CC BY
4УДК 37
Adambekova A.M.
Karaganda Buketov University (Karaganda, Kazakhstan)
МЕТ METHODOLOGICAL ANALYSIS OF THE CONTENT OF TEACHING AIDS IN SECONDARY SCHOOL MATHEMATICS
Аннотация: the article presents a methodological analysis of educational materials used in secondary school curricula in mathematics. The main goal is to evaluate the structure, content and pedagogical approaches to these materials, as well as to study how they contribute to the development of mathematical literacy and problem-solving skills in students. The analysis focuses on bringing educational materials in line with national standards, the effectiveness of learning strategies and the integration of modern educational technologies. In addition, the article examines to what extent these materials contribute to the development of critical thinking, logical reasoning and student involvement in mathematical research. Recommendations are offered on improving the content and educational design of mathematics textbooks and additional materials to improve learning outcomes in secondary school.
Ключевые слова: mathematical education, methodological analysis, curriculum design, secondary school, mathematical literacy.
The relevance of the research is due to the need to improve the quality of mathematical education in the context of modern digitalization and the introduction of new approaches to learning. In recent years, there has been an active introduction of interactive and multimedia technologies into the educational process, which requires a revision of traditional educational and methodological tools used in teaching mathematics. The main purpose of this study is to conduct a methodological analysis of the content of teaching aids in mathematics for secondary schools in order to identify their compliance with modern educational standards and society's requirements for the level of mathematical literacy of schoolchildren.
The study of this problem reveals the insufficient adaptation of existing materials to modern realities and the needs of students, which necessitates an in-depth analysis of their content. In the works of Russian researchers such as A.M. Alexandrov, N. P. Konovalov and L. V. Isayeva, attention is paid to the issues of methodological support for mathematical education and the effectiveness of educational materials. Foreign researchers such as J. Brown and P. Stevenson, consider innovative approaches to the construction of textbooks, focusing on the need to introduce modern techniques and technologies in the learning process.
The main focus of this study is on the analysis of the structure and content of textbooks, workbooks and other math textbooks used in secondary schools. Aspects such as the accessibility of the presentation of the material, the logical sequence of topics, the availability of examples of practical application of mathematical knowledge, as well as the use of interactive elements to increase the interest of students are considered. In addition, the role of visual aids and tasks of various levels of complexity for the development of mathematical thinking and problem-solving skills is being investigated.
The scientific novelty of the work lies in the systematization of approaches to the creation of educational materials in mathematics, as well as in identifying their strengths and weaknesses in terms of compliance with modern educational requirements. Special attention is paid to the analysis of the possibility of integrating digital technologies into educational materials to improve the assimilation of mathematics by schoolchildren.
The purpose of the study is to conduct a detailed methodological analysis of the content of educational and methodological tools in secondary school mathematics and make recommendations for their improvement in order to increase the effectiveness of mathematical education. The research objectives include analyzing existing approaches to the development of educational materials, assessing their impact on the formation of mathematical competencies, as well as identifying ways to improve the structure and content of textbooks in accordance with modern educational standards.
The analysis showed that despite the availability of high-quality manuals, many of them require improvement in terms of updating the content and introducing interactive technologies, which will contribute to the development of students' deeper understanding of mathematical concepts and increase their interest in the subject.
The theoretical significance of the research lies in expanding the understanding of the methodological foundations of the development of educational and methodological tools in mathematics. The research contributes to a deeper understanding of approaches to the creation of educational materials that meet the modern requirements of the educational process. Also, the theoretical significance lies in the analysis of the influence of various methods on the level of mathematical training of schoolchildren.
The practical significance of the research is related to the possibility of applying its results to improve existing educational systems, as well as to develop new textbooks that meet modern educational standards and requirements. The results of the study can be useful for teachers, methodologists and curriculum developers, as they allow improving the content of educational materials taking into account current pedagogical and methodological tasks.
The latest trends in education, such as the integration of digital technologies and multimedia elements, have a significant impact on the development of educational and methodological tools. Modern UMS in mathematics increasingly include interactive assignments, online tests, electronic textbooks and problem-solving applications. This contributes to the creation of a flexible educational environment that encourages independent learning of schoolchildren. However, despite the widespread use of such technologies, it is important to preserve the fundamental methodological principles that ensure the consistency and consistency of training.
Methodological analysis of educational materials allows us to evaluate them in terms of the following criteria: completeness and consistency of presentation of the material, compliance with the Federal State Educational Standard, the availability of differentiated tasks for students with different levels of training, the use of technology for the development of critical and logical thinking. It is important to note that the
successful assimilation of mathematical knowledge depends on how well the material is structured and how logically it is presented in textbooks and manuals.
