Interconnected Development of Geometric and Optical Representations: Diagnosis and Correction of Typical Errors
Interconnected Development of Geometric and Optical Representations: Diagnosis and Correction of Typical Errors
Manukyan Vardan, Nikoghosyan Gagik
Summary
Key words: interdisciplinary links, cognitive transfer, image construction, teaching methodology, education, knowledge
Within the scope of this research, we have conducted a comprehensive analysis of the cognitive problems arising at the intersection of geometry and physics courses in general education schools. The subject of the study is the typical errors made by students in the “Geometric Optics” section, which we have viewed as a consequence of incorrect transfer of mathematical knowledge. During the research, we aimed to identify the geometric misconceptions that lead to failures in solving optical problems and to develop methodological techniques for overcoming them. By applying methods for diagnosing typical errors and modeling “visual traps,” we have identified the direct impact of students’ difficulties related to angle construction, symmetry, and similarity theory on the path of light rays and the characterization of images. The scientific and methodological novelty of this study lies in the proposed “transfer model,” according to which an optical error is interpreted not as an isolated physical omission, but rather as the consequence of the incorrect projection or application of a geometric tool. We have confirmed that geometric “standardized” thinking, which is usually limited to diagrams depicted in a horizontal position, is the primary source of errors in optics. The results of the research allow us to state that success in topics involving thin lenses and mirrors is determined not by the mechanical reproduction of formulas, but by the stability of graphic-constructive skills. We have substantiated that targeted geometric exercises performed prior to the introduction of a physical law significantly reduce the likelihood of typical errors, contributing to the formation of systemic thinking and the competencies defined by subject standards.
DOI: https://doi.org/10.58726/27382923-2026.1ns-110