Порівняльний аналіз ефективності традиційних і сучасних методів навчання геометрії та алгебри в основній школі

Abstract

Today, there is an urgent need not only to adapt but also to fundamentally rethink traditional approaches to teaching such fundamental branches of mathematics as geometry and algebra, as the quality of instruction in lower secondary school largely determines students' further academic success in other fields. In this context, the analysis of the effectiveness of various methodological approaches gains particular significance, as it makes it possible not only to identify the strengths and weaknesses of each but also to define optimal ways of combining them to achieve maximum learning outcomes. The purpose of the article is to compare traditional and modern methods of teaching geometry and algebra in lower secondary school in order to determine the most effective instructional approaches. Methods. The study employed the method of synthesis to form a holistic understanding of the effectiveness of teaching approaches; the method of generalization to identify typical features and trends; the method of systematization to organize material according to content-based criteria. The comparative method was used to contrast traditional and modern teaching methods, and the empirical approach allowed for the analysis of practical experience in implementing educational technologies in mathematics instruction. Results. The effectiveness of traditional and modern methods of teaching algebra and geometry under the conditions of digital transformation of education has been assessed. The rationale for integrating classical methods with modern pedagogical practices—particularly blended learning—has been substantiated. The study analyzes the functional capabilities of digital tools such as GeoGebra, Desmos, Padlet, Mathigon, Jamboard, Kahoot, and Quizizz, which contribute to concept visualization, personalization of the learning process, and the development of key competencies and student motivation. It has been found that combining traditional and modern approaches within a blended learning model ensures a balance between the structured nature and flexibility of the educational process, preserving the strengths of classical pedagogy while expanding its potential through digital technologies. The study emphasizes that the successful implementation of innovative methods depends on the teacher's level of digital and methodological competence, the technical infrastructure of the educational institution, the psychological and pedagogical characteristics of students, as well as the teacher's ability to meaningfully integrate technologies into the logic of educational content. The need to develop effective teacher training models aimed at enhancing their ability to combine traditional and modern didactic approaches is outlined. Conclusions. The article emphasizes that the use of modern educational technologies in teaching algebra and geometry should be viewed as a means of optimizing the learning process, aimed at deep conceptual understanding, the development of critical and logical thinking, and the formation of skills for the practical application of knowledge. The integration of innovative methods should not displace traditional approaches, but rather complement them, creating conditions for more flexible, effective, and learner-centered educational interaction. Such a methodological synthesis supports the preparation of students for the realities of the modern world, where mathematical literacy serves as a foundation for further learning and professional growth.