In recent years, there has been a tendency in Kazakhstan to modernize the content of textbooks and teaching aids in mathematics. The research of Russian authors emphasizes the importance of an integrated approach to the formation of the content of the UMS, including not only the presentation of theoretical material, but also tasks that contribute to the development of analytical skills, critical thinking and creativity in students [4]. An important aspect is the use of modern digital technologies to create interactive manuals that facilitate the learning process and make it more interesting for students [5, 6].
In their research, the authors J. S. Aitkazinova and A. B. Kairbekova draw attention to the need to integrate interdisciplinary connections into textbooks on mathematics. This allows students to sthe connection of mathematics with other sciences such as physics, computer science and economics, which increases their motivation and interest in the subject [7]. In addition, these authors emphasize the importance of including tasks in educational materials that are focused on developing critical thinking skills and the ability to solve non-standard tasks [8].
The research methodology is based on a comprehensive analysis of the content of the UMS in mathematics used in secondary school. The analysis covers textbooks and manuals recommended by the Ministry of Education and Science of the Republic of Kazakhstan in terms of their structural construction, methodological approaches and compliance with the requirements of curricula. During the analysis, attention is paid to such aspects as the accessibility of the presentation, the use of examples and tasks of different levels of complexity, as well as the availability of tasks that contribute to the development of practical skills among students.
The study showed that most modern textbooks on secondary school mathematics in Kazakhstan comply with state standards and include a variety of tasks aimed at developing mathematical skills. However, some teaching aids need to be improved in terms of adaptation
Research conducted by Kazakhstani authors shows that high-quality textbooks contribute to the integration of theoretical knowledge with practical skills, which is especially important for schoolchildren who are just beginning to master complex mathematical concepts. Thus, according to V. P. Nikitin, modern textbooks in mathematics should take into account not only traditional teaching methods, but also be adapted to the new requirements of the digital age, including the use of interactive teaching methods and visual aids [6].
Despite the positive aspects of using modern UMS, there are a number of problems related to their content and application in practice. Firstly, some manuals do not pay enough attention to the development of critical thinking, which is one of the key tasks of mathematical education [7]. Secondly, educational materials often do not fully take into account the individual characteristics of students, which leads to a decrease in their motivation and interest in the subject [8]. For example, some tasks may be too difficult for some students and too simple for others, which creates an imbalance in the educational process.
Another important problem is the limited access to modern UMS, especially in rural schools in Kazakhstan, where the necessary infrastructure for the use of digital educational resources is not always available. This can significantly limit the opportunities for students to receive high-quality mathematical education and increase the gap between students from urban and rural areas [9].
The theoretical significance of the study lies in expanding the understanding of how UMS can contribute to the development of mathematical competencies and critical thinking among schoolchildren. The practical significance of the work lies in the possibility of using the findings of the study to develop new UMS that will take into account modern pedagogical approaches and the needs of students [10]. Thus, the analysis of the content of educational and methodological tools in secondary school mathematics makes it possible to identify key problems and prospects for their use in educational practice. In the context of the rapid development of technologies and the introduction of new teaching methods, it is important to create educational materials that will meet modern requirements and contribute to the development of students not
only basic mathematical skills, but also the ability to think independently and solve complex problems [11].
Nevertheless, despite the existing challenges, the potential of educational and methodological tools in mathematics in the educational process remains significant. Modern teaching materials can become an important tool for teachers, making it easier for them to complete routine tasks such as preparing assignments and checking homework, which allows them to focus on more important aspects of teaching, such as developing individual curricula and teaching methods adapted to each student [9].
One of the promising areas is the use of digital educational and methodological tools in the adaptive learning system. This allows you to create programs that take into account the level of training of each student, his speed of assimilation of material and preferred learning methods. UMS can collect data on student academic performance, which makes it possible to adjust educational materials in real time, providing more effective and personalized learning [5].
In addition, interactive digital textbooks and platforms can provide students with access to educational materials at any time and from any device. This is especially important in the context of distance and blended learning, which is becoming increasingly popular both in Kazakhstan and around the world. Resources such as online tests and math simulators help students consolidate their knowledge and receive instant feedback [2].
Educational and methodological tools in mathematics open up new opportunities for improving the educational process. They make learning more accessible, interactive and individualized. Nevertheless, it is important to take into account existing problems, such as the need to adapt materials to specific curricula and prepare teachers to use new technologies. In the future, with the development of technology, educational materials will become even more integrated into the learning process, which will increase academic performance and interest in mathematics among schoolchildren.
