PEDAGOGICAL AND PSYCHOLOGICAL FOUNDATIONS OF INTEGRATING MATHEMATICS EDUCATION

Аннотация

В статье рассматриваются психологические и педагогические основы интеграции в математическом образовании, уделяя внимание идеям обеспечения целостности научных знаний, а также мыслям и взглядам мыслителей прошлого. Исследуются усилия в области интеграции научных знаний и идеи педагогических ученых нашей республики относительно организации обучения на основе интегративных знаний в области естественных наук. В статье также рассматривается отсутствие взаимной интеграции между педагогическими и методическими учеными в объяснении сути образовательнойинтеграции. Ключевые слова:интеграция,перпендикуляр,целостность,математика,плоскость,логика. In Uzbekistan, the education system is undergoing fundamental reforms to elevate it to a new level in line with modern times and transition to a new stage of interaction between the state and society. To achieve this, every individual living in the present era must possess sufficient knowledge for the future of the country, ensuring its comprehensive development and progress. The preparation of independent-thinking, creative specialists who can consciously apply their knowledge inlife begins withschool education. According to academician N.N. Semenov, mandatory obedience in the teacher-student relationship should be replaced by free and conscious discipline. Furthermore, the main task of a teacher should be to develop students' ability to think independently and freely and to systematically enhance this skill. It is well known that in any legal and democratic state, students—and, more broadly, every member of society—should be educated to think freely, and theeducation system should be structured accordingly. In particular, one of the most essential conditions for mastering mathematics is developing students' thinking abilities, as full comprehension of the subject is only possible through cognitive growth. Global market integration and the rapid pace of scientific and technological progress require strengthening interconnections between all levels of education. This, in turn, necessitates an integrated approach to teaching andlearning. 13 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF2019:5.2222020:5.5522021:5.6372022:5.4792023:6.5632024:7,805 eISSN:2394-6334 https://www.ijmrd.in/index.php/imjrd Volume12,issue02(2025) In today's socio-economic conditions, the education system must align with democratic and market economy changes. It is crucial to ensure that the learning process is sufficiently supported by material, technical, and informational resources, provided with highly qualified scientific and pedagogical staff, and supplemented with high-quality textbooks, teaching methodologies, and literature. Additionally, establishing strong integration between education, science, and industry is essential. This, of course, requires giving great attention to mathematics and its development. The laws, theoretical concepts, and practical applications of mathematics continue to evolve in response to real-world demands. The advancement of mathematics requires a comprehensive, integrative understanding of itsessence, methodsof cognition, and tools. The concept of ensuring the integrative (holistic) nature of scientific mathematical knowledge is reflected in the works of past thinkers. More than 300 years ago, Euclid’s famous work Elements proved theorems using geometric methods, and even arithmetic problems were explained in the language of geometry. In those times, many algebraic identities were also demonstrated through geometric constructions. This suggests that arithmeticand algebra were integrated withgeometry. Moreover, the works of our ancestors, such as Al-Khwarizmi, Al-Farabi, Ibn Sina, A.R. Beruni, and M. Ulugh Beg, in fields like mathematics, astronomy, geography, medicine, and other sciences, discuss the relationship between quantity and quality, as well as the unity of natural, social, and applied sciences. Al-Khwarizmi’s famous work, Al-Kitab al-Mukhtasar fi Hisab al-Jabr wa al-Muqabala, which holds animportant place inthehistory of mathematics, consists ofthree sections: 1. The first section presents an algebraic method for solving first- and second-degree equations with a single unknown, ensuring that only non-negative roots are considered. He also provides a geometricanalysis of thesesolutions. 2. The second section is dedicated to geometry, where algebraic applications to measurement problems andcalculations related to quantities are discussed. 3. The third section explores the practical applications of algebra, particularly problems related to inheritance distribution. In the introduction of his work, Al-Khwarizmi also provides information about the contributions of past scholars to the development of science. His book covers both simple and complex arithmetic problems and emphasizes their necessity in legal and commercial matters such as inheritance distribution, drafting wills, property division, land measurement, canal construction, and