WAYS AND METHODS OF ORGANIZING INDEPENDENT WORK IN PRIMARY CLASSES BASED ON MODERN PEDAGOGICAL TECHNOLOGIES

Актуальні питання культурології. Випуск 24/2025 105 УДК: 373.3:37.015.3 ОСНОВНІ ФАКТОРИ, ЩО ВИЗНАЧАЮТЬ ОСОБИСТІСТЬ-ОРІЄНТОВАНИЙ ПЕДАГОГІЧНИЙ ПРОЦЕС У ПОЧАТКОВІЙ ОСВІТІ Зейналова Аїда БАБАК – докторант, Азербайджанський державний педагогічний університет, Баку Розглядається сутність та механізми впровадження особистісно-орієнтованих освітніх технологій у навчанні початкової школи. Підкреслюється, що забезпечення особистісно-орієнтованого підходу в процесі навчання вимагає від вчителя педагогічної компетентності, творчої активності та здатності адаптувати зміст навчання до індивідуальних потреб та особливостей розвитку учнів. У дослідженні наголошується, що ефективна реалізація особистісно-орієнтованої освіти залежить від створення позитивного соціально-освітнього середовища, зміцнення взаємодії вчителя та учня, розвитку навичок саморегуляції та самооцінки учнів. Аналізуються такі фундаментальні принципи, як індивідуальність, емоційно-ціннісна орієнтація та суб’єктивність процесу навчання. Зроблено висновок, що особистісно-орієнтоване навчання сприяє когнітивній самостійності, мотивації та самосвідомості учнів, тим самим покращуючи загальну якість освіти в початкових школах. Ключові слова: особистісно-орієнтоване навчання, початкова школа, педагогічні технології, індивідуальний розвиток, соціально-освітнє середовище, компетентність учителя. Стаття отримана 31.08. 2025 Стаття прийнята 22.10. 2025 Опублікована 26.12. 2025 UDC 372.851 WAYS AND METHODS OF ORGANIZING INDEPENDENT WORK IN PRIMARY CLASSES BASED ON MODERN PEDAGOGICAL TECHNOLOGIES Sabina Seyidli HAMZA – Doctoral Student, Azerbaijan State Pedagogical University https://orcid.org/0009-0006-1552-7499 doi [email protected] This article examines the development of students' independent activity, logical and creative thinking, and research skills in primary school mathematics instruction. The author notes that the primary goal of modern education is not simply the transfer of knowledge, but the development of students as individuals, with independent thinking and decision-making skills. Based on curriculum requirements, the use of interactive and student-centered methods, observation, problem-solving, question-and-answer models, and independent and creative assignments stimulates students' cognitive activity. The article demonstrates that by organizing independent work in mathematics lessons, students acquire knowledge through discovery, which develops their long-term memory and analytical and critical thinking. During the teaching process, teachers must consider the individual characteristics of each student and create conditions for them to freely express their opinions. The author concludes that the use of modern educational technologies has a significant impact on the development of mathematical thinking, independence, and research skills in primary school students. Key words: teaching mathematics, elementary grades, independent work, interactive methods, research skills, logical thinking, creative thinking, cognitive activity. Introduction. Today, the implementation of modern education in schools, including subject-based curricula, serves a specific purpose, which is the primary outcome of education. To achieve positive educational outcomes, it is essential to use an interactive teaching method. Interactive teaching fosters independence and life skills in students, creating ample opportunities for their personal development. We know from the experience of comprehensive schools that today's approach to education and students in comprehensive schools has radically and fundamentally changed. Teachers are not content simply imparting knowledge to students; they also strive to shape their worldview and intellectual development. In other words, preparing students for independent living has become the primary goal of student-centered education. The development of thinking plays a crucial and effective role in students' development as individuals. We know that subject-based curricula have been used in grades 1-4 since 2007. One of the main goals of the subject-based curriculum is the development and formation of students' logical, cognitive thinking. True, such issues were always a focus for teachers in the post-Soviet period, but the primary requirement of the curriculum at that time was simply to provide students with knowledge. At that time, preparing students as research participants was considered secondary. As a result, students weren't fully consciously aware of the theoretical and practical issues being studied, and memorization took precedence. Knowledge acquired in this way was not long-lasting [4; 801-822]. Consequently, students studied only science, but their logical thinking was not developed as effectively. In traditional learning, © Sabina Seyidli HAMZA, 2025 Стаття поширюється на умовах ліцензії CC BY 4.0 Альманах наукового товариства «Афіна» кафедри культурології та музеєзнавства Рівненського державного гуманітарного університету 106 students