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.

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.

This thesis explores the role of contextual tasks in the formation of mathematical literacy of students in math lessons at school. Mathematical literacy includes not only the ability to solve mathematical problems, but also an understanding of mathematical concepts and their application in real situations. Contextual problems are mathematical problems that are placed in a realistic context, which allows students to see the connection between mathematics and everyday life. The article discusses the advantages of using contextual tasks, methods of their construction, as well as the impact of contextual tasks on the development of mathematical literacy of students.

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.

The rapid digitalisation of engineering and the industry and the increasing technical uncertainty and complexity necessitate strengthening mathematical training among students of technical specialties. Probability theory and mathematical statistics develop analytical thinking competencies, including skills in mathematical modeling, interpretation of data, decision making under uncertainty during the design of models, components of devices and networks, evaluation reliability, safety, etc. This study develops and evaluates the professionally oriented approach to teaching stochastic methods integrating the theoretical mathematical knowledge with practical applications in engineering and information technologies. The proposed methodology incorporates the professionally oriented tasks considering the concepts of: reliability of electrical systems, probability of overload of transformer, diagnose of equipment using Bayes formula, electrical circuits using random processes, etc. Those tasks make students reflect on random phenomena, define probability models, carry out mathematical calculation, interpret results and justify decisions in professional contexts. To investigate the effectiveness of the proposed approach a 2 months quasi-experimental study with (n=23) a control group which studied the probability content and additional traditional and calculation tasks and (n=23) an experimental group which studied probability and performed additional contextual and professionally oriented tasks was conducted. Students completed pre-test and post-test assessment questionnaires, comparative statistical analysis and observation about learning engagement and common types of students’ errors followed the experiment. We found results improving in both groups but the experimental group resulted in a greater change in test scores, mean changing from 56.5% to 75.1% while in the control group the mean changed from 58.5% to 67.9%. Embedding stochastic methods into teaching through professionally oriented tasks appears to strengthen the connection between mathematical theory and its practical applications in system modelling while preparing students for their future professional careers.