Considering the pedagogical aspects of the combination of natural purity and artistic beauty of ecodesign in national art as an indicator of the everyday culture of an ethnic group, the authors use a variety of methods and techniques: analysis, systematization, questioning, narration, interpretation, processing of scientific literature and various sources. The results of the research will be presented to specialists in the field of art education and other professional fields in the form of scientific, pedagogical and practical materials. The pedagogical aspects of ecodesign in the education system are aimed at educating future generations in the spirit of harmony of nature and man, the integrity of ethnos and culture, the realization of the inseparable unity of art and life.

For the masters of modern art of Kazakhstan, along with the importance of samples of classical culture and discoveries of modernist art, Kazakh folk art is becoming a single field of tradition today. Intertextuality, constant dialogue with different layers of world and national painting and sculpture determine the search for new expressiveness in art. This article describes the role of intertextuality in the development of new forms of artistic statements, namely, as in the works of modern Kazakh sculptors (S.Bekbotayev, D.Sarbasov, Z.Kozhamkulov), jewelers (A.Mukazhanov), tapestry masters (A.Bapanov), the importance of the values of native culture as a space of cultural memory is preserved. Experiments with the material are perceived as a ritual, a creative act, a search for their own author's style, modern means of expression of the artist. It is shown that the danger of losing one's own national identity associated with the process of globalization explains the interest of the masters in the author's myth-making, designed to awaken the spiritual foundations of the nation in the minds of contemporaries. Through mechanical details, sculptors create new myths in order to streamline the ethical and psychological state of a modern person, while in the works of masters of decorative and applied art, bricolage is practiced as a combination of different materials and textures, meanings and images closest to the construction of a myth.

The concept of the study is determined by the understanding of the structure of the Kazakh traditional women's costume as a multifunctional socio-cultural phenomenon. The national costume, which is a system of socially significant deeply symbolic signs, is considered in this article as a model of competent design, which contributes to the improvement of design thinking and professional competencies of students-designers in the process of studying the discipline “Ethno-design”. Special attention is paid to the potential of traditional costume in the process of developing the research skills necessary for future specialists to correctly read the original source and design on its basis popular and competitive author's collections that combine tradition and innovation, and scientific projects for the preservation, modernization and popularization of folk values. In addition, the experience of national design is studied in order to understand the ability of the costume complex to reflect and shape the worldview, material and spiritual culture of the people. The information hidden in its compositional and constructive solution is valuable for modern design activities, which, in turn, have a great influence on the ideology of society and, therefore, should be aware of the high responsibility for generating new ideas and transforming the world, based on universal values.