memorized specific mathematical material, learned mathematical rules or properties, but when asked specific questions related to the material, they became confused, had difficulty answering, and were unable to reach the correct conclusion. Therefore, lessons based on modern teaching methods place special emphasis on developing students' observation skills, independence, critical thinking, and logical and mathematical reasoning. Main Text 1. Primary school teachers should create a motivation for students' independent learning during lessons, so that they can express their independent opinions on the problem (question) posed in accordance with their motivation, and show interest in finding effective solutions and methods for solving the problem under consideration. Therefore, developing such abilities in primary school students as observation, attentiveness, logical thinking, the ability to draw conclusions, etc., should be one of the most important tasks that a teacher must perform. In mathematics lessons, developing students' observation skills when studying a new topic, as well as when solving problems and examples, is not only a complex process but also a conscious perception by students of the knowledge acquired. The observation method organized during the teaching process largely depends on the stated goal. Therefore, each class teacher should be able to determine in advance the choice of objects and the purposes for which they will be used when planning their lesson. The model of the new curriculum for the subject is structured in such a way that daily observations of students' everyday activities should be an integral part of cognitive activity [6; 91-111]. According to the curriculum, students' observation of what they see in practical life and the drawing of mental conclusions must be an integral part of their daily thinking and cognitive activity. Whether in the process of reinforcing theoretical material or studying theoretical material, students cannot acquire the necessary knowledge without observation and cannot consolidate the acquired knowledge. Ensuring students' ability to independently observe and analyze is also a critical and necessary issue. Students' activity in this area manifests itself in two ways: a) intellectual activity; b) motor activity [9; 21-40]. During intellectual activity, similarities and differences between two objects are compared, contrasted, and generalizations are made. During physical activity, students attempt to construct a model of the observed object or subject, analyzing it comprehensively. During the learning process, questions posed by the teacher are of great importance, not only stimulating students' independent observation but also encouraging them to engage in independent observation. Questions should be formulated and posed in such a way that their answers necessarily involve exploratory and creative thinking. Sometimes, teachers pose questions in which none of the above situations arise, and students are satisfied with a simple answer. Each student's answer should be logically justified, and, consequently, appropriate, correct conclusions should be drawn. According to teachers' observations, the questions asked of students completely determine how well they have learned the mathematical material. Students independently search for answers to each question. Thus, students' thinking processes are thoroughly studied, including the rules for completing independent work. To determine how students independently solve mathematical problems, it is sufficient to ask not just one but several questions, thereby allowing the teacher to draw a definitive conclusion about how the students perceive the new material. Observing the work of experienced homeroom teachers teaching mathematics in grades 1–4, we concluded that these teachers most frequently ask students the following types of questions when teaching mathematics: • Questions requiring analysis of the conditions of a topic or problem; • Questions related to establishing relationships between the given and derived parts of a mathematical problem; • Questions identifying similarities or differences between a previous problem and a new problem currently being solved; • Questions asked to summarize observations made during the solution of a problem or study of a topic; • Questions requiring justification of the solution to a mathematical problem or proof of its correctness [3; 241]. Therefore, primary school teachers can develop students' intellectual activity by facilitating independent work during specific periods of the lesson and asking guiding questions on various aspects of independent work. In mathematics instruction, organizing learning through problem-solving on the topic under study is considered conducive to enhancing students' cognitive activity. This structured form of instruction fosters students' need for independent study. It should be noted that the pedagogical skill of the homeroom teacher plays a key role here. Thus, the teacher must be mindful of each student's individual characteristics, respect their