Results. The use of modern educational and methodological tools in mathematics is becoming an integral part of the educational process. Such tools help
to solve key tasks, including lesson planning, monitoring progress and providing feedback. One of the most promising areas is the introduction of digital UMS, which significantly increase the effectiveness of teaching by automating routine processes and providing a more personalized approach to each student [1].
One of the key advantages of using modern UMS is the ability to automatically assess students' knowledge. For example, testing and checking tasks can take a significant amount of time for teachers, especially in large classrooms. The introduction of technologies to automate this process provides a more objective and consistent approach to knowledge assessment. Such algorithms can analyze the performance of tasks based on the criteria laid down, which reduces the influence of the subjective factor and helps to ensure a more uniform assessment of student performance [4].
In this study, a methodological analysis of the content of teaching aids in mathematics in secondary school was carried out. The main attention was paid to the evaluation of textbooks, workbooks and manuals that are used for teaching mathematics, as they play a key role in the formation of mathematical knowledge and skills among schoolchildren. To collect data, an analysis of educational materials available in educational institutions was conducted, as well as surveys among mathematics teachers.
The study analyzed 15 math textbooks for grades 5-9, as well as 10 workbooks. The methodology of the analysis included such parameters as the compliance of the content of educational materials with modern educational standards, the availability of examples and tasks that contribute to the development of critical thinking, as well as the level of complexity and accessibility of the presentation of the material for students.
The results of the analysis showed that most textbooks meet modern requirements, but they lack tasks aimed at developing practical skills and solving real problems. It was also noted that many manuals have a monotonous approach to presenting the material, which may reduce students' interest in the subject.
Thus, it can be concluded that the content of educational and methodological tools in mathematics needs to be updated and varied. It is necessary to integrate modern
teaching methods and new approaches to learning in order to make the learning process more exciting and effective.
Discussion. A methodological analysis of the content of educational and methodological tools in mathematics identifies key aspects that must be taken into account when developing and using them. Despite the positive results, there are some limitations and problems that require attention.
Firstly, despite the achievements in the development of textbooks, there is often insufficient connection between theoretical material and practical tasks. This can make it difficult for students to apply their knowledge in real situations, which is extremely important for the formation of their mathematical literacy.
Secondly, although modern textbooks often include elements of innovative learning, insufficient attention is paid to the individualization of the educational process. Given the diversity of students, it is important to provide the opportunity to choose suitable assignments and materials, which will allow each child to work at their own pace and develop their own skills.
It is also worth noting that the availability of educational and methodological tools may vary. Not all schools have equal access to high-quality textbooks and manuals, which creates digital inequality. Education should be accessible to all students, and it is important to take into account the need to prepare teachers to use new techniques and technologies.
Recommendations. Considering the above, the following recommendations are proposed to improve the effectiveness of the use of educational and methodological tools in mathematics:
1. Updating educational materials: Educational institutions should regularly update educational and methodological tools so that they meet modern educational standards and requirements.
2. Variety of tasks: It is important to implement a variety of tasks and exercises that would develop not only theoretical knowledge, but also practical skills, critical thinking and creativity.
3. Individualization of learning: It is necessary to develop methodological materials that take into account the individual characteristics of students, giving them the opportunity to choose tasks and work rates.
4. Teacher training: It is important to ensure that teachers are trained to use modern teaching methods and technologies, which will allow them to use educational materials more effectively.
5. Monitoring and evaluation: Regular monitoring and evaluation of educational and methodological tools will help to identify their effectiveness and possible shortcomings, as well as identify areas for further improvement.
In conclusion, it can be emphasized that the methodological analysis of the content of teaching aids in mathematics in secondary school is an important tool for assessing the quality of educational materials and their compliance with modern requirements. The conducted research made it possible to identify both the strengths and weaknesses of existing textbooks and manuals, which, in turn, opens up opportunities for their further improvement.
The analysis showed that modern educational materials should not only be relevant, but also diverse, contributing to the development of critical thinking and practical skills of students. An important aspect is the availability of methodological support, which helps teachers to effectively use the proposed tasks. It is also necessary to take into account the individual needs of students, which requires flexibility and adaptability from textbooks.
The importance of professional training of teachers in the context of working with educational and methodological tools cannot be overestimated. Teachers must have the necessary skills and knowledge to successfully apply modern technologies and techniques in teaching mathematics.
As a result of the analysis, it was revealed that in order to increase the effectiveness of the educational process, it is necessary to integrate innovative approaches with traditional teaching methods. A hybrid approach combining different strategies can create a more dynamic and adaptive educational environment.
In conclusion, it can be said that the successful development of mathematical education in secondary schools depends on constant monitoring and improvement of the content of educational and methodological tools, which requires active cooperation of all participants in the educational process. Only through joint efforts can we ensure the quality of education and prepare students for a successful life in the modern world.
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