METHODOLOGY FOR SOLVING METRIC PROBLEMS IN DESCRIPTIVE GEOMETRY

Аннотация

This article explores methodological approaches to solving metric problems in the subject of Descriptive Geometry. It analyzes both theoretical and practical ways of developing students' spatial thinking, deep understanding of projection laws, and graphic representation skills when solving metric problems. The research demonstrates the effectiveness of a step-by-step methodical approach and visual tools used in the teaching process. Keywords: Descriptive geometry, metric problems, methodology, projection, spatial thinking, graphic representation, educational technologies. Descriptive geometry is one of the fundamental disciplines in technical and engineering education, playing a crucial role in developing students’ spatial https://scientific-jl.org/obr Выпуск журнала №-73 430 Часть–1_ июл–2025 ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ 2181- 3187 imagination, geometric reasoning, and graphic skills. Among its key practical components is the solution of metric problems, such as calculating distances, angles, lengths, and surface areas. This article focuses on developing an effective methodology for completing such tasks. The following research methods were applied: Theoretical analysis – a review of existing textbooks, teaching manuals, and methodological recommendations; Pedagogical observation – monitoring students' activity and comprehension during descriptive geometry lessons; Experiment – comparison of the effectiveness of different methodological approaches through control and experimental groups; Visual analysis – using graphic models, animations, and 3D software (AutoCAD, SketchUp) to solve problems. The experiment yielded the following outcomes: A step-by-step method (1. constructing the geometric model; 2. projecting; 3. measuring; 4. producing the final drawing) significantly improved students’ understanding; The use of graphic software enhanced spatial visualization skills; Visual aids (video lessons, animations) helped 85% of students grasp topics more quickly; Compared to traditional methods, interactive approaches were 1.5 times more effective. Common student mistakes included: incorrect placement of projections, inaccurate measurement of angles and distances, and ignoring physical characteristics of the geometric models. The study found that a visual-analytical teaching approach helped significantly reduce these errors. https://scientific-jl.org/obr Выпуск журнала №-73 431 Часть–1_ июл–2025 ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ 2181- 3187 Teaching metric problems in descriptive geometry is essential for fostering technical thinking, spatial imagination, and practical graphic skills in students. These skills are fundamental for future tasks in design, engineering calculations, and drafting. The research demonstrated that using a step-by-step methodology combining modeling, projection, and drawing leads to a 40–50% improvement in learning outcomes. In particular, the integration of interactive technologies (AutoCAD, SketchUp, GeoGebra) made lessons more engaging and effective. Additionally, incorporating verbal explanations, visual aids, and group work strategies further enhanced the learning process. Based on the findings, the following methodological recommendations are proposed: Use real-world examples to emphasize the practical relevance of metric problems; Develop a step-by-step teaching map for each topic; Analyze and address common student errors through personalized instruction; Integrate graphic software fully into the lesson process; Encourage independent problem-solving and graphical representation skills in students. In the future, the wider use of modern technologies in teaching descriptive geometry and the development of special methodological materials for distance and blended learning formats will be crucial. Furthermore, improving teachers’ qualifications and introducing new pedagogical approaches will significantly enhance the effectiveness of teaching metric problems.