Objective: The main goals of school mathematical education are the development of intellectual students, the formation of thought qualities characteristic of mathematical activities and the acquisition of specific mathematical knowledge, the skills and skills necessary for practical application, and the formation of research skills. Theoretical Framework: The problem and purpose of the study is to identify the possibilities of problem-searching tasks in mathematics as a way for school students to develop research skills in updated content situations. Method: A method has been developed to build selected skills based on the corresponding system. It has been established that collective or group forms are most effective in creating problem situations in the classroom. Group or individual forms are most effective for testing a hypothesis and finding a solution to a problematic task. Result and Conclusion: The article also highlights the main blocks of research skills of schoolchildren and problem-search tasks in algebra and geometry developed for these blocks and methods for the formation of these skills. The basic principles for constructing a system of tasks focused on the formation of each block and each skill that we have chosen are determined. Research Implications: Implementation of these goals necessitates updating the system of school mathematical education, which is designed to ensure a harmonious combination of the interests of the individual and society. Originality/value: It contributed to the activation of students’ activities and their positive motivation for learning activities carried out in the classroom and at home.

Good school geometry education not only develops logical thinking but also the spatial imagination and thinking of students. The main means of developing spatial thinking is solving stereometric problems and especially making drawings for these problems. In current practice, teaching students how to construct images of geometric shapes is a challenging task. Weaknesses in geometric preparation are manifested primarily in the inability to accurately depict geometric figures, perform additional constructions and analyze the constructed drawing. Therefore, creating precise and correct drawings, fostering a culture of working with visual effects and developing spatial thinking skills are all vital skills to teach students in geometry courses. In this regard, digital resources and specialized mathematics programs serve as powerful learning tools. The purpose of this study is to identify the significance of digital resources in solving geometric problems for the development of students' spatial thinking. This paper discusses the relationship between the type of spatial thinking and geometric problems for reasoning and digital technologies, presents digital educational materials and resources and provides recommendations for their integration into the educational program. The research methods of this study include observation, study and generalization of teaching experience, interviewing, surveying and testing students, development of methodology and digital resources. A pedagogical experiment was conducted to test the effectiveness of the developed methodology. The results showed the effectiveness of digital resources in the learning process with a noticeable improvement in students' spatial thinking skills observed due to the introduction of digital education.

Numerous issues with Kazakhstan's higher education system have been revealed by the digital advancement of the country. First, universities still have inadequate levels of digitization despite it being a significant component of the wider digitalization of education. The presence of organizational and legal barriers in the educational environment does not contribute to the digitalization of education. The issue of collaboration between teachers and students emerges in the context of educational digitalization. The study was conducted at Abai University and Almaty University of Humanities and Economics (Almaty, Kazakhstan). The experiment included 163 participants. The study revealed a lack of knowledge of digital literacy and motivation among learners for creating a digital environment and providing feedback. The use of cloud computing, video hosting and the coordination of offline and online activities on the internet were found to provide challenges for maintaining the security and privacy of personal information. This study demonstrates that significant advances in students' digital literacy have occurred following the introduction and testing of the author's academic program with EG participants to develop digital skills. Data from this study can serve as the foundation for creating strategies for digital skills development in universities and as a methodological basis for adapting educational programs for digital skills development.

This article examines the impact of contextual learning on the development of functional literacy of 5th grade students. The main purpose of the study was to identify the effectiveness of contextual tasks aimed at various spheres of life in improving the level of mathematical literacy and critical thinking among schoolchildren. The introduction of tasks related to personal, social, professional and scientific contexts has shown its high effectiveness. When developing contextual tasks, special attention was paid to such aspects as personal, social, professional and scientific. Repeated diagnostics after the implementation of these tasks showed a significant improvement in the level of functional literacy of students. The average scores in all contexts have increased significantly, which indicates an increase in skills in budget management, planning, organizing social projects, developing business plans and conducting scientific research. The results of the study emphasize the need to continue working in this direction, expand the range of contextual tasks and conduct regular diagnostics. The information gathered can be utilized to create fresh curricula and initiatives that will help kids’ functional literacy grow. As a result, incorporating contextual assignments into the curriculum enhances learning and equips students to handle challenges that arise in the real world. Keywords: Contextual learning, functional literacy, mathematical literacy, critical thinking, contextual tasks, learning tasks.

The purpose of the study is to solve this problem, which consists of substantiating, developing, and implementing a methodological system for preparing students for professionally oriented mathematics education in college. Professionally oriented mathematics education in colleges is advisable, as it helps students see the practical benefits and importance of mathematics in their future professional activities. This approach allows us to better prepare students for their future professions. Research problem: what are the leading directions, principles, content, and forms of methodological preparation of students for professionally oriented mathematics education in college? In achieving this goal, we distinguish a complex of professionally oriented tasks in the fact that they reflect specific scenarios and difficulties that specialists face in their professional activities, and this allows students to gain experience in specific tasks from their field. Research methods: interviewing and testing students, teachers; observation, study, and generalization of pedagogical experience; development of an author's methodology for preparing students for professionally oriented mathematics education in college. We identified criteria to verify the effectiveness of the training methodology, assessing the students’ assimilation of subject knowledge and their increased motivation for learning. The results of the pedagogical experiment show that the process of teaching mathematics in a college with a professionally oriented methodological learning system, implemented through the use of a set of professionally oriented tasks, contributes to an increase in the level of mathematical training and educational motivation of students.