Students’ Inconsistency when Solving a Geometry Problem in Three-Dimensional Context

Abstract

There is an issue regarding students' consistency in completing geometry assignments, as indicated by several research findings and assessments. Diagnosing how students integrate concepts in the conceptual design and understanding the reasons behind their inconsistency in completing assignments are the main focuses of this case study. This research was conducted with 58 high school students in Tanjungpandan, Indonesia. The data were obtained from students' answers to problems of the three initial levels of geometry thinking and retrospective reports about their answers. The data were analyzed based on three phases: the concept-eliciting and integrating phase, the relationship-eliciting phase, and the relationship-integrating phase. The study revealed that students' performance in geometry analysis aligned with the epistemological concept issue. Visual objects garnered the most attention from students, leading to their analysis techniques being primarily object-oriented. Some stages of property analysis were skipped, causing students to make claims about objects of thought when they should have been establishing relationships between properties to classify shapes through rigorous geometry analysis. Numerical computation remains an essential aspect of geometry analysis. The conceptual design has not yet reached the abstraction stage, resulting in experiments to solve problems not always yielding the correct solutions. In education, this highlights the need for a deep understanding of concept epistemology, efficient concept integration, and the cultivation of abstract thinking skills.