expressed mathematical ideas, and instill confidence in the validity of each idea. Furthermore, the teacher must determine in advance the sequence of teaching methods used in the lesson. Актуальні питання культурології. Випуск 24/2025 107 In teaching mathematics in grades 1–4, a number of methods and techniques are used, which share the following characteristics: • The teaching is based on the principle of a student-centered approach; • An exploratory approach, independence, and freedom of students; • Active independent thinking by students during the lesson; • Correctly guiding students in their search for a given problem (question); • Finding a solution to the problem through research; • Establishing close relationships between students and the teacher; • Ensuring collaboration between students; • A creative approach to connecting theoretical knowledge with real-life situations and its application [1; 25–32]. It should be noted that the main advantage of this learning structure is the creative delivery of knowledge to students. Developing students' enthusiasm for learning mathematics is based on their ability to resolve potential contradictions in their mathematical thinking. Real contradictions in the educational process can be resolved through independent work. In this case, the convergence of cognitive resources is fully ensured. Building students' independent work on a scientific and theoretical foundation eliminates the provision of ready-made knowledge. Students acquire knowledge primarily through «discovery». By independently solving a given mathematical problem in class or outside of class, students can approach the lesson creatively and retain the acquired knowledge for a long time. The use of this method in the educational process helps completely eliminate student passivity in the classroom, develop their mathematical and logical thinking, and significantly improve the quality of learning. The following reasons can be cited for improving the quality of mathematics instruction in grades 1–4 through independent work: • At the beginning of the lesson – in motivating learning and formulating the task; • Relying on students' mathematical and logical thinking and their independent, creative acquisition of knowledge. How can we foster students' emotional and volitional activity during independent work in the classroom? From research, it is clear that the advantage of the teaching methods used in schools today is that they develop students' logical thinking and cognitive activity, creating important conditions for independent knowledge acquisition. If we achieve the development of each student's logical thinking, we will also create conditions for their easy acquisition of life skills. The global education system also places particular emphasis on developing students' logical thinking. After all, through logic, students' overall intellectual level is raised, and their ability to independently acquire knowledge, skills, and abilities is formed and strengthened. Organizing and conducting independent mathematics work in grades 1–4 also fosters students' mathematical thinking: – Knowledge is acquired independently through student research and is retained for a long time; – Students develop skills such as logical, critical, and creative thinking, as well as independent decision-making; – Interest in the subject develops, and scientific research skills are strengthened; – Collaboration between students and the teacher is fostered. One of the key factors in organizing independent work in the classroom is students' deep understanding of the knowledge they have acquired, their desire to resolve contradictory situations, and the development of positive ideas. Each student strives to comprehensively justify the validity of their work. In this case, students sometimes perceive contradictions between previously acquired knowledge and knowledge they have acquired independently and strive to resolve them as quickly as possible. In this case, students justify their independently acquired knowledge and remember it for a long time. This is the essence of thought-provoking, educational learning in the truest sense of the word [1; 25-32]. The key features of developing students' creative research activities in mathematics during independent work can be defined as follows: - Creating a problem-solving situation related to the perception of new material during independent work at a specific stage of the lesson; - Stimulating students' active research to solve problems arising under the teacher's guidance; - Creating adequate conditions for the free acquisition, perception, and assimilation of new knowledge. The dictionary definition of «independent work» is the completion of a specific task without assistance. In a pedagogical context, it is used in conjunction with teaching methods. Independent work, performed under the Альманах наукового товариства «Афіна» кафедри культурології та музеєзнавства Рівненського державного гуманітарного університету 108 guidance of a teacher during a lesson, refers to the student's creative, independent