ENHANCING GEOMETRIC UNDERSTANDING: A GALILEAN GEOMETRY APPROACH TO DISTANCE CONCEPTS IN SCHOOL CURRICULUM

Abstract

This article presents a curriculum focused on teaching distance concepts in the context of Galilean geometry. The primary goal is to enhance students’ mathematical understanding, stimulate cognitive interest, and support the development of core competencies. At the core of the curriculum is Galilean geometry, which emphasizes the two-part nature of distance concepts. Unconventional units such as “step” and “cubit” are used throughout the curriculum to showcase historical and contemporary length measurements and encourage students to appreciate different perspectives. The curriculum introduces distance concepts using real-world examples, such as measuring the distance from Tashkent to Samarkand. Practical applications, such as planning intercity trips, highlight the utility of these units in everyday scenarios. Contemporary information technology and coding methods are integrated to demonstrate the importance of distance concepts in contemporary contexts. The curriculum delves into advanced topics, examining Minkowski geometry and making comparisons with Euclidean geometry. Practical application sections include questions to assess students’ understanding, and the table presented in the article facilitates monitoring of their knowledge across the curriculum and identifying areas for improvement. A proposed independent task encourages students to consolidate their knowledge of distance-related concepts. The curriculum concludes with a ‘Boomerang’ method that emphasizes collaborative learning and critical thinking. It is hoped that the proposed supplementary materials, discussion groups and assigned tasks will strengthen students’ understanding of Galilean geometry and its applications. Future studies are recommended to investigate whether this curriculum not only addresses the fundamental aspects of Galilean geometry but also encourages critical thinking, collaborative learning and a holistic understanding of geometry.

Keywords

• Critical thinking
• curriculum design
• distance concepts
• Galilean geometry
• real-world applications

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