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Ngoc Anh Nguyen
Hanoi Metropolitan University
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Students' problem-solving performance in geometric extremum tasks through an integrated vector and analytical approach Tien Da Nguyen; Ngoc Anh Nguyen; Kieu Anh Phan
Jurnal Elemen Vol 12 No 3 (2026): July
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/jel.v12i3.34344

Abstract

This study addresses the inherent limitations of traditional Euclidean approaches to geometric extremum and distance problems, which frequently result in unsystematic and difficult-to-generalize solutions. To overcome these challenges, a structured three-step mathematical modeling framework is introduced: (1) vectorization of the geometric configuration; (2) formulation of an analytical objective function; and (3) systematic optimization via derivatives or gradients. Methodologically, the research employs a constructive modeling strategy that translates complex spatial relationships into vector-based algebraic expressions, rigorously tested across eight purposively selected examples ranging from elementary plane geometry to advanced spatial dynamics. The results indicate that this framework effectively transforms intricate geometric constraints into tractable, variable-dependent functions, allowing derivative-based optimization to yield precise extremum values while bypassing ad hoc geometric constructions. Ultimately, this research contributes to the literature by bridging synthetic geometry and mathematical analysis, offering a robust, generalizable tool that clarifies the underlying mathematical structures and fosters the development of abstract thinking and generalization capabilities for future pedagogical applications.
Co-Authors Kieu Anh Phan Tien Da Nguyen