research, investigation, and study activities. If a student is engaged in the independent, creative use of theoretical material or acquired knowledge, then, in addition to enriching their memory with new scientific knowledge (information), they also systematically develop their thinking, creative thinking, research skills, the ability to acquire and assimilate new knowledge, and the ability to conduct research. Thinking and research are fully supported through the acquisition of knowledge. In reviewing our research and methodological studies on this issue, we discovered that today, the primary focus of instruction in comprehensive schools using modern educational technologies is: - developing students' thinking; - acquiring knowledge not in a pre-existing form, but through creative application; - independence and freedom of thought through interactions between students, teachers, and students etc. Various tools, methods, and teaching techniques are used to develop students' research skills in mathematics education. Today, in the educational process, based on curriculum requirements, the development of students' creative thinking and research skills occupy a special place. Independent work is crucial in developing mathematical thinking. Logical reasoning is used when considering any question or example. Therefore, it can be concluded that logical thinking is a manifestation of thinking. Logical thinking should be developed in students under the guidance of the teacher, but without their assistance. For this purpose, problem-solving situations are widely used in teaching mathematics. Problem-solving situations are one of the initial stages of independent work. At the beginning of the lesson, a problem on the topic is posed, and students attempt to solve it independently, using various tools. Students independently conduct various discussions about solving the problem and share their ideas with friends. Therefore, mathematical language is widely used to communicate problem-solving ideas to others. Each student has their own independent ideas about the problem, and when they share these ideas with each other, their thinking is broadened and deepened. To develop the thinking and research skills of students in grades 1–4 in mathematics, preliminary preparatory work is necessary. This is achieved by using the "from simple to complex" principle. In addition to providing students with mathematical knowledge, it is also crucial to develop their logical thinking. Practical work in elementary school plays a significant role in the development of mathematical thinking. Students must carefully read and study the instructions and be able to analyze them. To this end, independent work has received special attention in recent years. One type of independent work is the use of worksheets or cards in mathematics lessons. These cards or worksheets provide tasks for reflection on a topic, and by solving these written tasks, students express their own possible opinions on the topic. Naturally, students are greatly motivated to complete the tasks provided on the worksheets [6; 91–111]. Mathematics lessons require a special environment for developing creative thinking. Which arithmetic operation would you like to practice first in grades 1–4: addition, subtraction, multiplication, or division? As in other subjects, developing thinking in mathematics requires discussing relevant mathematical topics [8; 275–294]. As we have already noted, thinking is the foundation of students' creative activity. Therefore, in accordance with their mathematical knowledge, students independently carry out their unique activities. We would be right in saying that «the thinking and reasoning of each student is the logical structure of their future work». By developing students' creative thinking, we encourage them to develop new projects and think independently. Therefore, creating conditions for students' creative thinking and independent inquiry in the classroom is one of the main tasks of every teacher. Developing students' research abilities in mathematics lessons means they will be able to independently construct their future work. When teaching mathematics in grades 1–4, it's crucial to impart theoretical and practical knowledge to students not through provocation, but through creative exploration that they understand. Students should be able to consolidate mathematical concepts in their minds not only through understanding but also through creative application and logical formulation. Problem-solving and problem-solving, begun and completed in the early grades, plays a crucial role in developing each student's general worldview, broad thinking, and clear mathematical skills. To develop primary school students' mathematical thinking, it's essential to consider their level of knowledge and comprehension. These children require special (free) creative abilities and independence. Each mathematical topic studied must be clearly understood by students, and these topics must effectively guide them toward creativity. Building instruction around the requirements of an interactive method based on collaborative activity creates ample opportunities for proper guidance and encouragement of students' free, creative, and independent activity.The use of modern teaching methods is aimed at developing students' creative or research abilities. To develop students' research abilities in grades 1–4, it is essential to teach them how to use textbooks, workbooks, and tests. The teacher's selection of practical tasks relevant to the Актуальні питання культурології. Випуск 24/2025 109 topic being studied, from textbooks or various methodological literature, and the requirement to solve them also play an important role in developing students' research abilities. Conclusion. In general, when developing students' independent research skills, the following must be considered: Mathematics education requires developing students' research skills, in-depth study of theoretical knowledge, the ability to generalize it, and the ability to apply this knowledge to solving practical problems. This allows students to fully assimilate the acquired knowledge. Conversely, when solving practical problems, they extensively utilize methods of analysis and synthesis, formulate specific mathematical hypotheses, complete assignments, and verify their solutions. Based on many years of experience, I can note that active learning methods used in elementary school mathematics lessons today comprehensively and effectively develop students' cognitive activity and their creative research abilities. Based on the teacher's professionalism, it can be said that developing students' scientific thinking and research abilities can be achieved through independent work methods. During the lesson, conditions should be created for each student to express their independent opinions; freedom should be provided, students should be free from outside interference, and students should have the opportunity to verify the accuracy of their conclusions. References 1. Aghayev A. A. Modern approaches to the problem of pedagogical innovations. Azerbaijani school, 2013. No. 5. Р. 25-32. 2. Gamidov S. S. Methods of Teaching Mathematics in Primary School. Baku, 2012. 335 p. 3. Kazimov Z. F., Ibragimova A. F. Developmental and Entertaining Exercises in Mathematics. Baku, 2013. 241 p. 4. Gary R. Pike. Students’ Personality Types, Intended Majors, and College Expectations: Further Evidence Concerning Psychological and Sociological Interpretations of Holland’s Theory. Research in Higher Education. 2006. № 47, Issue 7. Р. 801-822. 5. Giuseppe Ritella, Kai Hakkarainen. Instrumental genesis in technology-mediated learning: From double stimulation to expansive knowledge practices. International Journal of Computer-Supported Collaborative Learning. 2012. № 7. Issue 2. Р. 239-258. 6. Helge I. Strømsø, Ivar Bråten. The role of personal epistemology in the self-regulation of internet-based learning. Metacognition and Learning. 2010. № 5, Issue 1. Р. 91-111. 7. Knowledge management e e-learning in ambito sanitario / M. Masoni, M. R. Guelfi, A. Conti, G. F. Gensini, Milan : Springer, 2011. Р. 65-72. 8. Mary Webb. Pedagogy with information and communications technologies in transition. Education and Information Technologies. 2012. № 19. Issue 2. Р. 275-294. 9. Tine van Daal, Vincent Donche, Sven De Maeyer The Impact of Personality, Goal Orientation and Self-Efficacy on Participation of High School Teachers in Learning Activities in the Workplace. Vocations and Learning. 2014. № 7. Issue 1. Р. 21-40. УДК 372.851 СПОСОБИ ТА МЕТОДИ ОРГАНІЗАЦІЇ САМОСТІЙНОЇ РОБОТИ В ПОЧАТКОВИХ КЛАСАХ НА ОСНОВІ СУЧАСНИХ ПЕДАГОГІЧНИХ ТЕХНОЛОГІЙ Сабіна Хамза СЕЇДЛІ – докторант, Азербайджанський державний педагогічний університет, Баку https://orcid.org/0009-0006-1552-7499 Розглядається розвиток самостійної діяльності учнів, логічного та творчого мислення, дослідницьких навичок у навчанні математики в початковій школі. Автор зазначає, що основною метою сучасної освіти є не просто передача знань, а розвиток учнів як особистостей, з самостійним мисленням та навичками прийняття рішень. Виходячи з вимог навчальної програми, використання інтерактивних та студентоорієнтованих методів, спостереження, вирішення проблем, моделей питань і відповідей, а також самостійних і творчих завдань стимулює пізнавальну активність учнів. У статті показано, що, організовуючи самостійну роботу на уроках математики, учні отримують знання через відкриття, що розвиває їхню довготривалу пам’ять та аналітичне й критичне мислення. Під час навчального процесу вчителі повинні враховувати індивідуальні особливості кожного учня та створювати умови для вільного висловлення ним своєї думки. Автор робить висновок, що використання сучасних освітніх технологій має значний вплив на розвиток математичного мислення, самостійності та дослідницьких навичок у учнів початкової школи. Ключові слова: викладання математики, початкові класи, самостійна робота, інтерактивні методи, дослідницькі навички, логічне мислення, творче мислення, пізнавальна діяльність. Стаття отримана 5.09. 2025 Стаття прийнята 26.10. 2025 Опублікована 26.12. 2025